12th EFTC

The twelfth European Fusion Theory Conference

24-27 September 2007

Madrid, Spain

Book of Abstracts

Laboratorio Nacional de Fusión - Ciemat

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Scientific Program Committee: D. Van Eester (Chairman) LPP-ERM/KMS, TEC, Belgium D. Borba IST, Portugal S. Cappello CNR, Italy F. Castejón CIEMAT, Spain H. De Blank FOM, TEC, The Netherlands O. Dumbrajs HUT, Finland S. Gunter IPP, Germany J. Heikkinen Tekes, Finland P. Helander IPP, Germany M. Lisak VR, Sweden V. Naulin Riso, Denmark M. Ottaviani CEA, France O. Sauter CRPP, Switzerland S. Sharapov UKAEA, United Kingdom M. Tokar FZJ, TEC, Germany M. Vlad INFLPR, Romania R. Zagorski IPPLM, Poland

Local Organizing Committee: F. Castejón (Chairman) CIEMAT, Spain A. López-Fraguas CIEMAT, Spain D. López-Bruna CIEMAT, Spain A. Medialdea CIEMAT, Spain

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PROGRAMME

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24/09/2007

07:30-08:40 Registration 08:40-9:30 Tutorial (50’) F. Zonca – ENEA, Italy “Physics of burning plasmas in toroidal magnetic field devices” 9:30-10:10 Topical (40’): W. Horton – Univ. of Texas at Austin, USA “The micro-tearing mode” 10:10-10:40 Coffee / tea + last registrations 10:40-11:20 Topical (40’): S. Benkadda – EDCS, France “Multi-scale interaction of magnetic islands and microturbulence in tokamaks” 11:20-12:00 Topical (40’): K.-H Spatschek –Univ. Dusseldorf, Germany “On the influences of stochastic magnetic fields on transport coefficients, runaway losses and heat flux patterns” 12:00-14:00 Lunch 14:00-15:20 Poster session 1 15:20-15:50 Coffee / tea 15:50-17:10 Poster session 1 Evening programme: Welcome drink (17:15 - …)

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25/09/2007

08:40-9:30 Tutorial (50’): J. Connor – UKAEA, UK “Rotation, stability and transport” 9:30-10:10 Topical (40’): T. Ribeiro – IPP-Garching, Germany “Edge turbulence simulations: self consistent MHD equilibrium and the X-point singularity” 10:10-10:40 Coffee / tea 10:40-11:20 Topical (40’): P. Xantopoulos – IPP-Greifswald, Germany “Gyro-kinetic Simulation of Micro-instabilities for the Stellarator Wendelstein 7-X” 11:20-12:00 Topical (40’): T. Tala – Tekes, Finland “The Physics of Internal Transport Barriers” 12:00-14:00 Lunch 14:00-14:40 Topical (40’): F. Ogando – Tekes, Finland “Neoclassical and turbulent processes in global full-f gyro-kinetic simulations” 14:40-15:20 Topical (40’): Y. Sarazin – CEA, France “Global full-f gyrokinetic simulations with GYSELA” 15:20-15:50 Coffee / tea 14:40-15:20 Lecture outside the Programme (50’) George Chiu. – Advanced Server Hardware System, USA “The Blue Gene Supercomputer Platform and Its Applications" 16:30-17:10 EFTC Programme Committee Meeting

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26/09/2007

08:50-9:30 Topical (40’): P. Helander – IPP-Greifswald Germany “Linear and nonlinear magnetic island dynamics in post-disruption plasmas with runaway electrons” 9:30-10:10 Topical (40’): S. Sharapov – JET, UK “Alfvén Spectroscopy for Advanced Scenarios on JET” 10:10-10:40 Coffee / tea 10:40-11:20 Topical (40’): A. Simakov – Los Alamos, USA “Magnetic topology effects on tokamak plasma flows” 11:20-12:00 W. Fundamenski – UKAEA-Culham, UK “On the relationship between ELM filaments and solar flares” 12:00-14:00 Lunch 14:00-15:20 Poster session 2 15:20-15:50 Coffee / tea 15:50-17:10 Poster session 2 Evening programme: Conference Dinner (20:30 - …)

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27/09/2007

08:50-9:30 Topical (40’): B. Breizman – IFS, Texas, USA “Energetic particle driven instabilities with frequency chirping” 9:30-10:10 Topical (40’): L. Chacon – Los Alamos, USA “PIXIE3D: efficient, fully implicit, 3D extended MHD code plasma modeling” 10:10-10:40 Coffee / tea 10:40-11:20 Topical (40’): N. Mellet – CRPP-EPFL, Lausanne, Switzerland “3-D warm effects for low frequency wave propagation” 11:20-12:15 CLOSING EFTC 12 TRANSPORTATION TO THE HOTELS

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Poster Session 1 P1.01 23 Effects of plasma elongation on drift wave-zonal flow turbulence. P. Angelino P1.02 24 Resistive Edge Modes in Stellarator and Tokamak Geometries. M. Ansar Mahmood P1.03 25 Turbulent transport of energetic ions. T. Dannert P1.04 26 Effects of Gyro-fluid Resonances on Turbulent Particle Pinches. A. Eriksson P1.05 27 Turbulent excitation of plasma oscillations in the acoustic frequency range. G. Falchetto P1.06 28 Redistribution of Energetic Particles by Background Turbulence. T. Hauff P1.07 29 2D Gyrofluid simulations of edge/SOL dynamics. J. Madsen P1.08 30 Parallel momentum in a 3D cylindrical plasma simulation. V. Naulin P1.09 31 Generation and Stability of Large Scale Magnetic Structures in Electron Drift Turbulence. M. Jucker P1.10 32 Turbulent transport in non-Ohmic plasma: an ion-cyclotron resonance heating case. N. Pometescu P1.11 33 A drift model of interchange instability. E. Benilov

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P1.12 34 Electron diffusion in a sheared unperturbed magnetic field and an electrostatic stochastic field. I. Petrisor P1.13 35 Diamagnetic effects on zonal flow generation in weak electrostatic turbulence. I. Petrisor P1.14 36 Multi-Accuracy-Level Burning Plasma Simulations. J.F. Artaud P1.15 37 Magnetic Nozzle and Plasma Detachment Scenario. B. N. Breizman P1.16 38 Fractional generalization of Fick’s law. I. Calvo P1.17 39 Influence of transport on EBW heating efficiency in magnetic confinement devices. A. Cappa P1.18 40 Nonlinear Dynamics of Multiple NTMs in Tokamaks. D. Chandra P1.19 41 On guiding center map. D. Constantinescu P1.20 42 Nonlinear visco-resistive dynamics of the Harris current sheet. K. Takeda P1.21 43 Analysis of ITER and DEMO steady-state scenarios with the CRONOS suite of codes. J. Garcia P1.22 44 Stability of Rotating Plasmas with Hall Effect. V. Ilgisonis P1.23 45 Formation and decay mechanisms of excimer molecules in silent plasma discharge. N. Larbi Daho Bachir

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P1.24 46 Particle transport in ECH plasmas of the TJ-II stellarator. D. López-Bruna P1.25 47 Pinch effects and chaotic motion in toroidal confinement devices. G. Spizzo P1.26 48 Different Methods for measuring Plasma displacement in Tokamaks. Construction & Compensation of Continuous Coils in IR-T1 Tokamak. R.Tarkeshian P1.27 49 Curvature particle pinch in tokamak and stellarator geometry. A. Mishchenko P1.28 50 Intermitent plasma transport in edge-localized mode. G. Kamberov P1.29 51 Contribution of slow particle dynamics to chaotic transport in RFP plasmas. I. Predebon P1.30 52 Numerical simulations on blob transport in TEXTOR-DED. D. Reiser

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Poster Session 2 P2.01 55 Resistive Wall Modes Stabilization the Presence of 3D Wall Structures. C.V.Atanasiu P2.02 56 3D nonlinear MHD simulations for ultra-low q plasmas. D. Bonfiglio P2.03 57 Fully implicit, nonlinear, parallel algorithm for the 3D collisionless reconnection study. D. Borgogno P2.04 58 Ordered magnetic topology in Reversed Field Pinch configurations. S. Cappello P2.05 59 Multiple Nested Beltrami regions as a Solution to the 3-D Toroidal MHD. R.L. Dewar P2.06 60 Influence of the safety factor profile on the nonlinear evolution of the 1/1 kink mode. R.L. Dewar P2.07 61 Energy losses by type I ELMs due to hot particle flows along perturbed magnetic field lines. A. Gupta P2.08 62 Modeling of non-linear Alfv en Eigenmode excitation with the SELFO code. K. Holmström P2.09 63 Nonlinear Dynamics of Magnetic Islands Inbedded in Micro­Turbulence. Muraglia P2.10 64 Magnetogravitational Instability of Rotating Hall Plasma with Electron Inertia and Radiative Effects. R. P. Pprajapati P2.11 65 Quasi-Single-Helicity states emerging from force-free equilibria: linear and nonlinear theory. E. Tassi

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P2.12 66 On existence of resistive magnetohydrodynamic equilibria. H. Tasso P2.13 67 Side conditioned axisymmetric equilibria with incompressible flows. G. N. Throumoulopoulos P2.14 68 Modeling of losses related to and frequency of type I Edge Localizad Modes and of ELM mitigation through external field perturbations. M. Z. Tokar P2.15 69 Study of toroidally confined plasmas in steady state using smoothed particle magnetohydrodynamics. C Toniolo P2.16 70 Stability analysis of internal ideal modes in low-shear tokamaks. C. Wahlberg P2.17 71 Simulations of NBI-ICRF synergy with full-wave TORIC package. R. Bilato P2.18 72 Contour Dynamics: Kinetic electron simulation of collisionless reconnection. H. J. de Blank P2.19 73 Quasi-linear theory of whistler waves destabilized by a relativistic runaway beam. T. Fülöp P2.20 74 Asymmetric Distributions of Energetic Circulating Ions and Sawtooth Control using ICCD and Unbalanced NBI. J. P. Graves P2.21 75 ICRF Mode Conversion Current Drive for Plasma Stability Control in Tokamaks. D. Grekov P2.22 76 Single particle orbits in anisotropic fully shaped plasmas. Martin Jucker P2.23 77 Nonlinear gyrofluid computation of ELM crash events. A. Kendl

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P2.24 78 Gyrokinetic simulations of shaping effects on turbulent heat and particle transport observed on the TCV tokamak. X. Lapillonne P2.25 79 Parallelization of a full-f semi-Lagrangian code: GYSELA. G. Latu P2.26 80 Self-consistent simulations of ICRH experiments: The CYRANO-BATCH code. E. Lerche P2.27 81 Many-particle approach to the gyrokinetic theory. A. Mishchenko P2.28 82 Impurity transport in ITER-like plasmas using fluid and gyrokinetic descriptions. H. Nordman P2.29 83 Plasma waves relativistic effects at the ICR frequency range. F. Castejón P2.30 84 Modelling of energetic ions behaviour in the n=1 kink distorted central core of the JET tokamak. A. Perona P2.31 85 When can Fokker-Planck equation describe anomalous transport? D.F. Escande P2.32 86 The trace ion module for the Monte Carlo code Eirene, a unified approach to plasma chemistry in the ITER divertor. Josef Seebacher P2.33 87 Challenges of rigorous 3-D Fokker-Planck modelling of ICRH heating. D. Van Eester

INVITED TALKS

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Multi-scale interaction of magnetic islands and micro-turbulence in tokamaks.

S. Benkadda1, M. Muraglia1, O. Agullo1, P. Beyer1, X. Garbet2

(1) Equipe Dynamique des Systèmes Complexes, Laboratoire PIIM. CNRS-Université de Provence(2) Association EURATOM-CEA. DRFC. CEA Cadarache.

Abstract.

In tokamaks, macro-scale MHD instabilities (magnetic islands) coexist with micro-scale turbulent fluctuations and zonal flows. Although several works were devotedto the study of macro-scale and micro-scale instabilities separately, only fewinvestigations were devoted to explore the mutual interaction between theseinstabilities [1, 2].We address here the multi-scale-nonlinear dynamics between macro-scale tearinginstabilities and gradient pressure driven (resistive interchange)micro-instabilitiesby solving reduced MHD equations numerically. We analyze the dynamics of thesystem and the nature of the regime as a function of the Prandtl number. It is foundthat, depending on the Prandtl number, the reconnection process is influenced bythe generation of external flows.In particular, we find that the system can reach a regime characterized by fourphases. First a linear growth of the magnetic island followed by a plateau phasewhere the island stops growing, becomes stable and a non linear saturated regimetakes place. During this late evolution of the island, the micro-scale interchangefluctuations begin to grow and the system reaches a hybrid regime which ischaracterized by the multi-scale competition between the island and themicroscopic fluctuations. Later, the kinetic energy reaches a non linear state wherea strong interaction between magnetic flows associated with the islands and zonalflows, generates violent magnetic reconnection. In the later phase the kineticenergy exhibit relaxation oscillations and the reconnection time becomes bursty.

[1] Mc Devitt, C. J., et al., Phys. Plasmas 13, 032302 (2006).[2] A. Ishizawa et al, IAEA proceedings, Chengdu 2006, TH/P2-21

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On the influences of stochastic magnetic fields on transport coefficients, runaway losses, and heat flux patterns Karl H. Spatschek* Institut für Theoretische Physik, Heinrich-Heine-Universität Düsseldorf D-40225 Düsseldorf, Germany Edge stochastization is a candidate for the plasma-wall-interaction control. In the present presentation, three aspects of stochastic plasmas are demonstrated, namely transport coefficients, runaway losses, and heat flux patterns. First, for stochastic magnetic flux functions with percolative contours the existing test particle transport theories are reviewed. Using the decorrelation trajectory method (DCT), the relation between the Lagrangian velocity correlation function and the Eulerian magnetic field correlation is discussed. Specific results are presented in the percolation regime corresponding to high Kubo numbers. For different percolative scenarios the diffusion is analyzed and strong influences of the percolative structures on the transport scaling are found. Numerical simulations of the A-Langevin equation confirm the semi-analytical predictions. Next, guiding-center motion is analyzed in relativistic invariant form for toroidal geometry. Including stochastic magnetic field components, a symmetric Hamiltonian mapping technique, leading to a 4-dimensional iteration procedure, is developed. The latter is analyzed in detail for increasing (relativistic) kinetic energies of the particles, i.e. runaway electrons. The dependency of the escape rates on the kinetic energy is calculated and compared to the escape rates for field lines. The non-relativistic limit of the model is derived. Quantitative results for the magnetic perturbations in a dynamic ergodic divertor (DED) of the TEXTOR experiment are shown, and predictions for runaway electrons are compared with experiments. Finally, we interpret heat flux patterns caused by stochastic magnetic fields. Experimental observations of heat fluxes on divertor plates of tokamaks show typical structures (boomerang wings) for varying edge safety factors. It is shown that the heat flux patterns follow from general principles of nonlinear dynamics. The pattern selection is due to the unstable and stable manifolds of the hyperbolic fixed points of the last intact island chain. Based on the manifold analysis, experimental observations can be explained in full detail. Quantitative results are presented in terms of the penetration depths of field lines. * in collaboration with S. Abdullaev, K.H. Finken, M. Jakubowski, M. Lehnen, M. Neuer, and A. Wingen

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PIXIE3D: An efficient, fully implicit, parallel,3D extended MHD code for fusion plasma modeling

L. Chacon

Los Alamos National Laboratory, Los Alamos, NM 87545

PIXIE3D is a modern, parallel, state-of-the-art extended MHD code that employs fullyimplicit methods for efficiency and accuracy. It features a general geometry formulation,and is therefore suitable for the study of many magnetic fusion configurations of interest.

PIXIE3D advances the state of the art in extended MHD modeling in two fundamentalways. Firstly, it employs a novel conservative finite volume scheme which is remarkablyrobust and stable, and demands very small physical and/or numerical dissipation [1].This is a fundamental requirement when one wants to study fusion plasmas with real-istic conductivities. Secondly, PIXIE3D features fully-implicit time stepping, employingNewton-Krylov methods for inverting the associated nonlinear systems. These methodshave been shown to be scalable and efficient when preconditioned properly. Novel precon-ditioned ideas (so-called physics based), which were prototyped in the context of reducedMHD [2, 3], have been adapted for 3D primitive-variable resistive MHD in PIXIE3D [4],and are currently being extended to Hall MHD [5]. PIXIE3D is fully parallel, employingPETSc [6] for parallelism.

PIXIE3D has been thoroughly benchmarked against linear theory and against other avail-able extended MHD codes on nonlinear test problems (such as the GEM reconnectionchallenge [7, 8]). We are currently in the process of extending such comparisons tofusion-relevant problems in realistic geometries.

In this talk, we will describe both the spatial discretization approach and the precon-ditioning strategy employed for extended MHD in PIXIE3D. We will report on recentbenchmarking studies between PIXIE3D and other 3D extended MHD codes, and willdemonstrate its usefulness in a variety of fusion-relevant configurations such as Tokamaksand Reversed Field Pinches [9].

References

[1] L. Chacon, Comput. Phys. Comm., 163 (3), 143-171 (2004)[2] L. Chacon et al., J. Comput. Phys. 178 (1), 15- 36 (2002)[3] L. Chacon et al., J. Comput. Phys., 188 (2), 573-592 (2003)[4] L. Chacon, 32nd EPS Conf. Plasma Physics, Tarragona, Spain, 2005[5] L. Chacon et al., 33rd EPS Conf. Plasma Physics, Rome, Italy, 2006[6] Satish Balay et al., http://www.mcs.anl.gov/petsc[7] J. Birn et al, J. Geophys. Res., 106 (A3), 3715-3719 (2001)[8] http://w3.pppl.gov/cemm/gem.htm[9] G. L. Delzanno et al., “Electrostatic mode associated with pinch velocity in RFPs,”

Phys. Plasmas, submitted (2007)

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On the relationship between ELM filaments and solar flares

W Fundamenski1, V Naulin2, T Neukirch3, O E Garcia2 and J Juul Rasmussen2

1Euratom/UKAEA Fusion Association, Culham Science Centre, Abingdon, OX14 3DB, UK‡2 Association Euratom–Risø National Laboratory, OPL-128 Risø, DK-4000 Roskilde,

Denmark3 School of Mathematics and Statistics, University of St. Andrews, St. Andrews, KY16 9SS,

United Kingdom

Both solar flares and edge localised modes (ELMs) involve magnetised plasma eruptionswhich sporadically eject field-aligned filamentary structures into the surrounding, low densityenvelope: the far scrape-off layer (SOL) in the case of the tokamak and interplanetary spacein the case of the sun. The erupting filamentary structures display many similarities and havebeen occasionally compared in the popular and specialist literatures. In this contribution,the dynamical evolution of solar flares and ELM filaments is separately reviewed, afterwhich the relationship between the two phenomena is examined. In particular, four familiesof dynamical theories of ELM filament evolution, classified according to the electric fieldordering and the absence/presence of magnetic reconnection at the X-point, are comparedwith experimental measurements on tokamaks. This comparison reveals that theories, whichencompass the drift ordering, offer better overall agreement with ELM filament observationsthan their MHD ordered counterparts. Although MHD ordered dynamics can describe thelinear and early non-linear phases of ELM evolution, they must be supplemented by driftordered dynamics to capture the saturation phase of the instability and the evolution offilamentary structures in the SOL. In other words, an integrated model of the ELM mustinclude finite gyro-radius terms, in particular gradient-B and curvature guiding centre driftsarising from non-uniformities in the magnetic field and diamagnetic drifts arising fromnon-uniformities in the thermodynamic variables. This is consistent with the observedresemblance between ELM filaments and turbulent eddies, or blobs, observed in the SOLduring ohmic and low confinement mode (L-mode) operation. In contrast, the dynamicalevolution of solar flares is shown to be predominantly MHD ordered, although drift orderedeffects play a role in some aspects of solar flare physics, eg. magnetic reconnection. It isconcluded that ELM filaments and solar flares are most likely governed by different regimesof magnetised plasma physics.

‡ This work was funded jointly by the UK Engineering and Physical Sciences Research Council and by theEuropean Communities under the contract of Association between EURATOM and UKAEA. The view andopinions expressed herein do not necessarily reflect those of the European Commission.

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Abstract for EFTC 2007: Madrid, September 2007

Alfvén Spectroscopy for Advanced Scenarios on JET

S.E. Sharapov

Euratom/UKAEA Fusion Association, Culham Science Centre, Abingdon,

Oxfordshire OX14 3DB, UK

Advanced tokamak scenarios on JET exhibit outstanding quality fusion-grade

plasmas, with internal transport barriers (ITBs) capable of supporting gradients ≅∇ iT

150 keV/m (with ( ) ≅0iT 40 keV), and with )(rq -profiles ranging from monotonic to

deep shear reversal, including the limiting case of toroidal current holes. It was found

experimentally, that in reversed shear JET discharges the ITB start from so-called

“ITB triggering events”, which are seen as increases in electron temperature within,

e.g. ≤ar / 0.4 by ee TT /∆ ≈ 10-30%. If main heating power is applied at this time, an

ITB is formed easily. Without an extra-heating power the improved confinement

effect is lost in about 100 msec. Here, we investigate the magnetic field topology at

the time of the ITB triggering events in JET plasmas. Alfvén spectroscopy based on

discrete spectrum of Alfvén eigenmodes (AEs) excited by ICRH-accelerated and/or

NBI-produced energetic ions is used for determining the evolution of the )(rq -

profiles. Recently developed interferometry diagnostics of AEs [1] significantly

extended time resolution and sensitivity of Alfvén spectroscopy on JET and made it

possible to perform the ITB triggering event studies with a high accuracy. The ITB

triggering events are found to occur when ( )tqmin passes values =minq integer

(majority of the cases), =minq half-integer, and when ( ) ∞→= 0rq (current hole is

triggered). This experimental data is compared to the “density of rational surfaces”

transport theory [2].

Acknowledgements

This work was funded by the UK Engineering and Physical Sciences Research Council and by the

European Communities under the contract of Association between EURATOM and UKAEA. The

views and opinions expressed herein do not necessarily reflect those of the European Commission.

[1] S.E. Sharapov et al., Phys. Rev. Lett. 93 165001 (2004)

[2] A.D. Beklemishev and W. Horton, Phys. Fluids B4 200 (1992)

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3D warm effects for low-frequency wave propagationin magnetically confined plasmas

N. Mellet, W.A. Cooper, L. Villard, P. Popovich, S. Brunner and T.M. Tran

Ecole Polytechnique Federale de Lausanne (EPFL)Centre de Recherches en Physique des Plasmas

Association Euratom-Confederation Suisse, CH-1015 Lausanne, Switzerland.

The study of wave propagation is an important topic in plasma physics as it can play aconsiderable role in heating or instability processes. The LEMan [1] code is designed totreat low-frequency waves e.g. in the Alfven and ion-cyclotron domain. In this range offrequencies, the main points of interest are heating in the ion-cyclotron domain (ICRH)and the global Alfven modes that can be driven unstable [2] by the fast ions resultingeither from fusion reactions or from neutral beam injection (NBI).

A warm model has been implemented in the LEMan code. To determine the correspond-ing dielectric tensor, the linearised Vlasov equation is solved by the same method used in[3], but retaining only the lowest order terms in the finite Larmor radius expansion. Inorder to compute the parallel gradient of the perturbed distribution function, the latteris decomposed in term of Fourier harmonics. A linear system is thus obtained and leadsto a dielectric tensor whose form corresponds to a convolution connecting together thecomponents of the Fourier series of the electric current density and field. Such a methodpermits to take into account the poloidal upshift of the parallel wave vector and to avoidusing approximations that are quite delicate in stellarator geometries.

In the Alfven range, the main kinetic effects that can be modelled with this formulationare the Kinetic Alfven Wave (KAW) and the electron Landau damping. Lack of symmetryin stellarator systems gives rise to a larger variety of global modes (TAE, HEA, MAE,etc...). These modes already exist in the cold model but can also be influenced by kineticeffects. Investigation will be done to see how the different methods act on the results.The computation of a straight helix has been done and points out the presence of ahelicity-induced Alfven eigenmode (HAE). Adding other effects like toroidicity to theprevious geometry will influence the spectrum and may modify the characteristics of theHAE.

References

[1] P. Popovich, W.A. Cooper and L. Villard, Comp. Phys. Comm., 175(4), 250 (2006).

[2] G.Y. Fu and J.W. Van Dam, Phys. Fluids A 1, 1949 (1989).

[3] S. Brunner and J. Vaclavik, Phys. Fluids B 5, 1695 (1993).

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Neoclassical and turbulent processes inglobal full-f gyrokinetic simulations

F. Ogando1,2, J.A. Heikkinen3, S.J. Janhunen1, T.P. Kiviniemi1, S. Leerink1, M. Nora1

1Euratom-Tekes Association, Teknillinen Korkeakoulu, Espoo (Finland)2Universidad Nacional de Educación a Distancia, Madrid (Spain)

3Euratom-Tekes Association, Valtion Teknillinen Tutkimuskeskus, Espoo (Finland)

The ELMFIRE full-f global gyrokinetic code[1] has been used for investigating GAM,ITG and TEM modes, as well as neoclassical transport and radial electric �eld in thelinear and non-linear regimes.

ELMFIRE has been successfully benchmarked against other codes in both linear growthrates and frequencies, and non-linear saturation of ion conductivity for the adiabaticCyclone-base case. New results are here presented for the kinetic electron case, comparedto Chen & Parker calculations [2]. The code also calculates the correct ion heat conduc-tivity values for both the neoclassical limit [3] and turbulent regime [4] (R/LT = 6.9; 9).

ELMFIRE has also been used for simulating neoclassical radial electric �eld in the FT-2tokamak. Good agreement is found in areas with low level of turbulence while showingdiscrepancies in the outermost layers of the plasma. The discrepancies have been quan-titatively justi�ed by action of turbulence and Reynolds stress on the plasma rotation.FT-2 tokamak plasma has been analyzed in more detail for testing against experimentalmeasurements. Doppler re�ectometry data have been calculated, as well as PDFs andgrowth of linear modes. Thanks to the increase of computational power, there is anongoing e�ort to simulate plasma self-organization in ASDEX Upgrade edge plasma.

ELMFIRE is based on a particle-in-cell algorithm with direct implicit treatment of po-larization drift and electron parallel movement. The algorithms in ELMFIRE will behere presented in more detail, as well as the current upgrade towards electromagneticcalculations (so far the magnetic �eld is �xed).

The facilities of CSC (Finnish IT Center for Science) and DEISA consortium have beenused in this work.

References

[1] J.A. Heikkinen et al., Contrib. Plasma Phys., 46/7-9, 490 (2006).

[2] Y. Chen et al., Nucl. Fusion, 43, 1121 (2003).

[3] F.L. Hinton et al., Rev. Mod. Phys., 48, 239 (1976).

[4] S.E. Parker et al., Phys. Plasmas, 6/5, 1709 (1999).

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Energetic Particle Instabilities with Frequency Chirping

Boris N. Breizman

Institute for Fusion Studies, The University of Texas, Austin, Texas 78712

The time scale for build-up of the energetic particle population in fusion plasmas is typically

much longer than the characteristic growth times of energetic particle-driven instabilities. This

feature draws special attention to nonlinear studies of unstable waves in near-threshold regimes.

One of the challenges here is to describe the long-time behavior of the wave-particle system in

the presence of particle sources and sinks as well as wave energy dissipation. Such a system is

known for its intricate nonlinear dynamics ranging from benign saturation of the unstable mode to

explosive growth that gives rise to strongly nonlinear phase space structures. The latter are

closely linked to frequency chirping phenomena. Experimental data from MAST, JET, DIII-D,

and NSTX show that rapidly changing frequencies can deviate significantly from the frequencies

of the known plasma eigenmodes. This deviation, once interpreted, should provide important

information about selective transport of energetic particles associated with self-consistent

evolution of the perturbed fields.

This talk presents an overview of recent progress in theoretical description and numerical

modeling of energetic particle instabilities with an emphasis on understanding frequency chirping

events and interactions between multiple phase-space structures. Of particular interest here is the

fishbone instability that involves both kinetic and MHD nonlinearities and has long presented a

challenge for numerical modeling. The main difficulty in the fishbone problem is the need to

resolve the structure of the narrow phase-space resonances, which is so far prohibitively

demanding for any of the existing global codes. This situation calls for an appropriate analytical

theory. Another important generic problem, which goes back to the basics of quasilinear theory,

is the transition from a single-mode dynamics to a multi-mode nonlinear scenario for kinetic

instabilities. The development of phase-space structures with frequency chirping adds an

interesting new aspect to this transition due to subsequent triggering of initially stable modes. In

addition to fast nonlinear chirping phenomena, there are noteworthy examples in which the

frequencies of nonlinearly saturated MHD modes evolve gradually due to slow time variation of

plasma parameters. Interpretation of such modes and their potential diagnostic applications will

also be discussed in the talk.

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Magnetic Topology Effects on Tokamak Plasma Flows

Andrei N. Simakov1, Peter J. Catto2, and Brian LaBombard2

1Los Alamos National Laboratory, Los Alamos, New Mexico, U.S.A. 2MIT Plasma Science and Fusion Center, Cambridge, Massachusetts, U.S.A.

Effects of magnetic topology changes on divergence-free plasma flow within axisymmetric magnetic flux surfaces inside and outside the separatrix of a tokamak are considered. In particular, changes in tokamak ion and impurity flows are studied [1] that are caused by (i) a switch from lower to upper X-point operation, (ii) the reversal of toroidal and poloidal magnetic fields and currents while preserving upper or lower single (or double) null operation, (iii) poloidal magnetic field or plasma current reversal, and (iv) toroidal magnetic field reversal. Alcator C-Mod scrape-off layer (SOL) flow measurements are interpreted using the flow transformation properties found for cases (i) and (ii). Case (i) can be understood by observing that up-down asymmetric single null operation introduces up-down asymmetric contributions to the flows that are not present in up-down symmetric double null operation. These contributions must clearly change sign in switching from lower to upper null operation. Then, the sum of one half the lower and upper single null plasma flows must be equivalent to the flow in an up-down symmetric double null configuration to the order required. This fact is verified by the experimental data from the SOL. The effects of transformation (ii) on plasma flow can be readily understood by observing that this transformation would be equivalent to first performing transformation (i) and then turning the tokamak over or vice versa (assuming the tokamak chamber were strictly up-down symmetric). Neglecting the chamber up-down asymmetry (which is relatively small for Alcator C-Mod except deep in the divertor) and observing that turning the tokamak over results in the reversal of plasma flow at a given fixed point on a flux surface one must conclude that transformation (ii) reverses up-down symmetric portions of plasma flow but leaves unchanged the up-down asymmetric portions. These conclusions are also confirmed by the Alcator C-Mod experimental measurements in the SOL. Even though up-down asymmetries in C-Mod complicate the interpretation of the measurements, in some cases these asymmetries can be factored out. Using density and temperature profile information allows us to evaluate the radial electric field profile. Moreover, knowledge of the effects of magnetic field topology changes on plasma flow allows the configuration with the strongest flow (or electric field) shear to be identified and thereby indicates the topology most likely to provide easiest access to H-mode operation. References [1] P. J. Catto and A. N. Simakov, Phys. Plasmas 13 (2006) 052507; ibid. 14 (2007) 029901.

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Abstract for EFTC 2007: Madrid, September 2007

Rotation, Stability and Transport J W Connor EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxon, UK, OX143DB Abstract Tokamak plasmas can frequently exhibit high levels of rotation and rotation shear. This can usually be attributed to various sources: injection of momentum, e.g. through neutral beams, flows driven by plasma gradients or torques resulting from non-ambipolar particle loss; however, the source sometimes remains a mystery, such as the spontaneous rotation observed in Ohmic plasmas. The equilibrium rotation profile is given by the balance of these sources with transport and other losses; the edge boundary conditions can play an important role in determining this profile . Such plasma rotation, particularly sheared rotation, is predicted theoretically to have a significant influence on plasma behaviour. In the first place, sonic flows can significantly affect tokamak equilibria and neoclassical transport losses. However, the influence of rotation on plasma stability and turbulence is more profound. At the macroscopic level it affects the behaviour of the gross MHD modes that influence plasma operational limits. This includes sawteeth, the seeding of neoclassical tearing modes, resistive wall modes and the onset of disruptions through error fields, mode locking and reconnection. At the microscopic level it has a major effect on the stability of ballooning modes, both ideal MHD and drift wave instabilities such as ion temperature gradient (ITG) modes. In the non-linear state, as unstable drift waves evolve into turbulent structures, sheared rotation also tears apart eddies, thereby reducing the resulting transport. There is considerable experimental evidence for these effects on both MHD stability and plasma confinement. In particular, the appearance of improved confinement modes with transport barriers, such as edge H-mode barriers and internal transport barriers (ITBs) appears to correlate well with the presence of sheared plasma rotation. This talk will describe the theory underlying some of these phenomena involving plasma rotation, on both macroscopic and microscopic scales. Some current theoretical challenges, such as reconciling sheared plasma rotation and ballooning mode theory, will be mentioned. Predicted effects on plasma stability, both for macroscopic MHD modes and for drift waves, as well as for transport will be discussed. The theoretical modelling of rotation and its effects will be linked to experimental observations on various magnetic confinement devices. Acknowledgements This work was funded by the UK Engineering and Physical Sciences Research Council and by the European Communities under the contract of Association between EURATOM and UKAEA. The views and opinions expressed herein do not necessarily reflect those of the European

Commission.

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Edge turbulence simulations: self consistent MHD equilibriumand the X-point singularity

T. T. Ribeiro1,2 and B. Scott1

1Max-Planck-Institut fur Plasmaphysik, EURATOM Association,D-85748 Garching bei Munchen, Germany

2Centro de Fusao Nuclear – EURATOM/IST Association,Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal

In the edge region of the tokamak the equilibrium and the turbulence interact strongly,and evolve together. This happens because the turbulent forcing is strong and fastenough to push the system out of an otherwise static equilibrium situation. Here, oneis concerned, in particular, with the MHD part of the equilibrium, as defined by thebalances (forces and divergences) describing the Pfirsch-Schluter current. The magneticvector potential component along the external magnetic field (A‖), which enters theMHD equilibrium, is a dynamical quantity evolved by the electromagnetic turbulencemodel. Its axisymmetric part yields the Shafranov shift, through the Pfirsch-Schlutercurrent. Since the shift is obtained from the current, it should not also be set by anMHD equilibrium solver, otherwise it would be double counted [1]. Here, one tries togeneralise the results obtained in the previous reference by using shifted-circles equilibria.Such particular simplified solution of the Grad-Shafranov equation is of relevance in thiscontext, as a starting point for addressing the general problem of treating the Shafranovshift consistently for arbitrary Grad-Shafranov solutions.

The X-point singularity is another paradigm relevant for edge turbulence. Its inclusionon the simplified equilibrium solution mentioned before (shifted circles) is foreseen. Theimpact on the turbulence of the deformation of the flux surfaces and the increase of thelocal magnetic shear [2] caused by the proximity to the X-point shall be assessed. Thiscan be done using simulations with the GEM model [3], with the geometrical informa-tion being calculated using the METRICS code [4], although in this case, due to thefield aligned coordinate system used, the domain can not contain the X-point itself, butonly approach it. Additionally, one can also study the same problem with a differentformulation of the field aligned coordinates, which uses the toroidal angle, and not thepoloidal one, as the coordinate along the magnetic field. In this case, the X-point can,in principle, be included in the domain, but one has to make sure that its topology iscorrectly represented. Note that the effort of not dropping the field aligned constraint ofthe coordinates is justified by the necessity to resolve enough degrees of freedom of thesystem under study with the computational resources available nowadays.

References

[1] B. Scott, Contrib. Plasma Phys. 46 2006 714[2] A. Kendl and B. Scott, Phys. Rev. Let. 09 (2003) 35006[3] B. Scott, Phys. Plasmas 12 (2005) 102307[4] T. Ribeiro, 30th EPS Conf. on Control. Fusion Plasma Phys. 27A (2003) P-2.152

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Linear and nonlinear magnetic island dynamics in post-disruption plasmas with

runaway electrons

Per Helander (IPP-MPG,Germany)

When a tokamak plasma survives a disruption, the current gets replaced by a beam of

ultra-relativistic (10 MeV) runaway electrons, which is embedded in the cool (10 eV),

resistive post-disruption bulk plasma. We study linear and nonlinear tearing modes in

such a two-component plasma. This is of importance since the runaway current

profile is likely to be more peaked than the pre-disruption current. The linear and

early nonlinear (Rutherford) dynamics is found to be determined by the cold plasma

component, so that unstable tearing modes are likely to grow quickly, but the

nonlinear saturation is determined by the runaway electrons, making the saturation

amplitude different.

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Global full-f gyrokinetic simulations with GYSELA

Y. Sarazin, V. Grandgirard, G. Darmet, G. Dif-Pradalier, X. Garbet, Ph. GhendrihAssociation Euratom-CEA, CEA/DSM/DRFC, CEA-Cadarache, France

The gyrokinetic description of turbulence allows one to investigate the impact of wave-particle resonances on the transport level, as well as a rigorous treatment of the dynamics ofzonal flows, which are known to contribute to the turbulence saturation. Various numericalapproaches can be envisaged to tackle the problem. The GYSELA code is based on a semi-Lagrangian scheme, which takes benefit from both the Eulerian and PIC approaches. The fullion distribution function is considered, allowing for the self-consistent treatment ofequilibrium and fluctuations. Several implications of such an approach will be highlighted.

First, in toroidal geometry, properly choosing the initial state reveals crucial in thosesimulations where the equilibrium and the fluctuations are resolved simultaneously.Especially, previous results report the self generation of large scale flows if the initial statedeparts from an equilibrium. Here, the dynamics of these flow is derived analytically,showing that an up-down asymmetric geodesic acoustic mode builds up first, linearly in time.It results from the vertical charge imbalance due to the magnetic field inhomogeneity. 5Dsimulations confirm these analytical results. Conversely, when initialising with an equilibriumdistribution function, i.e. depending on the motion invariants only, the vertical chargeseparation is naturally compensated by parallel flows

Second, when scale separation between equilibrium and fluctuations is no longer assumed, themean profile relaxation competes with the non linear couplings, which govern direct orinverse energy cascades, to saturate the turbulence level. In the 5D version of GYSELA,modelling the electrostatic branch of the Ion Temperature Gradient turbulence, coupling totwo thermal baths located at the radial boundaries provides the free energy to the system.While the linear regime allows one to recover the Cyclone base case, the non-linear turbulentregime exhibits the complexity of boundary layers where the energy flux is unconstrained.Especially, both the profile relaxation and the self-generated zonal flows are found tocontribute to the turbulence saturation. The resulting transport level is investigated whenvarying the parameter ρ*=ρi/a, the ratio of the ion Larmor radius over the minor radius. Whengoing to flux driven simulations in a 3D version of GYSELA modelling trapped ion modes,predator-prey cycles between the zonal flows and the turbulent radial transport are responsiblefor the largest relaxation events. In this case, heavy tail probability distribution functions offields such as the temperature are observed.

The proposed presentation will review the specific numerical features of the GYSELA codeas well as the physics and challenges of gyrokinetic turbulent transport.

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The Physics of Internal Transport Barriers T. Tala1, Y. Andrew2, K. Crombé3, X. Garbet4, N. Hawkes2, N. Kirneva5, P. Mantica6, S. Pinches2, A. Thyagaraja2 J. Weiland7 and JET-EFDA contributors* 1Association EURATOM-Tekes, VTT, P.O. Box 1000, FIN-02044 VTT, Finland 2EURATOM/UKAEA Fusion Association, Culham Science Centre, Oxon. OX14 3DB, UK 3Department of Applied Physics, Ghent University, Belgium 4Association EURATOM-CEA, CEA/DSM/DRFC Cadarache, St Paul-Lez-Durance, France 5RRC Kurchatov Institute, Moscow, Russia 6Istituto di Fisica del Plasma CNR-EURATOM, via Cozzi 53, 20125 Milano, Italy 7Association EURATOM-VR, Chalmers University of Technology, Göteborg, Sweden *See Appendix of M.L. Watkins et al., Fusion Energy 2006 (Proc. 21st Int. Conf. Chengdu 2006), IAEA Vienna (2006)

The Internal Transport Barriers (ITBs) were found more than a decade ago. Still for the time being, there are many open questions concerning their physics and dynamics. Several mechanisms are believed to affect the triggering and formation of the ITB, and subsequent dynamical processes, like expansion, strengthening and collapse of the barrier.

Regarding the question of dominant ITB formation mechanisms, many experimental results on JET are consistent with ITB dynamics controlled by the E×B flow shear and local magnetic shear. On the other hand, the actual triggering of the ITB is less clear. While the role of minimum value of the q-profile approaching an integer value is known to be significant [1], the actual role of q is delicate as the ITB is triggered before qmin reaches an integer value, indicated by the grand Alfven Cascades [2]. The prime candidate to explain the ITB triggering is the E×B flow shear. The increase in the E×B flow shear within the ITB is experimentally seen as a spin-up of the carbon poloidal velocity with the charge exchange resonance spectroscopy measurements [3]. Furthermore, the transport modelling with the Weiland and GLF23 transport models using the experimental poloidal velocity instead of the neo-classical one strongly supports the crucial role of E×B flow shear in triggering the ITB. The causality between the onset of the ITB and spin-up of the poloidal velocity has been studied extensively and will be reported here.

The role of magnetic shear is also undisputable. When the magnetic shear is negative enough, for example in the case of current hole, a strong ITB in the electron channel is observed, and often with very small E×B flow shear. The role of magnetic shear is less clear for ion heat transport channel. Certainly it facilitates the ITB formation, but whether it alone is able to trigger an ITB has not been proven. The role of stabilisation, the role of density peaking, the dilution effects due to impurities and fast particles are theoretically believed to affect the physics of ITBs. However, although some of them are found to play a role in some tokamaks, they have not been demonstrated to have such a universal role across the multimachine comparison as the E×B flow shear, magnetic shear and the q-profile.

Predicting the dynamics of the ITBs has turned out to be extremely challenging. Transport simulations across the multi-machine ITB database with the theory-based models show that in most cases, the models fail to predict the onset time correctly and often the location and strength of the ITBs are also incorrect. The use of neo-classical poloidal velocity in calculating the E×B flow shear is certainly one of the main reasons why most of the transport simulations of the ITB dynamics have so far failed. The results from the upgraded Weiland model with self-consistent prediction for the poloidal velocity are promising and probably the best way to obtain a large step in the predictive capability of simulating ITBs. Although the dynamics of the ITBs cannot be predicted satisfactorily with present theory-based transport models, the location and strength of the ITB can be controlled in real-time in experiments, and also on long, resistive time scale in fully predictive time-dependent transport simulations. [1] E. Joffrin et al., Nucl. Fusion, 43, 1167 (2003). [2] S. Sharapov et al., Nucl. Fusion 46 (2006) S868. [3] K. Crombe et al., Phys. Rev. Lett. 95 (2006) 155003.

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The Physics of Burning Plasmas in Toroidal Magnetic Field Devices

Fulvio Zonca

ENEA - C.R. Frascati - C.P. 65 - 00044 Frascati, Italy

Abstract:

Some of the crucial physics aspects of burning plasmas magnetically confined in toroidal systems are

presented from the viewpoint of nonlinear dynamics. Most of the discussions specifically refer to

tokamaks, but they can be readily extended to other toroidal confinement devices. Particular emphasis

is devoted to fluctuation induced transport processes of mega electron volts energetic ions and charged

fusion products as well as to energy and particle transports of the thermal plasma. Long time scale

behaviours due to the interplay of fast ion induced collective effects and plasma turbulence are

addressed in the framework of burning plasmas as complex self-organized systems. The crucial roles of

mutual positive feedbacks between theory, numerical simulation and experiment are shown to be the

necessary premise for reliable extrapolations from present day laboratory to burning plasmas.

Examples of the broader applications of fundamental problems to other fields of plasma physics and

beyond are also given.

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Gyrokinetic Simulation of Microinstabilities for the Stellarator Wendelstein 7-X

P Xanthopoulos and F Jenko

IPP-MPG

A numerical investigation of ion temperature gradient modes - considering_both adiabatic and kineticelectrons - and trapped electron modes is presented for the stellarator Wendelstein 7-X._The flux tubesimulations are performed by means of the gyrokinetic turbulence code GENE, employing Clebsch-type coordinates generated by field line tracing. _A linear study reveals substantial differences withrespect to axisymmetric geometries, which are attributed to the relative separation of regions with alarge fraction of helically trapped particles and those of pronounced bad_curvature._Nonlinear resultsare also presented, determining several turbulence characteristics, such as transport levels, Dimits shifteffects and the role of zonal flows and secondary instabilities.

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The Microtearing Mode

W. Horton

Institute for Fusion StudiesThe University of Texas at Austin, Austin, Texas, 78712, USA

Microtearing modes are driven by combinations of the electron temperaturegradient and the current density gradient, and thus may add to the anomalouselectron thermal flux in current carrying plasmas. The problem has a long historyin fusion research where generally the earlier results such as Connor et al. in PPCF(1990) find that the passing electron response and a stabilizing MHD responsefrom Δ′ over come the destabilization from the trapped electrons. They concludethat a typical tokamak system is unlikely to have unstable microtearing modes.There is experimental and gyrokinetic simulation evidence suggesting the presenceof microtearing modes perhaps coupled to the ETG modes. Without thetemperature gradient we benchmark a gyrofluid code with simulations [Horton etal. PoP, 012902 (2007)] showing coherent structures and dramatic magnetic energyreleases to the electron pressure from sheared magnetic fields –positive Δ′. Weperform a number of simulations looking for conditions when both the temperaturegradient and the current density gradient allow sustain electromagnetic turbulence

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20

POSTER SESSION 1

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22

Effects of plasma elongation on drift wave-zonal flow turbulence

P. Angelino¹, X. Garbet¹, V. Grandgirard¹, Y. Sarazin¹, Ph. Ghendrih¹, G. Dif-Pradalier¹,

S. Jolliet², A. Bottino³, B. F. McMillan², T. M. Tran², L. Villard²

¹Association Euratom - CEA, CEA/DSM/DRFC Cadarache

13108 Saint-Paul-lez-Durance, France

²Centre de Recherches en Physique des Plasmas,

Association Euratom - Confédération Suisse

EPFL, Lausanne, Switzerland

³Max Plank Institut für Plasmaphysik, IPP-EURATOM Association

Garching, Germany

The theoretical study of plasma turbulent transport is of central importance to fusion

research. Experimental evidence indicates that the confinement time is in fact a consequence

of the turbulent transport of energy. The magnitude of turbulent transport depends on the

turbulent state resulting from nonlinear saturation mechanisms. The ion heat anomalous

transport in the plasma core fusion devices seems to be dominated by a class of

microinstabilites, the toroidal ion temperature gradient driven modes (ITGs). ITG turbulence

is known to self organize to form coherent macroscopic structures extended in the direction

perpendicular to the gradient. These structures are essentially axisymmetric flows

denominated zonal flows. The amplitude of zonal flows can oscillate: these perturbations are

known as Geodesic Acoustic Modes (GAMs). Zonal flows act as a regulating mechanism on

plasma microturbulence, the saturated turbulent state being determined by the nonlinear

interactions between ITGs, zonal flows and GAMs [1].

We present an analytical study showing the strong impact that plasma geometry has on zonal

flow collisionless linear damping. The GAM frequency is shown to scale inversely with the

elongation and the aspect ratio. These results are supported by numerical linear analysis,

which in addition shows that the GAM damping rate and the undamped zonal flow

component are enhanced by elongation and smaller aspect ratio. The same parameters also

modify the ITG linear growth rates. Therefore linear analysis suggests that geometry can

play a role in the determination of the turbulent transport level. On the other hand, the extent

of this action can be quantified only by means of full nonlinear calculations. We present the

results of nonlinear gyrokinetic simulations in realistic tokamak magnetohydrodynamic

equilibria, focusing on the role of plasma elongation. The effect of the variation of this

parameter on the ion heat transport and zonal flow-GAM interactions is investigated in a

nonlinear saturated regime.

[1] P. Angelino, et al., Plasma Phys. Control. Fusion 48(5) 557 (2006)

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Resistive Edge Modes in Stellarator and Tokamak Geometries

M. Ansar Mahmooda, M. Perssona, and T. Rafiqb,1

aDepartment of Signals and Systems, and Euratom/VR Association,Chalmers University of Technology, S-41296 Goteborg, Sweden

bCenter for Plasma Theory and Computation, University of Wisconsin-Madison, USA

The reactive ion-temperature-gradient driven drift mode (or ηi mode) is a promising can-didate for explaining the anomalous transport in the core of tokamak plasmas. However,a strong influence of electron-ion collisions in the edge region gives a resistive nature tothe drift modes. So far, a lot of work has been done towards understanding of thesemodes in tokamak configurations, whereas a limited amount of work has been reportedin stellarators. In the present work, linear stability of the collisional ηi mode and theresistive ballooning mode in the electrostatic limit is studied in a three-dimensional Wen-delstein 7-X Stellarator geometry. The full magnetic field configuration is obtained usingthe variational moments equilibrium code VMEC. The reduced Braghinskii equations areused as a model for the electrons and an advanced fluid model for the ions. By employingthe ballooning mode formalism, the drift wave problem is set as an eignevalue equationalong a field line. The derived eigenvalue equation is solved numerically using a standardshooting technique and applying WKB type boundary conditions. The growth rates andreal frequencies of the most unstable modes and their eigenfunctions are calculated. Theeffects of collisions, density and temperature gradients and other geometrical quantitieson mode localization and stability are studied. Finally, the results are contrasted andcompared with those obtained for an ITER-like geometry.

1One of the authors, T. Rafiq, acknowledges the support of the U.S. DOE under Grants No. DE-FG02-99E54546 and DE-FG02-86ER53218.

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Turbulent transport of energetic ions

T. Dannert1, S. Gunter2, T. Hauff2, F. Jenko2

1Ecole Polytechnique Federale de Lausanne (EPFL), Centre de Recherches en Physiquedes Plasmas, Association Euratom-Confederation Suisse,

CH-1015 Lausanne, Switzerland2Institut fur Plasmaphysik, EURATOM-Assoziation, Boltzmannstr. 2,

D-85748 Garching, Germany

Anomalous transport of heat and particles is known to be a key issue for fusion devices.In the present paper the anomalous transport of fast ions is investigated. High transitfrequencies of the fast ions lead to the assumption that there is only very weak interactionwith the low-frequency turbulence. However, our results indicate a significant fast ionparticle transport due to the turbulence. To investigate this interaction, a second ionspecies is introduced into a saturated gyrokinetic turbulence simulation and the transporteffects of the turbulence on the fast ions is analyzed. The fast ion species can serve as amodel for ions which are introduced by neutral beam injection (NBI).

The simulation of the turbulence and the fast ions is done with the GENE [1, 2] code.The beam ions are treated as passive tracers but obey the fully gyrokinetic dynamics. Asmodel for the equilibrium beam ion distribution an unsymmetric Maxwellian with twodifferent temperatures in beam direction and in counter-beam direction is used. Thismodel and the resulting modifications to the gyrokinetic equations are discussed. Theinfluence of the turbulence on the particle distribution is presented, together with thedependencies on beam parameters. A link to the twodimensional studies of Hauff andJenko [3] is established and a physical picture of the processes involved will be shown.

The presented results have an impact on the NBI current drive and are a possible ex-planation for results reported from Asdex Upgrade [4], where the decrease of the currentdrive efficiency with higher input power was explained by a turbulent redistribution offast ions. Future experiments, which make extensive use of NBI current drive, may alsobe affected by this turbulent particle transport of energetic ions.

References

[1] F. Jenko et al., Phys. Plasmas 7 (2000), 1904

[2] T. Dannert and F. Jenko, Phys. Plasmas 12 (2005), 072309

[3] T. Hauff and F. Jenko, Phys. Plasmas 13 (2006), 102309

[4] S. Gunter et al., 31st EPS Conference on Plasma Phys. London (2004)

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Effects of Gyro-fluid Resonances

on Turbulent Particle Pinches

A. Eriksson and J. Weiland

Chalmers University of Technology, Euratom-VR, Goteborg, Sweden

Turbulent particle pinches, defined as anomalous inward particle fluxes, are experimen-

tally seen in tokamak plasmas but are not fully understood theoretically.

One thing that affects the magnitude and presence of these pinches is the description

of wave-particle interaction. From the fluid point of view, wave-particle interaction is

seen as fluid moments that are not relaxed on the confinement time scale. These fluid

moments are represented in the density response by a dissipative resonance.

We have investigated the effects of gyro-fluid resonances on particle pinches. Comparisons

are made with experimental data, gyro-fluid and gyro-kinetic simulations.

Gyro-fluid resonances are found to significantly reduce particle pinches. Experimental

comparisons show that the reduction is strong enough to suggest that fluid moments

without sources are relaxed on the confinement time scale.

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Turbulent excitation of plasma oscillations in the acoustic frequency range

G.L. Falchetto, M. Ottaviani, X. Garbet and A. Smolyakov*

Association EURATOM-CEA, CEA/DSM/DRFC, Centre de Cadarache

13108 Saint-Paul-Lez-Durance, France

*Department of Physics and Engineering Physics, University of Saskatchewan

Saskatoon, Canada

The impact of the geodesic curvature on flux-driven electrostatic ITG (Ion Temperature

Gradient) turbulence in the core of tokamak plasmas is studied by means of 3D global

numerical simulations. The emphasis of this work is on the dynamics of the axisymmetric

fluctuations.

A 3D Landau-fluid model is used; it consists of the evolution equations for the ion guiding

center density, the ion parallel velocity and the ion temperature (instead of the ion pressure as

in previous work [1]). The turbulence code ETAI3D [2] has been consistently modified to

solve for the improved model. The simulations evolve the equilibrium and the perturbed

fields as a whole. The coupling of poloidal harmonics induced by the curvature results, on one

side, in the presence of neoclassical transport and on the other, in the generation of

oscillations in the acoustic frequency range. Therefore, the simulations show both turbulent

and neoclassical transport effects.

The neoclassical thermal conductivity evaluated for the considered isotropic model, is found

to scale as the plateau conductivity. The conductivity computed in the simulations perfectly

agrees with that theoretical estimate. Geodesic Acoustic Modes (GAMs) [3] are only observed

transiently in the simulations. The GAM oscillations are strongly reduced in the final

turbulent stationary state.

The main peak in the poloidal velocity spectra is observed at a lower frequency. The detailed

analysis of the simulations in the turbulent stationary state, in particular by means of a

singular value decomposition (SVD) of the space-time data, shows that a quasi-coherent mode

having a radial wavelength somewhat larger than the ion Larmor radius, and frequency

somewhat lower than the acoustic one, is more effectively excited by the turbulence.

An extended analysis of the linear problem, allowing for finite radial wavelengths, led to

identify two classes of modes in the ion acoustic frequency range. One is associated with

GAMs, the frequency of which is up-shifted by finite Larmor radius effects, as it was also

shown via kinetic calculations in [4, 5]. The other branch is wavelength dependent. For a

typical turbulence wavelength it appears somewhat below the ion acoustic frequency and it

has essentially the character of a temperature oscillation.

Both GAMs and the lower frequency branch are resonances of the dynamics of the

axisymmetric fluctuations. Which of the two dominates in the turbulent state depends on the

relative strength of the various non-linear drives of which Reynolds stresses are just one

aspect.

References

[1] G. L. Falchetto and M. Ottaviani, Phys. Rev. Lett. 92, 025002 (2004).

[2] M. Ottaviani and G. Manfredi, Phys. Plasmas 6, 3267 (1999).

[3] N. Winsor, J. Johnson, and J. Dawson, Phys. Fluids 11, 2448 (1968).

[4] T. Watari et al., Phys. Plasmas 13, 062504 (2006).

[5] X. Garbet et al., in Theory of fusion plasmas, Joint Varenna-Lausanne International Workshop, edited by

AIP (Melville, New York, 2006), vol. 871 of AIP Conference Proceedings, p.342.

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Redistribution of Energetic Particles byBackground Turbulence

T. Hauff?, T. Dannert†, F. Jenko?

?Max-Planck-Institut fur Plasmaphysik, EURATOM-Association, D-85748 Garching,Germany

†Ecole Polytechnique Federale de Lausanne (EPFL), Centre de Recherches en Physiquedes Plasmas, Association Euratom-Confederation Suisse, CH-1015 Lausanne,

Switzerland

Although it is widely believed that fast particles – like alpha particles or beam ions –do not interact significantly with the background turbulence, our present understandingof this issue is still relatively poor. And as will be shown in our presentation, this basicintuition is not true in general. In order to understand the basic mechanisms determiningthe turbulent diffusion of fast particles, we perform direct numerical simulations of testparticles in prescribed electrostatic potentials. First, these potentials are random and two-dimensional; then, we consider three-dimensional potentials produced by the gyrokineticturbulence code Gene.Using an idealized isotropic potential with Gaussian statistics, numerous test particlesimulations are done varying both the gyroradius and the Kubo number of the potential.It is found that for Kubo numbers larger than about unity, the particle diffusivity isalmost independent of the gyroradius as long as the latter does not exceed the correlationlength of the potential. For smaller Kubo numbers, on the other hand, the diffusivityis reduced monotonically. The underlying physical mechanisms are identified and ananalytic approach is developed which favorably agrees with the simulation results. Theseinvestigations are then extended by introducing anisotropic structures like streamers andzonal flows as well as drift effects into the random potential. Analytic models are used toexplain these various effects.Additionally, we explore the issue under what conditions and for what timescales a non-diffusive transport behavior can be observed. Here, we find that non-diffusive transportdepends on the existence of quasi-stationary structures in the background plasma.Having developed a general picture of the behavior in simplified artificial potentials, testparticle simulations in realistic turbulent fields are presented. They are compared to theprevious results which enable us to understand the interaction between the wide numberof effects present at the same time, including drift orbit averaging. Finally, implicationsfor present-day experiments and ITER are discussed.

1

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2D Gyrofluid simulations of edge/SOLdynamics

J. Madsen, J. Stærk, O.E. Garcia, V. Naulin, A.H. Nielsen and J. Juul Rasmussen

1. Association EURATOM- Risoe National Laboratory, Danish Technical University, OPL-128, 4000Roskilde Denmark

Experimental observations show that the ion temperature outside the Last Closed FluxSurface (LCFS) may be comparable to or even higher that the electron temperature. .Earlier work [1][2] based on the cold ion approximation has been able to reproduceexperimental observations. We expect that by relaxing the cold ion approximation wewill be able to improve the understanding and predictions of interchange driventurbulence in the edge/SOL (Scrape Off Layer) regions. To account for finite ion-temperature effects we have developed a 2D gyrofluid model describing the dynamics inthe edge/SOL regions. The gyrofluid approach leads to tractable FLR (Finite LarmorRadius) corrected fluid equations.

Here we present results from the 2D gyrofluid code G-ESEL, which simulates local andnon-local [3] gyrofluid equations. The propagation of Gaussian “blob” like structures,show a larger coherence of the structures and an increased radial transport in the case offinite ion temperature. Also, we present turbulence simulations using G-ESEL andcompare them to the ESEL simulations for cold ions for typical TCV and JETparameters.

[1] O. E. Garcia, V. Naulin, A. H. Nielsen, and J. Juul Rasmussen, Phys.Rev. Lett. 92, 165003 (2004);Phys. Plasmas 12, 062309 (2005).[2] O.E. Garcia et al., Plasma Phys. Control. Fusion 48, L1-L10 (2006).[3] D. Strintzi and B. D. Scott , Phys Plasmas 11, 5452, (2004).

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Parallel momentum in a 3D cylindrical plasma simulation

V. Naulin1, P.H. Diamond2, Ö.D. Gürcan2 and J. Juul Rasmussen1

1.Association Euratom-Risoe National Laboratory Technical University of Denmark,P.O Box 49, DK 4000 Roskilde Denmark

2.Center for Astrophysics and Space Science Department, UCSD, La Jolla, USA

Understanding the transport of parallel momentum has become a high priority topic during thelast years, where its importance for plasma confinement has been recognized. Core plasmarotation is now routinely observed in tokamak discharges without external momentum input[1]. In particular, it is important that spontaneous generation of parallel momentum fromturbulence needs a symmetry breaking in the parallel wavenumber spectrum. In a recent paper[2] it was shown, that poloidal shear flows can provide the necessary asymmetry in the k-parallel spectrum, which will mediate the generation of the parallel flowHere we present results from simulations of a two fluid model of a cylindrical magnetizedplasma which is periodic in the parallel direction. The interaction of the drift wave type ofturbulence with the plasma profiles is included in the model, as well as parallel electron andion velocities. We investigate parallel flow generation in situations with and without poloidalshearing and compare the results to theoretical predictions..

[1] J.E. Rice et al., Nucl. Fusion 44, 379 (2004) ; 45, 251, (2005) ; Bortolon et al., Phys. Rev.Lett. 97, 235003 (2006).[2] Ö.D. Gürcan et al., Physics of Plasmas 14, 042306 (2007).

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30

Generation and Stability of Large Scale Magnetic Structures in Electron Drift Turbulence

M. Jucker1 and V. P. Pavlenko2

1Ecole Polytechnique Federale de Lausanne (EPFL), Centre de Recherches en Physique des

Plasmas, Association EURATOM-Confederation Suisse, 1015 Lausanne, Switzerland

2Uppsala University and EURATOM-VR Fusion Association, SE-751 20 Uppsala, Sweden The generation of large scale flows by underlying small scale turbulence is a well known

phenomenon in different areas of current research. Here, we turn our attention to the

magnetic electron drift mode turbulence. The corresponding turbulent magnetic fluctuations

are drift-type modes excited in non-uniform initially non-magnetized plasma, characterized

by a frequency range in-between the electron and the ion plasma frequencies. Within the

magnetic electron drift mode turbulence, we address the question of generation of large scale

magnetic fields by small scale turbulent magnetic fluctuations via turbulent Reynolds stress,

as well as their subsequent mutual interactions.

For the mathematical description we have to take into account that the total wave energy is

conserved and contains both the part stored in small as well as large scale structures. We

thus deal with a coupled system of two different parts of the same wave spectrum which

cannot be addressed in isolation. This necessitates a nonlinear theory capable of describing

magnetic electron drift wave and large scale magnetic fields spectra as interacting parts of

one and the same spectrum. Such a self-consistent nonlinear model has been developed via a

wave kinetic equation for a suitable action-like invariant. Having the spectral model

equations in our hand, we focus on the dynamics of interacting magnetic drift wave - large

scale field turbulence. The stability of such large scale structures is investigated in the

kinetic regime, and an instability criterion similar to the known Nyquist criterion in kinetic

wave theory is found. This criterion is then applied to a narrow wave packet, where we find

an amplitude threshold due to finite width of the wave spectrum in k-space.

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31

Turbulent transport in non-Ohmic plasma: an ion-cyclotron resonance heating case

N. Pometescu1 and B. Weyssow2

1Department of Physics, University of Craiova, Romania.

2 Physique Statistique et Plasmas, Université Libre de Bruxelles,, Belgium The combined effect of the electromagnetic turbulence and of the external radio-frequency heating on the radial and poloidal components of the ion particle flux in axis symmetric magnetically confined plasma is analyzed analytically from the drift kinetic equation. These two components of the transport, for passing particle regime, are derived in terms of the thermodynamic forces and of correlations of fluctuating quantities using the methodology of neoclassical transport theory based on the tokamak standard model of confining magnetic field. The formalism is applied to different types of instabilities in order to quantify the role of the heating versus turbulence on the transport, especially for the anomalous particle pinch [1]. References [1] N. Pometescu and B. Weyssow “Radial and poloidal particle and energy fluxes in a turbulent non-Ohmic

plasma: An ion-cyclotron resonance heating case” Physics of Plasmas, Vol.14, 022305 (2007)

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32

A drift model of interchange instability

E. Benilov and O. Power

University of Limerick, Limerick, Ireland

A set of asymptotic equations is derived, describing the dynamics of the flute mode in amagnetized plasma with cold ions, under a ‘local’ approximation (i.e. near a particularpoint). The asymptotic set is then used to calculate the growth rate of interchangeinstability in the slab model. It is shown that, unlike the MHD ordering, the drift oneallows instability to occur for either sign of the pressure gradient (i.e. for both ‘bad’ and‘good’ curvature of the magnetic field). It is also demonstrated that finite beta gives riseto an extra instability which does not exist in the small-beta limit.

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33

Electron diffusion in a sheared unperturbed magnetic field and anelectrostatic stochastic field

I. Petrisor1, M. Negrea1 and B. Weyssow2

1Department of Physics, Association Euratom-MEdC, Romania,University of Craiova, A.I.Cuza str.13, Craiova, Romania.

2Physique Statistique – Plasmas, Association Euratom-Etat Belge, Université Libre deBruxelles, Campus Plaine CP231, Bd. du Triomphe, 1050 Bruxelles, Belgium

The electron diffusion induced by a two-dimensional electrostatic turbulence, in a sheared slabapproximation of the toroidal magnetic geometry, is studied firstly using the decorrelationtrajectory method (DCT), secondly using direct numerical simulation. The former semi-analytical method allows us to go beyond the Corrsin approximation, well suited for a non-classical analysis of the particle trapping phenomena.

The numerical simulations assume an isotropic spectrum of electrostatic drift type turbulencethat is Gaussian for small wave-vectors and power-law k-3 for large wave-vectors. The ‘radial’and the ‘poloidal’ running and asymptotic diffusion coefficients of thermal electrons areobtained for physically relevant parameter values. An enhanced diffusion in the poloidaldirection is observed due to the magnetic shear.

The agreement between the semi-analytical method and the purely numerical method is pointedout.

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34

Diamagnetic effects on zonal flow generation in weak electrostatic turbulence

I. Petrisor1, M. Negrea1 and B. Weyssow2

1Department of Physics, Association Euratom-MEdC, Romania,University of Craiova, A.I.Cuza str.13, Craiova, Romania.

2Physique Statistique – Plasmas, Association Euratom-Etat Belge, Université Libre de Bruxelles,Campus Plaine CP231, Bd. du Triomphe, 1050 Bruxelles, Belgium

Intermittency in particle transport at the plasma edge is a quite common feature to all fusiondevices. It is observed in many different confinement regimes including complex situationsinvolving time dependent evolution of transport barriers and zonal flows as demonstrated inrecent papers.

The theories developed for the understanding of the anomalous particle transport therefore shouldcarefully take into account the non-Markovian and non-gaussian features of the underlyingturbulence. We consider specifically the zonal flow generated by an anisotropic electrostaticturbulence. As analytical tool, we adopt the decorrelation trajectory method since the methodretains correlations between stochastic processes beyond the Corrssin approximation.

We show that the fragmentation of the drift wave structures, which is a signature of the zonalflow generation, is not only influenced by the anisotropy parameter and the electrostatic Kubonumber but also by the diamagnetic Kubo number. The later depends on the level of turbulence(ratio between the correlation time and the correlation length) and the density scale length.

An original code for calculating the diffusion coefficients is used. The model Langevin equationsare derived from the wave Liouville equation adapted to the zonal flow. The dimensionalLagrangian correlations and diffusion tensor components are obtained in the case of theanisotropic weak electrostatic turbulence.

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35

Multi-Accuracy-Level Burning Plasma Simulations

J.F. Artaud, V. Basiuk, J. Garcia G. Giruzzi, P. Huynh,G. Huysmans, F. Imbeaux, J. Johner, and M. Schneider

Association EURATOM-CEA, CEA/DSM/DRFC, CEA-Cadarache, F-13108 St. Paul lez Durance.

The design of a reactor grade tokamak is based on a hierarchy of tools. We present here three codes that are presently used for the simulations of burning plasmas. At the first level there is a 0-dimensional code that allows to choose a reasonable range of global parameters; in our case the HELIOS code was used for this task [1]. For the second level we have developped a mixed 0-D / 1-D code called METIS that allows to study the main properties of a burning plasma, including profiles and all heat and current sources, but always under the constraint of energy and other empirical scaling laws [2]. METIS is a fast code that permits to perform a large number of runs (a run takes about one minute) and design the main features of a scenario, or validate the results of the 0-D code on a full time evolution. At the top level, we used the full 1D1/2 suite of codes CRONOS that gives access to a detailed study of the plasma profiles evolution [3]. CRONOS can use a variety of modules for source terms and transport coefficients computation with different level of complexity and accuracy: from simple estimators to highly sophisticated physics calculations. Thus it is possible to vary the accuracy of burning plasma simulations, as a trade-off with computation time. A wide range of scenario studies can thus be made with CRONOS and then validated with post-processing tools like MHD stability analysis. We will present in this paper results of this multi-level analysis applied to the ITER hybrid scenario [4]. This specific example will illustrate the importance of having several tools for the study of burning plasma scenarios, especially in a domain that present devices cannot access experimentally.

References

[1] J. Johner, Minimum dimension of an ITER like tokamak with a given Q, EUR-CEA-FC-1735 (2004)[2] J.F. Artaud et al, 32nd EPS Conference on Controlled Fusion and Plasma Physics, 2005[3] V. Basiuk et al., Nuclear Fusion 43, pp 822-, 2003.[4] J.F. Artaud et al.,13th International Congress on Plasma Physics (2006).

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36

Magnetic Nozzle and Plasma Detachment Scenario

B. N. Breizman

Institute for Fusion Studies, The University of Texas at Austin, Austin, TX 78712

Some plasma propulsion concepts rely on a strong magnetic field to guide the plasma

flow through the thruster nozzle. The question then arises of how the magnetically

controlled plasma can detach from the spacecraft. This talk presents a

magnetohydrodynamic detachment scenario in which the plasma stretches the magnetic

field lines to infinity.1 Such a scenario is of particular interest for high-power thrusters.

As plasma flows along the magnetic field lines, the originally sub-Alfvénic flow becomes

super-Alfvénic: this transition is similar to what occurs in the solar wind.2 In order to

describe the detachment quantitatively, the ideal MHD equations have been solved

analytically for a plasma flow in a slowly diverging nozzle. The solution exhibits a well-

behaved transition from sub- to super- Alfvénic flow inside the nozzle and a rarefaction

wave at the edge of the outgoing flow. The magnetic field in the detached plume is

almost entirely due to the plasma currents. It is shown that efficient detachment is

feasible if the nozzle is sufficiently long. In order to extend the detachment model beyond

the idealizations of analytical theory, a Lagrangian fluid code has been developed to

solve steady-stated MHD equations and to optimize nozzle efficiency by adjusting the

magnetic coil configuration. This numerical tool enables broad parameter scan with

modest computational requirements (single workstation). The code has been

benchmarked against the idealized analytical picture of plasma detachment and then used

to investigate more realistic nozzle configurations that are not analytically tractable. Most

recently, the code has been used to interpret experimental data from the Detachment

Demonstration Experiment (DDEX)3 facility at NASA Marshall Space Flight Center.

1 A. Arefiev and B. Breizman, “Magnetohydrodynamic scenario of plasma detachment in a magnetic

nozzle”, Phys. Plasmas 12, 043504 (2005) 2E. N. Parker, Astrophys. J., 128, 664 (1958)

3 D. Chavers et al., “Status of Magnetic Nozzle and Plasma Detachment Experiment”, CP813, Space

Technology and Applications International Forum, p. 465 – 473, AIP 2006

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37

Fractional generalization of Fick’s law

I. Calvo1, R. Sánchez2, B. A. Carreras3 and B. Ph. van Milligen1

1 Laboratorio Nacional de Fusión, Asociación EURATOM-CIEMAT28040 Madrid, Spain

2 Fusion Energy Division, Oak Ridge National LaboratoryOak Ridge, TN 37831, U.S.A

3 BACV Solutions Inc.Oak Ridge, Tennessee, U.S.A.

In the study of particle transport in magnetically confined plasmas it is common to construct

transport equations based on extensions of Fick’s law [1]:

Γ(x, t) = −D(x)∂xn(x, t) (1)

in which the particle flux is proportional to the particle density gradient (in general, the diffu-

sivity may also depend explictly ont and even on other fields). Such transport equations imply,

in particular, the existence of a characteristic length scale. However, numerical simulations and

experimental findings seem to suggest that this framework istoo restricted. Fractional differen-

tial equations provide a natural setup to formulate transport equations without a characteristic

length scale due to their intrinsic non-local character. The aim of the present work is to capture

the essential microscopic features underlying (1) and find its fractional generalization.

Continuous-Time Random Walks [2] give a suitable formalismto approach the dynamics

of n(x, t) from a microscopic point of view. The latter is described in terms of a General-

ized Master Equation [3, 4] whose key ingredient is a probability distribution ξ (∆x,∆t ;x′) =

p(∆x;x′)ψ(∆t ;x′) giving the probability that a particle located atx′ at timet ′ jump tox= x′+∆x

at timet = t ′+∆t . Fick’s law is obtained in the fluid limit as long asp(∆x;x′) possesses a certain

symmetry [5] (usually calledglobal detailed balance) and has finite moments of arbitrary order.

We construct the appropriate fractional generalization ofFick’s law by taking Lévy stable dis-

tributions (which only have a finite number of finite moments)which satisfy the global detailed

balance condition.

References

[1] A. Fick, Ann. Phys.23, 59 (1855).

[2] E. W. Montroll and G. Weiss, J. Math. Phys.6, 167 (1965).

[3] V. M. Krenke, E. W. Montroll and M. F. Schlesinger, J. Stat. Phys.9, 45 (1973).

[4] B. Ph. van Milligen, R. Sánchez and B. A. Carreras, Phys. Plasmas11, 2272 (2004).

[5] N. G. van Kampen,Stochastic Processes in Physics and Chemistry, North Holland, New

York 1981.

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38

Influence of transport on EBW heating efficiency in magnetic confinement devices.

A. Cappa, F. Castejón, D. López-Bruna, and M. Tereshchenko*

Laboratorio Nacional de Fusión. Asociación Euratom/Ciemat para Fusión.

28040,Madrid, Spain. * General Physics Institute, Russian Academy of Sciences, Moscow, Russia

The main advantage of the heating performed by electron Bernstein waves

(EBW) in the O-X-B1 regime (O mode injection that is converted into X mode, which is converted in Bernstein wave, strongly absorbed close to the cyclotron resonance layer at first harmonic) is that there is no cut-off density. Therefore, this heating system can work without upper density limit, still having all the advantages of electron cyclotron resonance heating (ECRH), which is localised in phase space due to its resonant nature.

The heating efficiency of Bernstein waves depends on the fraction of waves that

is transformed from O to X mode at the O mode cut off layer, then on the fraction of power converted into Bernstein waves at the upper hybrid resonance layer and, finally, on the final position of the absorption in the plasma. All these factors are related to the density profile, since the positions of the cut off and of the upper hybrid resonance layers depend on the actual plasma density profile. Besides, the absorption profile depends also on the temperature profile. Moreover, it is possible to observe that the former layers only appear for high enough plasma density, than can be obtained by gas puffing, as has been observed in the simulations performed for TJ-II stellarator [1].

For such reasons, particle transport is basic for understanding and guaranteeing

EBW heating. In this work, TJ-II plasmas are taken as a case example in order to simulate the full evolution of a plasma discharge that is created and heated by ECRH in a first step and finally is heated using EBW. The evolution of the discharge is simulated using the transport code ASTRA and the sequence of the discharge is as follows: O mode is launched on a steady state plasma with density lower than the O mode cut-off. Then a gas puff is injected in order to increase the plasma density over the level in which EBW heating is efficient [2] because O mode cut off and upper hybrid layer appear. EBW ray tracing calculations are performed every 5 ms in order to estimate the transmission and heating efficiency, using a weakly relativistic dispersion relation that has been introduced in the ray tracing code TRUBA [3].

[1] F. Castejón et al. Fusion Science and Technology 46 (2004) 327. [2] M. Tereshchenko et al. “Development and Use of 3D Ray/Beam Tracing Code for Plasma Heating by EBW in the TJ-II Stellarator” 30TH EPS Conference on Plasma Physics and Controlled fusion. St. Petersburgo, Russia, 2003. [3] F. Castejón, A. Cappa, M. Tereshchenko, S. S. Pavlov, and A. Fernández. “Weakly Relativistic and non- Relativistic estimates of EBW heating in TJ-II Stellarator”. To be published in Fusion Science and Technology, 2007 (In press).

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39

Nonlinear Dynamics of Multiple NTMs in Tokamaks

D. Chandra1,3, O. Agullo1, S. Benkadda1, X. Garbet2 and A. Sen3

1 Equipe Dynamique des Systemes Complexes, UMR 6633CNRS-Universite de Provence, 13397 Marseille, France2 Association Euratom-CEA, DRFC, CEA Cadarache,

13108 St-Paul-Lez-Durance, France3 Institute for Plasma Research, Bhat, Gandhinagar 382428, India

Neoclassical tearing modes are one of the most serious concerns for operation on a next-step fusion device such as ITER. They can indeed limit the achievable normalized plasmaparameter βN . Recently ASDEX and JET experiments show that multiple NTMs canget coupled and the occurence of one NTM can limit the growth of other NTM [1, 2].These experiments open up possibility to operate ITER at higher plasma pressure thananticipated earlier. Though there are some studies [3, 4] investigating the dynamics ofmultiple NTMs, it is still not yet fully understood. In this paper we perform numericalsimulations of multiple NTMs using a fully toroidal code [5] based on a set of generalizedreduced MHD equations. The results show a coupling between multiple NTMs whosedynamics is investigated and compared with previous results.

References

[1] S. Gunter, M. Maraschek, M. de Baar et al., Nucl. Fusion 44 (2004) 524.

[2] M.F.F. Nave, E. Lazzaro, R. Coelho et al., Nucl. Fusion 43 (2003) 179.

[3] Q. Yu, S. Gunter, K. Lackner et al., Nucl. Fusion 40 (2000) 2031.

[4] H. Lutjens and J-F Luciani, Phys. Plasmas 13 (2006) 112501.

[5] D. Chandra, A. Sen, P. Kaw et al., Nucl. Fusion 45 (2005) 524.

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40

On guiding center map

D. Constantinescu1 and B. Weyssow2

1Department of Physics, Association Euratom-MEdC, Romania,

University of Craiova, A.I.Cuza str.13, Craiova, Romania.2Physique Statistique – Plasmas, Association Euratom-Etat Belge, Université Libre de

Bruxelles, Campus Plaine CP231, Bd. du Triomphe, 1050 Bruxelles,

Individual particle trajectories in tokamak are studied in the framework of the finite

gyro radius guiding center approximation. In order to obtain relevant statistical information

on the tokamak plasma, the dynamics of the guiding centers, usually described in terms a set

of (stochastic) differential equations, is reduced to an Hamiltonian map obtained by the

method of Poincaré sections.

The elaboration of this category of maps meant for particle transport studies is a step

forward compared to previously used mapping methods, because the sensitivity to finite

gyro radius effects is included in the model. The consequence is that the map for the

canonically conjugated variables ( )!"!" PP ,,, is coupled to a kind of state equation,

( )!" !"# PfP ,,,= , which is needed to obtain the correct description of the trapped

particle.

The main types of trajectories (passing, banana, inverse bean, stagnation point,

external inverse bean) are identified and characterized in terms of the magnetic momentum by

using the method developed by C. Mercier, H. Capes, J. P. Morera. In figure 1 are presented

various types of trajectories of the guiding centre in a reversed shear magnetic configuration

(DIIID tokamak) The initial position of the particle is ( ) ( )0,0,1.0,,000=!"# , the parallel

velocity is 5.00||=! (corresponding to 40

0

=!P ) and the magnetic momentum is considered

in the interval [ ]250,0 .

Figure 1 Classification of the trajectories of the guiding centre in DIIID as a function of the magnetic momentum

Using the Hamiltonian map for particle trajectories in magnetic field configurations of

large tokamaks like ITER and JET, statistical aspects of particle anomalous transport of

contaminants with multiply ionized states as well as of helium ash in weakly stochastic

magnetic field are studied.

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41

Nonlinear visco-resistive dynamics of the Harris current sheet

K. Takeda1, O. Agullo1,∗ , S. Benkadda1, N. Bian1,4, A. Sen2 and and X. Garbet3

1 Equipe Dynamique des Systemes Complexes, 13397 Marseille, France2 Institute for Plasma Research, Bhat, Gandhinagar 382428, India

3 Association EURATOM–CEA, D.R.F.C., Cadarache, France4 School of Physics and Astronomy, University of Manchester, Manchester, U.K.

A numerical investigation of the visco-resistive evolution of the Harris sheet is presented.The linear growth rate of the tearing instability is found to have various power law scalingsin different visco-resistive regimes, in agreement with Porcelli’s theoretical work [1]. Ourmain focus is on the nonlinear regime of the instability at high values of the stabilityparameter ∆′. We analyze the dynamics of the mode and the nature of the regime as afunction of the Prandtl number Pm. It is found that, depending on the Prandtl regimeand in association with a poloıdal oscillation of the magnetic structure, a quadrupolarflow can be generated and or destroyed outside the sheet. The reconnection processappears to be influenced by the dynamics of the external quadrupolar flow generation.At large enough times, this non linear quadrupolar flow is poloidally advected at theAlfven velocity. At high Pm values, such an advection is inhibited by viscosity and, asa consequence, the latter contributes to a pronounced reduction in the amplitude of thepoloıdal oscillation.

References

[1] F. Porcelli, ”Viscous resistive magnetic reconnection”, Phys. Fluids 6 (1987) 1734.

∗e-mail: Olivier.Agullo@univ-provence.fr

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Analysis of ITER and DEMO steady-state scenarios with the CRONOS suite of codes

J. Garcia , J.F. Artaud, V. Basiuk, G. Giruzzi,

P. Huynh, F. Imbeaux and M. Schneider

Association EURATOM-CEA, CEA/DSM/DRFC, CEA-Cadarache, F-13108 St. Paul lez Durance.

Several conceptual studies of commercial fusion power plants have been carried out so far. In the European framework, these studies have finally led to a European final report on Power Plant Conceptual Study (PPCS), which has identified a range of possibilities for the power plant design [1]. In that report, four main designs for the commercial fusion power plant have been selected, primarily on the basis of 0-D modelling. In this framework, the CRONOS suite of codes [2] has been used with the aim of elaborating scenarios for DEMO by means of far more sophisticated tools than the 0-D analysis, i.e., integrated modelling by 1.5-D codes. This includes 2-D magnetic equilibrium, predictive transport calculations, detailed modelling of heating, current, particle and momentum sources, as well as impurity transport and radiation losses. These studies have shown some difficulties to have a scenario with q0>1 and high non-inductive current fraction [3]. Since the ultimate goal of magnetically confined fusion research is to develop commercial fusion reactors able to supply a continuous electrical power production of the order of 1.5 GW, a steady-state scenario with 100% of non-inductive current is desirable to avoid a pulsed power distribution system. For this purpose, scenarios with internal transport barrier (ITB) are adequate, since the bootstrap current provides a high current fraction whereas the heating systems can drive the rest of the current. In this work, we present an analysis of steady-state scenarios for ITER and DEMO carried out with the CRONOS suite of codes. The paper will mainly focus on the heating and current drive requirements for the formation and sustaining of an ITB with large bootstrap current fraction and high Q. It will be also shown that, in agreement with references [3] [4], synchrotron radiation can play a significant role in these scenarios due to the high temperatures obtained, therefore, the effect of this radiation on the final performance will be addressed. Results will be compared to those expected from 0-D studies in the case of DEMO [1]. References [1] Final Report on PPCS, EFDA(05)-27/4.10, 2005. [2] V. Basiuk et al., Nuclear Fusion 43, pp 822-, 2003. [3] J. Dies, J. Garcia et al., FT/P5-41 21st IAEA Fusion Energy Conference, 16 - 22 October, 2006 Chengdu, China. [4] F. Albajar et al., Nuclear Fusion 45, pp 642-, 2005.

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43

Stability of Rotating Plasmas with Hall Effect

V. Ilgisonis1, I. Khalzov1,2, and V. Lakhin1

1Russian Research Centre "Kurchatov Institute", Moscow 123182, Russia

2 University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2, Canada

Plasma rotation is known to affect stability thresholds and increments of unstable modes. It is important that sheared plasma rotation can play as stabilizing as destabilizing role depending on the type of equilibrium and on the type of exciting modes. As far as the modes are concerned, in the frame of MHD, plasma rotation can be a source of hydrodynamically unstable modes, can modify the modes known for static equilibria, and can produce the modes, which have no analogues in the static case. The structure of such modes may be quite different; in particular, there may be both localized and global modes. Magnetorotational instability (MRI) widely known in astrophysics is a good example of MHD mode, which may be not localized in the direction perpendicular to the magnetic field, and which usually does not appear in fusion papers. In this report, we consider the stability of moving cylindrical plasma using the unified approach for different modes in the frame of non-compressible MHD. The general dispersion law is demonstrated to be reduced both to the case of classical MRI [1,2] and to the Suydam stability condition for radially localized modes [3]. In the last case, we have shown that Alfven resonance, which destabilizes perturbation stable in the static case, has the physical origin similar to MRI. It makes reasonable to consider delocalization of unstable modes due to spread drive of instability. To compare the local and global mode approaches, for the classical MRI limit, we have calculated the spectrum and mode structure numerically, using the recently developed approach [4]. The comparison demonstrates rather good correlation with local theory; for Suydam limit, the role of delocalization appears to be more significant. Hall effect is another important thing which should be taken into account for localized modes in the case of high magnetic shear variations; this effect is also demonstrated both analytically and numerically. References [1] E. Velikhov, Sov. Phys. JETP, 36 (1959) 995. [2] Balbus S.A., Hawley J.F., Astrophys. J., 376 (1991) 214. [3] A. Bondeson et al., Phys. Fluids, 30 (1987) 2167. [4] I. Khalzov, V. Ilgisonis et al., Phys. Fluids, 18 (2006) 124107.

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44

FORMATION AND DECAY MECHANISMS OF EXCIMER

MOLECULES IN SILENT PLASMA DISCHRGE

N. Larbi Daho Bachir(1), S.Medina(2), A.Belasri(3) (1) Doctorat, institut de physique, Université d’Oran (USTO). ldb_djanet@yahoo.fr

(2) Doctorat, institut de physique, Université d’Oran (USTO).

(3) Professeur, Institut de physique, Université d’Oran (USTO).

Tel/Fax : 0213 041530462

Laboratory of Plasma physics, Conductors Materials and their Applications U.S.T.O Faculty of Science. Department of Physics U.S.T.O El M’NAOUR B.P. 1505 Oran

(ALGERIA)

Abstract: Dielectric barrier discharge or silent discharge is widely used in the field of plasma applications. A large variety of DBD assisted technologies, such as exhaust gas treatment, surface cleaning and incoherent vacuum ultraviolet (VUV) excimer lamps are under research. The excimer formation and decay processes are modelling and analysed in DBD [1]. Special interest is paid to the discharge structure and the processes occurring in the discharge areas. In order to study the electric parameters and the temporal evolution, a electrical circuit is modelling and the kinetic system of reaction is developed. The mechanisms of excimer formation are shown to depend on the discharge conditions. The temporal evolution of species and radiation are involved, such as molecular, metastable and ionic states, are determined. Physical model:

We consider the zero dimension model made up of three systems of equation coupled between them: Equations of the external circuit, electronic equation of Boltzmann and kinetic equations for the heavy species [2]. In the zero-dimensional kinetic model, plasma is regarded as a homogeneous and uniform medium whose conductivity is variable and is related to the evolution of the electronic density in plasma. Thus, the model consists of electric circuit, charged by variable resistors.

References: [1]Wen-Chao Zhu, Bai-Rong, Yong-Xi Yao, 2005 J.Phys.D:Appl.Phys.38 1396-1401 [2] thèse : Larbi Daho Bachir N “modélisation d’une décharge Xe à barrières diélectrique pour lampe à excimer” 2003 université USTO, Oran. Algérie.

Xe+

Xe**

Xe*

Xe2+

Xe2**

Xe2* 147 nm résonance ligne 172 nm

excimer radiation from Xe2*(

1,3∑u)

11.1 ev

7.2 ev

12.1 ev

8.3 ev

150 nm excimer radiation from Xe2*(Ou)

low pressure : atom of xenon high pressure: excimer of xenon

P1-23

45

Particle transport in ECH plasmas of the TJ-II stellarator

D. Lopez-Bruna, J. M. Reynolds, V. I. Vargas, J. Guasp, F. Castejon

Asociacion Euratom-CIEMAT, Madrid, Spain

An acknowledged difficulty in estimating particle diffusion in magnetic fusion machinesis determining the source in the particle balance equation. In this work we estimateparticle transport in ECH plasmas of the TJ-II stellarator using a Monte-Carlo code tocalculate the particle source from τp and the appropriate geometry of the machine/plasma.However, to calculate the recycling fluxes we must know the confinement time τp itself.First, for ECH plasmas in the TJ-II, particle inventory studies indicate that the recyclingfactor R ≈ 1 after some 15 discharges have followed the initial glow discharge at thebeginning of the experimental day [1], so we can select them. In the case of τp, weknow that it improves noticeably with density [2] even within the range of densitiesbelow the ECH cut-off limit (≈ 1.7 × 1019 m−3; corresponding to line averaged densityn ≈ 1.2× 1019 m−3). Since we lack a reliable theoretical transport model, we exploit thefact that stationary plasmas are reached. Thus, we tune a model for particle transportuntil, in an iterative process, a steady state based on the calculated distribution of theparticle source mimics the experimental profiles. The iterations are performed evolvingthe particle balance equation with the system ASTRA [3], which takes the source from aversion of the EIRENE code [4] adapted to the characteristics of the TJ-II. The results(see Fig. 1) are in fair accordance with the experiments [2].

Figure 1: Values of τp and net particle source for three discharges from a density scan.

References

[1] J. A. Ferreira, F. L. Tabares, D. Tafalla, Particle balance in TJ-II plasmas underboronized wall conditions, Proc. of the 32nd EPS Conf. on Contr. Fusion and PlasmaPhys., Tarragona, 27 June – 1 July 2005, ECA Vol. 29 C P-4.009 (2005).

[2] F. L. Tabares et al., Plasma Phys. Control. Fusion 43 (2001) 1023–1037.

[3] G. V. Pereverzev, P. N. Yushmanov, ASTRA Automated System for TRansport Anal-ysis, Max-Planck-Institut fur Plasmaphysik, Rep. IPP 5/98, Garching, February 2002.

[4] D. Reiter, The EIRENE Code User Manual, Version: 11/2005; http://www.eirene.de(2005).

P1-24

46

Pinch effects and chaotic motion in toroidal confinement devices

G. Spizzo1, R. B. White1, S. Cappello1, L.Marrelli1 and F. Sattin1

1Consorzio RFX, Euratom-ENEA Association, Corso Stati Uniti 4, 35127 Padova, Italy2Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, NJ 08543-0451

Particle transport in toroidal confinement devices is often described in terms of a diffusionconstant and an inward pinch velocity [1]: this phenomenological description can bejustified by a probabilistic approach (random walk) that simplifies the particle dynamicswhen the orbits are small enough compared to the system size. This results in a diffusiveexpression for particle flux. Then, the convective part of the particle flux can be related,for example, to spatial inhomogeneities in temperature or field curvature [2].

When magnetic chaos is present, but the system is not too far from the stochastic thresh-old, diffusion and pinch can be actually an expression of the subdiffusive nature of thetransport, brought about by the presence of a spectrum of long-distance Levy flights[3].This effect is shown by numerical modelling of the magnetic structure and associated par-ticle transport in conditions relevant for the reversed-field pinch experiment RFX-modbased at Consorzio RFX, Padova. Simulations reproduce the particle motion throughguiding center calculations of particle orbits embedded in the magnetic topology, ob-tained by 3D MHD simulations (code SpeCyl[4]). Results have been used to produce theprobability distribution functions (p.d.f.) of jump lengths and waiting times, providingthe kernel to integrate in the Montroll equation[5], which governs the evolution of particledensity in the Continuous-time random walk (CTRW) approach. This means that weobtain a transport equation using the knowledge of the kernel which comes directly fromthe actual particle dynamics. The difference of behavior between trapped and passingparticles has also been considered, and has a relevance comparable to subdiffusion indetermining the pinch effect.

Similar results can be applied to other systems with chaos induces particle transport, e.g.electron transport in Tokamaks. This work was partially supported by DoE contract No.DE-FG03-94ER54271.

References

[1] D. Gregoratto et al., Nucl. Fusion 38 (1998), 1199; L. Carraro et al., Plasma Phys.Control. Fusion, 42 (2000), 731; R. W. Harvey, O. Sauter et al., Phys. Rev. Lett., 88(2002) 205001; C. Angioni, Phys. Rev. Lett., 90 (2003) 205003; X. Garbet, PlasmaPhys. Control. Fusion, 46 (2004) B557;

[2] X. Garbet et al., Phys. Rev. Lett., 91 (2003) 035001, and references therein.

[3] G. Zaslavsky, Chaos, 8 (1998) 757.

[4] S. Cappello and D. Biskamp, Nucl. Fusion, 36 (1996) 571.

[5] Krenke-Montroll, J. Stat. Phys., 9 (1973) 45.

P1-25

47

Different Methods for measuring Plasma displacement in Tokamaks, Construction &Compensation of Continuous Coils in IR-T1 Tokamak

R.Tarkeshian, 1) M. Ghoranneviss, 1) K. Salem, 1) A. Talebi Taher, 1) P. Khorshid2)

1) Plasma Physics Research Center, Science & Research Campus, Islamic Azad University - P.O. Box 14665–678 - Tehran-Iran

2) Dept. of Physics: Mashhad Islamic Azad University, P.O. Box 91685-16491865 Mashhad, Khorasan

AbstractThe measurement of current-carrying plasma column displacement is very important for plasma positioncontrol. Two methods for this purpose are introduced; Discrete and Continuous Coils. In this paper, calculationand construction of these coils is explained. Multiple moment method [1, 2] has been used and derived forconstruction of sensing coils & measuring the Horizontal Displacement (H.D.) of plasma column. Also FourierTransform have been used and derived for continuous coils [3]. The comparison of their advantages anddisadvantages are investigated.For IR-T1 Tokamak, Two Cosine Rogowski coils & two Saddle Sine coils were designed and constructed,which have been placed diametrically around minor radius of torus. Then an electronic circuit was designed foradding and integrating the Cosine and Saddle Sine coils output with proper gain. The contribution and gain ofeach coil in final output is calculated [4, 5].For compensation of unwanted pickups voltage from the time varying fields such as Vertical, Toroidal, Ohmic,Plasma current, etc. each signal with adjustable gain is added to main signal, until removing the additional fieldeffect. Finally the signal which has been obtained holds good proportionality to H.D. In this circuit, for fast andmore accuracy response, high frequency and low offset Op-Amps (Operational Amplifier) are used.

Keywords: Tokamak, Horizontal Displacement, compensation, Rogowski coil.

References

[1] L.E. Zakharov, V.D. Shafranov, Sov.Phys.Tech.Phys.18 (2) (1973) 151[2] A.J.Wooton, Nucl. Fusion, 19-7 (1979) 987[3] V.S. Mukhavatov, V.D. Shafranov, Nucl. Fusion, 11 (1971) 605[4] R.Lopez-Callejas, Technical report in Spanish, ININ, 1999[5] R.Lopez-Callejas, Fusion engineering Design, 54 (2001) 21

P1-26

48

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49

INTERMITTENT PLASMA TRANSPORT IN EDGE-LOCALIZED MODE

G. Kamberov** *, L.Popova*(1), P.Marinov***, V.Hristov*

* Institute of Mathematics and Informatics BAS, Sofia, Bg** Stevens Institute of Technology, NJ US

*** Institute of Parallel Processing, BAS, Sofia, Bg(1) e-mail: lili_popovabg@yahoo.com

A B S T R A C T

We report results from a comparative analysis of published experimental data frommagnetically confined plasma in edge-localized mode (ELM). The data includes variousELM turbulences observed in different experimental (toroidal and linear) devices. Ouranalysis lead to establishing uniform conditions for intermittent transport characterizedwith typical structures propagating as filaments. An explanation of the mechanism isobtained by analyzing the calculation results from self-consistent Monte Carlo computersimulations of particle motion and collisions in the scrape-off layer (SOL) accountingfor the edge plasma characteristics in particular experimental conditions. A possiblemechanism for the intermittent transport is revealed: blob-like structures created by theself-organized plasma stream across the magnetic field lines achieving an evanescentquasi equilibrium over the whole SOL with a steep density gradient in the pedestalwhich in turn causes small density fluctuations to develop in growing bunches andconsequent propagation of filaments. The characteristic time is related with plasmaorganization in blobs and depends on the experimental conditions. It conforms theexperimentally observed recreation time of ELMs.

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50

Contribution of slow particle dynamics to chaotic transport inRFP plasmas

I. Predebon and R. Paccagnella

Consorzio RFX, Associazione Euratom-ENEA sulla Fusione, Padova, Italy

Kinetic descriptions of a plasma provide the expression of macroscopic quantities throughmoment equations, which usually need some simplifying hypotheses to be analyticallysolved. For turbulent plasmas this is particularly true, due to the hardly inspectablenature of particle dynamics. In this paper the derivation of particle and energy fluxesis described for a chaotic magnetic field, taking into account a full spectrum of particlevelocities. With the simplifying hypothesis that the magnetic field has a diffusive nature,keeping as guidelines the classical papers [1, 2], the contribution of slow particles turnsout to be relevant throughout the plasma, not only in the colder peripheral regions wherecollisional transport is expected to be dominant. The application of the model to theRFX-mod reversed field pinch shows for example an influence on transport even in thecore, by a factor ∼ 2 in the particle flux.

A second part of the paper is devoted to a critical analysis of the hypothesis at the base ofthe classical description of the diffusion process. In fact, the standard diffusion paradigmhas significant limitations whenever transport departs from Gaussianity, becoming superor sub-diffusive. In these cases the calculation of the fluxes will be provided by means ofa fractional diffusion model (e.g. [3]), so as to yield a qualitative comparison with thestandard case described above.

References

[1] A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett. 40, 38 (1978).

[2] R. W. Harvey et al., Phys. Rev. Lett. 47, 102 (1981).

[3] D. del Castillo Negrete, Phys. Plasmas 13, 082308 (2006).

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51

Numerical simulations on blob transport in TEXTOR-DED

D. Reiser1 and Y. Xu2

1Institute of Energy Research - Plasma Physics, Forschungszentrum Julich GmbH,

EURATOM Association, Trilateral Euregio Cluster,D-52425 Julich, Germany2Laboratoire de Physique des Plasmas - Laboratorium voor Plasmafysica,

Association ’EURATOM - Belgian state’, Ecole Royale Militaire - Koninklijke Militaire

School, Trilateral Euregio Cluster, B-1000 Brussels, Belgium

Three-dimensional numerical simulations of drift fluid turbulence have been performedto study the impact of resonant magnetic perturbation fields on the intermittent trans-port of particles (blob transport) in the edge-SOL-region of tokamaks. For this purposea non-linear 4-field-model (i.e. electric potential φ, the density n, the parallel magneticpotential A and the parallel ion velocity u, neglecting temperature dynamics) is employedand the computational domain set up in a way that it covers both regions of closed andopen field lines. The impact of resonant magnetic perturbations is taken into account bythe inclusion of a static magnetic field consisting of three island chains located aroundthe separatrix and reflecting scenarios studied at TEXTOR-DED. The first observationis that for the unperturbed magnetic configuration density blobs, i. e. macroscopic struc-tures of a size of a few cm, are formed in the vicinity of the separatrix and move radiallyoutwards. By switch-on of the resonant magnetic perturbation two significant effects ap-pear: the amplitudes of the intermittent density transport are strongly reduced and thetime averaged local radial E×B-flux changes sign at certain positions close to the sep-aratrix. By means of numerical probe measurements we compare the simulation resultswith experimental findings. It is shown that the numerically found density fluctuationsand E×B-fluxes bear a strong resemblance of the experimental results. The basic mech-anism for these effects induced by the magnetic perturbation is found in static structuresappearing due to the forced cancellation of parallel pressure gradient and parallel electricfield giving rise to resonant structures if magnetic islands are present.

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52

POSTER SESSION 2

53

54

Resistive Wall Modes Stabilization the Presence of 3D Wall Structures

C.V.Atanasiu1, S.Günter2, A.Moraru3 and L.E.Zakharov4

1Association Euratom MEdC Bucharest, Romania

2Association Euratom Max-Planck-Institut für Plasmaphysik, Garching, Germany 3Polytechnical University of Bucharest, Bucharest, Romania

4Plasma Physics Laboratory, Princeton University, Princeton, USA Writing the expression for the potential energy in terms of the perturbation of the flux function, and performing an Euler minimization, one obtains a system of ordinary differential equations in that perturbation [1]. This system of equations describes a tearing mode or an external kink mode, the latter if the resonance surface is situated at the plasma boundary. Usually, vanishing boundary conditions for the perturbed flux function at the magnetic axis and at infinity are considered. From single layer potential theory, we have developed an approach to fix “natural” boundary conditions for the perturbed flux function just at the plasma boundary, replacing thus the vanishing boundary conditions at infinity. It is known that the external modes are stabilized by the presence of a close-fitting perfectly conducting wall but become destabilized when the wall is assumed to have finite resistivity. Now, in the presence of a resistive wall, the boundary conditions of the external kink mode at the plasma boundary are determined by the reciprocal interaction between the external kink perturbation of the plasma and the toroidal wall (in its thin wall approximation). By using the concept of a surface current, the description and calculation of the stability of modes and the plasma response were greatly simplified [2]. A robustly accurate and effective method is presented to determine these surface currents in a wall with arbitrary holes, considering that the perturbation is given by toroidally coupled external kink modes. The normal component of the magnetic field perturbation, at the plasma boundary, has been considered as excited by toroidally coupled external kink modes and it is that component that gives the normal to the wall component of the exciting field causing the wall response via the induced eddy currents.

Figure 1. Eddy current stream function U(x,y,t) at=0.4833s, excited by a 3/2 external kink mode in a thin wall

References [1] C.V. Atanasiu, S. Günter, K. Lackner, A.Moraru, L.E.Zakharov et al., Phys. Plasmas 11, 5580 (2004).

[2] C.V. Atanasiu, A.H. Boozer, L.E. Zakharov et al., Phys. Plasmas 6, 2781 (1999).

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3D nonlinear MHD simulations for ultra-low q plasmas D. Bonfiglio , S. Cappello, R. Piovan

Consorzio RFX, Associazione Euratom-Enea sulla fusione, Padova, Italy

Nonlinear 3D MHD simulations for ultra-low q plasmas have been performed with the SpeCyl code [1] in the simple frame of visco-resistive zero pressure model. The ultra-low q (ULQ) configuration, which is a screw pinch characterized by a safety factor profile in the interval 0<q<1, is the intermediate state between the Tokamak and the Reversed Field Pinch. The experimental observation of the staircase-like behaviour in the evolution of the edge q-value, show that ULQ plasmas have the natural tendency to select discrete edge q-values which are about the major rational numbers, suggesting plasma self-organization [2,3]. In fact, the transition of qedge from a plateau level to the next one occurs in concomitance with the development of a kink deformation of the plasma column.

We present 3D nonlinear MHD numerical simulations in which starting from RFP configurations we drive the system toward Tokamak like conditions and vice-versa, exploring the whole ULQ region [4]. The typical staircase-like evolution of the edge q-value observed in experiments is also found in numerical simulations. Each phase of quiescent qedge is reached after the development of a helical kink instability, whose stabilization yields a nearly axisymmetric state, characterized by a slightly decreasing radial q profile with qedge near the mode rational number. Numerical simulations show finally that it is possible to sustain either of the two conditions, namely the helical configuration and the axisymmetric one, by freezing qedge at a suitable value.

This numerical study, and the preliminary experimental results obtained exploiting the flexibility of the experiment RFX-mod [3], indicate the possibility to explore the impact on transport of such different MHD behaviour within the same experiment.

References

[1] S. Cappello and D. Biskamp, Reconnection processes and scaling laws in Reversed Field Pinch magnetohydrodynamics, Nuclear Fusion 36, 571 (1996) [2] P. Brunsell, J. R. Drake, S. Mazur and P. Nordlund, Ultra-Low q and Reversed Field Pinch experiments in Extrap T1 with a resistive shell, Physica Scripta 44, 358 (1991) & refs therein [3] R. Piovan, S. Cappello, D. Terranova, L. Zanotto and M. Zuin First results of Ultra-Low q experiments in RFX-mod 12th IEA-RFP Workshop, Kyoto, Japan, 26-28 March 2007 http://nuclear.dj.kit.ac.jp/rfp2007/presentations.html [4] D. Bonfiglio, S. Cappello, R. Piovan, G. Spizzo, D. Terranova Preliminary results of 3D nonlinear MHD simulations for ultra-low q plasmas and OPCD RFP discharges 12th IEA-RFP Workshop, Kyoto, Japan, 26-28 March 2007 http://nuclear.dj.kit.ac.jp/rfp2007/presentations.html

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56

Fully implicit, nonlinear, parallel algorithm for the 3Dcollisionless reconnection study

D. Borgogno1, L. Chacon2, D. Grasso3

1Observatoire de la Cote d’Azur, CNRS, Nice, France2Los Alamos National Laboratory, Los Alamos, NM, USA

3Dipartimento di Energetica, Politecnico of Torino and CNISM, Italy

We present a new fully implicit, nonlinear, parallel algorithm suitable for exploring themagnetic reconnection process in collisionless regimes in three dimensional configura-tions. The algorithm solves the system of collisionless fluid equations in [1]. The nonlin-ear implicit time integration is performed using the Newton-Raphson iterative algorithm.Krylov iterative techniques are employed for the required algebraic matrix inversions, im-plemented Jacobian-free (i.e., without ever forming and storing the Jacobian matrix), andpreconditioned with a “physics-based” preconditioner [2, 3]. The parallelism is carriedout by PETSc libraries [4].

The scalability of the code with the spatial resolution and the number of processorshas been compared against an available explicit parallel code [1]. The accuracy of thealgorithm has been thoroughly benchmarked by reproducing recent reconnection results[5]. In particular, the remarkable performances of the implicit algorithm allowed us adetailed analysis, based on high spatial resolution numerical simulations, of the transitionto a turbulent regime, that occurs in the long term evolution of reconnection process incold electron plasmas [5].

as a confirmation of receipt

References

[1] D. Borgogno et. al., Phys. Plasmas., 12, 032309 (2005)

[2] L. Chacon et al., J. Comput. Phys. 178,(1), 15 (2002).

[3] L. Chacon et al., J. Comput. Phys. 188,(2), 573 (2003).

[4] Satish Balay et al., http://www.mcs.anl.gov/petsc

[5] D. Grasso et. al., Phys. Plasmas., 14, 055703 (2007)

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57

Ordered magnetic topology in Reversed Field Pinch configurations S. Cappello a, D. Bonfiglio a, G. Spizzo a, D. Terranova a, R. B. Whiteb

aConsorzio RFX, Associazione Euratom-Enea sulla fusione, Padova, Italy bPPPL-Plasma Physics Laboratory, Princeton University

The reversed field pinch (RFP) configuration for magnetic confinement has shown to develop a quasi-helical regime (quasi single helicity, QSH) with macroscopic plasma regions characterized by ordered magnetic surfaces. This is found both in experiments [1] and visco-resistive 3D MHD numerical computations [2]. Numerical force-free simulations indicate that pure ohmic helical symmetric (single helicity regimes, SH) stable equilibria exist for the RFP, which represent a target to approach in order to achieve conditions globally free of the transport channel associated with magnetic chaos [3, 4].

Recent experiments in RFX-mod have shown that a very efficient way to “stimulate” such a self-organization of the plasma column consists in oscillating the toroidal flux (so-called oscillating poloidal current drive, OPCD, technique) producing a pulsed pinching of the plasma mean field profiles [5]. This is systematically accompanied by the development of very clear QSH configurations, which are characterized by a significant increase of temperature and SXR emissivity. Similar effects have also been recently observed in the TPE-RX experiment [6] .

We present here results of visco-resistive 3D MHD numerical modelling aiming at clarifying the mechanism responsible for the stimulated helical organization observed in experiments. Preliminary results [7] indicate that the degree of helical order is actually modulated in amplitude and in particular amplifyied according to the oscillation imposed by the applied boundary condition representative of the experimental action. The conditions for chaos healing and the ensuing effect on test particle transport in terms of the MHD mode spectrum are also being investigated.

References

[1] P Martin et al., A new paradigm for RFP magnetic self-organization: results and challenges Plasma Phys. Control. Fusion 49 A177 (2007), Franz P et al Tomographic imaging of resistive mode dynamics in the Madison Symmetric Torus reversed-field pinch Phys. Plasmas 13 012510-1 (2006) & refs therein [2] S. Cappello,”Bifurcation in the MHD behaviour of a self-organizing system: the RFP”, Plasma Phys. Control. Fusion 46 B313 (2004) & refs therein [3] S. Cappello, D. Bonfiglio, D.F.Escande Magnetohydrodynamic dynamo in Reversed Field Pinch plasmas: electrostatic drift nature of the dynamo velocity field Physics of Plasmas 13, 056102 (2006) & refs therein [4] D.F. Escande, R. Paccagnella et al. ,” Chaos healing by separatrix disappearance and quasi-single helicity states of the reversed field pinch”, Phys. Rev. Lett. 85 3169 (2000) [5] M.E. Puiatti, S. Cappello et al. Analysis and modelling of the magnetic and plasma profiles during PPCD experiments in RFX Nuclear Fusion, 43 1057 (2003) [6] Y. Hirano, et al. Quasi-single helicity state by a small positive pulse of toroidal magneti field in TPE-RX reversed field pinch experiment Physics of Plasmas 13, 122511 (2006) [7] D. Bonfiglio, S. Cappello, R. Piovan, G. Spizzo, D. Terranova Preliminary results of 3D nonlinear MHD simulations for ultra-low q plasmas and OPCD RFP discharges 12th IEA-RFP Workshop, Kyoto, Japan, 26-28 March 2007 http://nuclear.dj.kit.ac.jp/rfp2007/presentations.html

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Multiple Nested Beltrami regions as a Solution to the 3-D Toroidal MHD Equilibrium Problem

R.L. Dewar1, M.J. Hole1, S.R. Hudson2 and M. McGann1

1Department of Theoretical Physics and Plasma Research Laboratory,

Research School of Physical Sciences and Engineering, The Australian National University, ACT 0200 Australia

2Princeton Plasma Physics Laboratory, PO Box 451, Princeton NJ 08543, USA A generalized energy principle for finite-pressure, toroidal magnetohydrodynamic (MHD) equilibria in general three-dimensional configurations is proposed. The full set of ideal-MHD constraints is applied only on a discrete set of toroidal magnetic surfaces (invariant tori), which act as barriers against leakage of magnetic flux, helicity and pressure through chaotic field-line transport. It is argued that a necessary condition for such invariant tori to exist is that they have fixed, irrational rotational transforms. In the toroidal domains bounded by these surfaces, full Taylor relaxation is assumed, thus leading to Beltrami fields: ∇ × B = λB, where λ is constant within each domain. Such equilibria and their stability have been studied in cylindrical geometry [1], generalizing the single Beltrami region study of Kaiser and Uecker [2]. Two distinct eigenvalue problems for λ arise in this formulation, depending on whether fluxes and helicity, or boundary rotational transforms, are fixed [3]. Beltrami states have been constructed in a three-dimensional toroidal region of annular cross section [3], a residue criterion being used to determine the threshold for connected chaos. References [1] M. J. Hole, S. R. Hudson and R. L. Dewar, Nucl. Fusion in press (2007) [2] R. Kaiser and H. Uecker, Q. Jl. Mech. Appl. Math., 57 (2004) 1 [3] S. R. Hudson, M. J. Hole and R. L. Dewar, Phys. Plasmas 14, 052505 (2007)

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Influence of the safety factor profile on the nonlinear evolutionof the 1/1 kink mode

H. Baty1 and M.-C. Firpo2

1Observatoire Astronomique de Strasbourg, 67000 Strasbourg, France2LPTP, Ecole Polytechnique, 91128 Palaiseau cedex, France

Simulations of the nonlinear evolution of the resistive kink instability have been per-formed in cylindrical geometry using a 3D numerical code with a full set of resistiveMHD equations [1]. Resistivity was chosen equal to η = 10−5, a value high enough toobserve a purely resistive kink mode yet small enough to contain finite-η effects. Sim-ulations were performed for different q-profiles. For instance, we considered profiles as

q(r) = q0

{1 + r2λ

[(qa/q0)

λ − 1]}1/λ

for different values of λ and fixed q0 and qa values.

The results are in qualitative agreement with a recent analytical modeling of the onsetof the nonlinear regime of the m = 1 resistive mode [2]. For a peaked current profile(e.g. λ = 0.4) saturation is observed at a very low level, while for flat ones (e.g. λ = 10)exponential growth at almost the linear growth rate continues far in the nonlinear regime.

0 100 200 300 400t�tA

-8

-7

-6

-5

-4

-3

Magneticenergyonm=1~A2

Figure 1: Time evolution of the magnetic energy in the m = 1 mode (in log10 scale) for threedifferent q-profiles obtained for λ = 0.4 (plain), λ = 1 (dashed) and λ = 10 (dot-dashed line)and q0 = 0.7, qa = 3. The bold horizontal line signals the level A2 ∼ η that marks the onset ofnonlinearities on m = 1 [2].

References

[1] H. Baty, J.-F. Luciani, and M.-N. Bussac, Nucl. Fusion 31 (1991) 2055.

[2] M.-C. Firpo, Phys. Lett. A 342 (2005) 263.

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Energy losses by type I ELMs due to hot particle flows alongperturbed magnetic field lines

A. Gupta and M. Tokar

1Institute for Energy Research, Plasma Physics, Forschungszentrum Juelich-52425,Germany

Various mechanisms are under consideration as responsible for energy losses from theedge transport barrier (ETB) during type I Edge Localized modes (ELM) in H-modeplasmas. Recently [1] a model has been proposed based on the assumption that the in-crease of transport by ELM bursts is due to flows along magnetic field lines perturbed byballooning-peeling MHD modes. In that consideration the energy losses due to convec-tion of thermal particles and heat conduction of electrons has been taken into account.However, escape of superthermal charged particles along perturbed field lines may alsocontribute substantially. Similarly to electron heat conduction this loss channel shoulddecrease with increasing plasma collisionality in agreement with experimental observa-tions.

In the present work the energy loss with superthermal particles is modelled by consideringparticles inside the separatrix starting to move along perturbed field lines from differentpositions and with diverse values of the initial perpendicular energy and parallel velocity.For these particles the equations for motion along field lines and energy conservation aresolved numerically by taking into consideration the forces from the ambipolar parallelelectric field and coulomb collisions with the background thermal particles which reducethe parallel velocity and total energy. The variation of the radial particle position dueto parallel motion is calculated by using the inclination angle of perturbed field linescalculated according to the model in Ref. [1]. Only particles which reach the separatrixwithin the ELM crash time contribute to the energy loss in question and this constrainsthe space of their initial position, perpendicular energy and parallel velocity. The totalloss is assessed by assuming a maxwellian distribution over the initial energy and velocityand simple step-wise profiles of the plasma density and temperature at the edge withsharp gradients in the ETB. The simulation results are compared with the experimentaldata [2].

References

[1] M.Tokar et al., Plasma physics Control. Fusion 49 (2007) 395.

[2] A.Loarte et al., Plasma physics Control. Fusion 45 (2003) 1549

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Modeling of non-linear Alfven Eigenmodeexcitation with the SELFO code

K. Holmstrom1, T. Bergkvist1 and T. Hellsten1

1Fusion Plasma Physics, Association EURATOM-VR,Royal Institute of Technology, Stockholm, Sweden.

Unstable Alfven Eigenmode (AE) excitation by fast ions can occur when the distributionfunction of the resonant ions is increasing along the AE characteristic in phase space.As a mode grows up, the distribution function flattens along the characteristics, and thedrive is reduced. Ion cyclotron interactions and collisions affect the phase evolution ofthe resonant ions. This decorrelates the interactions and causes diffusion in the orbitinvariants. If the distribution function is not restored or the interactions not decorre-lated, the resonant ions will instead undergo a superadiabatic oscillation along the AEcharacteristics. To describe the dynamics of the AE excitation, it is therefore necessaryto include the decorrelation of the AE interactions and the renewal of the distributionfunction in the unstable regions. An orbit averaged Monte Carlo operator describing thephase decorrelation between resonant ions and AEs has be developed and implementedin the SELFO code. The new operator takes into account the co-occurrence of decorrela-tion and AE interaction by monitoring the phase between the particle and the mode. Forfractions of orbits, time-weighted fractions of energy contributions from entire orbits areused. This addition to the SELFO code allows for self-consistent modeling of the non-linear interaction between fast ions and AEs, including the phase decorrelation. SELFOconsists of the orbit averaged Monte-Carlo code FIDO [1, 2], which given the wave fieldsolves for the distribution function in the three orbit invariants and the phase along theunperturbed drift orbit, coupled with the global wave code LION [3], which solves forthe wave field given the dielectric tensor and the distribution function.

References

[1] J. Hedin et al, Proc. Joint Varenna-Lausanne Workshop on Theory of Fusion Plasmas(1998)

[2] T. Bergkvist, T. Hellsten, T. Johnson and M. Laxaback, Nucl. Fusion, 45(2005)465

[3] L. Villard et al, Computer Physics Reports 4(1986)95 and Nucl. Fusion, 35(1995)1173

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Nonlinear Dynamics of Magnetic Islands Inbedded in Micro­Turbulence.

Muraglia1, O. Agullo1, S. Benkadda1, P. Beyer1, X. Garbet2

1.

[1] Equipe Dynamique des Systèmes Complexes, Laboratoire PIIM. CNRS­Université de Provence[2] Association EURATOM­CEA. DRFC. CEA Cadarache.

In   tokamaks,  macro­scale  MHD  instabilities   (magnetic   islands)   coexist  with  micro­scale turbulent fluctuations and zonal flows. Although many works were devoted to the study of macro­scale and micro­scale instabilities separately, only few investigations were devoted to explore the mutual interaction between these instabilities [1, 2].  We   address   here     the   multi­scale­nonlinear   dynamics   between   macro­scale   tearing instabilities and gradient pressure driven (resistive interchange)micro­instabilities by solving reduced  MHD  equations  numerically.  The  numerical   study   shows   the   existence  of   four regimes. First a linear growth of the magnetic island followed by a plateau phase where the island stops growing, becomes stable and a non linear saturated regime takes place. During this late evolution of the island, the micro­scale interchange fluctuations begin to grow and the system reaches a hybrid regime which is characterized by the competition between the island and the microscopic fluctuations. Later, the kinetic energy reaches a non linear state where a strong interaction between magnetic flows associated with the islands and zonal flows generates violent magnetic reconnection.

References

[1] McDEVITT, C. J., et al., Phys. Plasmas 13, 032302 (2006).[2] A. Ishizawa et al, IAEA proceedings, Chengdu 2006,  TH/P2­21

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63

Magnetogravitational Instability of Rotating Hall

Plasma with Electron Inertia and Radiative Effects

R.P.PPRAJAPATI AND R.K.CHHAJLANI

School of Studies in Physics, Vikram University, Ujjain-456010 (M.P.), India

Abstract

The problem of self-gravitational instability of infinitely extending homogeneous, viscous, magnetized, rotating plasma has been investigated incorporating the effects of finite electrical resistivity, thermal resistivity, thermal conductivity, Hall current radiative and finite electron inertia effect. The self-gravitating configurations have been taken here. It is assumed that the plasma is permeated by a transverse magnetic field and the axis of rotation is taken parallel and perpendicular direction to the magnetic field. With the help of relevant linearized perturbation equations of the problem, a general dispersion relation is obtained, using the method of normal mode analysis. Wave propagation is discussed for parallel and perpendicular directions to the magnetic field. The conditions of stability as well as instability are found in the present work. The stability of the configuration is discussed by applying Routh-Hurwitz criterion. The effects of electrical resistivity and Hall current on Alfven mode are discussed here. The conditions of thermal instability are obtained for a time dependent and density dependent heat-loss function. For parallel propagation of waves, it is found that the condition of radiative instability is independent of strength of magnetic field, Hall current, electron inertia, finite electrical resistivity, viscosity and rotation but for transverse propagation the condition of radiative instability is dependent of finite resistivity, strength of magnetic field and independent of rotation, electron inertia and viscosity. Numerical calculations have been performed to obtain the dependence growth rate of the unstable mode on the various physical parameters involved.

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Quasi-Single-Helicity states emerging from force-free equilibria:linear and nonlinear theory

E. Tassi1, F. Militello2, F. Porcelli1 and R.J. Hastie1,3

1Dipartimento di Energetica, Politecnico of Torino, Italy2IFS, University of Texas and CMPD

3Culham Science Centre, EURATOM/UKAEA Fusion Association, Abingdon, UnitedKingdom

A number of experiments carried out in several Reversed Field Pinches (see, e.g. [1]and references therein) have shown that plasma in such devices can settle into so-calledQuasi-Single-Helicity (QSH) states. These states are characterized by a magnetic spec-trum in which the amplitude of the mode with poloidal wave number m = 1 and withthe innermost resonant surface is much larger than the amplitude of all the other modes.QSH states can often exhibit a cyclic behavior [2] in which, at each cycle, the ampli-tude of the dominant helical mode initially grows in time, then saturates and eventuallyabruptly decays. QSH states are of interest not only because they represent an intriguingself-organization process but also because their occurrence can correspond to an im-provement in the particle confinement properties of the device [3]. However, a completetheoretical explanation for the occurrence of QSH states is still missing. In this contri-bution we propose that QSH states might emerge as consequence of a small deviation ofthe mean magnetic field from the linear force-free state predicted by the classical theoryby Taylor [4]. In particular we show [5] that, in cylindrical geometry, force-free equilibriafor which the parameter µ, defined as the ratio between the parallel current density andthe magnetic field, is a step function of the radius, can be linearly tearing unstable withrespect to the innermost resonant mode with m = 1 but stable with respect to all theother modes. A scenario is then depicted according to which a plasma initially relaxedto a tearing-stable Taylor state could subsequently become tearing-unstable and lead toa QSH state if even a small step in µ forms, due for instance to a peaking of the currentdensity caused by core ohmic heating.The results referring to the linear phase are complemented by nonlinear results [6] re-lated to the saturation phase. We derive an analytical relation that predicts the saturatedisland width w as function of the parameters of the inital stepped-µ equilibrium. In par-ticular it is found that, for small steps, w grows almost linearly with the step height ∆µbut the dependence becomes nonlinear as ∆µ increases.

References

[1] P. Martin et al, Nuclear Fusion 43, (2003) 1855.

[2] S. Ortolani and the RFX team, Plasma Phys. Contr. Fusion 48, (2006) B371.

[3] L. Frassinetti et al., Phys. Rev. Lett. 97, (2006) 175001.

[4] J. B. Taylor, Phys. Rev. Lett. 33, (1974) 1139.

[5] E. Tassi, R.J. Hastie and F. Porcelli, submitted to Phys. Plasmas (2007).

[6] E. Tassi, F. Militello, F. Porcelli and R.J. Hastie, in preparation (2007).

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On existence of resistive magnetohydrodynamic equilibria?

H. Tasso1, G. N. Throumoulopoulos2

1Max-Planck-Institut fur Plasmaphysik, Euratom Association,D-85748 Garching, Germany

2University of Ioannina, Association Euratom - Hellenic Republic,Section of Theoretical Physics, GR 451 10 Ioannina, Greece

A necessary condition for existence of general dissipative magnetohydrodynamic equi-libria is derived. The ingredients of the derivation are Ohm’s law and the existence ofmagnetic surfaces, only in the sense of KAM theorem. All other equations describing thesystem matter exclusively for the evaluation of the condition in a concrete case.

? Accepted for publication in Journal of Plasma Physics

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66

Side conditioned axisymmetric equilibriawith incompressible flows

G. N. Throumoulopoulos1, H. Tasso2, G. Poulipoulis1

1University of Ioannina, Association Euratom - Hellenic Republic,Section of Theoretical Physics, GR 451 10 Ioannina, Greece

2Max-Planck-Institut fur Plasmaphysik, Euratom Association,D-85748 Garching, Germany

Axisymmetric equilibria with incompressible flows of arbitrary direction are studied inthe framework of magnetohydrodynamics under a variety of physically relevant side con-ditions consisting for example in that the plasma temperature or the magnetic field mod-ulus are uniform on magnetic surfaces. To this end a set of pertinent non-linear ODEsare transformed to quasilinear ones and the respective initial value problem is solvednumerically with appropriately determined initial values near the magnetic axis. Severalequilibrium configurations are then constructed surface by surface. It turns out thatin addition to the usual configurations with a magnetic axis, the non field aligned flowresults to novel toroidal shell equilibria in which the plasma is confined within a coupleof magnetic surfaces. In addition, the flow affects the elongation and triangularity of themagnetic surfaces and opens up the possibility of changing the magnetic field topologyby creating double toroidal shell-like configurations.

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Modeling of losses related to and frequency of type I Edge Localized Modes and of ELM mitigation through external field perturbations

M.Z.Tokar¹, T.E.Evans², A.Gupta¹, R.Singh³, B.Unterberg1

¹Institut für Plasmaphysik, Forschungszentrum Jülich GmbH, Association FZJ-Euratom,

52425, Jülich, Germany; ²General Atomics, San Diego, California 92186-5606,USA;

³Institute for Plasma Research, Bhat, Gandhinagar-382428, India A model [1] to asses the particle and energy losses caused by type I Edge Localized Modes (ELM) is further developed. This model is based on the assumption that the increase of transport in the Edge transport barrier (ETB) during an ELM burst is due to flows along magnetic field lines perturbed by ballooning-peeling MHD modes. The model reproduces the experimentally found variation of losses with the plasma collisionality ν*, i.e., the weak dependence of the particle loss and significant reduction of the energy loss with increasing ν*. The ELM frequency is determined by considering the particle and energy balance during the relaxation phase between ELM bursts. This is done by assuming that on this phase the transport in the ETB is a neoclassical one. The effect of magnetic field perturbations from external resonant coils on the ELM behaviour is analyzed for the conditions of low and high ν*. The changes in the ETB parameter profiles observed in low collisionality plasma in DIII-D, where ELM were completely suppressed without deterioration of confinement, are interpreted [2]: the reduction of the density in plasmas of low collisionality is due to outflow of charged particles from the ETB along field lines which become inclined in the radial direction even between ELM bursts; the increase of the electron and ion temperatures in the barrier is caused by the reduction of perpendicular neoclassical transport with decreasing density and kinetic non-local effects in the heat transport along perturbed field lines. The found modification of the pressure gradient implies the stabilization of peeling-ballooning-MHD mode. References [1] Tokar M.Z., et al., Plasma Phys. Control. Fusion 49 (2007) 395 [2] Tokar M.Z., et al., Phys. Rev. Lett. 98 (2007) 095001

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Study of toroidally confined plasmas in steady state usingsmoothed particle magnetohydrodynamics.

C Toniolo1, B. Weyssow1, D. Price2

1Association EURATOM-Etat Belge, Statistical and Plasma Physics, Universite Librede Bruxelles, Campus plaine, CP 231, B-1050 Bruxelles

2School of Physics, University of Exeter, Stocker Rd, Exeter EX4 4QL, UK

Equilibrium of toroidally confined high temperature plasmas have been obtained ana-lytically or numerically by solving the Grad-Shafranov equation which depends on twomagnetic surface functions, the plasma pressure and the poloidal current. In the case ofthe toroidal Z-pinch, defined as an axisymmetric confinement where the magnetic field isin the poloidal direction (the angle defined in the toroidal cross section) the equilibriumis generally unstable. Coupling the poloidal field to a strong toroidal magnetic field maylead to a more stable equilibrium (in a small aspect ratio analysis) depending on theradial variation of the safety factor “q”.

We report on first results on toroidal equilibria and steady states obtained using asmoothed particle method approach. The calculations are performed using a three-dimensional binary tree hydrodynamic code originally developed by Benz [1] and sub-sequently modified by Price and Bate [2] to solve the ideal MHD equations. For thesimulations, a certain amount of artificial viscosity and resistivity is needed to compen-sate for too large (and unphysical) hydrodynamic and magnetic fluctuations, and thetoroidal solid wall is simulated using a boundary force which repulses particles approach-ing the edge. A statistical analysis of the velocity and magnetic components is performedshowing the appearance of MHD instabilities. The results obtained yet suggest that hightemperature magnetically confined plasmas and in particular shape related stability anal-ysis relevant to ITER can indeed be performed using the SPH method.

(a) (b)

Figure 1: (a) Positions of the gas particle inside the torus at a fixed time (in code units) and(b) a typical density profile with respect to the radial toroidal coordinate.

References

[1] W. Benz, A. G. Cameron, W. Press, R.L. Bowers, APJ, 348 (1990) 647.[2] D. J. Price and M. R. Bate, MNRAS, 377 (2007) 77.

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Stability analysis of internal ideal modes in low-shear tokamaks

C. Wahlberg1 and J. P. Graves2

1Department of Astronomy and Space Physics, EURATOM/VR Fusion Association, P.O. Box 515, Uppsala University, SE-751 20 Uppsala, Sweden

2Centre de Recherches en Physique des Plasmas, Association EURATOM-Confederation Suisse, EPFL, 1015 Lausanne, Switzerland

Tokamak equilibria with a wide, central region of very low magnetic shear are presently of large interest as potential operating scenarios for ITER. This class of equilibria includes the so-called ”hybrid scenario”, where q is slightly larger than unity in the low-shear region, as well as scenarios in which q is well above unity and relatively flat in the plasma core. Here we discuss the stability properties of ideal MHD modes resonant with the internal magnetic field in such plasmas [1]. Hastie and Hender [2] has previously analysed the stability of the quasi-interchange m = n = 1 mode as well as higher-order m = n > 1 ideal modes in low-shear equilibria with q ≈ 1 in the core plasma. The present work generalises the analysis in Ref. 2 to modes with m/n ≈ q in equilibria with arbitrary, but flat q in the core region. By modelling the pressure in the central plasma region with a parabolic profile, it is shown that, for tokamaks with large aspect ratio, the stability can be analysed from an exact solution of the ideal MHD equations. The exact solution gives a good overview of the complete, ideal MHD spectrum of low-shear equilibria, including the spectrum of pressure-driven, global instabilities that exist in low-shear equilibria with q < 1 in the plasma core due to violation of the Mercier criterion . Furthermore, the instabilities for q < 1 are found to appear as stable, global eigenmodes in equilibria where q > 1 in the core, and, for sufficiently high pressure, exactly one unstable mode with mode numbers m and n, with m > n, is shown to exist in equilibria where q ≈ m/n > 1. A simple, analytical expression for the stability limit of such modes is derived.

0')1( 2 >− pq

References [1] Wahlberg, C. and Graves, J. P., Phys. Rev. Lett., 2007 (submitted). [2] Hastie, R. J. and Hender, T. C., Nucl. Fusion 28, 585 (1988).

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Simulations of NBI-ICRF synergy

with full-wave TORIC package

R. Bilato

Max-Planck Institut fur Plasmaphysik - Euratom Association

Boltzmannstr. 2, D-85748 Garching, Germany

During the combined heating with waves in the Ion Cyclotron Range of Frequencies

(ICRF) and Neutral Beam Injection (NBI), the NBI fast-ions are further accelerated

as a consequence of the synergetic effects, in particular near the second harmonic

cyclotron resonance. This common experimental observation has been corroborated by

modelling and simplified numerical solvers over the years. Because of the importance

of the fast ion tail in the wave absorption and propagation, we have implemented

a NBI source in the Fokker-Planck SSFPQL solver interfaced with the spectral full-

wave TORIC solver. In our implementation the NBI ionization sources are calculated

directly by MonteCarlo codes, like FAFNER code. Due to the mathematical scheme

adopted in SSFPQL, it is possible to describe anisotropic sources such as NBI. We

discuss the numerical implementation and the preliminary results with reference to

ASDEX-Upgrade experiments.

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71

Contour Dynamics:Kinetic electron simulation of collisionless reconnection

H.J. de Blank and E.V. van der Plas

FOM-Institute for Plasma Physics Rijnhuizen,Association Euratom-FOM, Trilateral Euregio Cluster,P.O. Box 1207, 3430 BE Nieuwegein, The Netherlands

One of the long-standing problems in nonlinear plasma dynamics is the modelling offast magnetic reconnection rates observed in space and in magnetic fusion experiments.When collisional dissipation is weak, resistive reconnection cannot always explain the ob-served reconnection rates. However, faster than resistive reconnection rates are possibledue to electron inertia. Parallel electron compressibility can further accelerate this pro-cess, yielding fast reconnection rates comparable with those observed in tokamak plasmainstabilities [1].

The weak collisionality necessitates a kinetic description of the electrons during reconnec-tion [2]. We resolve the electron kinetics on the inertial scale de using Contour Dynamics(CD) in the plane perpendicular to the guide field. This method, taken from hydro-dynamics [3], simulates the electron motion in 2D with the evolution of a collection ofinteracting contours. The present plasma application exploits the fact that in a strongguide field, electrons with equal parallel velocities move together like an incompressiblefluid perpendicular to the field. We approximate the full electron distribution as a numberof such fluids.

We present the evolution of reconnecting instabilities of cylindrical symmetric currentdistributions, featuring transient scale collapse of the x-point current and nonlinear satu-ration and phase mixing. The effects of the current density distribution and temperaturegradients, and comparisons with 2-fluid theory are discussed.

References

[1] M. Ottaviani and F. Porcelli, Phys. Plasmas 2 (1995) 4104.

[2] H. J. de Blank, Phys. Plasmas 8 (2001) 3927, E. V. van der Plas and H. J. de Blank.Phys. Rev. Lett. 99 (July 6, 2007).

[3] P. W. C. Vosbeek and R. M. M. Mattheij, J. Comput. Phys. 133 (1997) 222.

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72

Quasi-linear theory of whistler waves destabilized by a

relativistic runaway beam

T. Fulop, G. Pokol, M. Lisak

Dept. of Radio and Space Science and Euratom-VR Association, Chalmers University

of Technology, Goteborg, Sweden

In a tokamak disruption a beam of highly relativistic runaway electrons (with energy of

order 20 MeV) is sometimes generated. Several tokamaks have reported that no runaway

generation occurs unless the magnetic field exceeds 2.2 T. A possible explanation for this

observation might be that the runaway beam excites whistler waves that may scatter the

electrons in velocity space and the beam cannot form. Recent work [Fulop et al Phys.

Plasmas, 13, 062506 (2006)] showed that the linear growth rates of these waves are such

that they are stable for high fields (so the runaway beam can form), but unstable for low

fields (so that it can prevent the beam from forming). The present work describes the

quasilinear evolution of the instability.

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Asymmetric Distributions of Energetic Circulating Ions andSawtooth Control using ICCD and Unbalanced NBI

J. P. Graves1

1Centre de Recherches en Physique des Plasmas, AssociationEURATOM-Confederation Suisse, EPFL, 1015 Lausanne, Switzerland

There is little doubt that various auxiliary heating systems are successfully and routinelycontrolling sawteeth. There is however some room for improving our understanding ofthe mechanisms that influence these important changes to the discharges. A mechanismthat appears to be common across ECCD, ICCD and unbalanced NBI discharges involvesthe effect of the q = 1 localised current drive perturbation on resistive diffusion duringthe sawtooth ramp. Nevertheless, it is important to look for explanations for sawtoothcontrol which may exist in ion based auxiliary systems, but may differ or not exist inelectron auxiliary means of sawtooth control. The reason for this is that monster saw-teeth, initially lengthened by trapped energetic ions, have up to the present day only beencontrolled using ICCD [1], while in ITER the primary method for sawtooth control couldbe ECCD. A mechanism based on the finite orbit width of parallel asymmetric energeticcirculating particles [2] is only non-negligible for ion based auxiliary systems. The presentcontribution examines the relevance of the latter in sawtooth control experiments, suchas those using ICCD [1] and NBI [3] at JET, by looking carefully at the role of circulatingions close to the trapped boundary. At such pitch angles the orbit width is largest, andthe parallel asymmetry of the distribution function has the greatest influence.

References

[1] L.-G. Eriksson et al, Phys. Rev. Lett. 92, 235004 (2004).

[2] J. P. Graves, Phys. Rev. Lett. 92, 185003 (2004).

[3] J. P. Graves et al, Plasma Phys. Control. Fusion 47, B121-B133 (2005); F. Nave etal, Phys. Plasmas 13, 014503 (2006)

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ICRF Mode Conversion Current Drive for Plasma Stability Control in Tokamaks

D. Grekov1, R. Koch2, A. Lyssoivan2, J.-M. Noterdaeme3 and J. Ongena4

1Institute of Plasma Physics, Kharkov, Ukraine

2Royal Military Academy, Laboratory for Plasma Physics /Association Euratom, Brussels, Belgium

3Max-Planck Institut fur Plasmaphysik, Garching, Germany 4Euratom/UKAEA Fusion Association Culham Science Centre, Abingdon, UK

There is a substantial incentive for the International Thermonuclear Experimental Reactor (ITER) to operate at the highest attainable beta (plasma pressure normalized to magnetic pressure), a point emphasized by requirements of attractive economics in a reactor. Recent experiments aiming at stationary high beta discharges in tokamak plasmas have shown that maximum achievable beta value is often limited by the onset of instabilities at rational magnetic surfaces (neoclassical tearing modes). So, methods of effective control of these instabilities have to be developed. One possible way for neoclassical tearing modes control is an external current drive in the island to locally replace the missing bootstrap current and thus to suppress the instability. Also, a significant control of the sawtooth behaviour was demonstrated when the magnetic shear was modified by driven current at the magnetic surface where safety factor equals to 1. In the ion cyclotron range of frequencies (ICRF), the mode conversion regime can be used to drive the local external current near the position of the fast-to-slow wave conversion layer, thus providing an efficient means of plasma stability control. The slow wave energy is effectively absorbed in the vicinity of mode conversion layer by electrons with such parallel to confining magnetic field velocities that the Landau resonance condition is satisfied. For parameters of present day tokamaks and for ITER parameters the slow wave phase velocity is rather low, so the large ratio of momentum to energy content would yield high current drive efficiency. In order to achieve noticeable current drive effect, it is necessary to create asymmetry in the ICRF power absorption between top and bottom parts of the plasma minor cross-section. Such asymmetric electron heating may be realized using:

- shifted from the torus midplane ICRF antenna in TEXTOR tokamak; - plasma displacement in vertical direction that is feasible in ASDEX-Upgrade; - the peculiarities of the design of new JET ITER-like ICRF antenna. Each radiating

strap of this antenna is divided to four parts in poloidal direction, connected to its own feeder.

The proper feeder phasing of JET new antenna may provide more than twice excess of m > 0 poloidal harmonics over m < 0 harmonics. The value of driven current is estimated as 300 - 500 kA for typical JET parameters.

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75

Single particle orbits in anisotropic fully shaped plasmas

Martin Jucker, Jonathan P. Graves and W. A. Cooper

Ecole Polytechnique Federale de Lausanne (EPFL), Centre de Recherches en Physiquedes Plasmas, Association Euratom-Confederation Suisse, CH-1015 Lausanne,

Switzerland

Present day devices employ sufficiently high power auxiliary heating such that the pres-sure associated with the corresponding energetic particles is of the order of the thermalpressure. In particular, for NBI and ICRH, the fast ions are distributed anisotropically,and this has been shown to influence the equilibrium and MHD stability. In the presentcontribution, we aim to explore the influence of anisotropy on single particle orbits, andultimately kinetic corrections to perturbations of MHD-like origin. New 3D single parti-cle orbit equations have been derived[1] and introduced into the guiding centre orbit codeVENUS. These new equations of motion allow for a treatment of the pressure anisotropyand electromagnetic perturbations. VENUS uses the well established equilibrium andstability codes VMEC and TERPSICHORE as inputs, and follows a single particle onits orbit around 2D or 3D configurations. As a first application, the magnetic drift pre-cession frequency is studied for both trapped and passing particles in a tokamak. Theeffects of parallel (P‖ > P⊥) and perpendicular (P⊥ > P‖) anisotropy are shown, includingpoloidal dependence of the perpendicular pressure due to anisotropy. Also, an analyticalexpression of the toroidal drift frequency for trapped particles including magnetic shear,plasma elongation and radial pressure gradients is derived. Thus a comparison with al-ready existing expressions is possible and all of them can be compared to independentorbit simulations. The VENUS code is also used for elucidating the effects of the differentparameters on the toroidal drift frequency. Another application is the modification offast particle orbits due to pressure anisotropy, especially for large orbit widths and smallinverse aspect ratio ε. Finally, the inclusion of electromagnetic perturbations allows foran investigation of MHD-like perturbations and their impact on particle orbits as well asresonance phenomena.

References

[1] W. A. Cooper et al., Phys. Plasmas, 13 (2006) 092501.

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Nonlinear gyrofluid computation of ELM crash events

A. Kendl1 and B.D. Scott2

1Institut für Theoretische Physik, Univ. Innsbruck / Association Euratom-ÖAW, Austria2Max-Planck-Institut für Plasmaphysik, Euratom-Association, Garching, Germany

First results on studies with a gyrofluid turbulence model on a nonlinear approach to simulation of the blow-out phase during an ELM crash are presented. The main aim is on an understanding of the physical mechanisms and scalings of the ballooning instability in H-mode like profiles that evolves into a fully turbulent phase during the crash.For this purpose, the electromagnetic 6-moment gyrofluid code GEM for both electrons and ions is used in global geometry with self-consistent q profile and Shafranov shift. For the initial profiles an ASDEX Upgrade H-mode shot (#17151) is chosen as base case. The instability, linear mode structure and final nonlinear cascade into the turbulent blow-out of the ballooning crash are analysed.Poloidal resolution convergence studies reveal the necessity of well-resolved nonlinear ELM simulations that span the whole range between system size and the gyro scale. The results are outside of both MHD and Braginskii regimes. A detailed scaling study on the mode structure, cascade properties and profile degradation is presented with respect to poloidal resolution, plasma beta, safety factor and gradient lengths.

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Gyrokinetic simulations of shaping effects on turbulent heatand particle transport observed on the TCV tokamak

X. Lapillonne, T. Dannert, O. Sauter, A. Marinoni, Y. Camenen,A. Pochelon, L. Villard and S. Brunner

Ecole Polytechnique Federale de Lausanne (EPFL)Centre de Recherches en Physique des Plasmas

Association Euratom-Confederation SuisseCH-1015 Lausanne, Switzerland

Experimental results from the ”Tokamak a Configuration Variable ” (TCV) experiment[1, 2] have shown a heat transport coefficient χe two times greater with a triangularityδ = +0.4 than in a case with δ = −0.4 in L-mode plasma. These results were themotivation for a systematic study of shaping effects, and especially triangularity, onturbulent transport using the flux-tube gyrokinetic code GENE [3, 4]. In order to enablesimulations of realistic tokamak plasma conditions and geometry, the code is extendedfrom the s-alpha approximation to general axisymmetric geometry using an interface withan ideal MHD equilibrium code, CHEASE [5].In a second stage the code will be used to compare numerical results with experimentaldata from Electron Internal Transport Barriers (eITBs) studies conducted at TCV in afully non-inductive discharge. The relative importance of Trapped Electron Modes andElectron Temperature Gradient modes will be investigated. The current status of thiswork will be presented.

References

[1] Y. Camenen and A. Pochelon, et al., Plasma Phys. Control. Fusion, 47 (2005) 1971.

[2] Y. Camenen and A. Pochelon, et al., to be published in Nuclear Fusion, Impact ofplasma triangularity and collisionality on electron heat transport in TCV L-modeplasmas.

[3] F. Jenko, W. Dorland, M. Kotschenreuther, and B.N. Rogers, Phys. Plasmas, 7 (2000)1904.

[4] T. Dannert and F. Jenko ,Phys. Plasmas , 12 (2005) 1.

[5] H. Lutjens, A. Bondeson, and O. Sauter, Comp. Phys. Com. , 97 (1996) 219.

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Parallelization of a full-f semi-Lagrangian code: GYSELA

G. Latu1, V. Grandgirard2, R. Belaouar 3, N. Crouseilles3 and E. Sonnendrucker3,4

1 INRIA Futurs, Scalapplix Project, Bordeaux, France2 CEA/DSM/DRFC, CEA-Cadarache, Saint-Paul-Lez-Durance, France

3 INRIA Lorraine, Calvi Project, Nancy, France4 IRMA, Universite Louis Pasteur, Strasbourg, France

The present work consists in the numerical simulation of tokamak plasmas. To study suchplasmas where the particles are confined along magnetic fields lines, gyrokinetic modelsare known to be a convenient way. The time evolution of the ionic distribution func-tion is self-consistently coupled by the electric potential through a quasi-neutrality typeequation. Gyrokinetic models take into account five dimensions of the phase space thatrepresent a great challenge to simulate since it is very demanding in terms of numerics.

Mainly two approaches can be envisaged to approximate gyrokinetic models; on the onehand, in PIC methods, the distribution function is considered as a sum of macro-particleswhereas the electromagnetic fields are evaluated on a fixed grid; on the other hand, Vlasovcodes use a grid of the phase space on which the kinetic unknown is determined. Thepresent code GYSELA is based on a full-f semi-Lagrangian scheme which takes benefitfrom both approaches.

The implementation of such a code remains a difficult task and important efforts have tobe done to perform an efficient parallelization of each step of the algorithm. In particu-lar, two important recent improvements of the GYSELA code will be highlighted: firsta parallel interpolation technique based on local cubic splines and second, a new solvingmethod of the quasi-neutrality equation (see Fig. 1). The integration of these two numer-ical methods together with an appropriate communication scheme significantly improvethe global time resolution and enable an efficient use of a large number of processors.

Figure 1: Comparison of the speedup for 2 quasi-neutrality equation solvers.

References

[1] G. Latu et al., Parallelization of a quasi-neutrality solver, in preparation.[2] G. Latu et al., Gyrokinetic semi-Lagrangian parallel simulation using a hybrid

OpenMP/MPI programming, submitted to PACT’07.

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Self-consistent simulations of ICRH experiments: The CYRANO-BATCHcode

E. Lerche(1), D. Van Eester and P. Lamalle

Laboratory for Plasma Physics, Association “EURATOM – Belgian State”,Trilateral Euregio Cluster, Royal Military Academy, Brussels

(1)ealerche@rma.ac.be

Self-consistent simulations of wave-particle interactions in tokamaks are becoming morepopular with the gradual increase in computational resources [1-5]. They have proven to be veryimportant for the understanding of some processes in recent RF experiments in tokamaks [1,3]and will be essential for more reliable predictions of the ITER scenarios.

In the case of high power ion-cyclotron resonance heating (ICRH), in particular, thedistribution function of the heated species is usually far from Maxwellian, and wave couplingwith injected beam ions (NBI) and fusion born alpha particles may be of strong importance formore reliable predictions of both the wave absorption and the wave propagation. Therefore, theMaxwellian description of the plasma particles traditionally adopted in full-wave simulations isnot satisfactory, and the dielectric response of the plasma species should be evaluated in terms ofgeneral particle distributions. This requires the numerical computation of the guiding-center orbitintegrals instead of the analytical approach used in the Maxwellian case (based on the plasmadispersion function).For that purpose, the full-wave code CYRANO [6] was coupled to the 2D quasi-linear Fokker-Planck BATCH [7] code. In practice, the two codes are looped and the fields produced by theCYRANO code (for the last received input distribution functions) are passed as input to theBATCH code, which evaluates the new distributions. The codes are consecutively iterated untilthe RF power densities computed by the two codes converge.

The first applications of the coupled CYRANO-BATCH numerical procedure will bepresented, including the comparison with simplified Maxwellian simulations and benchmarkingwith experimental data from recent JET experiments.

[1] M. Brambilla and R. Bilato, Nucl. Fusion 46, p.387 (2006).[2] M. Laxåback, T. Hellsten and T. Johnson, AIP Conf. Proc. 595, p.414 (2001).[3] E. Lerche, D. Van Eester, A. Krasilnikov and P. Lamalle, "D majority heating in JETplasmas: ICRH modelling and experimental RF deposition", to appear in AIP Conf. Proc. of 17thTopical Conference on RF Power in Plasmas, Clearwater, 2007.[4] F. Jaeger et al., Physics of Plasmas 13 (5), pp. 056101-056101-9 (2006).[5] A. Fukuyama et al., "Integrated Full-wave Analysis of ICRF Waves in Burning Plasmas", toappear in AIP Conf. Proc. of 17th Topical Conference on RF Power in Plasmas, Clearwater,2007.[6] P. Lamalle, PhD thesis - Université de Mons (1994); LPP-ERM/KMS Laboratory Report 101.[7] D. Van Eester, J. Plasma Physics 65, p.407 (2001).

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80

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81

Impurity transport in ITER-like plasmas using fluid and

gyrokinetic descriptions

H. Nordman1, T. Fulop1, J. Candy2, P. Strand1, J.Weiland1,

1Dept. of Radio and Space Science and Euratom-VR Association, Chalmers University

of Technology, Goteborg, Sweden2General Atomics, P.O. Box 85608, San Diego, California 92186-5608

Impurity and Helium ash transport in tokamaks is studied using an electrostatic fluidmodel for ion temperature gradient (ITG) and trapped electron (TE) mode driven turbu-lence and the results are compared with nonlinear gyrokinetic simulations using GYRO.Transport scalings with magnetic shear and impurity fraction are investigated, and thevalidity of the trace impurity approximation is studied. Comparisons between anoma-lous and neoclassical transport predictions are performed for ITER-like profiles based onASTRA modelling.

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82

Plasma waves relativistic effects at the ICR frequency range

Castejon F., Pavlov S.S., Tereshchenko M.

AbstractTheoretical description of plasma waves at the ECR frequency range requires one to take

into account mass variation relativistic effects, which can arise not only in hot but also incommon fusion plasmas and are essential for quasi-perpendicular waves propagation [1] andhigh harmonics regimes [2].

Those effects can naturally be separated into two parts since into theoretical descriptionthey are including by two ways. The first is connected with the use of linear kinetic equation inthe relativistic form and the use relativistic Maxwellian distribution of electrons for its resolving[3] and describes through plasma dispersion function (PDFs) relativistic effects, connected withlongitudinal to magnetic field a spatial disperion of plasma i.e. with longitudinal Dopplerextending of cyclotron zones of plasma waves and electrons interactions. The second way ismore obscure and connected with the use of Maxwellian equations (or dispersion relation)together with kinetic equation (relativistic or non-relativistic) and describes relativistic effects,connected with perpendicular spatial dispersion of plasma i.e. effects of finite plasmatemperature.

At the ICR frequency range arising relativistic effects seems much more exotic sincerelation of the relativistic parameter Tmc 0

2=µ ( 0m is the rest mass of plasma particles, T isthe plasma temperature), taken for ions to one for electrons is largeenough 310~eiei mm=µµ . However, at the quasi-perpendicular wave propagation regimethose effects of second sort can arise for fast waves (FW) near fundamental ICR harmonic atmoderate hot and reactor plasmas [4].

Results of the work [4] for FW absorption and dispersion near fundamental harmonicwere obtained on the base of the method of perturbations in the small relativisticparameter iµ1 and without demonstration of relativistic nature of those effects. Results arecorrect when longitudinal refractive index ω//// ckN = is large enough and, consequently,expansions in the parameter iλ converge fast. In opposite case it is necessary to perform theexact calculations in the parameter iµ1 .

The primary purpose of the present work is performing on the base [2] namely such kindof calculations for FW near fundamental in homogeneous plasma i.e. generalization results of [4]to the case of arbitrary

//N and demonstration of relativistic nature of these effects.

1. Fidone I., Granata G., and Meyer R.L., 1982, Physics of Fluids, 25, 2249.2. Castejon F., Pavlov S.S., 2006, Physics of Plasmas, 13, 072105.3. Trubnikov B.A. 1959 Plasma Physics and the problem of Controlled Thermonuclear

Reactions, (ed. M.A. Leontovich), vol.3, Pergamon.4. Castejon F., Pavlov S.S., Swanson D.G., 2002, Physics of Plasmas, 9(1), 111.

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83

Modelling of energetic ions behaviour in the n=1 kink distorted central core of the JET tokamak

A. Perona1, S. D. Pinches2, S. E. Sharapov2 and F. Porcelli1

1 Burning Plasma Research Group, Politecnico di Torino, 10129 Torino, Italy2 Euratom/ UKAEA Fusion Association, Culham Science Centre, Abingdon,  

Oxfordshire OX14 3DB, UK

The   1=n   kink perturbation is often observed in the form of a long­lived perturbation in plasmas of   the  Joint  European Torus  (JET).  The aim of   this  work   is   to   investigate   the behaviour of energetic ions in the presence of such   1=n  distortion of the plasma core in JET plasmas with the particle­following HAGIS (Hamiltonian GuIding System) code [1]. We have considered a plasma equilibrium reconstructed for a typical JET discharge, while the kink perturbation is provided by the linear ideal MHD CASTOR code and the amplitude of  the mode  is  extended  to a  finite value.   It   is  expected  that   the kink mode affects   the particle orbits, but how this happens, and what group of fast ions will be affected the most, depends on various parameters which characterize  the  ions at   the initial   time, when the perturbation is not yet present. In order to assess such effects the HAGIS code has been extended in order to display Poincaré plots for both the magnetic field lines and drift orbits of fast ions. Three characteristic types of unperturbed orbits initially localized inside the 

1=q  magnetic surface are considered: trapped banana orbits, accelerated with Ion Cyclotron Resonance   Heating;   passing   ions   (i.   e.   ions   circulating   in   the   poloidal   and   toroidal coordinates); and orbits close to the stagnation one. The changes in the orbit topology are investigated   both   for   a   static   1=n   kink   and   for   a   perturbation   whose   amplitude   is exponentially growing in time. In the first case, the stagnation and passing orbits show the most significant distortions, while the trapped ions are much less sensitive to the presence of the mode.  For  the growing perturbation,  the  trapped orbits  are,  again,   insensitive to  the changes in the perturbed magnetic topology. In this case, all passing ions originally starting near   the   1=q   unperturbed surface at  different  poloidal  positions   retain  their  circulating feature in the toroidal coordinate, but about one half of them become “poloidally localized”, so that they no longer circulate around the displaced magnetic axis.

References

[1] S.D. Pinches et al., Computer Physics Comm., 111 (1998) 133.

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When can Fokker-Planck equation describe anomalous transport ?

D.F. Escande1,2 and F. Sattin2

1UMR 6633 CNRS-Université de Provence, Marseille,France

2Consorzio RFX, Associazione EURATOM-ENEA sulla fusione, Padova, Italy

Modeling anomalous transport in magnetic fusion devices is a longstanding and difficult issue. Numerical simulation of this transport using fluid or kinetic models is a very successful approach, but low dimensional models are desirable to provide insight in transport mechanisms, rationales for confinement scaling laws, and tools for experimental data analysis. The Fokker-Planck Equation (FPE) is an age-old mathematical tool for describing transport processes. However the diffusive picture underlying FPE clearly breaks down in some cases. This was proved, e.g., for the transport in magnetized plasmas of tracer particles suddenly released in pressure-gradient-driven plasma turbulence, which exhibits strongly non gaussian features [1].

Notwithstanding this, its true limits and potentialities in the modeling of anomalous transport have not been fully considered. We address this issue for particle transport, by taking into account the Hamiltonian character of their dynamics. The FPE, applied to fusion plasmas, can model several anomalous features, including uphill transport, scaling of confinement time with system size, and convective propagation of externally induced perturbations. It can be justified for generic particle transport provided that there is enough randomness in the Hamiltonian describing the dynamics. Then, except for 1 degree-of-freedom, the two transport coefficients (the diffusive and the convective term) are largely independent. Diffusion is justified by locality of trapping in phase-space, or by locality in velocity of wave-particle resonance, then leading to a quasilinear estimate. On the other hand, FPE itself is an approximation of the more general Chapman-Kolmogorov Equation. However the assumptions justifying this approximation are not always correct. In this work we will point out some reasons and consequences of this breakdown, in particular when the small step-length approximation fails: the true features of the profiles are hidden by the inappropriate use of the FPE. References [1] D. del-Castillo-Negrete, B.A. Carreras, and V.E. Lynch, Phys. Plasmas 11, 3854 (2004)

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THE TRACE ION MODULE FOR THE MONTE CARLO CODE EIRENE, A UNIFIED APPROACH TO PLASMA CHEMISTRY IN THE ITER DIVERTOR

Josef Seebacher¹, Detlev Reiter² and Petra Börner²

¹ Association EURATOM­ÖAW, Institute for Theoretical Physics, University of Innsbruck, A­6020  Innsbruck, Austria

² Institute for Energy Research ­ Plasmaphysics, Forschungszentrum Jülich GmbH, EURATOM Association, Trilateral Euregio Cluster, D­54245 Jülich, Germany

Modelling of kinetic transport effects in magnetic fusion devices is of great importance for understanding the physical processes in both the core and and the scrape off layer (SOL) plasma. For SOL simulation the EIRENE code is a well established tool for modelling of neutral, impurities and radiation transport. Recently a  new  trace   ion   transport  module   (tim),   has  been  developed   and   incorporated   into  EIRENE.  The  tim essentially consists of two parts: 1) A trajectory integrator tracing the deterministic motion of a guiding centre particle in general 3D electric and magnetic fields.  2) A stochastic representation of  the Fokker­Planck collision operator in suitable guiding centre coordinates treating Coulomb collisions with the plasma background species. The TIM enables integrated SOL simulation packages such as B2­EIRENE, EDGE2D­EIRENE (2D) or EMC3­EIRENE (3D) to treat the physical and chemical processes near the divertor targets and in the bulk of the SOL in greater detail than before, and in particular on a kinetic rather than a fluid level. One of the physics applications is the formation and transport of hydrocarbon molecules and ions in the divertor in tokamaks, where the tritium codeposition via hydrocarbons remains a serious issue for next generation fusion devices like ITER. Real tokamak modelling scenarios will  be discussed with the code packages B2­EIRENE (2D) and EMC3­EIRENE (3D). A brief overview of the theoretical basis of the tim will be given including code verification studies of the basic physics properties. Applications to hydrocarbon transport studies in TEXTOR and ITER, comparing present (fluid) approximations in edge modelling with the new extended kinetic model, will be presented.

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Challenges of rigorous 3-D Fokker-Planck modeling of ICRH heating

D. Van Eester

Laboratory for Plasma Physics, Association “EURATOM – Belgian State”, ERM/KMS,Trilateral Euregio Cluster, Brussels, Belgium

Semi-analytical methods are adopted to evaluate the dielectric response of a plasma toelectromagnetic waves in the ion cyclotron domain of frequencies accounting for drift orbiteffects in an axisymmetric tokamak.

Various methods – each having its advantages and drawbacks - are adopted. One methodconsists in computing the actual bounce spectrum of the dielectric response. It is general butextremely time consuming. Another method relies on subdividing the orbit into elementarysegments in which the integrations can be performed analytically. This method is less generalbut allows speeding up the computation. The aim of the present paper is to provide an up-date of the modeling efforts attempting to formulate the quasi-linear diffusion aspects of RFheating in a flexible way that allows both 2-D and 3-D modeling (i.e. either accounting forfinite banana width effects and RF induced radial diffusion or not).

For the 3-D model, the adopted numerical resolution relies on a subdivision of the integrationdomain in tetrahedrons. This specific shape of the elementary volumes allows imposing theboundary conditions - in particular the non-local conditions across the curved trapped/passingboundary connecting one trapped to two passing orbits – in a way guaranteeing particle andenergy conservation. The particular chosen shape also readily permits zooming in on regionswhere more detail is required.

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AUTHOR INDEX

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Author Page(s) Agullo …………………………………………….…...…………………… 3, 40, 42, 63 Andrew …………………………...…………………...…………………………..… 16 Angelino …………………………...…………………………………..…….…….… 23 Ansar Mahmood ………………...……………………………………………....…… 24 Artaud ……………………………………..……………………………………… 36, 43 Atanasiu ………………………………………………………………………..…… 55 Basiuk ……………………………………………………………………….…… 36, 43 Baty …………………………………………………………………………...……… 60 Belaouar ………………………………………………………....…………………… 79 Benkadda …………………………………………………………...……… 3, 40, 42, 63 Benilov ……………………………………………………………..………………… 33 Belasri …………………………………………………………………………………45 Bergkvist ……………………………………………………………………………… 62 Beyer …………………………………………………………………………….… 3, 63 Bian ………………………………………………………………………………...… 42 Bilato …………………………………………………………………………........… 71 Börner ………………………………………………………………………….......… 86 Bonfiglio …………………………………………………………………….…… 56, 58 Borgogno …………………………………………………………………….……… 57 Bottino ……………………………………………………………....………….….… 23 Breizman ……………………………………………………………………….….10, 37 Brunner ………………………………………………………………………….... 8, 78 Calvo …………………………………………………………………………….…… 38 Camenen …………………………………………………………………………...… 78 Candy ………………………………………………………….......………………… 82 Cappa …………………………………………………………...…………………… 39 Cappello ………………………………………………………...…………… 47, 56, 58 Carreras ………………………………………………………….……………………38 Castejón ……………………………………………………………………… 39, 46, 83 Catto ……………………………………………………………..………….…..…… 10 Chacón …………………………………………………………………………… 5, 57 Chandra ……………………………………………………………………………… 40 Chhajlani ……………………………………………………………………….…..… 64 Connor ……………………………………………………………………….……… 12 Constantinescu …………………………………………………………………….… 41 Cooper ……………………………………………………………………………. 8, 76 Crombé ……………………………………………………………………..….…..… 16 Crouseilles …………………………………………………………………………… 79 Dannert ………………………………………………….……………..……. 25, 28, 78 Darmet ………………………………………………………………….………….… 15 de Blank …………………………………………………………………....………… 72 Dewar ………………………………………………………………………...……… 59 Diamond …………………………………………………………….………..……... 30 Dif-Pradalier ……..…………………………………………………………….… 15, 23 Eriksson …………………………………………………………….…………..….... 26 Escande ………………………………………………………………………….....… 85 Evans ………………………………………….......………………………………… 68 Falchetto ………………………………………...…………………….………….…. 27

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Firpo …………………………………………….……………………………………60 Fülöp ………………………………….………….……………………………… 73, 82 Fundamenski ……………………………………………….……………………….. 6 Garbet …………………………………….……………… 3, 15, 16, 23, 27, 40, 42, 63 Ghendrih ………………………………….……..……………………………… 15, 23 Garcia, J ………………………………….……………………………………… 36, 43 Garcia, O. E. ……………………………….……………………………………... 6,29 Ghoranneviss ……………………………………..………………………………… 48 Giruzzi …………………………………………………………………………… 36, 43 Grandgirard ………………………………………..……………………....… 15, 23, 79 Grasso ………………………………………………..……………………………… 57 Graves …………………………………………………..…………………… 70, 74, 76 Grekov ………………………………………………….....………………………… 75 Guasp ……………………………………………………...………………………… 46 Günter …………………………………………………………….……………….25, 55 Gupta …………………………………………………………………………… 61, 68 Gürcan ………………………………...…………………………….………….…… 30 Hastie …………………………………………………………………………………. 65 Hauff …………………………………...………………………….…………..…. 25,28 Hawkes …………………………………...………………………………….…….… 16 Heikkinen …………………………………..………………………………………… 9 Helander ……………………………………..……………………………….…… 14, 49 Hellsten ……………………………………….……………………………………… 62 Hole ……………………………………………..…………………………………… 59 Holmström ……………………………………………………………………………62 Horton ……………………………………………..………………..……….…….… 19 Hristov ……………………………………………..………………………………… 50 Hudson ……………………………………………..………………………………… 59 Huynh ……………………………………………….…………………………… 36, 43 Huysmans ……………………………………………..………………………………36 Ilgisonis ……………………………………………………………………………… 44 Imbeaux …………………………………………………..……………………… 36, 43 Janhunen …………………………………………………...…………………………. 9 Jenko …………………………………………………………….…….…...… 18, 25, 28 Jolliet ……………………………………………………………....………...…….… 23 Johner …………………………………………………………………………………36 Jucker …………………………………………………………….…………..…. 31, 76 Juul Rasmussen ………………………………………………………...…….. 6, 29, 30 Kamberov ………………………………………….………………………………… 50 Kendl ………………………………………………........…………………………… 77 Khalzov ……………………………………………………………………………… 44 Khorshid ………………………………………………………..…………………… 48 Kiviniemi ………………………………………………………….………………….. 9 Kirneva ……………………………………………………………………….……… 16 Koch ………………………………………………………………….........………… 75 Könies ………………………………………………………………………......….… 81 LaBombard ………………………………………………………………………….. 11 Lakhin …………………………………………………………………………………44 Lamalle ……………………………………………………………….....…………… 80 Lapillonne ……………………………………………………………….…………… 78 Larbi Daho Bachir ……………………………………………………….…………… 45

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Latu …………………………………………………………..........………………… 79 Leerink ……………………………………………………………………………… 9 Lerche ………………………………………………………………....…….……… 80 Lisak …………………………………………………………………......….……… 73 Lyssoivan …………………………………………………………………...….…… 75 López-Bruna ………………………………………………………………….… 39, 46 Madsen …………………………………………………………….………….……. 29 Mahmood …………………………………………………………….………..……. 24 Mantica …………………………………………………………………….….…..… 16 Marinoni ………………………………………………………………………..…… 78 Marinov ……………………………………………………………………………… 50 Marrelli ……………………………………………………………………….……… 47 McGann ……………………………………………………………………………… 59 McMillan …………………..…………………………………………..…………..… 23 Medina ……………………..………………………………………………………… 45 Mellet ………………………..………………………………………………………… 8 Militello ………………………..………………………………………………...…… 65 Mishchenko ………………………………………………………………...…… 49, 81 Moraru ………………………………………………………………………..……… 55 Muraglia …………………………………………………………………………… 3, 63 Naulin ………………………………………………………………………… 6, 29, 30 Negrea …………………………………………………………………………… 34, 35 Neukirch …………………………………………………………….………………… 6 Nielsen …………………………………………………………….….….…….……. 29 Nora ……………………………………………………….………….………………. 9 Nordman ………………………………………………………………...…………… 82 Noterdaeme …………………………………………………………………………… 75 Ogando ……………………………………………………………….…..…………… 9 Ongena ……………………………………………………………………......……… 75 Ottaviani …………………………………………………………….….…….…..…. 27 Paccagnella ……………………………………………………………………..…… 51 Pavlenko …………………………………………………………….…………...….. 31 Pavlov …………………………………………………………………….………...... 83 Perona …………………………………………………………………….......……… 84 Persson …………………………………………………………….…………...…..… 24 Petrisor …………………………………………………………………...………. 34, 35 Pinches ……………………………………………………………….…..……… 16, 84 Piovan …………………...…………………………………………………………… 56 Pochelon …………………...………………………………………………………… 78 Pokol ………………………........….………………………………………………… 73 Pometescu ………………………..…………………………………….……..…..…. 32 Popova …………………………….………………………………………………… 50 Popovich …………………………………………………………………………….… 8 Porcelli ……………………………...…………………………………………..… 65, 84 Poulipoulis ………………………….………………………………………………… 67 Power ………………………………………………………………………………… 33 Pprajapati ………………………………………………………………………………64 Predebon ………………………………………………………………………………51 Price …………………………………...……………………………………………… 69 Rafiq …………………………………………………………….…………...…….… 24 Reiser ………………………………………………………………………………… 52

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Reiter ………………………………….......………………………………………… 86 Reynolds …………………………………..………………………………………… 46 Ribeiro ………………………………...…………………………………….…….… 13 Salem ………………………………………………………………………………… 48 Sánchez ……………………………………………………………………………… 38 Sarazin ………………………………………………………………………….… 15,23 Sattin ……………………………………..……………………………………… 47, 85 Sauter …………………………………….......……………………………………… 78 Sen ……………………………………………..………………………………… 40, 42 Schneider …………………………………….………………………...………… 36, 43 Scott ……………………………………………………………………...…….… 13, 77 Seebacher …………………………………………………………………..………… 86 Sharapov .................................................................................................................. 7, 84 Simakov ……………………………………………………………………….…..… 11 Singh ……………………………………………………..…………………............… 68 Smolyakov …………………………………………………………….………….…. 27 Sonnendrücker ……………………………………………………………………….. 79 Spatschek ........................................................................................................................ 4 Spizzo …………………………………………………………………………… 47, 58 Staerk …………………………………………………………….………….………. 29 Strand ……………………........……………………………………………………… 82 Tala ……………………………………………………………………….………..… 16 Talebi Taher ………………….……………………………………………………… 48 Takeda ……………………….……………………………………………………… 42 Tarkeshian …………………………………………………………………………… 48 Tassi ……………………………………………………………………………………65 Tasso …………………………..……………………………………………..…… 66, 67 Tereshchenko …………………..………………………………………………… 39, 83 Terranova ……………………….…………………………………………………… 58 Throumoulopoulos ………………………………………...……………………… 66, 67 Thyagaraja ……………………….…………………………………………….…..… 16 Tokar ……………………………...………………………..…………………… 61, 68 Toniolo ……………………………..…………………………….…………………… 69 Tran .......................................................................................................................... 8, 23 Turkin ……………………………………………………………...………………… 49 Unterberg ……………………………………………………..……....……………… 68 Van der Plas ………………………………………………………….……………… 72 Van Eester ……………………………………………………………..………… 80, 87 Van Milligen ………………………………………………………………………… 38 Vargas …………………………………………………………………..…………… 46 Villard ................................................................................................................ 8, 23, 78 Wahlberg …………………………………………………………………..………… 70 Weyssow ………………………….…………………………….…… 32, 34, 35, 41, 69 Weiland ……………………………..……………………………………...…16, 26, 82 White …………………………………………………………………………… 47, 58 Xanthoupoulus ……………………………………………………………....…….… 18 Xu …………………………………………………………………………………… 52 Zakharov …………………………….……………………………………………… 55 Zonca …………………………………………………………………….…….….… 17