P. Strand

P.I. Strand,

With contributions/support fromW.A. Houlberg (ORNL), H. Nordman (CTH), A. Eriksson (CTH), J.

Weiland(CTH), G. Bateman(Lehigh), A. Kritz (Lehigh)

Multiple species extensions to the Weiland model and the

Semi-predictive DEA code

9th Meeting of the ITPA Confinement Database & Modeling Topical Group, 3-6 October, 2005, St. Petersburg,

P. Strand

Multiple Ion Species Drift Wave TransportStraightforward extension of the Weiland drift

wave model for ITG/TEM (Extended Drift Wave Model or ExtendeD Weiland Model):

– Arbitrary number of Ion Species• Each charge state treated as a single fluid

species– Separate descriptions of H, D and T transport

• Differs only through mass dependence in (first order) FLR term and k// dynamics

• FLR stabilisation gives different peak locations for growth rates in ksH.

– Transport is summed over extended ksH range to cover maximum growth rate for each hydrogenic species

– Modular, self-contained code distribution• Strict adherence to F95 standard • Strongly typed through automatic module

features• Parametric kinds (all system supported

precisions )• Data encapsulation with no global

dependencies– Fully compatible with and tested against

original disp9t description (Weiland)– Weak Ballooning problematic in multiple

species setting

Model can be used in different settings and allows for physical effects to be turned on/off to study impact on transport/stability.

Two versions used here:•Simple Baseline model (Electrostatic, no

k// effects, strong ballooning•Full physics (incl, collisions and

electromagnetic effects,…)

P. Strand

Density Evolution Assessor – DEA*A semi-predictive particle transport code

– Evolves arbitrary number of ion species assuming fixed temperatures.– Linked to the international profile database (Using MDSplus server).

• Targeted “read” from WDB being implemented. – Flexible geometry acces:

• Eqdsk files (EFIT, CHEASE, etc…)• Inverse coordinate solvers (VMEC output)• Simple 3-moment approximation available

– NCLASS for comprehensive neoclassical transport description.– EDWM for anomalous transport (ITG/TE)– Currently only prescribed source terms fully available– Modular structure, simple adaptive grid method(s)– Planned extensions (Summer and fall 05)

• Source terms (neutrals,…)– Frantic (implementation being tested), PELLET (ORNL code) being processed

• Improved access for experimental data– Input system is being changed to a more flexible/adaptable system

• Transport models (GLF23, …., ?) link to JET/ITM-TF Code integration effort • Explicit thermo-diffusion coupling (longer term)

AJAX

*DEA – Latin for ‘Goddess’

P. Strand

Effects of impurities on drift wave based D and T particle transport

Example studies with EDWM

P. Strand

Comparison of anom. D and T fluxes

Slight asymmetry in fluxes enters through first order FLR effects in the baseline version of Weilands fluid model. ITG driven mode only is excited for these parameters.

R/LTi = R/LTe = 3.75, Te/Ti = 1, (all species), R/LnC = 2, ft =0.4, fC = 0.01 R/Lne ambipolar

P. Strand

Tritium gradient scans

Impurity content (clockwise1%, 3% and 5%)

R/LT = 3.75, all speciesR/Ln = 2, Te/Ti = 1, ft = 0.4

R/Lne by ambipolarity

Tendency to equilibrate the density scale-lengths between species remain

P. Strand

Impact of an impurity species• DT particle transport is

reduced through stabilising carbon dilution.

However• Less peaked or inverted

Carbon profiles tend to enhance both D and T transport

• Impurity Driven ITG mode does not alter but rather increase these effects.

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P. Strand

Comparison of DW particle transport with neoclassical estimates

DIII-D like base case derived from Neon seeded shot #98775

P. Strand

Trace impurity scans for Ne, Ar and Wr/a = 0.52 r/a = 0.7

Strong Z- dependence of the neoclassical flux as expected, shift of W pinch may be explained through detailed balance of the thermodiffusion terms. Weak and inverted Z-dependence of anomalous transport as expected but comparatively weak D contrib.

P. Strand

Full response to non trace species

We note that D has a outward flux for hollow profile leading to an even stronger depletion and that it provides a pinch flow for already peaked profile whereas Ne has the opposite trend. (Nominal values R/LnD = 1.12 and R/LnNe (2.07))

Full response when a non-trace species is perturbed is much more complex andwould require more careful analysis.

P. Strand

Simple predictive example caseJET 37718 @ 53.8s

NB fuelled ELMy H-modeTaken from the PR98 International Profile Tokamak

Initial condition for simulation shown:

Beam particle contribution turned off

Flat Te profile => reduced TEM drive no anomalous inner core pinch.

P. Strand

Interpretative analysis: 37718 Deuterium transport in high coll. JET

ITG mode and TE modes excited at =0.25

•ITG modes drives an outward flux in inner core region•TE mode dominate transport in outer core defining a net pinch.

Anomalous contribution:

Neoclassical contributions•Ware pinch provides an inner core pinch contribution •Pinch not fully balanced by diffusive term•Other off-diagonal contributions are weaker except closer to edge

P. Strand

Time evolution: Peaking of nD Only Wall source availableBeam sources artificially turned off

The strong TEM driven pinchweaken as density peaks up.At 53.9s pinch has vanished andA weak outward flux persist for remainder of simulation

Neoclassical transport dominatedby Ware pinch => peaking of nD(0).

Axial peaking off-set by kineticBallooning mode as density increases.

Density profile determined byBalance between different neoclassical and anomalous terms.

P. Strand

SummaryTwo new code developments

– EDWM (Extended Drift Wave Model)• Closely linked to Weiland’s disp9t model• Arbitrary number of ion species• Extended wave-length spectra• Separate description for H, D and T, etc• Modular, Self-contained F95 coding

– DEA (Density Evolution Assessor)• Semi-predictive transport code for core particle transport• First test implementation with adaptive grids• NCLASS/EDWM models • MDSplus link to ITPA databases• Flexible geometry data access and processing

– Eqdsks (EFIT, CHEASE,…)– Inverse equilibrium solvers (VMEC)– Uses AJAX interface for moment solutions.– Intended to fill gap between interpretative analysis and fully pred. codes

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P. Strand

Summary Initial resultsEffect of impurities on D and T transport in core plasmas

– Deuterium and tritium transport coefficients may separate when their corresponding scale lengths differ for ITG dominated transport.

– Asymmetry in D and T fluxes due to (first order) FLR effects. – The presence of impurities does not appear to affect previous results to any larger

extent• Less peaked or inverted impurity (Carbon) profiles tend to increase both T and D transport• D and T particle transport is reduced through stabilising (Carbon) dilution• Impurity driven ITG modes does not alter but rather enhance the trends

Comparison with neoclassical fluxes– Dynamic coupling of Neoclassical and anomalous effects may be needed to explain

density peaking at least for high collisionality.– Trace impurity analysis shows anomalous and neoclassical particle flows of similar

magnitude• Profile effects enters in both components Neoclassical elements (thermo-diffusion and off-

diagonal elements) depends sensitively on gradient scalelengths of different species changing sign and magnitude of effective pinch flow relative to Ware pinch.

• Small changes in ITG/TEM drive terms may drastically change anomalous estimates– Non-trace analysis is much more complex but may still have anomalous and

neoclassical pinch velocities of similar magnitude. Diffusivities however dominated by anomalous contributions

P. Strand

Intentionally blank

P. Strand

ReferencesPhysics background: J. Weiland, IoP Publ., Bristol, 2000,

"Collectives Modes in Inhomogeneous Plasma”, and references therein

Numerical Techniques: G. Bateman, J. Weiland, H. Nordman, J. Kinsey. C. Singer, Phys. Scripta, 51, (1995)

Implementation: P. Strand, H. Nordman, J. Weiland, J.P. Christiansen, Nucl. Fusion, 38 (1998)

NCLASS: W.A.Houlberg et al., Phys. Plasmas 4 (1997), 3230

IPD databases: "The International Multi-Tokamak Profile Database", Nucl. Fus 40 (2000), 1955 And ITER Physics Basis, Chapter 2, Nucl. Fus, 39 (1999), 2175

P. Strand

Sensitivity to background gradients0.75 * Grad Ti 1.25* grad Ti

Effect of changing the background temperature gradients: Major change in anomalous transport as expected. Higher Z neoclassical estimates more strongly affected than lower Z. Results of analysis method strongly dependent on resolution of background profiles and their gradients..

P. Strand

Perturbative trace transport analysis

nS

ntN

nV

tot )()('

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Particle transport is generally described trough a diffusivity D and a pinch velocity V.

To avoid using a full transport matrix off-diagonal terms are lumped into the pinch term.

D and V cannot simultaneously be determined through steady state analysis.

Perturbative, timedependent analysis needed where:

• A Background close to SS• High resolution diagnostics• Assumption of time constant transport

coeffs during analysis

are all needed. VLR

RD

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nV n

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