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Fluctuations, turbulence and relatedtransport in the TORPEX simple

magnetized toroidal plasmaA. Fasoli, A. Diallo, I. Furno, D. Iraji, B. Labit,

G. Plyushchev, P. Ricci, C. TheilerCentre de Recherche en Physique des Plasmas, École Polytechnique Fédérale de Lausanne,

CH-1015 Lausanne, Switzerland

S. MüllerCenter of Energy Research, University of California, San Diego, La Jolla, CA 92093

M. PodestàDepartment of Physics and Astronomy, University of California, Irvine, CA 92697

F. PoliCenter for Fusion, Space and Astrophysics, University of Warwick,

Coventry CV4 7AL, United Kingdom

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Progress in understanding fluctuations, turbulence and related transport in magnetized plasmas is achieved in the basic plasma physics experiment TORPEX via high-resolution measurements of plasma parameters and wave fields throughout the plasma cross-section. Full spatio-temporal imaging of the electrostatic fluctuations is performed, using a multiple probe array or via conditional sampling of data obtained from movable probes.Electrostatic drift and interchange instabilities are characterized in terms of dispersion relation, driving mechanisms, and development into turbulence. Measurements of density fluctuation time series across the plasma cross-section in a variety of plasma conditions reveal universal aspects such as a quadratic relation between skewness and kurtosis. Blobs are observed to carry plasma from the high to the low-field side of the machine. The blob generation and ejection are related to a strongly sheared E×B flow. The blob effect on cross-field transport is investigated in details.Future research lines, such as active control of drift and interchange spectra using tunable antennas, optical turbulence imaging, and the study of the interaction of supra-thermal ions with turbulence, will be discussed.

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B

The toroidal device TORPEX

10-4-10-5 mbar

Neutral gas pressure

PRF < 50 kWInjected power @2.45GHz

≤1 sPulse duration

B ≤ 0.1 TMagnetic field

0.2 mMinor radius

1 mMajor radius

Helical configuration: Bz ≤ 5mTOpen field linesOptimal Bz to minimize

particle losses

~ 200 Langmuir probes: time averaged profiles, density fluctuations

Plasma production by microwaves injected from LFS (O-mode)

Primary ionization at EC layer, then main contribution from Upper Hybrid resonance (X-mode)

H, Ar, He, Ne, ..

ρs/a ~ 0.02

Gas

Ion sound Larmor radius

Te ~ 5 eV

Ti ≤ 1 eV

Electron temperatureIon temperature

n ~ 1016-1017 m-3Plasma density

S. H. Müller et al, Phys. Rev. Lett. 93 165003 (2004) A. Fasoli et al., Phys. Plasmas 13, 055902, (2006) M. Podestà et al., Plasma Phys. Control. Fusion 47, 1989 (2005); 48, 1053 (2006); 49,175 (2007)

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SOL-like configuration: time averaged profiles

Low PRF Separation between main plasma and source-free region[S.H. Müller, et al., PoP 14 110704 (2007)]

Large BZ Elongated (slab-like) profiles for r > 0 with sheared E x B vel. profile

Source-free regionMain plasma region

sourceUH layer

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Statistical and spectral properties of density fluct.

Main plasma region

Coherent oscillationsSingle coherent mode at f ~ 4kHzDouble-humped pdf

Source-free region

Intermittent eventsBroad-band spectraPositively-skewed pdf

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The mechanism is detailed using time-resolved measurements of two-dimensional profiles of electron density, temperature, plasma potential and E x B velocity.

These are obtained from conditionally sampled I-V characteristics of a Langmuir probe over many blob events.

Blobs are observed to form from a radially elongated structure that is sheared off by the ExB flow.

The structure is generated by an interchange wave that increases in amplitude and extends radially in response to a decrease of the radial pressure scale length.

The dependence of the blob amplitude upon this last quantity is also discussed.

Mechanism for blob generation

I. Furno et al, Phys. Rev. Letters 055004 (2008)

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Mechanism for blob generation

Coherent structures (interchange mode) move upwards with E x B velocity.A radially elongated structure forms from a positive cell.The structure breaks into two parts formation of the blob on LFS.Structures are convected by E x B flow.Strong shear in the E x B flowThe E x B flow shears off the structure and forms the blob.

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Mechanism for blob generationThe maximum (in space) |Lpe-1| increases.The interchange mode increasesfollowing the increase of |Lpe-1|.Existence of convective cells associated with plasma potential.The mode increase leads to a higher outflow VE x B and therefore to the elongation of the wave crest.

Select 8 classes of blob amplitudes.|Lpe-1|before and |Lpe-1|after do not show a strong dependence on blob size.|Lpe-1|max increases monotonically with blob size.The blob size depends on the increase of the local gradient.

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Role of the density gradient on intermittent cross-field transport events

C. Theiler et al, accepted for publication in Phys. Plasmas

Intermittent transport events (ITE's) are investigated with focus on the role of the density gradient. Conditional sampling reveals two different scenarios leading to ITE's.

In the first case, an interchange mode grows radially from a slab-like density profile and leads to an ITE. A novel analysis technique reveals a monotonic relation between the vertically averaged inverse radial density scale length and the probability for a subsequent ITE.

In the second case, the mode is already observed before the start of the ITE. It does not elongate in a first stage, but at a later time and in response to a steepening of the density profile.

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Scenario 1 Scenario 2

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Two distinct mechanisms for anomalous transport across the magnetic field are identified experimentally and quantified.

In the main plasma, the transport is dominated by the fluctuation-induced particle and heat flux associated with an interchange instability.

The heat flux is convective, with a negligible contribution from conduction.

In the source-free region (low-field side), the cross-field particle flux is due to the intermittent ejection of particles from the main plasma, resulting in macroscopic blobs propagating toward the outer wall.

Cross-field transport by fluctuations and blobs

M. Podestà et al., submitted to Phys. Rev. Lett.

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Particle transport, results

Main plasma: fluctuation-induced particle transport dominates

LFS: intermittent transport dominatesInstantaneous transport >> \Gamma_r

13 More details: B. Labit, in preparation

Toroidal flow and blob generationTime evolution of the z-averaged

toroidal velocity

At τ ~ -180 μs, the plasma accelerates locally

This pertubation propagates radially together with the density blob

The « toroidal velocity blob » is only ~20% of the surrounding velocity (to be compared with the density blob)Bl

ob d

etec

tion

Blobs are selected by amplitudes: (1+j/2)σ < Iref < (1.2+j/2)σ; j=2,3,…7

The toroidal acceleration increases with the blob amplitude

Linear relationship between the maximum pressure gradient and the minimum toroidal velocity

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Three-field simulations of interchange turbulence in the helimak configuration are presented.

The simulations show the presence of two turbulent regimes: a low and a high confinement regime.

By increasing the plasma source strength or reducing the vertical magnetic field, a transition to a high confinement regime occurs, in which a strong velocity shear limits the perpendicular transport, while the peakdensity and temperature increase and their gradients steepen up.

Nonlinear simulations

P. Ricci et al, submitted to Phys. Rev. Letters

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Nonlinear simulations: the model

Temperature

Source

( )e

e

e

Te

ee

TT

eeee

eeTe

nT

eee

n

eTzT

zn

nT

RD

dtd

SeTz

Tzn

nT

zTT

RTD

dtdT

SeTNz

nznT

zTN

RND

dtdN

/42

/32

2

/2

12

27

34

2

φφ

φ

φ

σ∂∂

∂∂φφ

σ∂∂φ

∂∂

∂∂

σ∂∂φ

∂∂

∂∂

−Λ

−Λ

−Λ

−+⎟⎠⎞

⎜⎝⎛ ++∇=

∇

+−⎟⎟⎠

⎞⎜⎜⎝

⎛−++∇=

+−⎟⎠⎞

⎜⎝⎛ −++∇=

AdvectionDiffusion

Interchange drive Parallel losses

Density

Potential

2-Fluid model, evolving N, φ, Te.∇B and curvature taken into account.2D geometry with dissipation in the parallel direction.Diffusion coefficients from Braginskii equations.Source terms from the experiment.

2D domain

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Nonlinear simulations: L-H transition

L

H

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Electrostatic instabilities develop in the bad curvature region and propagate consistently with the drift wave dispersion relation.

Wave number and frequency spectra are coherent at the location where the instabilities are generated, then broaden along the ExB convection.

The phase coupling between spectral components at different frequencies,measured at different locations over the plasma cross section, indicates that the transition from a coherent to a turbulent spectrum is mainly due to three-wave interaction processes.

Nonlinear interactions are measured between the linearly unstable mode and fluctuations with larger frequency, with transfer of energy away from the linearlyunstable mode.

Results consistent with a nonlinearity induced by the convection of densityfluctuations by the ExB fluctuating velocity.

Development of turbulence during ExB convection

F.M.Poli et al., Phys. Plasmas 14 52311 (2007)

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HFSLFS

δn/n0 increase from 12% to 15% @ f0δn/n0 increase from 10% to 40% @ f>f0

Development of turbulence during ExB convection

fl+fm=f0

fl+fm=2f0

|B(ωl,ωm)|

T(ω l ,ωm )∑f0

The mode loses its energy via nonlinear interactions during convection

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dPω (x)dx

= γωPω (x) + Re[Γω1 ,ω2ω B(ω l ,ωm )

ω l ≥ωmω=ω l +ωm

∑ ]

T(ω l ,ωm )

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A unique parabolic relation is observed to link skewness and kurtosis of around ten thousand density fluctuation signals, measured over the whole cross section of a toroidal magnetized plasma for a broad range of experimental conditions.

All the probability density functions of the measured signals, including those characterized by a negative skewness, are universally described by a special case of the Beta distribution.

Fluctuations in the drift-interchange frequency range (1

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In TORPEX

~30% with S

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An antenna tunable in vertical wave number is used to excite density perturbations.

Coherent detection is performed by means of Langmuir probes to directly determine both the wave vector and the plasma response induced by theantenna.

Comparison between the theoretical density response predicted by thegeneralized Hasegawa-Wakatani model, and the experimentally determined density response enables us the identification of one peak of the plasma response as a drift wave (not discussed here)

DW excitation by antenna

A. Diallo et al. Phys. Plasmas, 14 102101, (2007)

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DW excitation by antenna: Experimental Setup

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DW excitation by antenna: Synchronous detection of density response

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Ongoing investigations (1)Transfer of Energy Turbulence-Mean flow

Double gridded energy analyzer

Li 6+ source0.1 – 1 keV

Interaction between fast ions andturbulence

Source and detector are installed

Waiting for electronics

Search for a critical pressure gradient for interchange modes

Active control to suppress blobpropagation

Real time EC control Plate biasing

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Ongoing investigations (2)Non intrusive diagnostics:

LIF: under wayPlasma imaging with

fast framing camera

curr

ent [

A ]

loopvoltage [ V

]

Field lines are closed between t1 and t2

Ohmic transformer to close the field lineschange in the turbulence character?

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More details on our web site: http://crpp.epfl.ch/torpex