Turbulent Convection and Anomalous Cross-Field Transport in Mirror

Plasmas

V.P. Pastukhov and N.V. Chudin

Outline

1. Introduction.

2. Theoretical model.

3. Results of simulations for GAMMA 10 and GDT conditions.4. Discussion and comments.

Introduction. • anomalous particle and energy transport is one of the crucial problems for magnetic plasma confinement;

• low-frequency (LF) fluctuations and the associated transport processes in a wide variety of magnetic plasma confinement systems exhibit rather common features:

- frequency and wave-number spectra are typical for a strong turbulence;- intermittence; - non-diffusive cross-field particle and energy fluxes; - presence of long-living nonlinear structures (filaments, blobs, streamers, etc.); - self-organization of transport processes (“profile

consistency”, LH-transitions, transport barriers, etc.)

LF convection in magnetized plasmas is quasi-2D; inverse cascade plays an important role in the nonlinear evolution and leads to formation of large-scale dominant vortex-like structures; direct dynamic simulations of the structured turbulent plasma convection and the associated cross-field plasma transport appear to be a promising and informative method; relatively simple adiabatically reduced one-fluid MHD model demonstrate a rather good qualitative and quantitative agreement with many experiments; mirror-based systems are very convenient both for experimental and theoretical study of the structured LF turbulent plasma convection. Application to tandem mirror and GDT plasmas is reasonable;

Theoretical model• plasma convection in axisymmetric or effectively symmetrized shearless magnetic systems; • magnetic field can be presented as:

• convection near the MS-state for the flute-like mode:S = const ;

• ASM-method and adeabatic velocity field;

• stability of flute-like mode :

• small parameter

additional small parameter ( ) in paraxial systems admits considerable deviation from the MS state S = const

• characteristic frequencies of the

adiabatic convective motion

are much less than the characteristic frequencies of stable

magnetosonic

incompressible Alfven

longitudinal acoustic waves

UUr 2/ 1

• small parameter

additional small parameter ( ) in paraxial systems admits considerable deviation from the MS state S = const

• characteristic frequencies of the

adiabatic convective motion

are much less than the characteristic frequencies of stable

magnetosonic

incompressible Alfven

longitudinal acoustic waves

UUr 2/ 1

where:

• generalized dynamic vorticity is the canonical momentum:

• magnetic configuration is characterized by form-factors:

and U

and

• adiabatic velocity field has the form:

Set of reduced equations

),,(~

),(0 tt

are plasma potential and frequency of sheared rotation;

Simulations for symmetrized mirrors

Applicability reasons

• all equations are obtained by flux-tube averaging; as a result, effectively symmetrized sections (like in GAMMA 10) gives symmetrized contributions to linear terms in the reduced equations;

• axisymmetric central and plug-barrier cells gives a dominant contribution to the flux-tube-averaged nonlinear inertial term (Reynolds stress);

• non-axisymmetric anchor cells with anisotropic plasma pressure contribute mainly to linear instability drive and can be effectively accounted in a flux-tube-averaged form;

• in addition to a standard MHD drive we can model a “trapped particle” drive assuming that only harmonics with sufficiently high azimuthal n-numbers are linearly unstable due to a pressure-gradient.In other words we can assume for small n and for higher n;

• as a first example we present simulations for GAMMA 10 conditions with a weak MHD drive and without FLR and line-tying effects.

0 0

(c)

GAMMA 10 experiments

(c)

GAMMA 10 experimentsSimulations with low

sheared rotation

Vortex-flow contours

Pressure fluctuations contours

(c)

GAMMA 10 experimentsSimulations with low

sheared rotation

Vortex-flow contours

Pressure fluctuations contours

Turbulence suppression by high on-axis sheared-flow vorticity

Transport barrier is formed in experiments by generation of sheared flow layer with high vorticity

Te Increase Ti Increase

ExB flow; Barrier Formation

Turbulence

Cylindrical Laminar ExB Flow due to Off-Axis ECH Confines

Core Plasma Energies

X-Ray Tomography

Common Physics Importance for ITB and H-mode Mechanism Investigations

4 keV

5 keV

Suppress

VorticityPotential

(Note; No Central ECH)

Comparison of simulations with experiments

Soft X-ray tomography(experimint)

Without shear flow layer

With shear flow layer

Comparison of simulations with experiments

Simulations with low shear W = -1

Soft X-ray tomography(experimint)

Without shear flow layer

With shear flow layer

Comparison of simulations with experiments

Simulations with low shear W = -1

Simulations with

high shear W = - 6Soft X-ray tomography

(experimint)

Without shear flow layer

With shear flow layer

Results of simulations for regime with a peak of dynamic vorticity maintained near x=0.4 (r =7cm)

25 30 35 40 45 50 55 60 65 70 75 80 85t

-0 .5

0

0.5

x

Profiles of dynamic vorticity , entropy function , plasma potential , and plasma rotation frequency

0w00S

Chord-integrated pressure

(corresponds to soft X-ray tomography in GAMMA 10 experiments)

dyp0

0.0 0.5 1.0

-2.5-2.0-1.5-1.0-0.50.00.5w

0

x 0.0 0.5 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

x

S0

0.0 0.5 1.00.0

0.1

0.2

0.3

0.4

0.5

x

0.0 0.5 1.0-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1

x

Evolution of well-developed convective flows and fluctuations in the regime with peak of .0w

Results of simulations for regime with a potential biasing near x=0.7 (near r =10cm for GDT)

Profiles of dynamic vorticity , entropy function , plasma potential , and plasma rotation frequency

0w00S

Chord-integrated pressure

(corresponds to soft X-ray tomography in GAMMA 10 experiments)

dyp0

25 30 35 40 45 50 55 60 65 70 75 80 85t

-0.5

0

0.5

x

0.0 0.5 1.0-3

-2

-1

0

1

2w0

x

0.0 0.5 1.0-0.12-0.10-0.08-0.06-0.04-0.020.000.02

x

0.0 0.5 1.00.00.10.20.30.40.50.60.70.80.9

x

S0

0.0 0.5 1.0

-0.1

0.0

0.1

0.2

0.3

0.4

x

Evolution of well-developed convective flows and fluctuations in the regime with potential biasing

Discussion and comments (1)

• sheared plasma rotation in axisymmetric or effectively symmetrized paraxial mirror systems can strongly modify nonlinear vortex-like convective structures;

• this result was demonstrated by simulations for a weak MHD drive, but the similar and even stronger effect was obtained for the “trapped particle” drive as well;

• as a rule, the rotation does not stabilize plasma completely, however, the cross-field convective transport reduces significantly and the plasma confinement becomes more quiet

• the most quiet regimes were obtained in regimes where a peak of vorticity was localised at the axis;

• the above favorable results were obtained even without FLR and line-tying effects, which can additionally improve the plasma confinement;

Discussion and comments (2)

• in additional simulations with for all harmonics (i.e. without any MHD or “trapped particale” drives) low n-number fluctuations in the core disappear, while fluctuations with higher n-numbers still exist in both examples;

• accounting the above we can conclude that the core vortex structures were mainly driven by pressure gradient, while the edge vortex structures were maintained by Kelvin-Helmholtz instability generated by sheared plasma rotation;

• we can also conclude that the main effect of the sheared plasma rotation results from a competition between pressure driven and Kelvin-Helmholtz driven vortex structures.

0