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

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

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 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.

GAMMA 10 experiments

Simulations with low sheared rotation Vortex-flow contours Pressure fluctuations contours

GAMMA 10 experiments Simulations 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 T e IncreaseT i 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 Vorticity Potential (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 = - 6 Soft 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) Profiles of dynamic vorticity, entropy function, plasma potential, and plasma rotation frequency  Chord-integrated pressure (corresponds to soft X-ray tomography in GAMMA 10 experiments)

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

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  Chord-integrated pressure (corresponds to soft X-ray tomography in GAMMA 10 experiments)

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.