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
