Unified Plasma Fluid/kinetic Equations for Tokamak Microinstability and Turbulence Studies
Abstract
Unified fluid/kinetic equations for the plasma perturbed density (n), parallel flow velocity (u _parallel) and temperature (T) are developed by calculating the fluid moment closure relations kinetically. At first, a set of (unclosed) perturbed fluid equations for n, ~ u _parallel and T is developed using a drift ordering analysis and a new gyroviscous force (nablacdot {bf Pi}_{g }) derived from the stress tensor ( {bf Pi}) evolution equation. Thereafter, to develop linear closure relations for b cdot nablacdot{bf{~Pi }}_parallel and nablacdot q, a driftkinetic version of a ChapmanEnskogtype equation suitable for toroidal magnetic geometry is derived. In a sheared slab geometry this equation is solved using a moment approach and a physically realistic collision operator (Lorentz scattering operator plus the momentum restoring terms). The resultant closure relations for ~pi_parallel and q_parallel unify both the fluid and kinetic properties. In the fluid collisional limit the equations reduce to the wellknown Braginskii equations. In the adiabatic limit they reproduce the usual kinetic results, including Landau damping. It is shown that the ChapmanEnskogtype approach is more compatible with a fluidlike description of plasmas than the usual gyrokinetic approach. Remarkable simplification of these complicated closure relations is achieved. The results are compared with other recently developed Landau damping models and shown to be more accurate and complete. The unified fluid/kinetic equation set is valid for arbitrary values of nu/ omega (collisionality) and omega /kappa_parallelv _{t} (strength of Landau damping). Applications of these equations to a number of linear plasma microinstability problems are discussed. It is shown that many wellknown microinstabilities are covered by the equations derived in this thesis when appropriate limits are taken. Many generalizations of previous theories are achieved. For example, a generalized perturbed Ohm's law, and generalized nonlocal eigenvalue equations for electron and ion drift type modes and microtearing type modes are presented. The feasibility of including magnetic trapped particle effects in the fluid equations through the closure equations is also demonstrated. Taking into account only the major nonlinearities, these fluid/kinetic equations extend the HasegawaWakatani drift wave turbulence equations into regimes of arbitrary nu/ omega and omega/ k_parallelv_ {t}.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT........14C
 Keywords:

 DRIFT WAVES;
 LANDAU DAMPING;
 Physics: Fluid and Plasma;
 ChapmanEnskog Theory;
 Kinetic Equations;
 Landau Damping;
 Magnetic Fields;
 Magnetohydrodynamic Stability;
 Tokamak Devices;
 Toroidal Plasmas;
 Flow Equations;
 Flow Velocity;
 Lorentz Force;
 Parallel Flow;
 Plasma Density;
 Scattering;
 Stress Tensors;
 Turbulent Flow;
 Plasma Physics