Kinetic Theory of Trapped Electron Turbulence in Sheared Magnetic Field and Statistical Theory of Two  Drift Wave Turbulence.
Abstract
We have studied two subjects on drift wave turbulence in a magnetically confined plasma. The studies on trapped electron driven drift wave turbulence in a sheared magnetic field have focused on the nonlinear trapped electron dynamics and the effect of slablike eigenmode structure on nonlinear waveparticle interactions. Ion Compton scattering is shown to be the dominant nonlinear saturation mechanism due to the disparity in the three spatial scales: Delta (the trapped electron layer width), x_{t} (the turning point width), and x_{i} (the Landau resonance point) such that Delta < x_{t} < x_{i}, characteristic of the slablike eigenmode structure. Ion Compton scattering transfers the wave energy from long to short wavelengths where it is shear damped. As a consequence, saturated fluctuation spectrum phi ^2 (k_{theta}) ~ k_sp{theta}{alpha } (alpha = 2 and 3 for dissipative and collisionless trapped electron modes, respectively) develops in the region k_thetarho _{s}<1 and is heavily damped for k_thetarho_{s}>1 . The fluctuation level and transport coefficients predicted are considerably smaller than the mixing length type estimates due to the contribution of the wavenumbers of x_sp{t}{1} < k_sp {r}{'} <=q rho _sp{i}{1} to the nonlinear couplings, the radial localization of trapped electron response to Delta, and the weak turbulence factor< {gamma_sp {e}{l}overomega_ {vec k}}>_{ vec k}.The studies on the two field model (potential ~ phi and density ~ n) of drift wave turbulence have focused on the equilibrium statistical mechanics, the closure equations for the nonlinear evolution of the spectra < ~ n^2 > _{vec k}, < {~ phi}^2 > _{vec k}, and < {~ n}{~ phi} > _{vec k }, a H theorem, and turbulent relaxation process in a twofield drift wave turbulence. It is found that departure from the adiabatic relation {~ n} = {~ phi } allows for density transfer to small scales, which leads to rapid decorrelation between ~ n and ~ phi, while < {~ n} nabla ^2 {~ phi} > remains conserved. This transfer is dynamically inhibited by the presence of finite crosscorrelation < {~ n} nabla ^2 {~ phi} > . It is shown that in a weakly correlated twofield system, the nonlinear density transfer toward small scales is faster than the vorticity transfer. As a consequence, the decay process evolves to a dynamical aligned coherent vortex state characterized by: {~ n} = alpha_1 nabla^2 { ~ phi}, and nabla ^2 {~ phi} = alpha _2 {~ phi}.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1990
 Bibcode:
 1990PhDT........95G
 Keywords:

 Physics: Fluid and Plasma