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 slab-like eigenmode structure on nonlinear wave-particle 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 slab-like 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 two-field 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 cross-correlation < {~ n} nabla ^2 {~ phi} > . It is shown that in a weakly correlated two-field 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:
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Ph.D. Thesis
- Pub Date:
- January 1990
- Bibcode:
- 1990PhDT........95G
- Keywords:
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- Physics: Fluid and Plasma