Young‐ping Pao

Boltzmann collision operator with inverse-power intermolecular potentials. I

Abstract : The report studies the linearized collision operator in the Boltzmann equation with repulsive intermolecular potentials V(r) = a(r sup(-alpha)). It is shown that for alpha > 2 the collision operator has a purely discrete spectrum and its eigenfunctions are infinitely differentiable (L sup 2)-functions which are complete in (L sup 2). The proof relies on the formalism of pseudo-differential operators. The report contains two parts: Part I deals with the special case of alpha = 4, the Maxwells molecules, while Part II considers the general case of inverse-power potentials with alpha > 2. (Author)

The continuous MHD spectrum in toroidal geometries

The continuous spectrum for tokamak geometries is shown to be given by a reduced (one-dimensional non-singular) eigenvalue problem on the resonant surface. Properties of this reduced eigenvalue problem and singularity of the eigenfunctions for the continuous spectrum near the resonant surface are obtained.

Classical diffusion in toroidal plasmas

Time‐dependent classical diffusion in axisymmetric toridal plasmas with finite aspect ratio and finite beta is examined. The velocity component normal to the flux surfaces can be solved from a partial differentio‐integral equation in terms of instantaneous equilibrium quantities. A method for determining the other two velocity components is given which involves the use of convective and viscous terms in the momentum equation. Equations describing the evolution of magnetic field, plasma pressure, and density are presented.

Nonlinear behavior of linearly unstable magnetohydrodynamic modes

It can be shown that for linearly unstable magnetohydrodynamic modes near the threshold of linear instability, the mode amplitude A (t) evolves according to ∂2A/Λt2 =λ2A+αA3 which can lead to nonlinear stabilization, explosive instability, or eventual decay, depending on the sign of α. This is demonstrated explicitly for the m=1 kink modes in a sharp boundary plasma pinch.

Instabilities in toroidal plasmas

Surface‐preserving instabilities in axisymmetric toroidal plasmas are studied by a normal‐mode analysis. Their growth rates are calculated. Localized instabilities and noncircular diffuse pinches are also examined.

Classical diffusion in large‐aspect toroidal plasmas

Time‐dependent classical diffusion in large‐aspect toroidal plasmas with a circular section is studied for both low‐β and high‐β cases. In the low‐β case, both the fast and slow phases are examined and the difference between the slow phase and the quasi‐stationary theory is discussed.

Internal m=1 kink modes in tokamaks

A normal mode analysis is developed for m=1 kink modes in tokamaks with large aspect ratio and circular section. The result is applied to the internal kink modes where the q=1 surface is near the minor axis. It is shown that the m=k=1 internal kink modes, which are unstable in the screw pinch model, are also unstable in the toroidal geometry with even greater growth rates.

Instabilities and growth rates of low shear guiding center plasma pinches

Some instabilities and their growth rates are examined for low shear guiding center plasma pinches. Relations between these instabilities and the Suydam‐type instability are also discussed in terms of their growth rates.

Nonlinear evolution of longitudinal plasma waves

Long‐time nonlinear behavior of single‐mode longitudinal plasma waves is studied on the basis of the Vlasov equation with Fokker–Planck collision terms. The resonant layer, trapped island, collisional sublayers, and X‐point neighborhoods are analyzed. A nonlinear evolution equation is obtained and the wave‐generated current is also evaluated.

Kinetic theory of Bumpy Torus transport

The poloidal electric field is included in the Elmo Bumpy Torus (EBT) transport theory. The contribution of the poloidal electric field to the particle and energy fluxes is seen to be comparable to that of the curvature and gradient drifts.