Vortices of Two Dimensional Guiding Center Plasmas.
A system of two dimensional guiding center plasma in a square conducting boundary is used as a model to study the anomalous transport is magnetically confined plasma. An external gravitational force is introduced to simulate the curvature and gradient of the magnetic field. For finite boundaries, it is a Hamiltonian system with finite phase space and negative temperature states are allowed. The statistical equilibrium states of this system are described by the solutions of a Poisson's equation with self-consistently determined charge density. In the limit of zero gravity, it can be reduced to the sinh-Poisson equation (DEL)('2)u + (lamda)('2)sinh u = 0. Previous numerical efforts have found solutions with vortex structures. A novel method of generating general exact solutions to this nonlinear boundary value problem is presented. These solutions are given by. (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI). where E(,i)'s are constants and the dependence of (gamma)(,j)'s on x and y are given by a set of coupled first order nonlinear ordinary differential equations. These equations can be linearized to give u(x,y) in terms of Riemann theta functions u(x,y) = 2ln (THETA)(l + 1/2)(THETA)(l) . The phases l evolve linearly in x and y while nonlinear superposition is displayed in the solution u(x,y). The self-consistent Poisson's equation with gravity is studied numerically. Different branches of solutions are obtained and their relations to the zero gravity solutions are discussed. The thermodynamically most favored structure of the system carries the feature of a heavy ion vortex on top of the light electron vortex. Branches of solutions are found to merge into each other as parameters in the equations were smoothly varied. A critical value of gravitational force exists such that below which there is a possibility of hysteresis between different equilibrium states. With the help of the nonzero gravity solutions, we also have a clearer picture of the transition from negative to positive temperature states. Nonuniform positive temperature states with a heavy ion vortex at the bottom of the square boundary are also found when gravity is present.
- Pub Date:
- Physics: Fluid and Plasma