Vlasov stability of Bennett equilibrium

Abstract

A fully kinetic, non-local stability analysis of the Bennett equilibrium for a cylindrical plasma column is presented. The perturbations of the equilibrium distribution function constructed from the constants of motion may be divided into the adiabatic and non-adiabatic parts. The dominant trajectories of the particles are betatron orbits, and from an integration over these orbits the radial eigenmode equation is obtained. Expressing the electrostatic potential in terms of the vacuum eigenfunctions, i.e. the Bessel functions, yields a matrix dispersion relation. The wave-particle resonance in the analysis is spatially localized, owing to the betatron nature of the particle orbits. The eigenvalues of the problem are computed numerically.

Reconnection onset in the tail of Earth's magnetosphere

“…To solve the complex eigenvalue problem for the set of – one can use the finite element approach [ Sharma , 1983; Chen and Lee , 1985; Brittnacher et al , 1995, 1998; Daughton , 1998, 1999]. According to this approach, the potentials are expanded into a complete series of basis functions Ψ n which is convenient for the given problem, and in particular obeys the appropriate boundary conditions.…”

“…[18] To solve the complex eigenvalue problem for the set of equations (27) -(37) one can use the finite element approach [Sharma, 1983;Chen and Lee, 1985;Brittnacher et al, 1995Brittnacher et al, , 1998Daughton, 1998Daughton, , 1999. According to this approach, the potentials are expanded into a complete series of basis functions É n…”

Influence of the current profile on the growth rate of m = 1 kink modes in a pure z-pinch

“…Maxwell Laboratories [1], Los Alamos [2], Imperial College in London [3] and Royal Institute of Technology in Stockholm [4]. Although it is one of the oldest configurations, much of the physics of the pure z-pinch (with no axial magnetic field) is rather poorly understood, for example, kinetic effects on stability and transport [3,5], non-linear effects, and the influence of the current profile on stability [1,6].…”

Influence of Toroidal Flow on Stationary Density of Collisionless Plasmas

“…Finally, our findings show that equilibrium configurations leading to a globally confined plasma (a > 0) are unable to create unstable points and associated separatrices in the radial direction, which hints at some stability of these magnetic profiles when considering a confinement within a torus and no destruction of the adiabatic invariant, at least in the large aspect ratio limit, and as long as electric field effects can be neglected, and this is thus compatible with results discussed in (author?) [25] regarding special Bennett type solutions. As a perspective of this work, we may now consider to take into account global diamagnetic effects and see the possible influence of poloidal flow and current on the confinement.…”