Equilibrium and lowfrequency stability of a uniform density, collisionless, spherical Vlasov system
Abstract
Equilibrium and stability of a collisionless, spherical Vlasov system with uniform density are considered. Such an electron system is useful for the Periodically Oscillating Plasma Sphere (POPS) fusion system. In POPS the space charge of a uniformdensity spherical electron cloud provides a harmonic well for an underdense thermal ion population. Previous special solutions [D. C. Barnes, Phys. Plasmas 6, 4472 (1999)] are extended to arbitrary energy dependence. These equilibrium distribution functions and their first derivatives may be made nonsingular, in contrast to the previous solutions. Linear stability of general spherical equilibria is considered, and reduced to a onedimensional calculation by the introduction of a spherical harmonic decomposition. All azimuthal mode numbers are degenerate. Using this formalism, the lowfrequency stability of a collisionless, spherical Vlasov electron system coupled to a minority ion cloud is studied for the class of uniformdensity electron equilibria found. In the lowfrequency (adiabatic) limit, the general kinetic stability formalism can be integrated to find a closed form for the response of electron number density. The adiabatic response operator is shown to be selfadjoint. Computation of its eigenvalues proves the constantdensity electrons/thermal ions system in POPS to be mostly stable to ionelectron electrostatic modes. Unstable modes are avoided unless central electrons have an extremely small energy spread. These results may also be useful for the consideration of gravitational and beam systems.
 Publication:

Physics of Plasmas
 Pub Date:
 November 2002
 DOI:
 10.1063/1.1510667
 Bibcode:
 2002PhPl....9.4448B
 Keywords:

 52.58.Qv;
 52.27.Jt;
 Electrostatic and highfrequency confinement;
 Nonneutral plasmas