Equilibium and Stability of Spherical Vlasov Systems

Details Equilibium and Stability of Spherical Vlasov Systems Equilibium and Stability of Spherical Vlasov Systems

Apr 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002aps..aprb17014b&link_type=abstract

American Physical Society, April Meeting, Jointly Sponsored with the High Energy Astrophysics Division (HEAD) of the American As

Astronomy and Astrophysics

Astrophysics

Scientific paper

Collisionless systems with inverse square interaction potentials and possible background confining potentials are considered for the case of spherical symmetry and in the Vlasov limit. The equilibrium is the most general, with single-particle distribution function dependence on both total energy E and total angular momentum L. A new formulation of the full integral-equation stability problem is developed. For a general spherical harmonic perturbation potential, the 3D stability problem is reduced to a 2D problem in an arbitrary central plane of motion, then to a small number of coupled 1D problems involving only the radius. Normal modes depend only on the total mode number l, as is shown directly by this new formulation, with all m degenerate. This method has been used for the Coulomb (repulsive) case.[1] An equilibrium family with uniform central (electron) density is found, and the low-frequency response computed to show that these solutions may provide stable confinement of a massive second (ion) species. These methods may be applied to a particle bunch in the beam frame, and some stability results appropriate to this case are presented. Application to the gravitational (attractive) case is also described, and some initial analytic results are presented. [1] D. C. Barnes, L. Chacón, J. M. Finn, “Equilibrium and Low-frequency Stability of a Uniform Density, Collisionless, Spherical Vlasov System,” submitted to Phys. of Plasmas (2002).

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