More uniform perturbation theory of the Vlasov equation

The classical phenomenon of electron plasma oscillations has been investigated from new aspects. The applicability of standard normal-mode analysis of plasma perturbations has been judged from comparisons with exact numerical solutions to the linearized initial-value problem. We consider both Maxwellian and non-Maxwellian velocity distributions. Emphasis is on perturbations for which αλD is of order unity, where α is the wavenumber and λD the Debye distance. The corresponding large-Debye-distance (LDD) damping is found to substantially dominate over Landau damping. This limits the applicability of normal-mode analysis of non-Maxwellian distributions. The physics of LDD damping and its close connection to large-Larmor-radius (LLR) damping is discussed. A major discovery concerns perturbations of plasmas with non-Maxwellian, bump-in-tail, velocity distribution functions f0(ω). For sufficiently large αλD (of order unity) the plasma responds by damping perturbations that are initially unstable in the Landau sense, i.e. with phase velocities initially in the interval where df0/dw > 0. It is found that the plasma responds through shifting the phase velocity above the upper velocity limit of this interval. This is shown to be due to a resonance with the drifting electrons of the bump, and explains the Penrose criterion.

Section: Assumptionsmentioning

confidence: 99%

Large-Debye-distance effects in a homogeneous plasma

Scheffel

Lehnert

1989

“…where £ is the new independent velocity variable (Lewak 1969). With the transformation (2.1), (1.1) becomes…”

Section: Perturbationmentioning

confidence: 99%

The effects of ion-ion coffision on a ion-acoustic plasma pulse

Espedal

1971

“…In a previous paper [Lewak (1969), see also Pfirsch (1966) for related treatment], it was shown that the Vlasov equation in the Semi-Lagrangian (S.L.) formulation, may be written in a form resembling the fluid equations.…”

mentioning

confidence: 99%

A note on the semi-Lagrangian formulation of the Vlasov equation

Lewak

1970

Self Cite

In a previous paper [Lewak (1969), see also Pflrsch (1966) for related treatment], it was shown that the Vlasov equation in the Semi-Lagrangian (S.L.) formulation, may be written in a form resembling the fluid equations.plus Maxwell's equations with the source terms given bywhere n is the determinant of the tensor Tij = ∂gi/∂ζj, and N is the constant mean number density of electrons. The averaging notation < > here is defined bywhere f(σ) is the electron distribution function to be specified. The equations assume for simplicity a uniform fixed ion background, although this is not a necessary restriction and equations (1) and (2) need only an obvious modification to account for ions. The force fields in (1) are related to the electric field E and magnetic field B in the plasma by .