Adiabatic nonlinear waves with trapped particles: II. Wave dispersion

Abstract

A general nonlinear dispersion relation is derived in a nondifferential form for an adiabatic sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of trapped electrons. The linear dielectric function is generalized, and the nonlinear kinetic frequency shift ${\omega }_{\mathrm{NL}}$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield ${\omega }_{\mathrm{NL}}\propto \sqrt{a}$, as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation. Such beams are formed whenever the phase velocity changes, because the trapped distribution is in autoresonance and thus evolves differently from the passing distribution. Hence, even adiabatic ${\omega }_{\mathrm{NL}}(a)$ is generally nonlocal.

submitted together with Papers I and III

References in corpus (5)

• Langmuir wave filamentation instability
• Self-consistent Langmuir waves in resonantly driven thermal plasmas
• Adiabatic nonlinear waves with trapped particles: I. General formalism
• Nonlinear dispersion of stationary waves in collisionless plasmas
• Adiabatic nonlinear waves with trapped particles: III. Wave dynamics

Cited by in corpus (5)

• Axiomatic geometrical optics, Abraham-Minkowski controversy, and photon properties derived classically
• Nonlinear frequency shift of electrostatic waves in general collisionless plasma: unifying theory of fluid and kinetic nonlinearities
• Adiabatic nonlinear waves with trapped particles: I. General formalism
• Adiabatic nonlinear waves with trapped particles: III. Wave dynamics
• On the nature of kinetic electrostatic electron nonlinear (KEEN) waves