Nonlinear Interaction of a Small Cold Beam and a Plasma

Abstract

Recently, a simple model was proposed for the nonlinear interaction of a low-density monoenergetic electron beam and a relatively cold infinite homogeneous one-dimensional plasma. The essential feature of this model is the observation that after several e-foldings the bandwidth of the growing waves is so narrow that the electrons interact with a very nearly pure sinusoidal field. In terms of this single wave model, a properly scaled solution of the nonlinear beam-plasma problem which depends analytically on all the basic parameters of the problem (i.e., plasma density, beam density, plasma thermal velocity, and beam drift velocity) is presented. This solution shows that the single wave grows exponentially at the linear growth rate until the beam electrons are trapped. At that time the wave amplitude stops growing and begins to oscillate about a mean value. During the trapping process the beam electrons are bunched in space and a power spectrum of the higher harmonics of the electric field is produced. Both the oscillation in wave amplitude and the power spectrum are given a simple physical interpretation.

Envelope equation for the linear and nonlinear propagation of an electron plasma wave, including the effects of Landau damping, trapping, plasma inhomogeneity, and the change in the state of wave

“…1. As is wellknown, these oscillations in sin(ψ) translate into oscillations in the wave amplitude during the nonlinear stage of the cold beam-plasma instability [36]. Now, a smooth distribution, like the Maxwellian distribution used in Fig.…”

Large-amplitude oscillations and chaos in a Hamiltonian plasma system with many degrees of freedom

“…The nonlinear development of a perturbation in a collisionless plasma is a topic thoroughly investigated in the literature, both analytically and numerically [1][2][3]. Even in its simplest, one-dimensional, formulation, it can reveal new features, which happen to be of interest for a variety of physical systems, whenever these features derive from the quite generic Hamiltonian structure of the system, as in the present case.…”

“…The essential features of the fully nonlinear dynamics of the system are retained in this model, even if a single wavelength is taken into account [1,7]. The Hamiltonian (1) has the following constant of motion:…”

Anomalous electron diffusion across a magnetic field in a beam–plasma system

“…1 In the nonlinear regime, quasilinear and single wave nonlinear theory are well understood. 2,3 Numerous numerical simula tions have been performed for strongly nonlinear plasma turbulence under various initial and boundary conditions. 4 Experimentally, beam-plasma in teraction has been used for plasma production and heating, 3 radiation gen eration, 6 current drive, 4 and active space experiments.…”

“…2,3 Numerous numerical simula tions have been performed for strongly nonlinear plasma turbulence under various initial and boundary conditions. 4 Experimentally, beam-plasma in teraction has been used for plasma production and heating, 3 radiation gen eration, 6 current drive, 4 and active space experiments. 7 Here we report on the results of two-dimensional numerical simulations of beam-plasma instability in a magnetic field.…”