Two-dimensional electrostatic E×B trapping

Abstract

The nonlinear motion of a charged particle in a uniformly magnetized, two-dimensional plasma is analyzed in the presence of finite amplitude electrostatic waves traveling in the plane perpendicular to the magnetic field. In a strongly magnetized plasma, no particle trapping occurs in a single electrostatic traveling wave of arbitrary amplitude, since the induced E×B motion is orthogonal to the direction of wave propagation. However, particle orbits can be trapped when there are at least two mutually orthogonal components of the electrostatic field with finite wave amplitude cE⊥/B⩾ω/k⊥ such that a particle drifts one wavelength in a waveperiod. Exact integrability of the two-wave system implies that there is no stochastic particle behavior. Perturbation of this nonlinear equilibrium by additional waves with incommensurate phase velocities will destroy the coherent island structure and lead to stochastic diffusion. The threshold amplitude for strong nonlinear behavior in the coherent wave case helps to explain the many-wave turbulence criterion for the onset of particle diffusion in a two-dimensional plasma.