Resonant Excitation of High Amplitude Oscillations and Hydrodynamic Wave Breaking in a Streaming Cold Plasma

Abstract

The excitation of large amplitude electron oscillations in a streaming cold plasma and the minimum threshold of wave breaking in the resonant region are investigated analytically as a function of flow velocity. The problem is reduced to the solution of a driven harmonic oscillator with time varying eigenfrequency ωp(t) in a self-consistent, stationary ion density profile. An analytical solution is presented and applied to the correct wave breaking criterion in a streaming plasma. Wave breaking sets in when the driver amplitude Êd obeys the inequality which shows that the threshold is proportional to the driver frequency ω and to the flow velocity at the resonance point, vc; however, it is independent of the density scale length. Resonance ends at η = π/2. The denominator assumes there the value 2.759. η is a dimensionless time which measures the transit time of a volume element through resonance.