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 cop(<) 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 obeys the inequality me(ovc v \ -f ir/eii 2 j" drj, — oo which shows that the threshold is proportional to the driver frequency co and to the flow velocity at the resonance point, vc; however, it is independent of the density scale length. Resonance ends at rj = jr/2. The denominator assumes there the value 2.759. rj is a dimensionless time which measures the transit time of a volume element through resonance.