Triplet and beam interaction in a plasma

Abstract

The interaction of three waves requires wavelength and frequency matching conditions. Without the presence of a particle beam, if the conditions are satisfied and if the frequency of the envelope is lower than the lowest frequency of the waves, they exchange energy and the evolution of the envelope of each wave is given by a constant plus a sinusoidal function. On the other hand, if a particle beam propagates within electrostatic and electromagnetic fields with no wavelength and frequency match, the energy exchange between the modes is done due to the particles. One of the modes could be amplified in this scheme. In the present work, we propose a model where a nonrelativistic particle beam propagates in a plasma within two electromagnetic modes and one electrostatic mode with wavelength and frequency matching conditions. Then, the waves are allowed to exchange energy between themselves and with the particle beam as well. We present new features in comparison to the isolated triplet interaction and to the beam-wave interaction. These features are relevant for a more realistic triplet interaction model.

Thermal effects in a triplet and beam interaction in a plasma

“…As seen in Ref. 16, the regular dynamics of the envelopes is completely destroyed by the interaction: the longitudinal mode is excited, growing exponentially. After saturation, the amplitude of the longitudinal mode begins to oscillate around a mean value with two characteristic frequencies: the highest one is related to the frequency of the plasma, while the lowest one is related to the frequency of the triplet (in the case of no particles).…”

“…In a previous work, 16 it was shown that when an initially cold beam, even for a very small charge, is allowed to interact with a triplet, the dynamics of the system is completely changed. Besides the triplet interaction, the particles interact with the waves and with themselves.…”

“…[19][20][21]29,30 In the case of Ref. 16, in the absence of the triplet interaction, the growth rate of the longitudinal mode should be reduced as the initial velocity spread increases, as well as the amplitude of the longitudinal mode at the moment of the breakdown of the laminar regime (in the phase-space). This result is expected according to Refs.…”

“…This Lagrangian is identical to the dimensionless Lagrangian of Ref. 16. In the present work, we allow the particle beam to have an initial velocity distribution (initial conditions of the particles).…”

“…If the triplet interaction is turned off, as one of the cases studied in Ref. 16, the growth rate (that is exponential) of the longitudinal mode is a function of the initial velocity of the beam. This result is similar to the result obtained from the one-dimensional high gain FEL theory.…”