Amplification and acceleration of soltons by an ion beam

We consider the interaction of an ion-acoustic soliton with a weak ion beam whose velocity is near the soliton velocity. Ostrovskii, Petrukhina, and Fainshtein
¹
have used a model in which the plasma is weakly nonlinear but the beam nonlinearity is neglected. Based on this model, a type of "transient" amplification was found. However, in the regime in which the difference between the beam and soliton velocities are sufficiently small, the nonlinear effects in the beam are typically stronger than the plasma nonlinearities. Therefore, we consider the case of weak plasma nonlinearity but strong ion beam nonlinearity, i.e., q ø
₀
>m
_i
(v
₀
- v
₅
)
²
/2, where q, m
_i
, v
₀
are the charge, mass, and velocity of the beam ions, and ø
₀
and v
₅
are the maximum potential and the velocity of the soliton. In this regime, the beam ions are reflected by the soliton in the waveframe. It is shown that if initially v
₀
>v
₅
, the soliton is amplified, accelerated, and compressed by the beam, and eventually reaches a stationary state with a velocity equal to the beam velocity. Conversely, if initially v
_0
5
, the soliton is attenuated, decelerated, and decompressed. The soliton behavior and the time scale on which the beam-soliton interaction takes place is presented.