Fast and slow beam mode ion-acoustic solitons in plasmas with counterstreaming cold protons

Abstract

It was recently shown (Lakhina et al (2020), Physica Scr. 95, 105601) that in a plasma of hot electrons and two counterstreaming warm proton beams, a slow ion-acoustic solitary mode occurred, where the soliton speeds decreased from the critical acoustic speeds, while the amplitudes increased. This contradicts conventional wisdom that solitons are inherently ‘super-acoustic’, the soliton speeds exceeding the linear acoustic speed, and that amplitudes grow with soliton speed. To elucidate and further elaborate on these findings, a simpler model is considered, in which the ion beam species are cold, neglecting their thermal effects. This retains the essence of the physics, but simplifies the analysis. It permits a full parametric discussion of the existence ranges for such solitons, not only for the critical Mach numbers, but also for the limit amplitudes, by using fluid density restrictions for the ions. If the beam speed exceeds a threshold, two acoustic regimes are found: a fast beam mode with the usual super-acoustic solitons, and a slow beam mode, where solitons are sub-acoustic, at least in the laboratory frame. This confirms the earlier result, but shows that it is primarily a beam effect, rather than an ion thermal effect. The observation can be explained: in the ion beam frame, the solitons are indeed super-acoustic. However, those travelling in the negative direction are swept forwards by the fast beam and hence are observed in the laboratory frame as being sub-acoustic. A similar approach is used for a case of asymmetric proton beams, with unequal ion densities and beam speeds.