Kinetic instability of ion acoustic mode in permeating plasmas

In plasmas with electron drift (current) relative to static ions, the ion acoustic wave is subject to the kinetic instability which takes place if the directed electron speed exceeds the ion acoustic speed. The instability threshold becomes different in the case of one quasi-neutral electron-ion plasma propagating through another static quasineutral (target) plasma. The threshold velocity of the propagating plasma may be well below the ion acoustic speed of the static plasma. Such a current-less instability may frequently be expected in space and astrophysical plasmas. PACS: 52.35.Fp, 52.35.Qz, 52.35.Dg In an un-magnetized plasma with a macroscopic velocity of the electron component ~ve0 = ve0~ez relative to static singly-charged ions, a kinetic instability of the ion acoustic mode sets in, described by the growth rate ωi= ( π 8 )1/2 kcs [( me mi )1/2(ve0 cs − 1 ) − τ 3/2 exp ( − τ 2 )] (1) Here, cs = (κTe/mi) 1/2 is the ion sound speed, and τ = Te/Ti. The necessary condition ve0 > cs[1 + (mi/me) τ 3/2 exp(−τ/2)] (2) may imply a rather high electron current magnitude. A similar description of the ion acoustic mode and the growth rate may be obtained also in the case of a magnetized plasma with the equilibrium magnetic field ~ B0 = b0~ez and for perturbations propagating in the direction of the electron current ~ve0 = ve0~ez that is parallel to the magnetic field vector. The instability described by (1) is a purely kinetic, collision-less, electron inertia effect. Its two-fluid counterpart however is a strictly electron-collision effect. The instability in (1) appears due to the Doppler shift term (the one containing ve0), which may determine the sign of the growth rate. However, a much lower instability threshold may be obtained in the case of two interpenetrating (permeating) plasmas. This is then a current-less instability, where now the Doppler shift of ions appears to play the main role. This will be demonstrated in the forthcoming text. Such permeating plasmas can be created in lab conditions, while in space this happens to be a rather frequent situation, for example in the case of colliding astrophysical clouds, in the propagation of plasmas originating from the explosions of novae and supernovae and moving through the surrounding plasmas, and also in the case of solar and stellar winds. In the case of the solar wind, one electron-ion quasi-neutral component is generated mainly in the polar regions (fast wind), while the other electron-ion quasi-neutral component (slow wind) originates from lower latitudes, yet at large distances from the origin there may be overlapping between the two. A most obvious example of such permeating plasmas is seen also in the solar atmosphere where plasma streams from lower layers are seen continuously propagating along magnetic field structures towards and through the solar corona. From the text and results that follow it will become clear that the present general study of two interpenetrating plasmas comprises also, as special cases, various examples of plasmas containing some additional (electron or ion) species. In all of these examples we have one fast flowing plasma whose parameters we shall denote by the subscript f , and one slow moving (target) plasma with the parameters denoted by the subscript s. In fact, the target plasma can be non-moving (or ’static’,