Abstract
In this manuscript the dispersion relations of streaming instabilities, by using the unique property (neutralized in charge and current by default) of plasma shells colliding, have been generalized and studied. This interesting property for interpenetrating beams enables one to find the general dispersion relations without any restrictions used in the previous works in this area. In our previous work [H. Mehdian et al., ApJ. 801, 89 (2015)], employing the plasma shell concept and boost frame method, the general dispersion relation for filamentation instability has been derived in the relativistic classical regime. But in this paper, using the above mentioned concepts, the general dispersion relations (for each of streaming instabilities, filamentation, two-stream and multi-stream) in the non-relativistic quantum regime have been derived by employing the quantum fluid equations together with Maxwell equations. The derived dispersion relations enable to describe any arbitrary system of interacting two and three beams, justified neutralization condition, by choosing the inertial reference frame embedded on the one of the beams. Furthermore, by the numerical and analytical study of these dispersion relations, many new features of streaming instabilities (E.g. their cut-off wave numbers and growth rates) in terms of all involved parameters have been illustrated. The obtained results in this paper can be used to describe many astrophysical systems and laboratory astrophysics setting, such as collision of non-parallel plasma shells over a background plasma or the collision of three neutralized plasma slabs, and justifying the many plasma phenomena such as particle accelerations and induced fields.
Highlights
ApJ. 801, 89 (2015)], employing the plasma shell concept and boost frame method, the general dispersion relation for filamentation instability has been derived in the relativistic classical regime
For the cases studied in the previous researches with the above neutralization condition, mentioned simplification conditions rarely occur in astrophysical systems
It is notable that since this work has been done in non-relativistic quantum regime, the boost of frame is not needed in the present study, in contrast of our previous work in Ref. 1
Summary
In. 2010, Michno and Schlickeiser (in order to consider the microphysical details of the energy conversion in relativistic and non-relativistic outflows) investigate the solutions of the linear plasma dispersion relation in classical and unmagnetized anisotropic beam plasma consisting of two overall-neutral particle beams propagating with arbitrary velocities in the same direction.[21] in our previous work, by expressing the above mentioned limitative assumptions which had been applied theretofore, we employed the cold fluid equations, together with Maxwell’s equations, as well as plasma shell concept and boost frame method to obtain general dispersion relations for the filamentation instabilities in relativistic classical regime.[1] by observing the more plasma systems in quantum regime (in astrophysics and laboratory), finding the general dispersion relations for streaming instabilities in this regime would be extremely important in future researches.
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