Abstract
Counterstreaming beams of charged particles are frequently observed in the laboratory and space plasma systems, and they are responsible for supplying the free energy of the system in the absence of temperature anisotropies. Such systems are unstable and give rise to excitation of various electrostatic and electromagnetic plasma waves. This work is intended as a supplement to the previous investigations of the Maxwell-Jüttner distributed counterstreaming plasmas on the basis of the covariant (fully relativistic) formulation. Here, we aim to find analytical solutions of the dispersion relations and investigate the properties of the growth rate for the electrostatic and electromagnetic modes propagating parallel to the background magnetic field. The influences of the important parameters of the beam, namely, velocity, temperature, the relative intensity of the two streams, and the strength of the stationary magnetic field, on the growth rates of the longitudinal and transverse modes are compared. The analytical evaluation of the parallel modes reveals several interesting results. First, for all investigated modes, the growth rate is minimum only if the particle distribution function is exactly symmetric. Second, the behavior of the electrostatic and electromagnetic instabilities by varying the beam temperature is totally opposite. Third, increasing the drift velocity, the growth rate exhibits a maximum at a certain velocity; however, beyond that, wave damping occurs. Finally, under the same conditions, the external magnetic field has a destabilizing (stabilizing) effect on the left (right)-hand branch of the transverse modes.
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