A comparative study of the filamentation and Weibel instabilities and their cumulative effect. II. Weakly relativistic beams

Counterstreaming plasma systems with intrinsic temperature anisotropies are unstable against the excitation of Weibel-type instabilities, namely filamentation and Weibel instabilities, and their cumulative effect. Here, the analysis is extended to counterstreaming plasmas with weakly relativistic bulk velocities. while the thermal velocities are still considered to be non-relativistic. Such plasma systems are relevant for fusion plasma experiments and the more violent astrophysical phenomena, such as jets in gamma-ray burst sources. Simple analytical forms of the dispersion relations are derived in the limit of a small transverse temperature or a large temperature anisotropy of the beams. The aperiodic growing solutions are plotted systematically for the representative cases chosen in Paper 1 (Lazar et al. 2009 J. Plasma Phys. 75, in press), In the limit of slow non-relativistic plasma flows, the numerical solutions fit well with those obtained in Paper 1, but for weakly relativistic streams an important deviation is found.