The relativistic kinetic Weibel instability: General arguments and specific illustrations

A general description is developed of the kinetic Weibel [Phys. Rev. Lett. 2, 83 (1959)] instability in relativistic plasmas for arbitrary plasma distribution functions. Then general conditions for the existence of the relativistic instability are given as well as the influence of limits on the wave-number range and so on the instability rate. A comparison with previous works on bi-Gaussian distributions is also provided. Furthermore, ultrarelativistic and also weakly anisotropic relativistic distributions are investigated in general. Finally, isolated Weibel modes (in which both the frequency and wave number are fixed) are derived for asymmetric relativistic plasma distributions and constraints on these isolated modes are presented.