Linear Theory of Temperature Anisotropy Instabilities in Magnetized Thermal Pair Plasmas

A rigorous study of the dispersion relations of weakly amplified and weakly propagating transverse fluctuations with wave vectors ( k B ) parallel to the uniform background magnetic field B in an anisotropic bi-Maxwellian magnetized pair plasma is presented. Earlier work, based on the weakly-amplified limit, is extended to the case of weakly propagating solutions, which includes in particular aperiodic fluctuations, by the appropriate Taylor expansion of the plasma dispersion function. It is shown that six different transverse right-handed (RH) and left-handed (LH) polarized modes can be excited whose dispersion relations and instability threshold conditions are derived. The existence and instability conditions are derived in terms of the combined temperature anisotropy A = T /T , the parallel plasma beta = 8 nekBT / B 2 and the electron plasma frequency phase speed w = p,e / (kc) . The pair Alfven and cyclotron instabilities are the only two weakly amplified solutions, whereas the four weakly propagating solutions are the mirror, firehose, cool magnetized Weibel and cyctronic fluctuations, respectively. The four weakly propagating solutions are aperiodic with vanishing real phase speeds R = 0 if the plasma positrons and electrons have the same temperature anisotropy. The mirror and cool magnetized Weibel fluctuations reduce to the known hot and cool Weibel instabilities in the limit of an unmagnetized plasma. PACS Numbers: 52.25.Xz --52.27.Ep --52.35.-g --94.30.cq