WEIBEL INSTABILITY IN RELATIVISTICALLY HOT MAGNETIZED ELECTRON-POSITRON PLASMAS

A linear stability analysis is carried out for the Weibel instability in relativistic magnetized electron-positron-pair plasmas, with the propagation direction parallel to the background magnetic field. The instability in the ultrarelativistic regime, with the typical Lorentz factor gamma much greater than unity, is emphasized for its relevance to astrophysical sources of synchrotron radiation. Detailed stability properties are examined, in the ultrarelativistic regime, for two model distribution functions, the water-bag distribution function, and a smooth distribution function. The dispersion relations are obtained in closed analytic forms for both distribution functions. The necessary and sufficient conditions for instability are determined when the temperature along the background magnetic field is cold (T(parallel-to) = 0). The dispersion relations are solved numerically with T(parallel-to) not-equal 0 over a wide range of system parameters to determine the detailed dependence of the instability on the strength of the background magnetic field and the temperature anisotropy. The present analysis shows that both a decrease in temperature anisotropy and an increase in the background magnetic field can cause a significant decrease in growth rate. For the smooth distribution function, it is found that, for a given plasma density, the system stabilizes completely when the background magnetic field is stronger than the moderate threshold value [(omega(p+/-)/omega(c+/-))2 less-than-or-equal-to 2/pi], corresponding to T(parallel-to) = 0. As the temperature anisotropy decreases, the threshold magnetic field decreases.