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 pr opagation direction parallel to the background magnetic field. The ins tability in the ultrarelativistic regime, with the typical Lorentz fac tor gamma much greater than unity, is emphasized for its relevance to astrophysical sources of synchrotron radiation. Detailed stability pro perties are examined, in the ultrarelativistic regime, for two model d istribution functions, the water-bag distribution function, and a smoo th distribution function. The dispersion relations are obtained in clo sed analytic forms for both distribution functions. The necessary and sufficient conditions for instability are determined when the temperat ure along the background magnetic field is cold (T(parallel-to) = 0). The dispersion relations are solved numerically with T(parallel-to) no t-equal 0 over a wide range of system parameters to determine the deta iled dependence of the instability on the strength of the background m agnetic field and the temperature anisotropy. The present analysis sho ws that both a decrease in temperature anisotropy and an increase in t he background magnetic field can cause a significant decrease in growt h rate. For the smooth distribution function, it is found that, for a given plasma density, the system stabilizes completely when the backgr ound magnetic field is stronger than the moderate threshold value [(om ega(p+/-)/omega(c+/-))2 less-than-or-equal-to 2/pi], corresponding to T(parallel-to) = 0. As the temperature anisotropy decreases, the thres hold magnetic field decreases.