Quasilinear Stabilization of the Transverse Instability

The transverse instability is studied for the case of an infinite unmagnetized plasma with small electron temperature anisotropy. Growth rates and normal modes are found. Relativistic corrections to the growth rate have a stabilizing effect. The distribution function satisfies a diffusion equation with an additional flow term. The diffusion term causes the anisotropy to disappear and thus stabilizes the instability. The flow term is a perfect time derivative and makes no contribution to the net change in the distribution function between initial and final states which have negligible wave spectra.