Detailed properties of the Weibel instability in a relativistic unmagnetized plasma are investigated for a particular choice of anisotropic distribution function F($p_{\perp }^2$,$p_z$) that permits an exact analytical solution to the dispersion relation for arbitrary energy anisotropy. The particular equilibrium-distribution function considered in the present analysis assumes that all particles move on a surface with perpendicular momentum $p_{\perp }$=p${^}_{\perp }$=const and are uniformly distributed in parallel momentum from $p_z$=-p${^}_z$=const to $p_z$=+p${^}_z$=const. (Here, the propagation direction is the z direction.) The resulting dispersion relation is solved analytically, and detailed stability properties are determined for a wide range of energy anisotropy.

• Received 9 June 1986

DOI:https://doi.org/10.1103/PhysRevA.35.2718