A simple analytical model for the Weibel instability in the non-relativistic regime

The Weibel instability is prompted by a temperature anisotropy within a plasma. We present an analytical model based on a non-relativistic two temperatures waterbag distribution function. The model is exactly solvable in terms of the stability condition, the growth rate for any wave vector and temperature parameters, the maximum growth rate and the wave number for which it is reached.