As a simple example of Weibel instability, consider an electron beam with density n b 0 and initial velocity v 0 z propagating in a plasma of density n p 0 = n b 0 with velocity − − v 0 z . The analysis below will show how an electromagnetic perturbation in the form of a plane wave gives rise to a Weibel instability in this simple anisotropic plasma system. We assume a non-relativistic plasma for simplicity.