Spatial structure and time evolution of the Weibel instability in collisionless inhomogeneous plasmas

The magnetic field generated in an initially unmagnetized and anisotropic inhomogeneous plasma by the development of the Weibel instability is strongly nonuniform. For the case of a plasma where the anisotropy arises from two (relativistic) counterstreaming electron beams it is shown, both analytically and numerically, that this instability develops a spatial ''resonant''-type singularity. The largest magnetic field is generated around this singularity and has opposite polarities. In the case of one-dimensional (1D) perturbations, a current layer is formed very rapidly at the resonance position, almost independently of the characteristic scale of the initial perturbation. In 2D, numerical simulations show that a chain of current vortices is formed.