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

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Abstract
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.