Nonlinear development of the Weibel instability and magnetic field generation in collisionless plasmas

The Weibel instability is expected to be one of the mechanisms at play in the generation of quasi-static magnetic fields by high-intensity laser pulses propagating with relativistic amplitudes in underdense plasmas. This instability can be excited in a plasma with two electron populations: the background cold electrons and the high energy electrons accelerated by the laser radiation. Here we investigate the nonlinear stage of the evolution of this instability both analytically and numerically. We consider both the non-relativistic and the relativistic regimes within the frame-work of a cold two-electron fluid plasma description, where ions are assumed to be at rest and to provide a uniform neutralizing background.