Kinetic saturation of the Weibel instability in a collisionless plasma

We investigate the nonlinear saturation of the Weibel instability in an initially unmagnetized plasma in which two electron streams propagate in opposite directions. We then estimate the fraction of the kinetic energy of the counter-streaming electrons that is transformed by the instability into magnetic energy. In a fluid cold plasma description this instability evolves nonlinearly into smaller and smaller spatial scales. The introduction of a kinetic plasma description resolves these spatial singularities and shows that the instability saturates when the effective electron gyroradius in the generated magnetic field becomes of the order of the electron collisionless skin depth. This corresponds to an approximate energy equipartition.