• Weibel instability
• magnetic reconnection
• Hamiltonian fluid
• collisionless plasma

Magnetic fields topology plays a fundamental role in plasma dynamics by imposing strong constraints to particle dynamics and to the energetic of the system. On large spatial- and on slow time-scales, the key role played by magnetic fields is the consequence of the cancellation of the electric ones. This is particularly relevant for space plasmas and magnetically confined plasmas. On the other hand, in typical conditions of laser-plasma interactions, the magnetic field usually becomes important when particle kinematics becomes relativistic.
Here we have studied the nonlinear evolution of two basic plasma phenomena in a non-collisional framework, magnetic reconnection (or magnetic fields annihilation) due to electron inertia effects, and its, let's say, inverse process, the generation of magnetic fields by plasma anisotropies (in particular the electron momentum anisotropy leading to the current filamentation instability).