Hamiltonian fluid reduction of the 1.5D Vlasov–Maxwell equations

We consider the Vlasov–Maxwell equations with one spatial direction and two momenta. By solving the Jacobi identity, we derive reduced Hamiltonian fluid models for the density, the fluid momenta, and the second order moments, related to the pressure tensor. We also provide the Casimir invariants of the reduced Poisson bracket. We show that the linearization of the equations of motion around homogeneous equilibria reproduces some essential features of the kinetic model namely, the Weibel instability.