A new Eulerian variational principle is presented for the exact Vlasov-Maxwell equations [1]. This variational principle is based on constrained variations of the Vlasov distribution in an eight-dimensional extended phase space. The standard energy-momentum conservation law is then derived explicitly by the Noether method. This new variational principle can be applied to various reduced Vlasov-Maxwell equations in which fast time scales have been asymptotically eliminated (e.g., low-frequency gyrokinetic Vlasov-Maxwell theory

[2]).

[1] A.J. Brizard, Phys. Rev. Lett. 84, 5768-5771 (2000).

[2] A.J. Brizard, Phys. Plasmas 7, 4816-4822 (2000).