With use of a recent variational formulation of the Maxwell-Vlasov and guiding-center theories [D. Pfirsch, Z. Naturforsch. A 39, 1 (1984)], the energy-momentum and angular momentum tensors for such theories are derived and the corresponding local conservation laws are proven. The energy-momentum tensor is shown to be symmetric in its spatial components while the angular momentum density is naturally antisymmetric.

The following theorem is proved in the article: An MHD-unstable configuration with a dissipationless plasma surrounded by vacuum and possibly superconducting walls cannot be stabilized by introducing walls of finite electrical conductivity.

Hamiltonian or variational formulations of the Maxwell-Vlasov equation naturally yield expressions for the free energy available upon perturbation of an equilibrium. The noncanonical Hamiltonian, Hamilton-Jacobi, and Lagrangian formulations are used to obtain such expressions. It is concluded that all interesting equilibria are either linearly unstable or possess negative-energy modes.