Free-energy expressions for Vlasov equilibria
- 1 October 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 40 (7) , 3898-3910
- https://doi.org/10.1103/physreva.40.3898
Abstract
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.Keywords
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