Physics
Scientific paper
Jan 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984phfl...27..192l&link_type=abstract
Physics of Fluids (ISSN 0031-9171), vol. 27, Jan. 1984, p. 192-196. Research supported by the U.S. Department of Energy.
Physics
35
Collisionless Plasmas, Plasma Dynamics, Poisson Equation, Vlasov Equations, Distribution Functions, Maxwell Equation, Ponderomotive Forces, Time Dependence
Scientific paper
A class of exact, time-dependent solutions of the nonlinear, one-dimensional Vlasov-Poisson equations is determined by applying a result of Lewis and Leach (1982) on invariants of time-dependent Hamiltonian systems. Potential energies for which an invariant quadratic in the momentum exists are found to occur in exact solutions of the Vlasov-Poisson equations, in which case the distribution functions are functions of quadratic functions in the momenta. The special case of locally Maxwellian single-species solutions is discussed. The solutions for a single-species plasma, or a multispecies plasma where the charge-to-mass ratios are all equal, can be obtained by translating stationary solutions of the Vlasov-Poisson equations rigidly with an arbitrarily time-dependent displacement. If the charge-to-mass ratios are unequal, the solutions can be obtained by translating stationary solutions of modified Vlasov-Poisson equations with a displacement that depends quadratically on time.
Lewis Ralph H.
Symon K. R.
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