Abstract
A new class of exact solutions of the Vlasov–Poisson equations based on the Jeans’ theorem is considered. The self-consistent solutions for the evolution of the system from given initial particle distributions make use of particular invariants of particle motion with predetermined spatial structure. The relation between the time-dependent coefficients of the latter and the macroscopic plasma quantities, or moments of the distribution function, are obtained. As an illustration, the evolution of an expanding plasma with oscillations of the electron and ion expansion fronts is presented.
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