Abstract
A class of exact one-dimensional oscillating solutions of the Vlasov–Poisson system describing a one-component plasma in a parabolic electrostatic potential well is considered. Through a separation of variables procedure, a system of ordinary differential equations describing the moments of the velocity distribution function is obtained. The moment equations can be decoupled at any order from the higher ones without approximations. Oscillating-pattern solutions for the resulting finite and exact systems are found.
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