Abstract
A collisional trapped non-neutral plasma is described by a hydrodynamical model in one-dimensional geometry. For suitable initial conditions and velocity fields, the Lagrangian variables method reduces the pressure dominated problem to a damped autonomous Pinney equation, representing a dissipative nonlinear oscillator with an inverse cubic force. An accurate approximate analytic solution derived from Kuzmak-Luke perturbation theory is applied, allowing the assessment of the fully nonlinear dynamics. On the other hand, in the cold plasma case, the Lagrangian variables approach allows the derivation of exact damped nonlinear oscillations. The conditions for the applicability of the hot, pressure dominated or cold gas assumptions are derived.
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