Nonlinear oscillations of non-neutral plasmas in a time-dependent harmonic trap

Abstract

A non-neutral plasma is confined in a quasi-1D device and described by a fluid model. The use of the Lagrangian variables method together with a certain Ansatz for the velocity field reduces the problem essentially to ordinary differential equations satisfied by a scale function. In the case of thermal dominated plasma, the governing equation is the Pinney equation, having a close connection with the time-dependent harmonic oscillator. For a slowly varying frequency of the trap potential, an approximate solution is derived and shown to be accurate in the adiabatic limit. In the case of negligible thermal effects, the resulting non-homogeneous time-dependent oscillator equation for the scale function is also approximately solved, in the adiabatic limit. The validity conditions of the thermal dominated and Coulomb dominated cases are determined. The results are applied to a confined antiproton plasma, with implication on antimatter atom experiments.