Nonuniform non-neutral plasma in a trap

An analytical model for breathing oscillations in a nonuniform non-neutral plasma slab is developed. The plasma is relatively small and warm with the smallest dimension only of several Debye lengths. Nonuniformity in the equilibrium results in a frequency shift associated with pressure and boundary effects. The plasma size and temperature, being related to the frequency shift, can therefore be evaluated from frequency measurements. In particular, for small nonuniform plasmas the frequency of the breathing mode is twice that predicted by the cold fluid theory. Nonlinear oscillations are also considered and the pressure is shown to have an important effect on the dynamics. Analytical solutions for linear and nonlinear oscillations are obtained and compared with that from one-dimensional particle-in-cell simulations. Good agreement is found.