Time-dependent Trapped Plasmas: Nonlinear Dynamics, Symmetries and Invariants

We investigate the nonlinear dynamics of a single-component plasma confined in a time-dependent harmonic trap with regard to aspects of symmetry and invariant functions in a variational approximation. The system is described as a fluid in an isentropic adiabatic regime by a system of partial differential equations (pde). A convenient change of variables, along with a Gaussian ansatz for the number density distribution, allows a consistent mathematical description in terms of ordinary differential equations (ode). From this formulation, we follow up with an analysis concerning the corresponding differential operators algebraic structure and Noether symmetries in specific physical regimes. For each studied case, proper invariants are identified. As a result, the obtained conserved quantities capture an interplay between the internal plasma dynamics and the time modulation of the trap, resulting in a sharp restriction for the system evolution.