Plasma Dynamics in a Dual-Frequency Paul Trap Using Tsallis Distribution

Abstract

This paper theoretically analyzes the motion of a collection of charged particles in a dual-frequency Paul trap. We derive analytical expressions for the single particle trajectory and the plasma distribution function assuming Tsallis statistics to see how this trap configuration is different from a conventional Paul trap. The introduction of a secondary RF frequency in a dual-frequency Paul trap allows for a modification of the spatial extent of confinement of charged particles. The plasma distribution function and temperature have been found to be periodic if the two driving frequencies are rationally related and the resulting period of plasma oscillation is given by the LCM of the time periods corresponding to the two driving frequencies and their linear combinations. The plasma temperature is spatially varying and the time-averaged plasma distribution has been found to be double humped beyond a certain spatial threshold, indicating the presence of certain instabilities. The effect of dual frequency in a Paul trap on the energy level shifts of the atomic orbitals has been investigated and the uncertainties in second order Doppler and Stark shift are found to be of the same order as that of a single-frequency Paul trap.