Time Evolution of Tsallis Distribution in Paul Trap

Motion of individual charged particles inside a Paul trap is very well understood, but the understanding of collective dynamics offers a challenge and opens up avenues for investigation. This problem has been addressed earlier by solving the 1-D Vlasov equation assuming the initial distribution to be Gaussian. In this paper, we generalize this solution by taking a Tsallis distribution, since in some Paul trap experiments, the plasma distribution has been reported to have power law tails. The time averaged distribution function is found to be doubled humped in velocity beyond a spatial threshold and the hump moves away from the bulk as the Tsallis parameter is increased from 1. The plasma temperature is found to vary quadratically with the spatial coordinate.