The influence of plasma density on the optimal beam loading in plasma wake field accelerator

In the beam driven plasma wakefield accelerators, the optimal beam loading can be achieved by changing the total charge of the witness beam while keeping all other beam parameters the same． Under the optimal beam loading condition, the witness beam will have the minimal relative energy spread growth during the acceleration process inside the plasma． When the witness beam does not have the proper charge for the optimal beam loading, it will be either less loaded or over loaded inside the plasma wake． In this paper, we proposes that the beam-loading condition can be modified by changing the plasma density with fixed beam parameters． Furthermore, the final relative energy spread of the witness beam can be mitigated by using a longitudinally non-uniform plasma. These are shown in the simualtion results that uses the QuickPIC code． In addition, we also show that the density ramps in the plasma wake field accelerator experiments will not lead growth on trailing beam’s energy spread but will instead reduce it．