Bubble core field modification by residual electrons inside the bubble

Abstract

Bubble core field modification due to the nondepleted electrons present inside the bubble is investigated theoretically. These residual electrons induce charge and current densities that can induce the bubble core field modification as well as the bubble shape change. It is found that the electrons entering into the bubble move backward at almost light speed and would weaken the transverse bubble fields. This reduces the ratio of longitudinal to transverse radius of the bubble. For the longitudinal bubble field, two effects compensate with each other because of their competition between the enhancement by the shortening of bubble shape and the reduction by the residual electrons. Therefore the longitudinal field is hardly changeable. As a comparison we perform particle-in-cell simulations and it is found that the results from theoretical consideration are consistent with simulation results. Implication of the modification of fields on bubble electron acceleration is also discussed briefly.