Focusing characteristics of the relativistic electron beam transmitting in ion channel

Based on the beam-plasma system model established in this paper, the trajectory of the electron beam in the ion channel is studied quantitatively through the envelope equation. Under different initial system parameters, the focusing transmission conditions of the beam in the ion channel are discussed. Then, a series of particle-in-cell simulations are performed, which generally versifies the theoretical results and shows some further details of the focusing behavior of the beam. It is found that the deceleration of some electrons around the focusing point or the beam-plasma interaction at the ion channel boundary will result in the generation of the residual electrons, which forms the electron return current that leads to the new instabilities influencing the focusing characteristics of the beam.