3D simulation of periodic cusped magnetic focusing sheet electron beam

When the sheet electron beam is transmitting in solenoid magnetic fields, Diocotron mode or Diocotron instability comes into being, which could lead to collapse of beam propagation. In this paper, Diocotron mode theory is derived from Maxwell equations. Forces on electrons is analyzed in periodic cusped magnetic(PCM) focusing, and the result shows PCM can restrain Diocotron mode. Using 3D PIC program, formation of Diocotron mode is analyzed, and PCM focusing sheet electron beam and restraining Diocotron mode are simulated. The effect of Diocotron mode in sheet electron beam is also studied with changed PCM magnitude. The results show that space charge force and magnetic force need rebalance, which leads profile of beam to be thicken, when PCM magnitude is reduced.