Particle simulation of proton beam propagating in background plasma

Numerical simulations have been conducted on the propagation of a long proton beam in the background plasma with the help of 2D3V PIC code. The simulations show that the plasma improves the propagation of the proton beam obviously. And for long distance propagation, the proton beam has a more stationary profile when propagating in the bulk plasma compared to propagating in the plasma slab. The plasma wave excited by the beam can modulate the density of the proton beam, influencing the beam’s stable propagation, and the results of the simulations confirm that the proton beam with a smooth edge-density profile can minimize the excitation of plasma waves．