In a plasma wakefield accelerator operating in the blowout regime, the strong space charge of a dense electron beam can cause significant radial motion of the background plasma ions. This ion motion changes the originally uniform ion density and alters the linear transverse focusing force of the wake, which affects the beam dynamics and its betatron radiation. In this work, we study this radiation process using theoretical models and simulations. Numerical simulations are performed using QuickPIC, a quasi-static three-dimensional (3D) particle-in-cell (PIC) code, along with its specialized radiation post-processing tool. We employ a mathematical model to describe the collapsed ions and calculate the modified focusing force. Based on this, we analyze how the non-uniform ion distribution impacts the radiation power. By comparing the theoretical calculations with PIC simulations under different beam conditions, we aim to explain the basic physical mechanism of betatron radiation when ion motion is present.
 

Ion Motion,betatron radiation,PIC simulations