A particle-based field ionization algorithm in quasi–static PIC codes

Particle-in-cell (PIC) simulation code, especially the quasi–static PIC code, has been an indispensable tool to the development of the plasma wake field accelerator (PWFA). Such an advanced accelerator scheme uses a drive particle beam or a laser pulse to generate wake fields inside a plasma for accelerating another particle beam. The acceleration gradient can be 10 GeV  or higher in the PWFA, which makes it a promising candidate as the main acceleration method in the future high energy electron–positron colliders or x-ray free electron laser facilities. In the plasma wake field acceleration, the plasma can be generated by ionizing the neutral gas with the Coulomb field around the particle beam or the electric field of the laser pulse. Therefore, the field ionization process plays a key role in the plasma wake field acceleration experiments. The 3D PIC code QuickPIC, which is based on the quasi–static approximation, has been widely used for efficiently modeling the PWFA problems including the field ionization process. However, the current field ionization algorithm in QuickPIC cannot simulate mobile ions. In this work, we developed a particle-based ionization method in order to track the motion of ions that generated during the ionization process. We also implement the new algorithm in another quasi–static PIC code QPAD, which additionally applied the azimuthal Fourier decomposition method compared with QuickPIC. The comparison of simulation results between the old and new algorithm and between QuickPIC and QPAD are presented. The comparison shows that for the plasma wake field acceleration simulation without the plasma ion motion, the particle-based method works as well as the old algorithm in both codes of QuickPIC and QPAD. When including the mobile ions in the field ionized plasma, QuickPIC and QPAD with the particle-based method show a well agreement with each other.