Grid dependent noise and entropy growth in anisotropic 3d particle-in-cell simulation of high intensity beams

The numerical noise inherent to particle-in-cell (PIC) simulation of 3d anisotropic high intensity bunched beams in periodic focusing is compared with the analytical model by Struckmeier [Part. Accel. 45, 229 (1994)]. The latter assumes that entropy growth can be related to Markov type stochastic processes due to temperature anisotropy and the artificial "collisions" caused by using macro-particles and calculating the space charge effect. The PIC simulations are carried out with the TRACEWIN code widely used for high intensity beam simulation. The resulting noise can lead to growth of the six-dimensional rms emittance. The logarithm of the latter is shown to qualify as rms-based entropy. We confirm the dependence of this growth on the bunch temperature anisotropy as predicted by Struckmeier. However, we also find a grid and focusing dependent component of noise not predicted by Struckmeier. Although commonalities exist with well-established models for collision effects in PIC-simulation of extended plasmas, a distinctive feature is the presence of a periodic focusing potential, wherein the beam one-component plasma extends only over relatively few Debye lengths. Our findings are applied in particular to noise in high current linac beam simulation, where they help for optimization of the balance between the number of simulation particles and the grid resolution.