ABSTRACT
Numerical simulation has become a major tool for modeling and theoretical understanding of beam propagation as well as for accelerator design. Most simulations today are being performed using the Particle-In-Cell (PIC) approach. This method combines Lagrangian particle motion with grid based computation of the mean self fields, a deposition and interpolation step making the link between the two parts. The PIC method enables to perform cost effective simulations and becomes especially efficient compared to grid based Vlasov methods when dimensionality increases. The drawback of PIC methods is their inherent numerical noise which decreases only slowly when the number of particles is increased. Moreover. in the PIC method, the phase space is populated with particles according to the value of the distribution function, i.e. more particles are put in regions of phase space where the distribution function is larger. This means that low density regions of phase space are very sparsely populated with particles. which makes the resolution very poor in these areas. This aspect of PIC methods makes them inefficient for simulations where what happens in those regions is of major importance. like beam halo formation. Note that populating phase space uniformly with particles of different weights does not help and makes things even worse for highly non linear problems, as particles of different weights mix, making light weight particles useless.
