A Probability Function to FIT Radial Distributions in PARMILA Simulation Beams

Proton or deuteron beams in linear accelerators have halos much too large to be described by the normal distribution. When the beam core is fitted to a normal distribution, the actual amount of beam past a given number of standard deviations is orders of magnitude above the normal distribution prediction. Knowing the distribution obeyed by beams would be helpful in evaluating beam spill using computer codes. Toward this end, a probability distribution has been found that fits PARMILA-generated radial beam distributions. The fitting distribution is a mixture of two generalized gamma (gg) distributions and fits both the beam core and the tail reasonably well. Its predictions in the halo region are substantially larger than normal distribution predictions. The distribution is described, examples of fits are given, and the ability to fit the tail is discussed.