Simulation of the Space Charge Effect in RHIC

Space charge forces, representing the weak-strong case, are simulated by kicks from a line charge having a 2D-Gaussian transverse charge distribution. A series of particles having initial coordinates consistent with the dimensions of the injected beam are tracked sequentially, and tunes are obtained from analysis of the coordinates, x, x, y, and y, at the end of each turn. Stability is tested using 30K turn tracking runs during which the momentum error varies as = ̂sin(2 Qst).