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 30 K turn tracking runs during which the momentum error δ varies as δ=δˆsin(2πQ_st)