Modeling of beam focusing and kink instability for colliding relativistic electron and positron beams

A simulation code has been developed and exercised to study the time evolution and resultant liminosity of intersecting pulses of electrons and positrons. Under the extreme conditions of high current and small radius recently proposed for the SLAC facility, the pulses mutually pinch to a smaller mean radius than that achieved by free flight alone. The effective luminosity is enhanced by a factor of approx. 3 in the best case, corresponding to zero initial emittance and pulse length equal 1/4 the mean betatron wavelength. Gaussian profiles in the longitudinal and transverse coordinates are preferred over flat profiles in order to minimize disruptive oscillations in radius which reduce luminosity. A second potential source of disruption is the kink instability. This is always present to some degree during the interaction of opposed pulses. However, the maximum growth rate is only one half the angular betatron frequency and therefore mode growth is limited to a very low level if the pulses are short compared with a betatron wavelength