Effects of direct space charge on the transverse mode coupling instability

The effects of direct space charge forces on the Transverse Mode Coupling Instability (TMCI) are studied using numerical techniques. We have implemented a third order symplectic integrator for the equation of motion, taking into account non linear space charge forces coming from a Gaussian shaped bunch. We performed numerical simulation for the Super Proton Synchrotron (SPS) bunch at 26 GeV of kinetic energy, using either resistive wall or broad band transverse wake elds. In both cases the result of applying direct space charge, leads to an intensity threshold increase up to 100% for the resisitve wall wake.