Experience with OpenMP for MADX-SC

MADX-SC allows the treatment of frozen space charge using beam-beam elements in a thin lattice, i.e. one can take advantage of the standard set-up of MAD-X lattices without the need for specialized codes for the space-charge (SC) evaluation. The idea is to simulate over many turns without the problem of noise as in the PIC SC codes. For the examples under study, like the PS and RHIC, it would be desirable to simulate up to 1 million turns or more. To this end one had to make an effort to optimize the scalar speed and, most importantly, get a speed-up of approximately a factor of 5 using OpenMP.