Dynamic aperture effects due to linear coupling

The coupling introduced by the random a1 can produce considerable distortion of the betatron motion. For a given initial xo, xo', yo, yo', the maximum x and the maximum y for the subsequent motion can be considerably larger when coupling is present. The maximum x and y can be used as a measure of the betatron distortion. One effect of this betatron distortion shows up in the dynamic aperture, in a loss in the stability limit, ASL, found by tracking. The betatron distortion causes the particle to move further out in the magnets, where it sees stronger non-linear fields. Previous tracking showed a loss in ASL due to random a1 and b1. It was noticed then that the loss in ASL was associated with a betatron motion distortion which was primarily a linear effect. For a given initial x, x', y, y' the xmax and ymax in the high-Β magnets were considerably larger for those random a1 distributions which produced the smaller ASL. The studies described in this report show that the stability limit, ASL, depends on the starting location around the ring. This variation in ASL around the ring can be correlated with the variation in the betatron distortion for particles starting at different places around the ring. It is proposed that the average of the ASL found by starting at each of the QF, the focusing quadrupoles in the arcs, can be taken as a measure of the dynamic aperture. It is found that the average ASL is reduced by about 15% by the random a1 multipoles expected in RHIC