Effects of a Bon-Linear Lens on the Stored Proton Beam in the ISR

In order to simulate the beam-beam effect in a proton storage ring, at values of the beam-beam tune-shift much higher than those attainable with proton beams in the ISR, a non-linear lens has been installed. It consists of a pair of bars inside the vacuum chamber, about 1 m long and capable of carrying currents pp to 1000 A, corresponding to a linear tune-shift of about 0.1. The current bars, running parallel to the beam at a distance of a few mn above and below it, create a highly non-uniform magnetic field. It has the same symmetry as space charge at a head-on intersection, and excites all nonlinear resonances nhQh + nvQv = p for which both nh and nv are even. The beam decay rate has been measured as a function of the betatron tunes and the tune shift ¿Q caused by the non-ljnear lens. When ¿Q changes between 0 and 0.05 the decay rate changes by about 3 orders of magnitude, and depends strongly on the betatron tunes. A computer simulation shows that at ¿Q ¿ 0.05 the stochtsticity limit is reached.