Investigation of Stochastic Beam Growth with a Non-Linear Lens

The problem of the onset of stochastic motion in a non-linear system is of considerable importance for the understanding of the long-time stability of beams in hadron storage rings in the presence of strong high-order non-linear resonances. A non-linear lens has been installed in the SPS in order to simulate resonances driven by the beam-beam effect or by magnetic field imperfections in superconducting storage rings. In this paper, a criterion for the onset of stochastic motion is derived and compared with the results of computer simulations and of experiments performed on the machine.