Magnetic optics calculations for cylindrically symmetric beams with space charge

The purpose of this report is to discuss a new approach for doing magnetic optics calculations in the presence of space charge. Our approach is based on the self-consistent calculation of the transfer map, M, that describes the motion of individual particles. Since our approach is based on the computation of M, it is the only method that provides for the direct calculation of aberrations in beam tranport systems with space charge. In this report, we will treat cylindrically symmetric beams in beam transport systems consisting of drifts and solenoids. We will derive ordinary differential equations for a third order representation of M. We will show how this formalism can be used to predict rms beam size and emittance growth caused by nonlinear optical effects and nonlinear space charge effects. Since our method does not rely on 'pushing particles', it is much faster than particle simulation. (However, it is not as generally applicable as particle simulation.) As a specific example, we will consider the focusing of a cold beam by a solenoid. We will show that predictions of beam evolution based on our method are in good agreement with particle simulation. (author) 20 refs., 10 figs