Beam stability in a solenoid-focused betatron

The solenoid-lens betatron uses periodic solenoid focusing to increase the current that can be injected into a betatron. A dispersion relation for the negative-mass instability in this device is derived using a multiple-length-scale method to average over the nonuniform toroidal field. The result qualitatively resembles the dispersion relation for the conventional betatron but has a finite transition energy and suppresses growth rates. Both effects are due to the solenoid focusing. It is shown that for a space-charge-dominated equilibrium finite beam radius has a strong stabilizing influence even in the absence of an energy spread. Results of 3-D numerical simulations confirm the predicted stability at low-toroidal mode numbers. High toroidal-mode numbers show anomalously large growth rates but saturate nonlinearly in a relatively benign manner. (author) 18 refs., 9 figs., 1 tab