Analytic and Numerical Studies of the Modified Betatron

The modified betatron concept has been proposed as a means, of accelerating high current (kiloamp) electron beams to high energy. This device employs a toroidal magnetic field to overcome the space-charge limit on the current in a conventional betatron at low energy. In this paper, we look at the injection, equilibrium and stability of the modified betatron. The main emphasis is on stability. An analytic dispersion relation is derived using a cold-fluid model of the beam. The results are compared to three-dimensional simulations performed with the electromagnetic PIC code IVORY. The nonlinear development of the negative mass instability is followed in the simulations.