Equilibrium and Stability Properties of the Solenoidal Lens Betatron

The solenoidal lens betatron uses a series of solenoidal lenses arranged around a race-track shaped drift-tube to provide strong transverse focusing for a high-current electron ring. Equilibrium behavior of the circulating beam is examined for parameters close to those of the University of New Mexico machine currently under construction. The tolerance of the beam to mismatches in the toroidal and vertical fields is evaluated analytically and using a particle simulation code. The linear and nonlinear development of the negative-mass instability in the device is also studied. Stability behavior comparable to that in a conventional betatron (i.e., one with no toroidal magnetic field) is found. Growth rates are compared to those obtained from an analytic model.