Improved Long-Wavelength Dispersion Relation for the Negative Mass Instability in High Current Conventional and Modified Betatrons

摘要

A new linear dispersion relation, taking proper account of toroidal curvature effects on the electromagnetic fields, has been derived for the negative mass installability in high current betatrons. (The low frequency and paraxial approximations are employed). The dispersion relation typically gives growth rates which are smaller than those from earlier analyses and are in better agreement with simulation code results. Applying these findings to the Office of Naval Research racetrack induction accelerator design suggests that it may be safe from severe negative mass instability development with only a modest beam energy spread. (Author)