Conditions for stable operation in a helical quadrupole focusing accelerator

A number of high-current accelerator designs utilize strong focusing in the form of helical quadrupole and axial guide fields. Operation in certain parameter regimes can cause electromagnetic instabilities. We find that the electron beam centroid can be i) orbit unstable, independent of the waveguide modes, ii) three-wave unstable or iii) fully stable. Analytic expressions for the various stability conditions are obtained in the limit of zero beam current. The stability conditions are verified via particle simulation in each regime.