Stability regimes in a helical quadrupole focusing accelerator−theory and simulation

Abstract

The inclusion of helical quadrupole (stellarator) and axial guide fields in high current spiral line or recirculating accelerator configurations provides a high tolerance to energy mismatch and confines the beam against space charge forces. Such a configuration is studied via three-dimensional particle simulation. It is found that the electron beam centroid motion can interact with the external fields and with the TE11 waveguide mode to obtain (i) highly unstable particle orbits, (ii) the electromagnetic three-wave instability, or (iii) a fully stable beam. Theoretical stability conditions are presented in the limit of zero beam current and are found to be good predictors of simulation results. Minor departures from the stability conditions at high current are discussed in terms of the full linear dispersion relation. Saturation of the instability without beam loss is observed in some cases. This is the result of detuning in the relativistic cyclotron wave number as the beam energy and axial velocity decrease. The effectiveness of this detuning mechanism is evaluated for the various regimes.