Parametric instabilities in 3D periodically focused beams with space charge

Abstract

Parametric resonances of beam eigenmodes with a periodic focusing system under the effect of space charge—also called structural instabilities—are the collective counterparts to parametric resonances of single particles or of mechanical systems. Their common feature is that an exponential instability is driven by a temporal modulation of a system parameter. Thus, they are complementary to the more commonly considered space charge single particle resonances, where space charge pseudo-multipole terms are assumed to exist already at finite level in the initial distribution. This article elaborates on the characteristics of such parametric instabilities in 3D bunched beams—as typical in linear accelerators—for modes of second (envelope), third and fourth order, including the transverse coupled “sum envelope instabilities” recently discovered for 2D beams. Noteworthy results are the finding that parametric resonances can be in competition with single particle resonances of twice the order due to overlapping stopbands; furthermore the surprisingly good applicability of the stopband positions and widths obtained from previously published 2D linearised Vlasov stability theory to the 3D non-Kapchinskij-Vladimirskij particle-in-cell code studies presented here.