A weak microwave instability with potential well distortion and radial mode coupling

In attempts to minimize the impedance of an accelerator by smoothing out its vacuum chamber, improvements are typically first made by reducing the inductive part of the impedance. As the inductance is reduced, however, the impedance becomes increasingly relatively resistive, and as a consequence, the nature of potential well distortion changes qualitatively. An inductive impedance lengthens the bunch (above transition) while maintaining more or less a head-tail symmetry of the bunch longitudinal distribution. A resistive impedance does not change the bunch length as much, but tends to cause a large head-tail asymmetry. We explore two ways which might in principle allevial this instability mechanism. (i) add a higher harmonic cavity: A higher harmonic rf voltage with appropriate and amplitude may compensate for the head-tail asymmetry and thus raise the instability threshold. (ii) operate the accelerator with a negative momentum compaction factor {eta}:(12) With {eta} > 0, the distorted beam distribution leans toward the head of the bunch; the bunch tail sees large wakefields. Operating with {eta} < 0 could conceivably help because the beam distribution now leans toward the tail of the bunch. Both (i) and (ii) were explored in this paper. We found that a higher harmonic cavity of a modest voltage can indeed eliminate this instability, while the advantage of operating with {eta}< 0 is less obvious