TMCI with Resonator Wakes

TL;DR

This paper investigates the transverse mode-coupling instability (TMCI) caused by high-frequency resonator wakes using the NHT solver, revealing complex mode interactions and proposing an interval of thresholds instead of a single value.

Contribution

It introduces a novel approach to defining TMCI thresholds by considering an interval due to multiple mode couplings and decouplings, accounting for Landau damping effects.

Findings

Multiple mode couplings complicate threshold definition.

Threshold interval is bounded by low and high intensity limits.

High intensity threshold follows Zotter's scaling, but with a different factor.

Abstract

Transverse mode-coupling instability (TMCI) with a high-frequency resonator wake is examined by the Nested Head-Tail Vlasov solver (NHT), where a Gaussian bunch in a parabolic potential (GP model) is represented by concentric rings in the longitudinal phase space. It is shown that multiple mode couplings and decouplings make impossible an unambiguous definition of the threshold, unless Landau damping is taken into account. To address this problem, instead of a single instability threshold, an interval of thresholds is suggested, bounded by the low and high intensity ones. For the broadband impedance model, the high intensity threshold is shown to follow Zotter's scaling, but smaller by about a factor of two. The same scaling, this time smaller than Zotter's by a factor of four, is found for the ABS model (Air Bag Square well).