Characterisation and mitigation of RF knockout during beam stacking

TL;DR

Beam stacking in FFAs enables higher extracted currents but RF knockout, driven by finite cavity dispersion, can cause beam loss. The work derives the RF knockout mechanism, establishes the resonance condition $Q_x = \pm \frac{\omega_{RF}}{\omega_{rev}} + n$, and demonstrates that knockout-induced betatron growth scales with $V_{RF}$ and ramp rate $\alpha$. It validates two mitigation strategies at ISIS: local cancellation with three cavities and global cancellation with symmetrically placed cavities, finding that local cancellation eliminates kicks within a turn but may impact acceleration, while global cancellation provides robust suppression of knockout-driven oscillations without compromising acceleration. The results support global cancellation as a viable path for high-intensity FFAs and future spallation neutron sources, expanding the operational knockout-free frequency range through symmetry and careful cavity placement.

Abstract

Beam stacking allows a Fixed Field alternating gradient Accelerator (FFA) to increase the extracted beam current whilst also allowing for a flexible time structure making FFAs a promising candidate for future spallation neutron sources and high beam intensity applications. For successful beam stacking, beam loss caused by RF knockout must be avoided. RF knockout can occur during beam stacking because of the finite dispersion function at the RF cavity location, which is unavoidable in a scaling FFA. In this work, the RF knockout resonance is characterised and through a series of experiments at the ISIS Neutron and Muon Source, we show that it is possible to suppress the loss from RF knockout.

Figures (14)

• Figure 1: Shows an example beam stacking RF programme with linear RF ramps. At the end of this programme, two coasting beams will have been stacked at the extraction orbit.
• Figure 2: A diagram of the fundamental (harmonic 2) RF cavity positions in the ISIS ring, the superperiods are numbered from $0$ to $9$. Each cavity is located at the same point in the superperiod.
• Figure 3: A diagram showing how the displacements from RF knockout are cancelled in a single turn using 3 successive cavities. $a_1, a_2$ and $a_3$ are the displacements at each cavity, $\nu_1$ and $\nu_2$ is the phase advance between the cavities.
• Figure 4: An example radio frequency cavity programme used to study RF knockout at ISIS. In this example the cavity frequency ramps from 1.42MHz to 1.96MHz or $2.1$ to $2.9$ times the coasting beam revolution frequency. The RF knockout conditions ($n=2$ and $n=7$) in this frequency range are indicated by the dashed lines.
• Figure 5: Beam current showing loss resulting from two RF knockout resonances.