Parametric mapping of the efficiency$\unicode{x2013}$instability relation in plasma-wakefield accelerators

TL;DR

This study uses particle-in-cell simulations to explore the efficiency–instability relation in plasma-wakefield accelerators, identifying conditions that minimize beam-breakup instability and proposing methods to dampen oscillations.

Contribution

It provides a parametric mapping of the efficiency–instability relation and demonstrates how initial energy spread and ion motion can reduce instability growth.

Findings

The efficiency–instability relation acts as a lower limit on instability strength.

Only specific normalized wake radii and fields reach the minimal instability.

Initial energy spread and ion motion can dampen the instability growth.

Abstract

High efficiency is essential for plasma-wakefield accelerators to be a cost-effective alternative in high-power applications, such as a linear collider. However, in a plasma-wakefield accelerator the beam-breakup instability can be seeded by a transverse offset between the driver and trailing bunch. This instability, which rapidly increases the oscillation amplitude of the trailing bunch, grows with higher power-transfer efficiency from the driver to the trailing bunch [V. Lebedev et al., Phys. Rev. Accel. Beams 21, 059901 (2018)]. In this paper, we use particle-in-cell simulations to investigate the efficiency$\unicode{x2013}$instability relation that constrains the driver-to-trailing-bunch power-transfer efficiency in beam-driven plasma accelerators. We test the relation using a grid of simulations across all parameters that affect the beam-breakup instability, assuming a uniform accelerating field (optimal beam loading) and no ion motion. We find that the previously proposed efficiency$\unicode{x2013}$instability relation represents a lower limit on the strength of the instability for a given efficiency. For each normalized wake radius, only a certain accelerating field reaches this lowest value of the transverse instability; deviating from this point can increase the growth rate by several orders of magnitude. Lastly, we highlight how the oscillation-amplitude growth of the trailing bunch can be reduced or damped with an initial uncorrelated energy spread and the presence of ion motion.