Landau damping of transverse head-tail instabilities with a pulsed electron lens in hadron synchrotrons

TL;DR

This paper analyzes how pulsed electron lenses can mitigate head-tail instabilities in hadron synchrotrons by inducing tune spreads that lead to Landau damping, supported by analytical models and particle tracking simulations.

Contribution

It provides a detailed Vlasov formalism for combined longitudinal and transverse detuning effects of pulsed electron lenses on beam stability.

Findings

Pulsed electron lenses create tune spreads with static and dynamic components.

The static component induces Landau damping, enhancing stability.

The dynamic component modifies effective impedance, affecting nonzero head-tail modes.

Abstract

A pulsed electron lens produces a betatron tune shift along a hadron bunch as a function of the longitudinal coordinates, which is a longitudinal detuning. An example of transverse detuning are the tune shifts due to octupole magnets. This paper considers a pulsed electron lens as a measure to mitigate the head-tail instabilities. Using a detailed analytical description within a Vlasov formalism, the coherent properties of the longitudinal and transverse detuning are presented. The analytical predictions are compared with the results of the particle tracking simulations. A pulsed electron lens is demonstrated to be a source of tune spread with two components: a static one, leading to Landau damping; and a dynamic one, leading to an effective impedance modification, which we demonstrate analytically and in our particle tracking simulations. The effective impedance modification can be important for beam stability due to devices causing a longitudinal detuning, especially for nonzero head-tail modes. The Vlasov formalism is extended to include the combination of longitudinal and transverse detuning. As a possible application at the SIS100 heavy-ion synchrotron (FAIR at GSI Darmstadt, Germany), a combination of a pulsed electron lens with octupole magnets is considered.