Computation and Numerical Simulation of Focused Undulator Radiation for Optical Stochastic Cooling

TL;DR

This paper develops formulas for calculating the corrective kick in optical stochastic cooling and validates them through numerical simulations, advancing the understanding of beam cooling at optical frequencies.

Contribution

It introduces new analytical formulas for the corrective kick in OSC and validates them with wave-optics simulations, enhancing the precision of modeling in optical stochastic cooling.

Findings

Formulas for the corrective kick in OSC are derived.

Validation of formulas against wave-optics simulations confirms their accuracy.

Enhanced understanding of beam cooling mechanisms at optical frequencies.

Abstract

Optical stochastic cooling (OSC) is a promising technique for the cooling of dense particle beams. Its operation at optical frequencies enables obtaining a much larger bandwidth compared to the wellknown microwave-based stochastic cooling. In the OSC undulator radiation generated by a particle in an upstream \pickup" undulator is amplified and focused at the location of a downstream "kicker" undulator. Inside the kicker, a particle interacts with its own radiation field from the pickup. The resulting interaction produces a longitudinal kick with its value depending on the particles momentum which, when correctly phased, yields to longitudinal cooling. The horizontal cooling is achieved by introducing a coupling between longitudinal and horizontal degrees of freedom. Vertical cooling is achieved by coupling between horizontal and vertical motions in the ring. In this paper, we present formulae for computation of the corrective kick and validate them against numerical simulations performed using a wave-optics computer program.