Transverse-Longitudinal Coupling by Space Charge in Cyclotrons

TL;DR

This paper introduces a method to analyze and compute the effects of space charge on beam dynamics in cyclotrons, focusing on transverse-longitudinal coupling and providing numerical tools for practical applications.

Contribution

It derives first-order equations for transverse-longitudinal coupling in azimuthally symmetric cyclotrons and presents a numerical algorithm for AVF cyclotrons, validated against existing codes.

Findings

Eigenellipsoid of the beam is calculated.

Transfer matrix is block-diagonalized.

Results are validated with TRANSPORT.

Abstract

A method is presented that enables to compute the parameters of matched beams with space charge in cyclotrons with emphasis on the effect of the transverse-longitudinal coupling. Equations describing the transverse-longitudinal coupling and corresponding tune-shifts in first order are derived for the model of an azimuthally symmetric cyclotron. The eigenellipsoid of the beam is calculated and the transfer matrix is transformed into block-diagonal form. The influence of the slope of the phase curve on the transverse-longitudinal coupling is accounted for. The results are generalized and numerical procedures for the case of an AVF cyclotron are presented. The algorithm is applied to the PSI Injector II and Ring cyclotron and the results are compared to TRANSPORT.