Multiparticle simulation of adiabatic excitation of longitudinal parametric resonances

K A Brown,W Fischer,T Roser,M Bai

doi:10.1103/physrevstab.4.014001

Abstract

In order to further understand phenomena observed during studies of adiabatic excitation of longitudinal bunch shape oscillations [M. Bai et al., Phys. Rev. ST Accel. Beams 3, 064001 (2000)], we have developed a simulation using a one-turn map. In this report we will present the physical foundations for the simulation and the methods used in the simulator. We will present simulation results using parameters of actual experiments, along with the corresponding experimental results.

Highlights

In Ref. [1] it was shown that, by exciting longitudinal bunch shape oscillations adiabatically, longitudinal emittance can be preserved and the driven bunch shape oscillations can be maintained for a long period
The physical foundations for the simulation are given in the discrete synchrotron equations for a stationary bucket, in which the amplitude of the rf voltage is modulated
With loop gains of 17 dB and greater the system does a very good job at compensation, reducing to better than 1% any beam loading distortion [5,6]

Summary

INTRODUCTION

In Ref. [1] it was shown that, by exciting longitudinal bunch shape oscillations adiabatically, longitudinal emittance can be preserved and the driven bunch shape oscillations can be maintained for a long period. The physical foundations for the simulation are given in the discrete synchrotron equations for a stationary bucket, in which the amplitude of the rf voltage is modulated. 1 g2 is the phase slip factor, ns is the synchrotron tune at zero amplitude without modulation, and p is the parqticle momentum. The unstable fixed point at the origin and the two stable fixed points are clearly visible. The modulation tune nm ෇ 0.000 87 is below but close to the resonance interval. When the amplitude of the modulation is large, the approximations of the Hamiltonian (3) are no longer valid, it still provides qualitative guidance of the particle. To study more extreme conditions we return to the Hamiltonian (2) and track individual particles

SIMULATION OF LONGITUDINAL MOTION WITH MODULATED FOCUSING STRENGTH

COMPARING SIMULATION RESULTS TO EXPERIMENTAL RESULTS

SUMMARY