Formulation of electron motion in a storage ring with a betatron tune varying with time and a dipole shaker working at a constant frequency

Toshihiko Hiraiwa,Hitoshi Tanaka,Kouichi Soutome

doi:10.1103/physrevaccelbeams.24.114001

Toshihiko Hiraiwa, Hitoshi Tanaka + Show 1 more

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https://doi.org/10.1103/physrevaccelbeams.24.114001

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Abstract

In order to reduce the beam density efficiently for a safe beam abort, we analytically studied the motion of an aborted electron beam undergoing a sinusoidal kick by a beam shaker working at a constant frequency. Since the rf power is switched off, the betatron tune changes gradually with time due to chromatic effects. Chromatic aberration, together with a finite energy spread, enhances the dilution effect of the beam density, while the change in betatron tune with time causes a phase slippage that suppresses the growth of oscillation amplitude by the beam shaker. In order to treat such a situation properly, we formulated the motion of an aborted electron beam, taking into account nonlinear chromatic effects, under the adiabatic condition that the change in betatron tune is much slower than the betatron oscillation. In addition, by considering the case of a linearly varying betatron tune, it is shown that the response of an aborted electron beam can be interpreted as a superposition of waves, i.e., diffraction of waves. Our investigation not only provides a criteria for the determination of shaker's frequency for a safe beam abort but also has applications to resonance crossing phenomena.

Highlights

In an electron storage ring, the stored electron beam is usually aborted by turning off the rf power for acceleration
In order to reduce the beam density efficiently for a safe beam abort, we analytically studied the motion of an aborted electron beam undergoing a sinusoidal kick by a beam shaker working at a constant frequency
In order to treat such a situation properly, we formulated the motion of an aborted electron beam, taking into account nonlinear chromatic effects, under the adiabatic condition that the change in betatron tune is much slower than the betatron oscillation

Summary

INTRODUCTION

In an electron storage ring, the stored electron beam is usually aborted by turning off the rf power for acceleration. The second is to install graphite beam absorbers with a highmelting point and a long radiation length at dispersive sections to absorb the vertically spread electron beam These countermeasures prevent high-density beams from hitting vacuum chambers directly and ensure a safe beam abort. During the beam abort process, the betatron tune of an electron beam varies gradually due to chromatic effects as the electron beam loses its energy turn-by-turn by synchrotron radiation In this case, it is not trivial which frequency is most effective for spreading the electron beam in the phase space, and how much the beam density can be decreased.

FORMULATION OF THE ABORTED BEAM MOTION WITH A SINUSOIDAL FORCE

COMPARISON TO PARTICLE TRACKING SIMULATION

DECOHERENCE OF BETATRON MOTION

LINEARLY VARYING TUNE AND ANALOGIES TO LIGHT DIFFRACTION

SUMMARY