Standing wave model of regenerative beam breakup in recirculating electron accelerators

doi:10.1016/0167-5087(83)90057-1

Nuclear Instruments and Methods in Physics Research

Volume 204, Issues 2–3, 1 January 1983, Pages 269-284

https://doi.org/10.1016/0167-5087(83)90057-1 Get rights and content

Abstract

This work is based on a standing wave theory of regenerative beam breakup in recirculating accelerators. Experiments performed at the Stanford superconducting recyclotron confirm the validity of this theory for two pass beam breakup. The theory is extended to multiple passes. Methods are discussed for estimating the values of field integrals of hybrid structure modes and beam transfer matrix elements for typical recirculation systems. Predictions are made for the beam breakup starting currents in various proposed accelerators and these are summarized by approximate formulae.

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Cited by (16)

Further studies on beam breakup growth reduction by cavity cross-couplings in recirculating accelerators: effects of long pulse length and multiturn recirculation
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Cavity cross-coupling was recently found to reduce beam breakup (BBU) growth in a recirculating accelerator known as the Spiral Line Induction Accelerator (SLIA). Here, we extend the analyses in two respects: long beam pulse lengths and a SLIA upgrade geometry which accelerates a 10 kA, 35 ns beam to 25 MeV via a 70 cavity, 7 turn recirculation.
We found that when the beam pulse length τ exceeds the beam's transit time τ′ between cross-coupled cavities. BBU growth may be worsened as a result of the cross-couplings among cavities. This situation is not unlike other long pulse recirculating accelerators where beam recirculation leads to beam breakup of a regenative type. Thus, the advantage of BBU reduction by cavity cross-coupling is restricted primarily to beams with τ<τ′, a condition envisioned for all SLIA geometries.
For the 70 gap, 7 turn SLIA upgrade, we found that cavity cross-coupling may reduce BBU growth up to factors of a thousand when the quality factor Q of the deflecting modes are relatively high (like 100). In these high Q cases, the amount of growth reduction depends on the arrangement and sequence of beam recirculation. For Q⪅20, BBU growth reduction by factors of hundreds is observed, but this reduction is insensitive to the sequence of beam recirculation. The above conclusions were based on simple models of cavity coupling that have been used in conventional microwave literature. Not addressed is the detail design consideration that leads to the desired degree of cavity coupling.
The polytron as a cw electron accelerator in the 10 GeV range
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This article is concerned with a generalized microtron, characterized essentially by the number of magnet pairs in its bending system. It is shown that the most serious physical energy limit of the microtron, emittance growth due to synchrotron radiation, may be overcome if this number is raised essentially above what has been considered in the past. The main properties of such “polytrons” are investigated and several design examples for 15 GeV output energy are discussed.
Analyse de la stabilite de faisceau dans un accelerateur lineaire avec passages multiples en prenant en compte les effets de toutes les cavites
1987, Nuclear Inst. and Methods in Physics Research, A
The interaction of a beam with the deflecting modes of the cavities can make it unstable when the energy transferred to the mode is greater than the power lost in the walls. In a single cavity, the mechanism of the regenerative beam breakup has been clearly described. In the case of multiple passes the instability appears at a level of current in general much lower and is indeed the most severe limitation. The current threshold was evaluated earlier either in the impulse approximation or considering only one cavity where the mode is supposed to be excited ignoring the other cavities. The purpose of this paper is to take into account the effects of all the cavities whose deflecting mode frequencies coincide or overlap. The analysis is based upon the theory of the stability of the feedback systems and a simulation code in the time domain confirms the results. The only restrictive assumptions are the following: the displacement of the beam is supposed not to vary inside a cavity and the structure of bunched beams is neglected. A similar feedback analysis involving discrete-time systems which takes into account the bunched structure of the beam showed that the values of the BBU currents are exactly the same if the frequency of the deflecting mode does not coincide with the harmonics of the repetition frequency of the bunches [14].
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Filling pattern dependence of regenerative beam breakup instability in energy recovery linacs
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^∗∗: Present address: Lawrence Berkeley Laboratory, Building 88, Berkeley, CA 94720, U.S.A.

⁺: Present address: University of California San Francisco, Physics Research Laboratory, 460 Carlton Court, South San Francisco, CA 94080, U.S.A.

⁺⁺: Present address: University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A.

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Standing wave model of regenerative beam breakup in recirculating electron accelerators

Abstract

Nucl. Instr. and Meth.

IEEE Trans. Nucl. Sci. NS-26

IEEE Trans. Nucl. Sci. NS-26

Argonne National Laboratory, ANL-PHY-79-2

IEEE Trans. Nucl. Sci. NS-28

IEEE Trans. Nucl. Sci. NS-22

HEPL 869