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abstract:
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In one mode of operation of an electron ring accelerator (ERA), at the end of compression rings are slowly moved through the radial integral betatron resonance Q_r=1. Although the coherent radial oscillation frequency of the ring as a whole remains below unity, the oscillation frequencies of individual electron are (incoherently) caused to pass through the resonance because of the additional focusing from ions trapped in the ring. In this paper the effect of field errors on ring major and minor radii is evaluated-theoretically-for the cases in which the spread in the square of the electron oscillation frequency ( Delta(2)) is (a) much smaller and (b) much larger than the contribution to the square of the oscillation frequency from the ions ( Lambda(2)).
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