Open AccessCROSSING OF AN INCOHERENT INTEGRAL RESONANCE IN THE ELECTRON RING ACCELERATOR
Author(s) -
C. Pellegrini
Publication year - 1970
Language(s) - English
Resource type - Reports
DOI - 10.2172/938547
Subject(s) - betatron , oscillation (cell signaling) , resonance (particle physics) , physics , ring (chemistry) , electron , atomic physics , lambda , ion , square (algebra) , nuclear physics , chemistry , mathematics , quantum mechanics , geometry , biochemistry , organic chemistry
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{sub r} = 1. Although the coherent radial oscillation frequency of the ring as a whole remains below unit, 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}{sup 2}) is (a) much larger and (b) much smaller than the contribution to the square of the oscillation frequency from the ions ({Lambda}{sup 2}). It is shown that for the ERA, where case (b) applies, the increase in ring minor dimensions, for given field errors and rate of resonance crossing, is less than in case (a) by a factor of ({Delta}/{Lambda}){sup 2}. Numerical examples show that the degradation of ring quality in case (b) should, with suitable attention to the design and construction of the ERA apparatus, be acceptably small