Theory of the alternating-gradient synchrotron
- Brookhaven National Laboratory, Upton, New York (United States)
The equations of motion of the particles in a synchrotron in which the field gradient index n=-(r/B){partial_derivative}B/{partial_derivative}r varies along the equilibrium orbit are examined on the basis of the linear approximation. It is shown that if n alternates rapidly between large positive and large negative values, the stability of both radial and vertical oscillations can be greatly increased compared to conventional accelerators in which n is azimuthally constant and must lie between 0 and 1. Thus aperture requirements are reduced. For practical designs, the improvement is limited by the effects of constructional errors: these lead to resonance excitation of oscillations and consequent instability if 2v{sub x} or 2v{sub z} or v{sub x}+v{sub z} is integral, where v{sub x} and v{sub z} are the frequencies of horizontal and vertical betatron oscillations, measured in units of the frequency of revolution. The mechanism of phase stability is essentially the same as in a conventional synchrotron, but the radial amplitude of synchrotron oscillations is reduced substantially. Furthermore, at a ''transition energy'' E{sub 1}{approx_equal}v{sub x}Mc{sup 2} the stable and unstable equilibrium phases exchange roles, necessitating a jump in the phase of the radiofrequency accelerating voltage. Calculations indicate that the manner in which this jump is performed is not very critical. (c) 2000 Academic Press, Inc.
- OSTI ID:
- 20216983
- Journal Information:
- Annals of Physics (New York), Vol. 281, Issue 1; Other Information: PBD: 10 Apr 2000; ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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