Theory of the AlternatingGradient Synchrotron
Abstract
The equations of motion of the particles in a synchrotron in which the field gradient indexn=(r/B) ∂B/∂rvaries 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 2ν_{x} or 2ν_{z} or ν_{x}+ν_{z} is integral, where ν_{x} and ν_{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_{1}≈ν_{x}Mc^{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.
 Publication:

Annals of Physics
 Pub Date:
 April 2000
 DOI:
 10.1006/aphy.2000.6012
 Bibcode:
 2000AnPhy.281..360C