A Note on the Amplitude of Betatron Oscillations
- Univ. of Michigan, Ann Arbor, MI (United States); Midwestern Universities Research Association (MURA), Urbana, IL (United States)
H. R. Crane has proposed that certain resonance orbits in a strong focussing synchrotron with non-linearities might be stable and that particle paths might lie close to and oscillate about these orbits. The most stable orbits might then be those where the betatron wavelength is an integral number of magnet periods. In the case of either this machine or a near-perfect linear strong focussing machine, the amplitudes of betatron oscillation would depend largely on injection conditions. Courant and Snyder (EDC/HSS-1) (referred to hereafter as C and S) consider the amplitude of oscillations resulting from an error in injection angle of particles injected at the equilibrium radius. The justification for this treatment is that the diameter of beam spots from Van de Graaf's and linear accelerators can be made small relative to the aperture of projected strong focussing machines, while the angular divergence of the beam is still of the order of .001 radians.
- Research Organization:
- Univ. of Michigan, Ann Arbor, MI (United States); Midwestern Universities Research Association (MURA), Urbana, IL (United States)
- Sponsoring Organization:
- US Atomic Energy Commission (AEC)
- NSA Number:
- NSA-11-003113
- OSTI ID:
- 4336516
- Report Number(s):
- MURA--13; MAC-LWJ-1
- Country of Publication:
- United States
- Language:
- English
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