Effects of Radial Straight Sections on the Betatron Oscillation Frequencies in a Spiral Sector FFAG Accelerator

Technical Report · Tue Oct 21 04:00:00 EDT 1958

DOI:https://doi.org/10.2172/4259157· OSTI ID:4259157

Morton, Phil L. ^[1]

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1. Midwestern Universities Research Association (MURA), Madison, WI (United States)

It is desirable to introduce radial straight sections into spiral sector accelerators in order to accommodate accelerating cavities of reasonable design and magnet windings. Such straight sections make the accelerator non-scaling, i.e., in general the betatron oscillation frequencies vary with energy and resonances may be crossed. These effects were investigated analytically in the linear approximation. The equations of motion are now functions not only of the accelerator parameters but also of the geometry of the radial straight sections and of the equilibrium orbit radius. If the number of spirals per revolution is N and the number of radial straight sections per revolution is p, then all harmonic numbers n < 1/2 q, where q equals p divided by the greatest common divisor of p and N, do not contribute to the change of betatron oscillation frequencies with energy. since the contributions of a harmonic to the frequencies decrease as the harmonic number increases, it appears that the variation of betatron oscillation frequencies with energy can be kept within acceptable limits.

• Research Organization: Midwestern Universities Research Association (MURA), Madison, WI (United States)
• Sponsoring Organization: US Atomic Energy Commission (AEC)
• NSA Number: NSA-13-004773
• OSTI ID: 4259157
• Report Number(s): MURA--434
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
ACCELERATORS
BETATRONS
CAVITY RESONATORS
COILS
CONFIGURATION
ENERGY
EQUATIONS
FREQUENCY
MAGNETS
MICROWAVES
MOTION
NUMERICALS
OPTICAL SYSTEMS
ORBITS
OSCILLATIONS
PLANNING
RADIO WAVES
RESONANCE
SPIRAL SECTOR ACCELERATORS
VARIATIONS