A study of some coherent electromagnetic effects in high-current particle accelerators
- Univ. of California, Berkeley, CA (United States)
Two coherent effects by which particles circulating in an accelerator may lose energy are considered. The vacuum tark is assumed to be a toroid with rectangular cross section, highly conducting walls, a major radius very much larger than its cross sectional dimensions, and no discontinuities or windows. The beam configuration is assumed to be given and to be unaffected by the energy losses. The beam is assumed to have a negligible crosssectional area. Expressions for the electromagnetic fields arising from the given current and charge distribution are presented in three different forms. The first loss mechanism considered is the drugging of image charges through the walls of finlte conductivity. This is found to be a small effect for circulating currents of the order of 1 amp. A proof is developed that in such a vacuum tank there exist eigenmodes with phase velocities in the azimuthal direction that are less than the velocity of light. It is then possible for a relativistic beam to be in resonance with such a mode. It is shown that the excitation of these modes leads to a negligible energy loss in the types of vacuum chambers considered. The interaction of the beam with a radiofrequency cavity that provides the accelerating mechanism of the machine is discussed. The passage of the beam induces a back voltage on the cavity. The total voltage is the sum of the back voltage and the externally applied voltage. A Hamiltonian for synchrotron motion is employed that makes possible the simultaneous solution of Maxwell's equations and the Vlasov equation, so that a self-consistent distribution of particles in synchrotron phase space is determined. The induced voltage is of the order of magnitude of the product of the total circulating current in the accelerator and the shunt impedance of the nf cavity. It has the net effect of reducing the total cavity voltage and shifting its phase relative to the applied voltage. The stable phase angle must then be increased for the particles to remain in phase with the accelerating radio frequency. The decrease in total voltage and increase in stable phase angle result in a decrease in stable phase space available for acceleration. It is shown that the consequences of the induced voltage may be alleviated by increasing the voltage applied to the cavity.
- Research Organization:
- Univ. of California, Berkeley, CA (United States)
- Sponsoring Organization:
- US Atomic Energy Commission (AEC)
- DOE Contract Number:
- W-7405-ENG-48
- NSA Number:
- NSA-14-023648
- OSTI ID:
- 4148818
- Report Number(s):
- UCRL-9124
- Resource Relation:
- Other Information: Orig. Receipt Date: 31-DEC-60
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ACCELERATORS
BEAMS
BOLTZMANN-VLASOV EQUATION
CIRCUITS
CONFIGURATION
CURRENTS
DISTRIBUTION
EFFICIENCY
ELECTRIC CHARGES
ELECTRIC CONDUCTIVITY
ELECTRIC FIELDS
ELECTRIC POTENTIAL
ELECTROMAGNETIC FIELDS
ELECTROMAGNETIC WAVES
ELECTROMAGNETISM
ELEMENTARY PARTICLES
ENERGY
EQUATIONS
ERRORS
EXCITATION
FAILURES
FREQUENCY
IMAGES
INDUCTION
LOSSES
MATHEMATICS
MAXWELL EQUATIONS
MICROWAVES
MOTION
OPERATION
OSCILLATIONS
PHASE SPACE
RELATIVITY THEORY
RESISTORS
RESONANCE
SPECTRAL SHIFT
STABILITY
SYNCHROTRONS
VACUUM
VARIATIONS
VELOCITY
VESSELS
WAVEGUIDES
WINDOWS