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Flux Diffusion and Acceleration in a High Current Modified Betatron.

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Memorandum rept.,

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An analytic and numerical scheme is developed to determine self-consistent equilibria in modified betatrons. As the beam undergoes adiabatic changes, its behavior is determined by a series of time dependent equilibria. At any time these equilibria are characterized by the number of particles in a drift P sub theta surface, and the toroidal flux through a P sub theta surface. The evolution of the drift surfaces is followed during beam acceleration and self-flux diffusion, and beam equilibria are found for various levels of flux diffusion compensation. As the beam accelerates, it reaches a certain energy at which it makes a transition from diamagnetic to paramagnetic poloidal drift. This transition is characterized by a change in topology of the P sub thetas. Depending on the change in shape at transition, the new P sub theta surface can either be confined in the liner or run into the liner. Conditions for confined orbits at the transition are given for parameters of the NRL modified betatron experiment. During flux diffusion, it is found that large adjustments in external fields are necessary to maintain equilibrium. It may be possible to overcome this difficulty by placing a set of external coils at the liner to compensate for the decaying eddy currents. When the distribution of currents in these coils mimic the surface currents exactly, no adjustments in external fields are necessary. However, beam equilibrium is very sensitive to the azimuthal error in this distribution. Author

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  • Particle Accelerators

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