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Acceleration of an Electron Ring in a Modified Betatron with Transverse Pressure.

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Memorandum rept.,

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An analytic and numerical scheme is developed to follow the adiabatic evolution of a beam with non-zero transverse pressure in a modified betatron. These calculations are made using improvements to previous zero pressure models in regimes where, as before, the poloidal inertia is ignored. The evolution of the beam is determined as a series of time independent equilibria with pressure appearing in our fluid approach as a gradient in the fluid equations of motion. The evolution of the pressure during adiabatic acceleration is determined by kinetic theory. The series of equilibria are then characterized by the constant number of particles within a drift P sub theta surface, the conserved toroidal flux inside a P sub theta surface, and the self-consistently evaluated pressure distribution from magnetic moment conservation. As in the case of zero pressure, it is found that the beam makes a transition from diamagnetic to paramagnetic orbits when it reaches a certain energy, and that the transition manifests itself by a change in the topology of the P sub theta surfaces during acceleration. As compared to our zero pressure results, it is found that the poloidal drift of the beam is significantly faster, so that measurement of this rotation frequency is a possible diagnostic for pressure. Despite the faster drift, however, the paramagnetic transition occurs at about the same energy in both cases. Finally it is observed that the higher polodial drift frequency associated with this pressure forces the beam toward the Brillouin limit much sooner than in the cold beam case, and that contrary to simple estimates, the pressure increases rather than decreases during acceleration due to a coupling between toroidal and poloidal motion.

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  • Particle Accelerators

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