Self-consistent field theory of plasma betatrons

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Abstract
A quasi-stationary, self-consistent field theory is developed for the space-charge neutralized plasma betatron. It is found that the equilibrium orbit shrinks in the first phase of the acceleration process, and this sets a limit to the number of particles which can be accelerated. Exceeding this limit the beam collapses. During the acceleration process, the beam passes through a betatron damping dominated and a self-pinching phase, and finally enters the relativistic regime. Limits where these phases set in, as well as the beam behaviour in different phases is given.