Separatrix formalism for superconducting linear accelerators

Yu. Senichev; A. Bogdanov; R. Maier

doi:10.1103/PhysRevSTAB.6.124001

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Separatrix formalism for superconducting linear accelerators

Yu. Senichev, A. Bogdanov, R. Maier

DOI 10.1103/PhysRevSTAB.6.124001 · Physical Review Special Topics - Accelerators and Beams

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Abstract

Superconducting cavities provide high accelerating gradient in linear accelerators. However, it is desirable to have a constant geometry of the accelerating cells in order to simplify manufacturing. Such geometry leads to a nonsynchronism. A separatrix formalism has been developed for a superconducting linear accelerator based on a model of stationary separatrixes overlapping, and an effective separatrix, moving together with a quasisynchronous particle. This formalism is applied to two cases: either the phase velocity changes from cavity to cavity, or the phase velocity is constant for cavities, belonging to one family. Solving Hamiltonian equations, it is shown qualitatively and quantitatively, how the quasisynchronous phase velocity has to be adjusted either by a stepped phase velocity or by a stepped rf phasing in order to minimize the effect of nonsynchronism in the first or the second case.