Abstract
The paper investigates the stability of equilibrium orbits of charged particles in one variant of the ultrarelativistic cyclotron. The Bogoljubov-Krylov method of averaging is used to show that one of the pairs of principal equilibrium orbits, which were found in the first part of the paper, is stable while the second is unstable. The stability limit is identical with the limit of the existence of equilibrium orbits. The dependence of the frequencies of betatron oscillations on the field parameters is shown in the stability diagrams. Brief mention is made of the magnet of the variant of an ultrarelativistic cyclotron with axially scalloped equilibrium orbit.
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References
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Sedláček, Z. Stability of equilibrium orbits in isochronous ultrarelativistic cyclotron II. Czech J Phys 14, 158–166 (1964). https://doi.org/10.1007/BF01688835
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DOI: https://doi.org/10.1007/BF01688835