Vlasov equation approach to space charge effects in isochronous machines

A. J. Cerfon, O. Bühler, J. Guadagni, F. I. Parra, J. P. Freidberg

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Starting from the collisionless Vlasov equation, we derive two simple coupled two-dimensional partial differential equations describing the radial-longitudinal beam vortex motion associated with space charge effects in isochronous cyclotrons. These equations show that the vortex motion can be intuitively understood as the nonlinear advection of the beam by the E × B velocity field, where E is the electric field due to the space charge and B is the applied magnetic field. The partial differential equations are also formally identical to the two-dimensional Euler equations for a fluid of uniform density. From this analogy, we explain why elongated beams develop spiral halos and a stable round core while round beams are always stable. Solving the coupled equations numerically, we find good agreement between our model and Particle-In-Cell simulations.

Original languageEnglish (US)
Title of host publicationCYCLOTRONS 2013 - Proceedings of the 20th International Conference on Cyclotrons and their Applications
PublisherJoint Accelerator Conferences Website (JACoW)
Pages310-314
Number of pages5
ISBN (Electronic)9783954501281
StatePublished - Mar 2014
Event20th International Conference on Cyclotrons and their Applications, CYCLOTRONS 2013 - Vancouver, Canada
Duration: Sep 16 2013Sep 20 2013

Publication series

NameCYCLOTRONS 2013 - Proceedings of the 20th International Conference on Cyclotrons and their Applications

Conference

Conference20th International Conference on Cyclotrons and their Applications, CYCLOTRONS 2013
CountryCanada
CityVancouver
Period9/16/139/20/13

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ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Cerfon, A. J., Bühler, O., Guadagni, J., Parra, F. I., & Freidberg, J. P. (2014). Vlasov equation approach to space charge effects in isochronous machines. In CYCLOTRONS 2013 - Proceedings of the 20th International Conference on Cyclotrons and their Applications (pp. 310-314). (CYCLOTRONS 2013 - Proceedings of the 20th International Conference on Cyclotrons and their Applications). Joint Accelerator Conferences Website (JACoW).