@inproceedings{be3fc23494b04054976f9e1a6ecbe0e7,

title = "Vlasov equation approach to space charge effects in isochronous machines",

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.",

author = "Cerfon, {A. J.} and O. B{\"u}hler and J. Guadagni and Parra, {F. I.} and Freidberg, {J. P.}",

year = "2014",

month = mar,

language = "English (US)",

series = "CYCLOTRONS 2013 - Proceedings of the 20th International Conference on Cyclotrons and their Applications",

publisher = "Joint Accelerator Conferences Website (JACoW)",

pages = "310--314",

booktitle = "CYCLOTRONS 2013 - Proceedings of the 20th International Conference on Cyclotrons and their Applications",

note = "20th International Conference on Cyclotrons and their Applications, CYCLOTRONS 2013 ; Conference date: 16-09-2013 Through 20-09-2013",

}