Author: Guadagni, J.V.
Paper Title Page
WE2PB02 Vlasov Equation Approach to Space Charge Effects in Isochronous Machines 310
  • A.J. Cerfon, O. Bühler, J.V. Guadagni
    Courant Institute of Mathematical Sciences, New York University, New York, USA
  • J.P. Freidberg, F.I. Parra Diaz
    MIT/PSFC, Cambridge, Massachusetts, USA
  Starting from the collisionless Vlasov equation, we derive two simple coupled two-dimensional fluid 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 ExB velocity field, where E is the electric field due to the space charge and B is the applied magnetic field. This explains why elongated beams develop spiral halos while round beams are always stable. Solving the coupled equations numerically, we find good agreement between our model and 3-D Particle-In-Cell OPAL simulations*.
* J.J. Yang, A.Adelmann, M. Humbel, M. Seidel, and T.J. Zhang, Physical Review Special Topics Accelerators and Beams 13, 062401 (2010)
slides icon Slides WE2PB02 [1.166 MB]