Paper  Title  Page 

WE2PB02  Vlasov Equation Approach to Space Charge Effects in Isochronous Machines  310 


Starting from the collisionless Vlasov equation, we derive two simple coupled twodimensional fluid equations describing the radiallongitudinal 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 3D ParticleInCell 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 WE2PB02 [1.166 MB]  