Antoine Cerfon, CIMS
Vortex Dynamics in Cyclotrons

Abstract: Cyclotrons are compact particle accelerators that are used on a regular basis for fundamental research in nuclear physics, for cancer treatment, and for radioisotope production. New applications have recently emerged that require cyclotrons to accelerate very intense beams of charged particles. At these high intensities, electrostatic interactions between the particles have a significant effect on the beam dynamics, and the beam behaves like a plasma. This new regime is poorly understood, and direct numerical simulations are computationally costly.

In this talk, we start from the Vlasov equation for the charged particles and use an asymptotic analysis to derive simple fluid equations describing beam dynamics in cyclotrons. Remarkably, these equations are formally identical to the two-dimensional Euler equations for a fluid of uniform density. This analogy explains several results observed in Particle-In-Cell simulations and experiments. It also allows us to make new conjectures regarding the stability of beams.