Vortex dynamics and shear layer instability in high intensity cyclotrons

TL;DR

This paper models high intensity cyclotron beam dynamics using fluid mechanics, revealing that beam breakup results from classical shear flow instabilities, and offers scaling laws and predictions for nonlinear evolution.

Contribution

It introduces a fluid dynamics analogy for cyclotron beam behavior, providing new insights into beam instabilities and their nonlinear development.

Findings

Beam breakup caused by shear flow instability.

Scaling laws for instability growth.

Predictions for nonlinear beam evolution.

Abstract

We show that the space charge dynamics of high intensity beams in the plane perpendicular to the magnetic field in cyclotrons is described by the two-dimensional Euler equations for an incompressible fluid. This analogy with fluid dynamics gives a unified and intuitive framework to explain the beam spiraling and beam break up behavior observed in experiments and in simulations. In particular, we demonstrate that beam break up is the result of a classical instability occurring in fluids subject to a sheared flow. We give scaling laws for the instability and predict the nonlinear evolution of beams subject to it. Our work suggests that cyclotrons may be uniquely suited for the experimental study of shear layers and vortex distributions that are not achievable in Penning-Malmberg traps.