John M. Jowett

Introductory statistical mechanics for electron storage rings

These lectures concentrate on statistical phenomena in electron storage rings. A stored electron beam is a dissipative, fluctuating system far from equilibrium whose mathematical description can be based upon non−equilibrium statistical mechanics. Stochastic differential equations are used to describe the quantum fluctuations of synchrotron radiation which is the main cause of randomness in electron dynamics. Fluctuating radiation reaction forces can be described via stochastic terms in Hamilton’s equations of motion. Normal modes of particle motion, radiation damping effects, quantum diffusion in single−particle phase space are all discussed in this statistical formalism. (AIP)

Electron dynamics with radiation and nonlinear wigglers

The physics of electron motion in storage rings is described by supplementing the Hamiltonian equations of motion with fluctuating radiation reaction forces to describe the effects of synchrotron radiation. This leads to a description of radiation damping and quantum diffusion in single-particle phase-space by means of Fokker-Planck equations. For practical purposes, most storage rings remain in the regime of linear damping and diffusion; this is discussed in some detail with examples, concentrating on longitudinal phase space. However special devices such as nonlinear wigglers may permit the new generation of very large rings to go beyond this into regimes of nonlinear damping. It is shown how a special combined-function wiggler can be used to modify the energy distribution and current profile of electron bunches.

Does the transition to chaos determine the dynamic aperture

We review the important notion of the dynamic aperture of a storage ring with emphasis on its relation to general ideas of dynamical instability, notably the transition to chaos. Practical approaches to the problem are compared. We suggest a somewhat novel quantitative guide to the old problem of choosing machine tunes based on a heuristic blend of KAM theory and resonance selection rules.