Introduction to Electrodynamics for Microwave Linear Accelerators

This collection of notes and exercises is intended as a workbook to introduce the principles of microwave linear accelerators, starting with the underlying foundation in electrodynamics. We review Maxwell's equations, the Lorentz force law, and the behavior of fields near a conducting boundary. We go on to develop the principles of microwave electronics, including waveguide modes, circuit equivalence, shunt admittance of an iris, and voltage standing-wave ratio. We construct an elementary example of a waveguide coupled to a cavity, and examine its behavior during transient filling of the cavity, and in steady-state. We go on to examine a periodic line. We then turn to examine the problem of acceleration in detail, studying first the properties of a single cavity-waveguide-beam system and developing the notions of wall Q, external Q, [R/Q], shunt impedance, and transformer ratio. We examine the behavior of such a system on and off resonance, on the bench, and under conditions of transient and steady-state beam-loading. This work provides the foundation for the commonly employed circuit equivalents and the basic scalings for such systems. Following this we examine the coupling of two cavities, powered by a single feed, and go on to consider structures constructed from multiple coupled cavities. The basic scalings for constant impedance and constant gradient travelling-wave structures are set down, including features of steady-state beamloading, and the coupled-circuit model. Effects of uniform and random detuning are derived. These notes conclude with a brief outline of some problems of current interest in accelerator research.