Introduction to Electrodynamics for Microwave Linear Accelerators

Abstract

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.

High-power radio frequency pulse generation and extration based on wakefield excited by an intense charged particle beam in dielectric-loaded waveguides.

“…In the presence of an infinitely long charged particle bunch train with bunch spacing T b and bunch charge q, a second term representing the power increase per unit length due to the wakefield must be added to Equation 2.11 (Whittum 1998)…”

Single-mode beam-cavity interaction in relativistic klystrons

“…We define a modal current density, J ऋ घtङ, by computing the overlap of the time-dependent current density with the spatial profile of the mode electric field, as in (2).…”

Introduction to Microwave Linacs

“…We m a y express the time-averaged balance of forces as . A more precise calculation provides the coecient 1.57 [1].…”

“…2 we start with the problem of acceleration and develop the logic behind the multi-cell structure, and the electromagnetic elds it can support. Detailed calculations aren't really necessary here, but may be found in [1]. Appreciating the character of the elds we m a y provide for acceleration, we determine what manner of beam may benet from them.…”