U.S. Particle Accelerator School

U.S. Particle Accelerator School

Education in Beam Physics and Accelerator Technology

Cornell University

Microwaves for Accelerator Engineers and Physicists

James Sebek, SSRL/SLAC

**Purpose and Audience **

The purpose of this course is to teach the fundamentals of microwave physics and engineering, emphasizing the applications to accelerators. The target audience includes practicing electrical engineers and physicists, as well as students in those fields, who want to study the design of RF structures and systems for accelerators and to understand the interaction of the beam with those structures. The level of the course will be at an elementary graduate level, but should be accessible to advanced undergraduates in the field.* *

**Prerequisites
**The student should be proficient in vector calculus (gradient, divergence, curl, etc.) at the level of Vector Calculus by Marsden and Tromba and have an undergraduate knowledge of electromagnetism at the level of Introduction to Electrodynamics by David J. Griffiths, or Fields and Waves in Communication Electronics, by Ramo, Whinnery, and Van Duzer.

**Objectives **

An accelerator or storage ring requires an external RF system to supply energy to the particle beam; the beam, itself, also generates RF fields as it travels through the accelerator. One needs a solid knowledge of the electromagnetic theory of fields and waves to understand either of these topics. An accelerator microwave engineering course covers microwave theory, concentrating on its applications to the components of a typical high power accelerator system, including waveguides, cavities, klystrons, circulators, couplers, etc. A physics course concerning RF in accelerators covers subjects such as beam-generated fields, beam impedances, wakefields, longitudinal equations of motion, and cavity-induced instabilities. The goal of this course is to treat both groups of subjects and to give the student a solid foundation upon which to build specialized knowledge in areas such as accelerator RF systems, low impedance vacuum chamber component design, and the understanding, diagnosis, and control of instabilities.

**Instructional Method **

The course will have classroom instruction for five to six hours per day, divided into morning and afternoon sessions. The majority of the classroom instruction will be lectures, but appropriate time will be devoted to review and discussion of homework. Readings, from the text and other sources, and homework problem sets will be assigned each day. These assignments are expected to be completed outside of the class sessions. A small number of the homework problems may introduce the students to some useful computer codes. For these problems, a computer lab will replace one of the classroom sessions.

**Course Content **

The course will start with a brief review of mathematical preliminaries, followed by basic electromagnetic fields and waves. The engineering theory will be developed describing the properties of passive devices, such as transmission lines, waveguides, cavity resonators, couplers, and circulators. Applications such as tuning, matching, and coupling power into and out of these devices will be discussed. Periodic structures will be discussed in order to introduce linacs. The operation of a klystron will be discussed. The physics theory will develop the field distributions created by the beams and the impedance generated by the structures and walls in the vacuum chamber. Applications geared toward the design of low impedance vacuum chamber components and beam pickups will be discussed. The longitudinal equations of motion and synchrotron motion will be developed, followed by a discussion of wakefields and beam impedance. An application of these concepts will discuss longitudinal instabilities and present techniques for characterizing and reducing them.

**Reading Requirements **

*(to be provided by the USPAS)* "Foundations for Microwave Engineering", Second Edition, by Robert E. Collin, Wiley-IEEE Press, 2000. Supplementary notes and readings will be provided.

**Credit Requirements **

Homework assignments will be given each day. Students are encouraged to discuss the homework among themselves in order to better learn the material, but are expected to work out and complete their solutions independently. Homework will count for 70% of the course grade. A take-home final exam will count for the other 30%.