U.S. Particle Accelerator School

U.S. Particle Accelerator School

Education in Beam Physics and Accelerator Technology

Old Dominion University

Microwave Electron Accelerators

David Whittum, ViewRay, Inc; Rich Kowalczyk, L3 Technologies, Inc

**Purpose and Audience **

This course will introduce microwave linear accelerators starting from Maxwell’s equations and the Lorentz force law. Students are typically senior undergraduates or graduate students in physics, applied physics, or electrical engineering. Auditors have included accelerator systems operators and technicians, mechanical and manufacturing engineers. Students should have completed freshman calculus and should be comfortable with basic concepts of RLC circuits.

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Prerequisites
**Algebra, trigonometry, calculus, undergraduate electrodynamics and mechanics.

It is the responsibility of the student to ensure that he or she meets the course prerequisites or has equivalent experience.

Students will learn how to describe the behavior of an accelerator in the time or frequency domain, and to explain the theory behind cold-test measurements, and observations with beam. They will use CAD tools to design a structure including the input coupler. They will become familiar with the practical design trade-offs and the manufacturing and operational aspects of normal conducting microwave accelerators. They will be able to analyze their accelerator application and describe it in conventional terms.

There are two lectures each morning with a 20-minute break in between. After lunch there will be a computer lab. On some afternoons there will be a homework review session or a special topic lecture. An important resource for this course is the (optional) evening homework and study session, where students usually work together on problems. Instructors will come by a couple of times during the evening to help with homeworks if needed. All homeworks and exams are open book, and collaboration is encouraged except for the final exam, where the honor system is in force.

Structure modeling and design are developed from an elementary point of view, with computer lab exercises for illustration. Topics include quality factor, [R/Q], shunt impedance, loss factor, VSWR, Slater's theorem, external coupling, cell-to-cell coupling, Brillouin curve, tuning errors, tuning, tolerances, field-symmetry. The behavior of standing-wave and travelling-wave structures is analyzed on and off resonance, in cold test, and in operation with beam loading. Additional topics influencing linac design will be selected based on student interest and may include rf systems, instrumentation, beam dynamics, wakefields. It is important for students to fill out the course questionnaire available on the web to express their particular interests and applications. Illustrations and exercises will be drawn from practical problems in industrial, medical and high energy physics applications.

References may be found at the course URL. Reading will consist of two sets of notes that will be distributed to enrolled students beforehand. (1) Introduction to Electrodynamics for Microwave Linear Accelerators (SLAC-PUB-7802) and (2) Introduction to Microwave Linacs (SLAC-PUB-8026). The first chapter of (1) should be read before the course. Lectures will proceed more along the intuitive lines of (2), albeit with mathematical forays as needed in the style of (1). A detailed lecture schedule will be posted at the course URL.

Credit is based on exercises given in seven homeworks, one midterm, and one final exam. Each part of each exercise carries a weight of at least one point, and more difficult exercises will carry up to 4 points. Points for the course usually total about 150, with typically 20 points each for midterm and final. Extra credit opportunities will appear frequently.

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Old Dominion University course number:** Phys 865, "Linear Accelerators"