U.S. Particle Accelerator School

U.S. Particle Accelerator School

Education in Beam Physics and Accelerator Technology

University of California, Davis

Introduction to Low-Level Radio Frequency Systems, Technology and Applications to Particle Accelerators

John Fox, Stanford University and SLAC; Claudio Rivetta, SLAC

**Purpose and Audience**

This course is intended to bring accelerator physicists and operators, who have backgrounds in particle dynamics and general understanding of accelerator systems, to a better understanding of the functions in LLRF systems. The class is also valuable for those with RF engineering or electrical engineering backgrounds who want to better understand the interplay between the RF systems and the particle beam in an accelerator. The course will be taught at an advanced undergraduate/early graduate level.

**Prerequisites**

An undergraduate background in electromagnetics and classical mechanics. Some general familiarity with electrical engineering signal concepts such as transfer functions and signals in the time and frequency domains.

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

**Objectives**

To introduce fundamental concepts of particle interaction with RF fields for LINAC and circular accelerators. We also intend to introduce accelerator phycists to RF technology concepts and the role of low-level radio frequency systems in controlling RF fields in cavity structures. We will introduce electrical engineers to accelerator and beam dynamics. We will highlight the role of LLRF systems to stabilize fields in amplitude and phase in practical accelerator systems. We will develop a formalism to understand the limits of performance of typical systems, impacts of noise and imperfections. We endeavor to develop closer ties between physicists and engineers at national and international facilities and to use conference and workshop literature to understand this specialized topic.

**Instructional Method**

The class will use lectures, tutorial discussion sessions and computer lab exercises. The lectures will present advanced undergraduate/early graduate-level Physics and Engineering topics. The tutorial sessions will use interactive discussions between students, a teaching assistant and the instructor to highlight concepts from the lectures, answer questions, review papers from the literature and allow students to give short presentations on technical topics. The computer labs will be structured as opportunities for the class to calculate and simulate various aspects of beams interacting with RF fields, understand the responses of LLRF systems interacting with RF power stages and the beam dynamic system.

**Course Content**

Lectures with tutorial discussions and lab sessions with Matlab/Simulink will be presented; if possible a short hands-on RF concepts lab will be included. The class will have 4 days of lecture followed by tutorial/lab. The last day will allow student presentations of topical papers from the accelerator literature that feature the concepts of the class.

Day 1

Review of accelerator fundamentals, concepts such as beam emittance, energy distributions, transverse and longitudinal focusing. General structures of linear and circular accelerators. Review through example existing facilities such as light sources, high energy colliders and LINAC/FEL facilities. Introduction of RF cavity structures commonly used to apply RF fields on beams. Behavior of Normal Conducting vs. Superconducting RF cavity systems. Concepts of resonance, resonance control, shunt impedance and interactions of particle beams with fields in cavities. Synchrotron oscillations in circular machines and phase space concepts for particle distributions. Matlab exercises on energy compression, beam distributions and impact of cavity voltages/phases on beam properties.

Day 2

Review of time domain/frequency domain formalisms, Fourier transforms, and concepts of Linear Time Invariant systems. Introduction to feedback and feedforward control applied to simple systems. Continuous-time and discrete-time formalism, sampling concepts, RF concepts, and RF signal processing introductions. RF concepts such as filters, oscillators, heterodyned systems, and basics of signal detection and amplitude/phase, I/Q representation of signals. Definitions of noise and implications of signal/noise in processing systems. Examples of RF technology such as mixers, amplifiers, directional couplers, diode detectors, etc. Introduction of digital down conversion, applications of sampling for discrete-time systems. Matlab exercises on simple control and signal processing concepts. If possible RF devices and RF concepts lab.

Day 3

Review of example LINAC and circular machine RF and LLRF systems. Examples chosen to highlight the variety of techniques in use. Analog and digital implementations. Impact of direct and comb feedback loops on impedance and stability in circular machines. Examples of the role LLRF control plays in LINAC energy chirps, beam properties and operational considerations. System-level issues such as synchronization of multiple RF stations in a large facility. Operational needs including system diagnostics, fault files, etc. Tutorial conference literature, paper reviews and study. Focus on papers from LLRF workshops and IPAC/PAC conferences.

Day 4

Impacts of technical imperfections, limits of LLRF system performance and implications for beam properties (energy spread, longitudinal emittance, stability). Examples of LLRF architectures, mitigation techniques in use at LHC, SuperKEKB (PEP-II examples). Impact of RF and LLRF system noise in hadron vs. lepton facilties. State-of-the-art limits on accelerator capabilities and implications for LLRF systems for future machines. Tutorial: students (singly or in small groups) select final presentation topic, literature review, preparation of final report. Instructors work with students to guide content, selection of good examples based on students backgrounds and interests. Papers may focus on accelerator operations, machine limits, technology and implementation of LLRF systems, etc. Use of the conference literature for examples, explain why the designers chose the path they did and what benefits/drawbacks were experienced in the operation or testing of the system.

Day 5

Student final project presentations. Each group presents via slides and brief written report. Class discussions and emphasis of class concepts by the instructors.

**Reading Requirements**

This course will use materials from “Handbook of Accelerator Physics and Engineering” (*provided by the USPAS*) by Alexander W. Chao and Maury Tigner, World Scientific (1999) (this textbook will be provided by the USPAS); “Microwave Engineering” by David Pozar (fourth edition), John Wiley and Sons Publishers (2011); "Planar Microwave Engineering: A Practical Guide to Theory, Measurement and Circuits" by Thomas H. Lee, Cambridge University Press (2004). Reading will also be assigned from Physical Review Special Topics (Journal articles), and Conference papers from the LLRF Workshops (JACOW website) and IPAC and PAC conferences (JACOW website).

**Credit Requirements**

Students will be evaluated as follows: RF lab exercises (25%), final report (75%).

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UC Davis course number:** 163EDN671 Advanced Topics