U.S. Particle Accelerator School
U.S. Particle Accelerator School
Education in Beam Physics and Accelerator Technology

Introduction to Digital Low-Level Radio Frequency Controls in Accelerators


Northern Illinois University

Course Name:

Introduction to Digital Low-Level Radio Frequency Controls in Accelerators


Larry Doolittle, Qiang Du and Carlos Serrano, Lawrence Berkeley National Lab

Purpose and Audience
This course is intended for both accelerator scientists and engineers with a background in electronics, RF or software, and operators or technicians who are interested in the design of Low-Level Radio Frequency (LLRF) control systems for particle accelerators and light sources. The course focuses on all aspects related to the controls of electromagnetic fields in RF cavities: from the electromagnetic theory to the implementation of digital feedback systems using Field Programmable Gate Arrays (FPGAs). LLRF systems are important since there is a direct correlation between the accuracy of RF controls and particle beam characteristics that determine the quality of the science they produce: from brightness in a light source to luminosity in a collider.

Undergraduate-level coursework in applied mathematics including linear algebra, differential equations, and calculus is required. Undergraduate-level Electricity and Magnetism, including electromagnetic waves is required. Basic knowledge of circuit theory at an undergraduate level is required. Some exposure or experience with basic digital signal processing concepts and RF techniques (mixers, heterodyne detection, filters) is recommended. Familiarity with programming languages (we will employ Python) and control theory is recommended. Some exposure or experience with FPGA design is recommended but not required. It is recommended that students enrolling also take Fundamentals of Timing and Synchronization with Application to Accelerators in the second week of this USPAS session to increase understanding of important related concepts.

It is the responsibility of the student to ensure that they meet the course prerequisites or have equivalent experience.

The course will cover the basics of LLRF, from theory to practice, to provide students with an overview of the Physics associated with the controls of electromagnetic fields in RF cavities, along with the necessary background to analyze and understand the controls aspects involved in LLRF. Since LLRF system designs involve a combination of analog, digital and feedback controls, the course will cover engineering concepts involved in each one of those components, providing an overview of the engineering design considerations in the implementation of LLRF systems in particle accelerators.

Instructional Method
The course is centered on hands-on, practical exposure to LLRF systems through lab exercises. These Lab exercises will be held in the afternoons. Preceding morning lectures will cover fundamental concepts needed in the afternoon laboratory exercises. Outside of the class hours, students will complete regular homework assignments, carry out data analysis of the lab experiments performed that day, and write reports. The class will be open in the evenings with instructors and/or teaching assistants available to address questions on either the coursework or lab experiments. Homework and lab reports will be graded and overviewed in class recitation sections.

Course Content
Students will be introduced to important aspects related to the feedback controls of RF fields in resonant cavities. RF cavities are used to accelerate particle beams, decelerate or bunch them, or more broadly produce an exchange of energy between an external power source and the particle beam. In order to control these exchanges, the electromagnetic fields in the resonant cavities need to be precisely maintained and tuned to their desired levels using feedback controls, since they are subject to external disturbances and sometimes even naturally unstable.

This coursework will cover the theory underlying components of an RF feedback chain, from the RF cavities themselves to the high-power RF sources that feed them. In doing so, we will examine how the electromagnetic properties can be manipulated to bring the expressions into more familiar engineering expressions associated with circuits and control theory. Once the system is described in these terms, it can be analyzed both analytically and numerically. We will explore both avenues in theory and in practice through software simulations in order to gain understanding of the fundamental aspects of RF controls systems.

RF fields are controlled using a combination of analog and digital electronics, and those systems are monitored and controlled from computers in an accelerator facility. We will cover fundamentals of the RF techniques used in order to accurately measure the RF fields in a cavity. These techniques traditionally involve heterodyne detection and use RF components such as mixers, analog filters, etc. We will explore signal processing principles behind these concepts, paying particular attention to performance metrics that define the stability of the RF field, e.g. measurement noise, crosstalk, etc. From there, we will transition into the digital domain and explore digital signal processing techniques, control theory and their application to the control of fields in an RF cavity. We will explore more complicated systems involving many measurement points and actuators, including how machine learning techniques can be applied when there is not a good analytical representation of the problem at hand, or it is just too complicated for a human to process.

After the fundamentals are covered, students will be exposed to engineering aspects associated with the construction of RF control systems in particle accelerators. Coverage will range from design optimization for performance to operational and software control aspects.

All the concepts above will be covered in a combination of lectures and practical exercises or laboratory sessions, where the student will gain exposure to both the underlying theory and the practical implementation of RF controls in particle accelerators. Lab sessions will be based on hands-on measurements with RF equipment, software simulations, and real-time controls using FPGAs.

Reading Requirements
A collection of papers from LLRF literature and a copy of notes by the instructors will be provided. Text to be provided by the USPAS:  RF Linear Accelerators Second Edition by Thomas P. Wangler (Wiley 2008). Other suggested references include: 

Credit Requirements
Students will be evaluated based on performance in lab sessions (50% grade) and homework (50% grade).

USPAS Computer Requirements
There will be no Computer Lab and all participants are required to bring their own portable computer to access online course notes and computer resources. This can be a laptop or a tablet with a sufficiently large screen and keyboard. Windows, Mac, and Linux-based systems that are wifi capable and have a standard web browser and mouse are all acceptable. You should have privileges for software installs. If you are unable to bring a computer, please contact uspas@fnal.gov ASAP to request a laptop loan. Very limited IT support and spare loaner laptops will be available during the session.

Northern Illinois University course number: PHYS 790D Special Topics in Physics - Beam Physics
Indiana University course number: Physics 671 Advanced Topics in Accelerator Physics
Michigan State University course number: PHY 963 "U.S. Particle Accelerator School"
MIT course number: 8.790 Accelerator Physics