Fundamentals of Radio Frequency Control for Particle Accelerators

Overview

Modern particle accelerators use electromagnetic energy at RF frequencies to accelerate particles. This course outlines the fundamental concepts needed to understand the monitoring and control of the electromagnetic fields. Often this area of study is called “Low Level RF”. This course was taught at the CERN CAS course on “RF for Accelerators”, 18 June - 01 July 2023, Berlin Germany.

1. Spectrum Analysis

  • Fourier Series
  • Fourier Transforms
  • Spectrum Analysis
  • Power Spectral Density

2. Modulation

  • AM Modulation
  • FM Modulation

3. Noise

  • Thermal Noise
  • Band Limited Noise
  • Noise Circuit Model
  • Noise Power Spectral Density
  • Noise in an Amplifier
  • Effective Noise Temperature
  • Noise Figure of Systems

4. Control Theory

  • Laplace Transforms
  • Initial and Final Value Theorems
  • Circuit Elements
  • Low Pass Filter Frequency Response
  • Impulse Response
  • High Pass Filter
  • Poles and Zeros
  • Bode Plots
  • Feedback
  • Phase Lock Loop

5. Frequency Control

  • LLRF & HLRF
  • Frequency Sources
  • Complete RF System
  • Phase focussing
  • Beam phase transfer function
  • Phase locked RF System
  • Cavity Cavity Detuning
  • AC Coupled Phase loop