This book begins with an overview of the RF control concepts and strategies. It then introduces RF system models for optimizing the system parameters to satisfy beam requirements and for controller design. In addition to systematically discussing the RF field control algorithms, it presents typical architecture and algorithms for RF signal detection and actuation. Further, the book addresses the analysis of the noise and nonlinearity in LLRF systems to provide a better understanding of the performance of the RF control system and to specify the performance requirements for different parts of the RF system.
Today, accelerators require increased RF stability and more complex operation scenarios, such as providing beam for different beam lines with various parameters, and as a result LLRF systems are becoming more critical and complex. This means that LLRF system developers need have extensive knowledge of the entire accelerator complex and a wide range of other areas, including RF and digital signal processing, noise analysis, accelerator physics and systems engineering.
Providing a comprehensive introduction to the basic theories, algorithms and technologies, this book enables LLRF system developers to systematically gain the knowledge required to specify, design and implement LLRF systems and integrate them with beam acceleration. It is intended for graduate students, professional engineers and researchers in accelerator physics.
Author(s): Stefan Simrock, Zheqiao Geng
Series: Particle Acceleration and Detection
Publisher: Springer
Year: 2022
Language: English
Pages: 395
City: Cham
Preface
Contents
Abbreviations
Chapter 1: Introduction
1.1 RF Systems of Particle Accelerators
1.2 Principles of Beam Acceleration
1.2.1 Acceleration in Standing-Wave Cavities
1.2.2 Acceleration in Traveling-Wave Structures
1.3 Disturbances to RF Fields
1.3.1 Electronic Noise
1.3.2 Temperature and Humidity
1.3.3 Mechanical Vibrations
1.3.4 Beam Loading
1.4 LLRF Systems Overview
1.4.1 Requirements and Architecture
1.4.2 Context in Particle Accelerators
1.4.3 A Brief History
1.5 Summary
References
Chapter 2: RF Control Strategy
2.1 Feedback and Feedforward Control
2.2 Amplitude/Phase and In-Phase/Quadrature Control
2.3 RF Control Loop Architecture
2.3.1 Generator Driven Resonator
2.3.2 Self-Excited Loop
2.3.3 Phase-Locked Loop
2.4 Analog and Digital Control
2.5 Single-Cavity and Vector-Sum Control
2.6 Summary
References
Chapter 3: RF System Models
3.1 General Assumptions
3.2 RF Modeling Method
3.2.1 RF Signal Description
3.2.2 Principle of RF Signal Detection
3.2.3 Phasor Laplace Transform
3.3 Single-Cell Cavity Model
3.3.1 Parallel RLC Circuit Model
3.3.2 Cavity Phasor Transfer Function
3.3.3 Cavity Step Response
3.3.4 Cavity Response to RF Power
3.3.5 Cavity Response to a Single Bunch
3.3.6 Cavity Response to a Bunch Train
3.3.7 Cavity Equation with Voltage Drives
3.3.8 Interaction Between Cavity Voltage and Beam
3.3.9 Forward and Reflected RF Power
3.3.10 Mechanical Model
3.4 Multi-cell Cavity Model
3.4.1 Coupled RLC Circuit Model
3.4.2 Multi-cell Cavity Phasor Equations
3.4.3 Passband Modes
3.4.4 Transient in Cavity Cells with RF Drive
3.5 Traveling-Wave Structure Model
3.5.1 Filling of Structures
3.5.2 Structure Phasor Transfer Function
3.6 Modeling of Important RF Devices
3.6.1 Transmission Line Model
3.6.2 RF Amplifier Model
3.6.3 RF Pulse Compressor Model
3.7 Application of RF System Models
3.8 Summary
References
Chapter 4: RF Field Control
4.1 Requirements to RF Field Control
4.2 Generator Driven Resonator Control
4.2.1 Feedback Stability for Single-Cell Cavities
4.2.2 Feedback Stability for Multi-cell Cavities
4.2.3 Active Disturbance Rejection Control
4.2.4 Advanced Control Algorithms
4.2.4.1 Optimal Control
4.2.4.2 Robust Control and Adaptive Control
4.2.4.3 Model Predictive Control
4.3 Self-Excited Loop Control
4.3.1 Free-Running SEL
4.3.2 SEL with Amplitude Limiter
4.3.3 SEL with Feedback Control
4.4 Phase-Locked Loop Control
4.4.1 Introduction to PLL
4.4.2 Modeling of PLL for Cavity Control
4.4.3 Feedback Analysis of PLL
4.4.3.1 Control Goals Analysis
4.4.3.2 Controllability Analysis
4.5 Adaptive Feedforward
4.5.1 Adapt Feedforward with Feedback Actuation
4.5.2 Iterative Learning Control
4.5.2.1 FIR Model of RF System
4.5.2.2 ILC Algorithm
4.6 Cavity Resonance Control
4.6.1 Detuning Measurement
4.6.1.1 RF Frequency Scanning
4.6.1.2 Phase Slope at RF Pulse Decay
4.6.1.3 Solving Cavity Equation
4.6.1.4 Cavity Input-Output Phase Shift
4.6.2 Cavity Tuners
4.6.2.1 Motor Tuner
4.6.2.2 Piezo Tuner
4.6.2.3 Cooling Water Temperature
4.6.3 Tuning Control Scheme
4.6.3.1 Tuning Control with Feedback
Coupling with Phase Feedback Loop
Issues of Feedback with Piezo Tuners
4.6.3.2 Tuning Control with Adaptive Noise Cancellation
4.6.3.3 Feedforward Control for Pulsed Cavities
4.6.4 Ponderomotive Effects
4.6.4.1 Introduction to Ponderomotive Instability
4.6.4.2 Static Instability Analysis
4.6.4.3 Mitigation of Ponderomotive Instability
4.7 Summary
References
Chapter 5: RF Detection and Actuation
5.1 RF Detection Schemes
5.1.1 Amplitude and Phase Detectors
5.1.2 Analog I/Q Demodulator
5.1.3 Down-Converter and IF Sampling
5.1.4 Direct RF Sampling
5.2 RF Detection Algorithms
5.2.1 I/Q Demodulation
5.2.1.1 I/Q Sampling and Demodulation Algorithm
5.2.1.2 Harmonics Aliasing of I/Q Sampling
5.2.2 Non-I/Q Demodulation
5.2.2.1 Non-I/Q Sampling
5.2.2.2 Harmonics Aliasing of Non-I/Q Sampling
5.2.2.3 Non-I/Q Demodulation Algorithm
5.2.2.4 Frequency Response of Non-I/Q Demodulation
5.2.2.5 Non-I/Q Demodulation for Transient RF Measurement
5.2.3 Digital Down-Conversion
5.2.4 Handling of Time-varying Frequency
5.2.5 RF Detection with Reference Tracking
5.2.5.1 Reference Tracking with PLL
5.2.5.2 Reference Tracking with Hilbert Transform
5.2.5.3 Direct Reference Phase Tracking
5.3 RF Actuation Schemes
5.3.1 Direct Up-Conversion
5.3.2 Single Sideband Up-Conversion
5.3.3 IF Up-Conversion
5.4 Summary
References
Chapter 6: Noise in RF Systems
6.1 General Description of Noise
6.1.1 Basic Concepts of Noise
6.1.2 Estimation of PSD and SNR
6.1.2.1 Discrete Fourier Transform
6.1.2.2 PSD and SNR Calculation
6.1.3 Correlation of Noise
6.1.3.1 Description of Correlation
6.1.3.2 PSD of the Sum of Two Noises
6.1.4 Additive Noise and Parametric Noise
6.1.5 White Noise and 1/f Noise
6.1.6 Noise Factor
6.1.7 Phase Noise and Amplitude Noise
6.1.7.1 Phase Noise
6.1.7.2 Amplitude Noise
6.1.7.3 Signal with Amplitude and Phase Noise
6.1.8 Additive Noise and RF Jitter
6.1.9 Frequency-Domain Meaning of RMS Value
6.1.10 Drift and Jitter
6.2 Noise Model of Basic RF Components
6.2.1 Two-Port Passive RF Components
6.2.2 Power Splitter and Combiner
6.2.3 RF Amplifier
6.2.4 Mixer
6.2.5 Frequency Divider and Multiplier
6.2.6 Analog-to-Digital Converter
6.2.6.1 ADC Noise Model
6.2.6.2 Noise Added by ADC
6.2.6.3 Measurement of Noise Added by ADC
6.2.7 Digital-to-Analog Converter
6.2.7.1 DAC Noise Model
6.2.7.2 Noise Added by DAC
6.3 Noise Transfer in RF Control Loops
6.3.1 Noise Transfer in Feedback Control
6.3.2 Noise Transfer in Pulse-to-Pulse Control
6.4 RF System Noise Specification
6.4.1 Noise Specification Strategy
6.4.2 Accelerator Global Noise Model
6.4.2.1 Noise Specification of Linacs
6.4.2.2 Noise Specification of Synchrotrons
6.4.3 Specification of RF Reference Phase Noise
6.5 RF Station Noise Model
6.5.1 RF Station Noise Overview
6.5.2 RF Reference Phase Noise
6.5.3 RF Driving Chain Noise
6.5.4 RF Measurement Chain Noise
6.5.5 Estimation of RF Measurement Chain Noise
6.5.6 Estimation of RF Driving Chain Noise
6.5.7 Estimation of RF Field Noise
6.5.8 Validation of RF Station Noise Model
6.5.9 Specification of RF Component Noise
6.6 RF Detector Drift Correction
6.6.1 Reference Tracking
6.6.2 Drift Calibration
6.6.3 Beam-Based Feedback
6.7 Summary
References
Chapter 7: Nonlinearity in RF Systems
7.1 Basic Concepts
7.1.1 1-dB Compression Point
7.1.2 Third-Order Intercept Point
7.1.3 AM-PM Conversion
7.1.4 Nonlinearity Induced RF Detection Error
7.1.5 Nonlinearity Induced RF Driving Disturbances
7.2 Nonlinearity of RF Amplifiers
7.2.1 Look-Up Table Model
7.2.2 Analytical Model
7.2.3 Dynamical Model
7.3 Handling of Amplifier Nonlinearity in RF Control
7.3.1 RF Amplitude Control with High Voltage
7.3.2 Gain Scheduling
7.3.3 LUT-Based Linearization
7.3.4 Linearization Loop
7.4 Summary
References
Chapter 8: Timing and Synchronization
8.1 Overview
8.2 Master Oscillator
8.2.1 RF and Laser Oscillator
8.2.2 Synchronization of Two Oscillators
8.3 Timing System
8.3.1 Timing Fiducial Generation
8.3.2 Common Subharmonic
8.3.3 Client Trigger Generation
8.4 Synchronization System
8.4.1 Synchronization Signal Distribution
8.4.2 Phase Drift Mitigation
8.4.2.1 Phase-Stable Coaxial Cable
8.4.2.2 Temperature and Humidity Stabilization
8.4.2.3 Active Drift Compensation
8.4.2.4 Phase-Averaging Coaxial Line
8.4.3 Client Synchronization
8.4.3.1 RF Signal Extraction
8.4.3.2 Frequency Synthesis
8.4.3.3 Synchronization of Laser Oscillator
8.5 Robust Timing Relations
8.5.1 Timing Relation Highlight
8.5.2 Timing Relation Uncertainty
8.5.3 Strategies for Robust Timing Relations
8.5.3.1 Frequency Selection
8.5.3.2 Timing Relation Diagnostics
8.5.3.3 Reference Tracking
8.5.3.4 Frequency Divider Resynchronization
8.5.3.5 Race Condition Handling
8.6 Summary
References
Chapter 9: LLRF Applications
9.1 Overview
9.2 Parameter Optimization
9.2.1 RF Pulse Shaping
9.2.2 DAC Offset Correction
9.2.3 Parameter Scanning
9.3 RF Calibration
9.3.1 Beam-Induced Transient
9.3.1.1 Physical Meaning of Beam-Induced Transient
9.3.1.2 Measurement of Beam-Induced Transient
9.3.2 Accelerating Voltage and Beam Phase Calibration
9.3.2.1 Accelerating Voltage Calibration with RF Drive Power
9.3.2.2 Accelerating Voltage and Beam Phase Calibration with Beam-Induced Transient
9.3.2.3 Accelerating Voltage and Beam Phase Calibration with Beam Energy
9.3.3 Cavity Input Power and Phase Adjustment
9.3.4 Vector-Sum Calibration
9.3.4.1 Vector-Sum Calibration Algorithm
9.3.4.2 Vector-Sum Calibration Error
9.3.5 Cavity Forward and Reflected Signals Calibration
9.3.6 RF Signal Power Calibration
9.4 RF System Identification
9.4.1 Cavity Input Coupling Factor Identification
9.4.2 System Gain and System Phase Identification
9.4.3 Cavity Parameters Identification
9.4.3.1 Basic Equations
9.4.3.2 QL and Δω Identification at RF Pulse Decay
9.4.3.3 QL and Δω Identification During RF Pulse
9.4.3.4 Identification of Beam Drive
9.5 Beam Loading Compensation
9.6 Summary
References
Index
