Transient analysis of RF cavities under beam loading

The conventional electrical model analogy of a RF cavity is a shunt RLC circuit supplied by two current sources representing the RF amplifier and the beam. In the literature, the impedance of the cavity is often calculated in the Fourier domain. This type of cavity modelling has two drawbacks: First, it assumes a perfect matching between the cavity and the amplifier therefore it neglects the reflected voltage. And, second, it does not provide any information about the cavity transient response, for example at start-up or upon beam arrival, while this information can be very important for the design of the regulation loops. In this work we will remove these drawbacks by calculating the cavity impedance in Laplace domain taking the reflected voltage into account. We will then modify our model so that it also includes the influence of the beam on the cavity. For transient RF simulations, though, a typical problem is the long simulation time due to the relatively slow transient response compared to the RF period. To overcome this problem, finally, we will use a mathematical method to map the cavity frequency response from RF to baseband to reduce the simulation time significantly.Peer ReviewedPostprint (author’s final draft

Low level rf system for the European Spallation Source's Bilbao linac

Design and some performance results of the pulsed digital low level radio frequency (LLRF) for the radio frequency quadrupole (RFQ) systems of Rutherford Appleton Laboratory-front end test stand and the future European Spallation Source Bilbao linac are presented. For rf field regulation, the design is based on direct rf-to-baseband conversion using an analog in-phase quadrature (IQ) demodulator, high-speed sampling of the I/Q components, baseband signal processing in a field-programmable gate array (FPGA), conversion to analog, and IQ modulation. This concept leads to a simple and versatile LLRF system which can be used for a large variety of rf frequencies and virtually any LLRF application including cw, ramping, and pulsed. In order to improve the accuracy of the probe voltage measurement, errors associated with the use of analog IQ demodulators have been identified and corrected by FPGA algorithms and proper setting of the feedback loop parameters. Furthermore, a baseband-equivalent model for the rf plant is developed in MATLAB-Simulink to study the RFQ transient response under beam loading in the presence of phase and delay errors. The effect of the unwanted resonant modes on the feedback loop stability and the LLRF considerations to avoid such instabilities are discussed and compared to some other machines such as the ILC and the European free electron laser. The practical results obtained from tests with a mock-up cavity and an RFQ cold model verify that amplitude and phase stabilities down to a fraction of one percent and one degree and phase margins larger than ±50° can be achieved with this method preserving the linearity and bandwidth of the feedback loops. © 2011 American Physical Society.Peer Reviewe

1 A New Method for Clock Recovery in MPEG Decoders ∗

We propose and analyze a new method for reconstruction of the reference clock which is needed for correctly timing the decoding and presentation of video and audio streams in MPEG decoders. Clock recovery is possible by transmitting time stamps called Program Clock References (PCR’s) in the bit stream at the rate of at least 10 per second. The PCR’s are generated at the encoder by sampling the System Time Clock (STC) which runs at 27 MHz ± 30 ppm.Since the decoder’s free-running system clock frequency doesn’t exactly match the encoder’s STC, the reference time is reconstructed by means of a Phase Locked Loop (PLL) and the received PCR’s. Always, there’s a difference between the values of the incoming PCR’s and the values they should have when received by the decoder. This difference (Jitter) in input at the receiver’s PLL to a LPF whose output controls the instantaneous frequency of a VCO (Voltage Controlled Oscillator). The frequency variations of the VCO should be restricted according to the system’s clock specifications. This can be done by increasing the order of the LPF but at the expense of increasing the locking-time of the PLL which requires a high amount of buffering. In this paper, we take a new and different approach to solve the problem of clock recovery. In our proposed method, a fixed frequency oscillator is utilized to store the incoming times of the PCR’s and the reference clock is reconstructed by finding the LMS (Least Mean Square) Best Fit line for the last several hundred PCR values. The LMS Best Fit process is repeated by receiving every new PCR to keep the LMS line up-to-date. The proposed method is advantageous because it drastically reduces the required hardware for clock recovery. Significance of the new method is verified by computer simulations

A transient model for RF cavity analysis under beam loading

There are two important considerations in the development of an electrical model for RF cavities to be used for system analysis or LLRF loop design, being: transient response and cavity impedance mismatch. In the literature, however, either one or both of these issues are often neglected depending whether the RF cavity is being looked at from high-power or low-level RF perspectives. In this work, a transient model for storage ring RF cavities under beam loading is developed so that it represents the important RF aspects of the cavity such as impedance mismatch and reflected voltage as well as its transient response, for example at start-up or upon beam arrival. As a special case, the model is applied to the RF cavity of the ALBA storage ring to study the effects arising from beam loading, system start-up and delays on the performance of the LLRF regulation loops. For the simulation of the regulation loops in time domain a mathematical technique is introduced to map the RF frequency to baseband, leading to the baseband-equivalent model of the cavity with almost the same results as the conventional cavity model but with significantly higher simulation speed

Transient analysis of RF cavities under beam loading

The conventional electrical model analogy of a RF cavity is a shunt RLC circuit supplied by two current sources representing the RF amplifier and the beam. In the literature, the impedance of the cavity is often calculated in the Fourier domain. This type of cavity modelling has two drawbacks: First, it assumes a perfect matching between the cavity and the amplifier therefore it neglects the reflected voltage. And, second, it does not provide any information about the cavity transient response, for example at start-up or upon beam arrival, while this information can be very important for the design of the regulation loops. In this work we will remove these drawbacks by calculating the cavity impedance in Laplace domain taking the reflected voltage into account. We will then modify our model so that it also includes the influence of the beam on the cavity. For transient RF simulations, though, a typical problem is the long simulation time due to the relatively slow transient response compared to the RF period. To overcome this problem, finally, we will use a mathematical method to map the cavity frequency response from RF to baseband to reduce the simulation time significantly.Peer Reviewe

A transient model for RF cavity analysis under beam loading

There are two important considerations in the development of an electrical model for RF cavities to be used for system analysis or LLRF loop design, being: transient response and cavity impedance mismatch. In the literature, however, either one or both of these issues are often neglected depending whether the RF cavity is being looked at from high-power or low-level RF perspectives. In this work, a transient model for storage ring RF cavities under beam loading is developed so that it represents the important RF aspects of the cavity such as impedance mismatch and reflected voltage as well as its transient response, for example at start-up or upon beam arrival. As a special case, the model is applied to the RF cavity of the ALBA storage ring to study the effects arising from beam loading, system start-up and delays on the performance of the LLRF regulation loops. For the simulation of the regulation loops in time domain a mathematical technique is introduced to map the RF frequency to baseband, leading to the baseband-equivalent model of the cavity with almost the same results as the conventional cavity model but with significantly higher simulation speed

Transient analysis of RF cavities under beam loading

The conventional electrical model analogy of a RF cavity is a shunt RLC circuit supplied by two current sources representing the RF amplifier and the beam. In the literature, the impedance of the cavity is often calculated in the Fourier domain. This type of cavity modelling has two drawbacks: First, it assumes a perfect matching between the cavity and the amplifier therefore it neglects the reflected voltage. And, second, it does not provide any information about the cavity transient response, for example at start-up or upon beam arrival, while this information can be very important for the design of the regulation loops. In this work we will remove these drawbacks by calculating the cavity impedance in Laplace domain taking the reflected voltage into account. We will then modify our model so that it also includes the influence of the beam on the cavity. For transient RF simulations, though, a typical problem is the long simulation time due to the relatively slow transient response compared to the RF period. To overcome this problem, finally, we will use a mathematical method to map the cavity frequency response from RF to baseband to reduce the simulation time significantly.Peer Reviewe

Low level rf system for the European Spallation Source’s Bilbao linac

Design and some performance results of the pulsed digital low level radio frequency (LLRF) for the radio frequency quadrupole (RFQ) systems of Rutherford Appleton Laboratory–front end test stand and the future European Spallation Source Bilbao linac are presented. For rf field regulation, the design is based on direct rf-to-baseband conversion using an analog in-phase quadrature (IQ) demodulator, high-speed sampling of the I/Q components, baseband signal processing in a field-programmable gate array (FPGA), conversion to analog, and IQ modulation. This concept leads to a simple and versatile LLRF system which can be used for a large variety of rf frequencies and virtually any LLRF application including cw, ramping, and pulsed. In order to improve the accuracy of the probe voltage measurement, errors associated with the use of analog IQ demodulators have been identified and corrected by FPGA algorithms and proper setting of the feedback loop parameters. Furthermore, a baseband-equivalent model for the rf plant is developed in MATLAB-Simulink to study the RFQ transient response under beam loading in the presence of phase and delay errors. The effect of the unwanted resonant modes on the feedback loop stability and the LLRF considerations to avoid such instabilities are discussed and compared to some other machines such as the ILC and the European free electron laser . The practical results obtained from tests with a mock-up cavity and an RFQ cold model verify that amplitude and phase stabilities down to a fraction of one percent and one degree and phase margins larger than ±50° can be achieved with this method preserving the linearity and bandwidth of the feedback loops

Implementation Issues and First Results of the ESS Beam Current Monitor System

The BCM system of the European Spallation Source needs to measure several beam parameters including pulse profile, charge, current, pulse width and repetition frequency. Moreover, it will measure differential beam currents using several ACCT pairs along the linac. This is particularly important at low beam energies where BLMs cannot be used for measuring beam losses. Due to the ESS-specific requirements, the BCM software and firmware will be customized. Also, parts of the electronics may need to be customized to be consistent with the ESS standard electronics platform, hence facilitate maintenance and maximize synergy with other systems. Technical challenges include maintaining signal integrity and a fast response despite large variations in the sensor cable length and ambient temperature, as well as minimizing the effect of the ground voltage fluctuations. This paper gives a general overview of the design and focuses on a few technical issues that are particularly important for satisfying the performance requirements. Also, BCM test results in laboratory conditions as well as preliminary results with the ESS ion source will be presented

System Overview and Current Status of the ESS Beam Position Monitors

It is planned to install more than 140 button BPMs along the ESS linac. The BPMs will be used to measure the beam position and phase in all foreseen beam modes and to provide input to the Machine Interlock System. The phase measurement is mainly intended for cavity tuning and Time-Of-Flight energy measurements. A customized BPM detector based on the European XFEL button style has been designed for the cold linac through a collaboration with DESY. Large buttons with diameters up to 40 mm are foreseen to provide enough S/N ratio not only with the nominal beam, but also with a low-current or a de-bunched beam. A demo MTCA.4 system has been procured and successfully integrated into EPICS. Also, a customized Rear Transition Module for down-mixing the BPM signals will be developed with SLAC. Electronics tests with a BPM test bench are currently going on at ESS. BPM installation in the linac is foreseen for 2017 and afterwards