Baseband Modeling of Superconducting RF Cavity in Digital Domain

Abstract

Modern day particle accelerators use resonating RF structures known as RF cavities to generate high electric field inside the gap of cavity to enhance the kinetic energy of the particle for beam acceleration. Worldwide the RF Cavity structures used for this purpose are made using normal conducting material or superconducting material. The main aim of the RF control is to maintain the stability of high electric field gradient inside the gap at given instance by controlling the amplitude and phase of the RF field generated inside the cavity. Normal conducting mode mainly differ from superconducting mode in terms of available bandwidth for establishing the amplitude and phase lock of the cavity field as it has more bandwidth availability in normal conducting case. Understandably, due to stringent bandwidth limitations, the amplitude-phase control of field inside the superconducting RF cavity is difficult. Most importantly, for achieving superconductivity, huge amounts of Liquid Nitrogen, Liquid Helium, high degree of evacuation is required. Also, the RF cavities in operate either in continuous wave mode (CW) or in pulsed mode as per the requirement. Thus, developing and testing of any control mechanism electronics for these cavities in actual poses a huge challenge since multiple test iterations are desired which is not economical or sustainable as it requires to run liquid helium plant and associated infrastructure for such purpose. So, in order to perform iterative design, development and deployment in an economical manner, cavity simulators need to be developed to mimic the behaviour of the cavity characteristics in terms of its electrical and mechanical parameters in the laboratory itself. In the present paper, the electrical and mechanical model of a superconducting RF cavity is mathematically built on the Simulink platform of MATLAB. The models are then converted to fixed point format and uploaded on to an Intel FPGA device to develop a digital equivalent of a superconducting RF cavity. As these cavities operate in high frequency region so, in order to reduce the simulation time, baseband (low frequency) model is generated and tested. In the physical implementation of the control electronics on the FPGA platform, the control algorithms are preceded by an analog down-conversion filter block followed by ADC to capture low frequency inputs. Like input, at the output end, DAC output is fed to analog up-conversion block to match the frequency of the cavity operation. 

In the Simulink model, the cavity is represented by differential equations governing its electrical and mechanical equivalents. While the electrical model remains the same, the mechanical model will vary based on the operation of cavities. As in case of pulsed cavity operation, Lorentz Force Detuning is severe and dynamic with time variance [1-3], but in continuous wave case, its nature is static and time invariant [5].

Control of the RF cavities can be achieved in either of two modes, Generator Driven Resonator (GDR) or Self Excited Loop (SEL) [4]. The cavity simulator developed in this research work is applicable to truly test both the control mechanisms. Electrical characteristics of IUAC’s Quarter-Wave Resonator in SEL domain are simulated in this paper for the purpose of developing and testing digital control mechanism. Results of cavity characteristics are found to be matching the experimental data available. This development thus has rendered future control test process as somewhat easier and sustainable.