SRF Cavity Simulator for LLRF Algorithms Debugging

The availability of niobium superconducting cavities, either due to a lack of a real cavity or due to the time needed for the experiment set up (vacuum, cryogenics, cabling, etc.), is limited, and thus it can block or delay the development of new algorithms such as low level RF control. Hardware-in-the-loop simulations, where an actual cavity is replaced by an electronics system, can help to solve this issue. In this paper we present a Cavity Simulator implemented in a National Instruments PXI equipped with an FPGA module. This module operates with one intermediate frequency input which is IQ-demodulated and fed to the electrical cavity’s model, where the transmitted and reflected voltages are calculated and IQ-modulated to generate two intermediate frequency outputs. Some more advanced features such as mechanical vibration modes driven by Lorentz-force detuning or external microphonics have also been implemented. This Cavity Simulator is planned to be connected to an mTCA chassis to close the loop with a LLRF control system. ELECTRICAL MODEL An equivalent electric circuit can be used to model a superconducting cavity, [1], where the power amplifier and beam are represented as current generators, the fundamental power coupler as a transformer and the cavity as an RLC-circuit. Figure 1 shows the equivalent circuit of the fundamental mode of a cavity connected to an RF power source, where �cav represents the transmitted voltage to the cavity, �ref the reflected voltage sent to the circulator in order to protect the RF power source, and the circuit components are defined in terms of the cavity parameters: √� � = (1) � = √�� (2) = �h 0 = 0 (3) where h is the shunt impedance used in accelerator physics. The ratio of the transformer depends on the coupling of the cavity β, � = √��0. The envelope of the RF transmitted voltage in the cavity can then described by the differential equation (4) where � / = � 0� , L = +�, ∆� the cavity detuning and �cav = (�cav , �cav�), �amp = (�amp , �amp�) are the real and imaginary parts of cavity voltage and the driven current respectively. � �� �cav = (−� / −∆� ∆� −� / ) �cav + + ( �� / �� / ) �amp � (4) The reflected voltage is calculated with the following equation: �ref = �cav � − �0�amp (5) Figure 1: Electrical equivalent circuit of a superconduct-