Superconducting cavities are responsible for beam acceleration in superconducting linear accelerators. Challenging cavity control specifications are necessary to reduce RF costs and to maximize the availability of the accelerator. Cavity detuning and bandwidth are two critical parameters to monitor when operating particle accelerators. Cavity detuning is strongly related to the power required to generate the desired accelerating gradient. Cavity bandwidth is related to the cavity RF losses. A sudden increase in bandwidth can indicate the presence of a quench or multipacting event. Therefore, calculating these parameters in real-time in the low-level RF system is highly desirable. A real-time estimation of the bandwidth allows a faster response of the machine protection system in case of quench events, whereas the estimation of cavity detuning can be used to drive piezoelectric tuner-based resonance control algorithms. In this article, a new FPGA-based estimation component is presented. Such a component is designed to be used either in continuous wave or pulsed operation mode with loaded quality factors between 106 and 108. Results of this component with FLASH, EuXFEL, CMTB, and ELBE are presented.

Vacuum tube amplifiers are the most widespread type of Radio Frequency (RF) sources used to produce high power signals needed for beam acceleration in superconducting cavities. At Deutsches Elektronen-Synchrotron (DESY), megawatt rated klystrons are used to produce millisecond-long RF shots for pulsed operation in particle accelerators. In contrast, inductive output tubes are used to provide a continuous RF signal for Continuous Wave (CW) operation. In both cases, the amplifiers suffer from amplitude dependent nonlinearity between the driving and generated signals. This nonlinearity complicates the setup operations of the Low Level RF (LLRF) system and makes it harder to regulate the accelerating field. Therefore a way to linearize the amplifier is highly valuable. This paper covers the design, implementation, and test of an FPGA-based predistortion linearization unit. The first results on the performance of this component in linearizing the amplifiers of running CW and pulsed superconducting accelerators are presented. Such a component uses programmable interpolating Look Up Tables (LUT) that are addressed using the squared value of the requested signal amplitude. This component only adds 64 ns latency to the RF control system without relying on any vendor-dependent FPGA component. Other benefits of using programmable interpolating LUT are low FPGA usage of FPGA resources and flexibility in terms of the type of amplifier to be corrected. The benefits of using this linearizer for klystrons and inductive output tubes are presented and quantified.

Modern superconducting radio-frequency linear accelerators require the cavity bandwidth and detuning to be within a specified range to maximize the efficiency of the machine. To correctly estimate these states during operation, the measured RF signals should be calibrated. Due to the finite isolation of the waveguide directional couplers, cross-coupling effects in the forward and reflected channels complicate the calibration of the RF signals in Low-Level RF control systems. Past work proposed a compensation method employing least-squares optimization. This method requires the directivity of the directional couplers to be much higher than one. Additionally, the algorithm requires a tuning parameter to optimize the calculated calibration. However, for some accelerating systems, finding an acceptable value for such a parameter is challenging and time-consuming. Other methods strongly depend on the forward-reflected ratio during the field decay phase. This, in some circumstances, may decrease the accuracy due to noise or systematic errors. In this paper, we present a way to overcome these limitations by performing a global nonlinear least square optimization constrained by energy conservation laws. The method is tested with L-band superconducting resonators at loaded quality factors of $4.6\cdot 10^6$ and $2.8\cdot 10^7$.

The High Duty Cycle (HDC) upgrade is a proposed improvement to the existing European X-ray Free Electron Laser (EuXFEL) to extend the pulsed RF duty factor from the actual value of around 1% to more than 5% up to Continuous Wave (CW). To implement this upgrade, the loaded quality factor (Q_L) of the superconducting cavities will increase by more than one order of magnitude. This will result in shrinking the cavity bandwidth to values as low as a few Hertz. Since the Lorentz Force Detuning (LFD) experienced during the accelerating field buildup is of hundreds of Hertz, the Low-Level RF (LLRF) system has to accurately track and control the cavity resonance frequency to obtain the desired accelerating gradient. Moreover, ponderomotive instabilities have to be suppressed to achieve stability during beam acceleration. Since LFD is a repetitive disturbance in cavity frequency, the correction to its effects can be implemented as a feedforward compensation on the piezoelectric tuners of the cavity. Initial results on the simulation of feedforward resonance control in the HDC regime are discussed in this proceeding.

Enabled by progress in superconducting technology, several continuous wave linear accelerators are foreseen in the next decade. For these machines, it is of crucial importance to track the main cavity parameters, such as the resonator bandwidth and detuning. The bandwidth yields information on the superconducting state of the cavity. The detuning should be minimized to limit the required power for operation of the cavity. The estimation of these parameters is commonly implemented in the digital electronics of the low-level rf control system to minimize the computation delay. In this proceedings paper, we present a way to compute the bandwidth and detuning using a Luenberger observer. In contrast to previous methods, the state observer yields estimations at the native control system sample rate without explicitly filtering the input signals. Additionally, the error convergence properties of the estimations can be controlled intuitively by adjusting gain parameters. Implementation considerations and test results for the derived observer are presented in the manuscript.