Real-time cavity simulator-based low-level radio-frequency test bench and applications for accelerators

A Low-level radio-frequency (LLRF) control systems is required to regulate the rf field in the rf cavity used for beam acceleration. As the LLRF system is usually complex, testing of the basic functions or control algorithms of this system in real time and in advance of beam commissioning is strongly recommended. However, the equipment necessary to test the LLRF system, such as superconducting cavities and high-power rf sources, is very expensive; therefore, we have developed a field-programmable gate array (FPGA)-based cavity simulator as a substitute for real rf cavities. Digital models of the cavity and other rf systems are implemented in the FPGA. The main components include cavity baseband models for the fundamental and parasitic modes, a mechanical model of the Lorentz force detuning, and a model of the beam current. Furthermore, in our simulator, the disturbance model used to simulate the power-supply ripples and microphonics is also carefully considered. Based on the presented cavity simulator, we have established an LLRF system test bench that can be applied to different cavity operational conditions. The simulator performance has been verified by comparison with real cavities in KEK accelerators. In this paper, the development and implementation of this cavity simulator is presented first, and the LLRF test bench based on the presented simulator is constructed. The results are then compared with those for KEK accelerators. Finally, several LLRF applications of the cavity simulator are illustrated.

Figure 1

Diagram of typical LLRF control system and rf cavity.

Figure 2

Cavity simulator structure. Both the cavity model and the disturbance model are incorporated in the simulator.

Figure 3

Comparison of bode plots from $u_r$ to $V_{c,r}$ and $V_{c,i}$. Left: $u_r\to V_{c,r}$, right: $u_r\to V_{c,i}$. The bode plot of the continuous-time (blue) and discrete-I (green) cases are very different; however, the discrete-II (red) case is very similar to the continuous-time case.

Figure 4

Electrical and mechanical models of cavity system. Electro-mechanical interaction is considered here.

Figure 5

Structure of cavity model in FPGA. The parameters $a$, $b$, and $c$ are selected based on difference equations (9) and (14).

Figure 6

Structure of klystron model. The parameter $a$ is equivalent to $1-e^{-2\pi f_{\text{kly}}{T}_s}$.

Figure 7

Structure of ripple model in FPGA. The parameter “frp” in the figure represents the ripple frequency, and the ripple amplitude is scaled by the parameter “$G_r$”.

Figure 8

Structure of microphonics model in FPGA. The measured microphonics data obtained from the real cavity data are prestored in the LUT. The parameter “$G_m$” input port is used to control the amplitude of the microphonics.

Figure 9

MicroTCA FPGA board used performing digital algorithms in cavity simulator.

Figure 10

Cavity simulator-based test bench for LLRF system. The cavity simulator model is implemented in FPGA #1 (indicated by red block). Noted that only the ADCs and DACs in use are plotted in the figure.

Figure 11

Comparison of pick up, incident, and reflected cavity signals measurement based on cavity simulator (blue) and real STF nine-cell cavity (red) under “$\mathrm{FF}+\mathrm{FB}$” operation. The parameters of the cavity and mechanical models were mainly selected based on one of the nine-cell cavities in the STF2 ($Q_L\approx 4.8\times {10}^6$, $E_{\text{acc}}\approx 25\mathrm{MV}/\mathrm{m}$).

Figure 12

Comparison of LFD between measurement based on cavity simulator (blue) and real STF2 nine-cell cavity (red).

Figure 13

Comparison of beam-loading effects between measurement based on cavity simulator (blue) and real STF nine-cell cavity (red).

Figure 14

Beam-induced change in the cavity gradient corrected by the gradient drop [%] versus rf phase [deg] for the cavity at STF. The arrow indicates the on-crest beam acceleration.

Figure 15

Comparison of oscillations in cavity pickup signal caused by the $8\pi /9$ mode measured from cavity simulator (blue) and real cERL nine-cell cavity (red). The oscillation frequency in the figure is approximately 1.72 MHz (closed to the value for one of the cavity in the main linac of cERL). Algorithms to generate the $8\pi /9$ mode were developed based on the difference equations in (14).

Figure 16

Comparison of microphonics measured from cavity simulator-based LLRF system (blue) and LLRF system from cERL main linac (red) under FF operation. The cavity parameters were selected based on the cERL nine-cell cavity in the main-linac ($Q_L\approx 10\times {10}^6$). (a) FF and (b) FB control.

Figure 17

Comparison of power-supply ripples measured based on cavity simulator (blue) and real cERL two-cell cavity (red) under FF operation. The ripple frequency was set to 300 Hz, close to the real case. (a) FF and (b) FB control.

Figure 18

(Upper) 1.6-ms and $800\text{−}\mu \mathrm{A}$ beam current measured by oscilloscope and (lower) simulated current used in simulator.

Figure 19

Comparison of beam-loading effects for cavity simulator-based LLRF system (blue) and LLRF system for cERL injector (red) under FB operation. The cavity parameters were selected based on the cERL nine-cell cavity in the injector ($Q_L\approx 1.2\times {10}^6$) and the P gain for feedback was approximately 50.

Figure 20

Closed-loop operation based on cavity simulator with and without filter. In the without filter case (blue line), even a very low gain (P gain $\approx 20$) resulted in system oscillation, because of the existence of the $8\pi /9$ mode. In the with-filter case, the system was stable, even with high P gain up to 300.

Figure 21

Measured cavity pick-up signal on cavity simulator in presence of 0.8-mA beams. The blue and red waveforms represent the PI and “$\mathrm{PI}+\mathrm{DOB}$”-based control, respectively.