CERN’s Super Proton Synchrotron 200 MHz cavity regulation upgrade: Modeling, design optimization, and performance estimation

CERN’s Super Proton Synchrotron (SPS) accelerates protons to $450\mathrm{GeV}/c$ and transfers them into the Large Hadron Collider (LHC). It is currently one of the limiting factors in increasing the beam intensity and thus the luminosity of the LHC. As part of the LHC injectors upgrade project, the SPS 200 MHz rf system has been modified during the CERN long shutdown 2 (January 2019–April 2021), resulting in a new layout containing two additional cavities. The goal is to improve longitudinal stability required for the planned doubling of the beam intensity for the high luminosity LHC. In parallel with the upgrade of the high-power rf, a new low-level rf (LLRF) system has been designed, including a new cavity field regulation system. This work presents a model of the beam-rf interaction which includes a detailed representation of the LLRF controlling the cavity. This model is used to determine the optimal LLRF design for maximum loop stability and beam loading compensation. Finally, the performance of the upgraded LLRF is estimated.

Figure 1

SPS rf and LLRF block diagram.

Figure 2

Three-section cavity. Left: $Z_g(f)$ after compensation of the $\tau /2$ delay. Right: real (red) and imaginary parts of $Z_b(f)$.

Figure 3

Four-section cavity. Left: $Z_g(f)$ after compensation of the $\tau /2$ delay. Right: real (red) and imaginary parts of $Z_b(f)$.

Figure 4

SPS feedback block diagram.

Figure 5

$H_{\mathrm{cav}}(f)$ filter response and phase for three- and four-section cavity.

Figure 6

Measured and simulated total cavity voltage phase, with feedforward off (left) and feedforward on (right). Feedback is on for both figures.

Figure 7

Feedforward/feedback beam loading compensation. Total beam induced rf voltage from four three-section cavities and two four-section cavities.

Figure 8

Transmitter power for three-section cavity.

Figure 9

Transmitter power for four-section cavity.

Figure 10

Uncompensated beam loading with nonideal feedforward gain (feedback off). Vertical markers indicate the extent of the batch.

Figure 11

Uncompensated beam loading with nonideal feedforward gain (feedback on). Vertical markers indicate the extent of the batch.

Figure 12

Uncompensated beam loading for different OTFB bandwidth/gain and ideal feedforward. The batch is indicated with vertical dashed lines.

Figure 13

Coupled cavity feedback block diagram. Solid lines show feedback inputs from cavities the LLRF system controls. Dashed lines show feedback inputs from other cavities.

Figure 14

Uncompensated beam loading with coupled feedback (three-section cavity only). The feedforward is also on. The batch is indicated with vertical dashed lines.

Figure 15

Uncompensated beam loading with coupled feedback. The feedforward is also on. The batch is indicated with vertical dashed lines.

Figure 16

Transmitter power for three-section cavity with coupled feedback.

Figure 17

Transmitter power for four-section cavity with coupled feedback.

Figure 18

Transmitter power with detuning, clamping, and band-limited transmitter response. Steady state required power with (continuous) beam shown for comparison. The batch is indicated with vertical dashed lines.

Figure 19

$H_{\mathrm{cav}}(f)$ filter comparison. Left: three-section cavity. Right: four-section cavity.

Figure 20

Beam phase with original and new filters.

Figure 21

Transmitter power comparison Left: three-section cavity. Right: four-section cavity.

Figure 22

Induced voltage with proposed design.

Figure 23

Beam phase with baseline design.

Figure 24

Transmitter power with proposed design. First and last bunch for each batch are indicated with vertical dashed lines. Left: three-section cavity. Right: four-section cavity.

Figure 25

Impulse response to generator current. Diagonal term $h_{gs}(t)$ normalized. For $\mathrm{\Delta }{f}_0\tau =0$ (left) and $\mathrm{\Delta }{f}_0\tau =0.2$ (right).

Figure 26

Impulse response to generator current. Off-diagonal term $-h_{gc}(t)$ normalized. For $\mathrm{\Delta }{f}_0$ $\tau =0$ (left) and $\mathrm{\Delta }{f}_0$ $\tau =0.2$ (right).

Figure 27

Impulse response to beam current. Diagonal term $h_{bs}(t)$ normalized. For $\mathrm{\Delta }{f}_0\tau =0$ (left) and $\mathrm{\Delta }{f}_0\tau =0.2$ (right). The top trace is the even-symmetric part, the middle trace shows the odd-symmetric and the bottom trace is the sum that is causal.

Figure 28

Step response to beam current (normalized). The time index refers to the 31.25 MHz rate. The top left trace is the response to the real part of the impedance (even-symmetric impulse response), the top right trace shows the odd-symmetric part and the bottom trace is the sum.

Figure 29

Even-symmetric (left) and odd-symmetric impulse responses of the feedforward FIR filter.

Figure 30

Compensation voltage due to the feedforward (blue) and beam induced voltage (orange). Left: voltage caused by the even-symmetric impulse response compared to the one caused by the real part of cavity impedance (perfect superposition). Right: voltage caused by the odd-symmetric impulse response compared to the one caused by the imaginary part of cavity impedance.

Figure 31

Left: Compensation voltage (blue) and beam induced voltage (orange). Right: Compensation error.