Coupled bunch mode zero correction using orbit measurements and rf system phase feedback

The target bandwidth of the Advanced Photon Source Upgrade (APS-U) fast orbit feedback (FOFB) is dc-1000 Hz where the synchrotron tune will be between 100 and 560 Hz. This overlap places coupled bunch mode 0 (CBM0) induced horizontal position offsets within the FOFB bandwidth range, affecting our ability to achieve APS-U goals for beam stability. In this article, we present a new feedback technique to damp CBM0 oscillations using the existent FOFB controller framework with no additional hardware and software requirements. Based on the theory of synchrotron oscillations, we developed a feedback algorithm that uses the beam horizontal position measurements at dispersive beam position monitors (BPM) as input and the low level rf (LLRF) phase as an actuator. We demonstrated via experiments in the present APS storage ring that this configuration can correct CBM0 oscillations, and also it can work simultaneously with orbit feedback used to damp ordinary betatron orbit. The simulation model for the proposed orbit to rf phase feedback system is implemented in matlab/simulink to guide us in the controller design. Simulation responses are in good agreement with measurements.

Figure 1

Orbit to rf phase feedback configuration.

Figure 2

Angle between dispersion and betatron orbit ${\theta }_{\eta }$ when 440 BPMs in the ring are used to define orbit.

Figure 3

Angle between dispersion and betatron orbit ${\theta }_{\eta }$ when 16 BPMs are used to define orbit.

Figure 4

Block diagram showing orbit to rf phase feedback integrated into APS-U prototype FOFB system. The orbit feedback loop is shown in “black” and orbit to rf phase feedback loop is shown in “red.”

Figure 5

Block diagram showing the experimental setup for the orbit to rf phase feedback tests.

Figure 6

Beam phase and BPM position responses measured for 1 A step input.

Figure 7

Open loop chirp responses, the $x$ axis is instantaneous chirp frequency. A resonant peak at synchrotron frequency is observed in $\varphi$ and $x$ responses.

Figure 8

Closed loop chirp responses $K_d=-5\times {10}^{-6}$, $x$ axis is instantaneous chirp frequency. Resonant peaks are suppressed compared to open loop responses in Fig. 7.

Figure 9

Comparison of BPM position frequency response magnitudes for different $K_d$ gains. Resonant peak magnitude is reduced with an increase in $K_d$.

Figure 10

Comparison of pulse responses for different $K_d$ gains. Faster damping of the synchrotron oscillations is achieved with an increase in $K_d$.

Figure 11

Comparison of beam frequency spectrum measured in open and closed loop configurations.

Figure 12

Comparison of measured input disturbance attenuation at corrector drive.

Figure 13

Comparison of measured input disturbance attenuation at phase drive.

Figure 14

Comparison of ac rms orbit motion measured in different feedback configurations.

Figure 15

Underdamped oscillation fit of BPM position response to 1 A phase step

Figure 16

Main window of simulink model.

Figure 17

Validation of closed loop simulation model with pulse input applied to phase drive.

Figure 18

Validation of closed loop simulation model with sine sweep input applied to phase drive.

Figure 19

Main window of the simulation model for FOFB+CBM0 correction configuration.

Figure 20

Input disturbance attenuation at corrector drive with FOFB+CBM0 correction.

Figure 21

Input disturbance attenuation at phase drive with FOFB+CBM0 correction.