High-resolution, low-latency, bunch-by-bunch feedback system for nanobeam stabilization

We report the design, operation, and performance of a high-resolution, low-latency, bunch-by-bunch feedback system for nanobeam stabilization. The system employs novel, ultralow quality-factor cavity beam position monitors (BPMs), a two-stage analog signal down-mixing system, and a digital signal processing and feedback board incorporating a field-programmable gate array. The field-programmable gate array firmware allows for the real-time integration of up to fifteen samples of the BPM waveforms within a measured latency of 232 ns. We show that this real-time sample integration improves significantly the beam position resolution and, consequently, the feedback performance. The best demonstrated real-time beam position resolution was 19 nm, which, as far as we are aware, is the best real-time resolution achieved in any operating BPM system. The feedback was operated in two complementary modes to stabilize the vertical position of the ultrasmall beam produced at the focal point of the ATF2 beamline at KEK. In single-BPM feedback mode, beam stabilization to $50\pm 5\mathrm{nm}$ was demonstrated. In two-BPM feedback mode, beam stabilization to $41\pm 4\mathrm{nm}$ was achieved.

Figure 1

Schematic of the ATF layout, with the ATF2 focal point indicated as the IP [8].

Figure 2

Schematic of the ATF2 IP region, showing the final-focus magnets including quadrupoles (QF1FF, QD0FF) and sextupoles (SD0FF, SF1FF), and the elements of the FONT IP feedback system including dipole cavity BPMs IPA, IPB and IPC, reference cavity BPMs Ref $x$ and Ref $y$, and the stripline kicker IPK.

Figure 3

Schematic of the electric and magnetic field lines of (a) the TM010 mode for a circular cylindrical cavity BPM and (b) the TM210 mode (or $x$-dipole mode) for a rectangular cylindrical cavity BPM. The waveguides which couple to the TM210 mode are shown. There are also corresponding waveguides which couple to the $y$-dipole TM120 mode.

Figure 4

Schematic of the (a) cylindrical reference cavity BPMs and (b) rectangular dipole cavity BPMs [13].

Figure 5

Schematic of the IP BPM configuration, showing the IPAB mover block, with submovers ${\mathrm{m}}_1$, ${\mathrm{m}}_2$, and ${\mathrm{m}}_3$, on which IPA and IPB are mounted, and the IPC mover block with submovers ${\mathrm{m}}_{\mathrm{C}}$, ${\mathrm{m}}_{\mathrm{D}}$ and ${\mathrm{m}}_{\mathrm{E}}$. The nominal IP location, as used for beam-size measurements, is indicated.

Figure 6

Simplified block diagram of the two-stage down-mixing process of the dipole and reference cavity signals from GHz-level to baseband. The 700 MHz bandwidth band pass filters on the dipole cavity signal are centered on the dipole cavity frequency, $f_{\mathrm{dip}}$, and those on the reference cavity signal are centered on the reference cavity frequency, $f_{\mathrm{ref}}$. Diagram adapted from [17].

Figure 7

Block diagram of the FONT5A digital board showing the primary input and output signals used.

Figure 8

Photograph of the FONT5A digital board with the case removed [28, 29].

Figure 9

Representative digitized $I$, $Q$ and $q$ waveforms from IPC, for two-bunch-train operation with a bunch spacing of 280 ns. The waveforms were sampled at intervals of 2.8 ns.

Figure 10

Example vertical position calibration of IPA, using an 11-sample integration range: (a) $\frac{I}{q}$ and $\frac{Q}{q}$ versus trigger number; (b) $\frac{Q}{q}\text{versus}\frac{I}{q}$ (points); the line shows a least-squares fit to determine ${\theta }_{IQ}=-1.093\pm 0.006\text{radians}$; (c) the data points show $\frac{I^{\prime }}{q}$ versus QD0FF mover position, the red error bars show the standard error on the mean values at each QD0FF setting and the red line shows a least-squares fit, which yields $k=0.184\pm 0.002\mu {\mathrm{m}}^{-1}$.

Figure 11

Resolution vs number of samples integrated; the location of each integration window was chosen so as to optimize the geometric resolution. Results for the geometric (black) and fitting method for each BPM (green, gold, blue) are shown. The error bars represent the statistical uncertainty on the resolution.

Figure 12

Diagrams of feedback loops showing dipole cavity BPMs (IPA, IPB and IPC) and stripline kicker (IPK). (a) Single-BPM feedback with beam measurement and stabilization illustrated at IPC (red). (b) Two-BPM feedback, illustrated for position measurements at IPA and IPC (purple) with beam stabilization at IPB (red).

Figure 13

Photograph of the IP stripline kicker.

Figure 14

Schematic illustrating the principle of the direct latency measurement by adding a controlled delay to the kicker drive output signal.

Figure 15

The deflection of bunch-2 as a function of $\mathrm{\Delta }t$ (# 2.8 ns samples) defined in Fig. 14. The red line shows a sigmoid fit of the form $f(\mathrm{\Delta }t)=p_1+\frac{p_2-p_1}{1+10^{p_3-p_4\mathrm{\Delta }t}}$, where $p_1$, $p_2$, $p_3$ and $p_4$ are fit parameters. The dashed lines show the latency definition at 90% of maximum deflection.

Figure 16

Distributions of bunch positions measured at IPC, for bunch-1 (left) and bunch-2 (right) with feedback off (blue) and feedback on (red).

Figure 17

(a) IPC bunch-2 position versus bunch-1 position and (b) bunch-2 position versus trigger number; for feedback off (blue) and feedback on (red).

Figure 18

Distributions of bunch-1 (left) and bunch-2 (right) positions measured at IPB, with feedback off (blue) and feedback on (red). Feedback was performed in 2-BPM mode, stabilizing at IPB using beam position measurements from IPA and IPC.