Multiharmonic rf feedforward system for compensation of beam loading and periodic transient effects in magnetic-alloy cavities of a proton synchrotron

Beam loading compensation is a key for acceleration of a high intensity proton beam in the main ring (MR) of the Japan Proton Accelerator Research Complex (J-PARC). Magnetic alloy loaded rf cavities with a Q value of 22 are used to achieve high accelerating voltages without a tuning bias loop. The cavity is driven by a single harmonic ($h=9$) rf signal while the cavity frequency response also covers the neighbor harmonics ($h=8,10$). Therefore the wake voltage induced by the high intensity beam consists of the three harmonics, $h=8,9,10$. The beam loading of neighbor harmonics is the source of periodic transient effects and a possible source of coupled bunch instabilities. In the article, we analyze the wake voltage induced by the high intensity beam. We employ the rf feedforward method to compensate the beam loading of these three harmonics ($h=8,9,10$). The full-digital multiharmonic feedforward system was developed for the MR. We describe the system architecture and the commissioning methodology of the feedforward patterns. The commissioning of the feedforward system has been performed by using high intensity beams with $1.0\times {10}^{14}$ proteins per pulse. The impedance seen by the beam is successfully reduced and the longitudinal oscillations due to the beam loading are reduced. By the beam loading compensation, stable high power beam operation is achieved. We also report the reduction of the momentum loss during the debunching process for the slow extraction by the feedforward.

Figure 1

The frequency response of the accelerating gap and the harmonics covered by the impedance.

Figure 2

A simplified block diagram of the MR LLRF control system.

Figure 3

Typical waveform of the wake voltage just after K1–K4 timings. (Top) K1, (second top) K2, (third top) K3, and (bottom) K4 timing.

Figure 4

Harmonic components of the wake voltage.

Figure 5

A conceptual diagram of the rf feedforward method. The feedforward module generates $-i_{\mathrm{beam}}$ so that the wake voltages are canceled.

Figure 6

Block diagram of the multiharmonic rf feedforward system for the MR.

Figure 7

Signal flow of the segmented waveform capturing.

Figure 8

A schematic of segmented waveform data processing.

Figure 9

A comparison of the impedances and the feedforward transfer function of cavity #8: (top) in case of constant gain and phase patterns for all harmonics; (bottom) the result after two iterations.

Figure 10

A comparison of the harmonic components of cavity #8 gap voltage without and with feedforward; (top) full accelerating cycle; (bottom) magnified plot during injection period.

Figure 11

Transfer functions of the feedforward system #8 after commissioning: (top) injection period; and (bottom) near extraction.

Figure 12

Mountain plots of the WCM signals during the injection period (left) without and (right) with feedforward. Bottom plots are magnified ones just after K1 injection timing.

Figure 13

Mountain plots of the WCM signals from injection to extraction (left) without and (right) with feedforward. Bottom plots are magnified ones of the K1 injected bunches around the smoothing period.

Figure 14

Typical momentum deviation ($dp/p$) calculated by using the BPM signals (top) without and (bottom) with feedforward.

Figure 15

Typical beam loss monitor signal in the arc sections without and with feedforward.

Figure 16

Comparison of the momentum deviation during the debunching process, without feedforward and gap short, with feedforward, and with gap short.