Advanced simulation study on bunch gap transient effect

Bunch phase shift along the train due to a bunch gap transient is a concern in high-current colliders. In KEKB operation, the measured phase shift along the train agreed well with a simulation and a simple analytical form in most part of the train. However, a rapid phase change was observed at the leading part of the train, which was not predicted by the simulation or by the analytical form. In order to understand the cause of this observation, we have developed an advanced simulation, which treats the transient loading in each of the cavities of the three-cavity system of the accelerator resonantly coupled with energy storage (ARES) instead of the equivalent single cavities used in the previous simulation, operating in the accelerating mode. In this paper, we show that the new simulation reproduces the observation, and clarify that the rapid phase change at the leading part of the train is caused by a transient loading in the three-cavity system of ARES. KEKB is being upgraded to SuperKEKB, which is aiming at 40 times higher luminosity than KEKB. The gap transient in SuperKEKB is investigated using the new simulation, and the result shows that the rapid phase change at the leading part of the train is much larger due to higher beam currents. We will also present measures to mitigate possible luminosity reduction or beam performance deterioration due to the rapid phase change caused by the gap transient.

Figure 1

Illustration of the ARES cavity structure (Ref. [9]). The accelerating (A-)cavity is coupled to the storage (S-)cavity via a coupling (C-)cavity. The C-cavity has a parasitic-mode (0 and $\pi$-mode) damper. An illustration of the coupled pendulum model is also shown.

Figure 2

Examples of the observed phase modulation caused by a bunch gap transient in KEKB operation. (a) LER with a beam current of 660 mA and (b) HER with 470 mA. The solid lines indicate the results of the simulation reported in Ref. [11], which used equivalent single-cell cavities operating in the accelerating mode.

Figure 3

Implementation of feedback loops in the simulation.

Figure 4

Simulation results of the phase modulation due to a 10% bunch gap for KEKB operation. (a) LER with the ARES cavities only and (b) the vector sum of ARES and SCC for HER.

Figure 5

Simulation results of the phase modulation in the ARES cavities (a) and SCCs (b) for HER to calculate the vector sum shown in Fig. 4.

Figure 6

Comparison of the result of the new simulation for LER (dashed red line) with the observed data (dots) and the previous simulation (solid black line). The observed data and the previous simulation are replotted from Fig. 2.

Figure 7

Simulation results of the amplitude (left) and phase (right) modulation due to the 2% bunch gap in ARES. The calculations are done for LER at SuperKEKB.

Figure 8

A plot of the simulated phase modulation shown in Fig. 7, enlarged to show the empty gap region.

Figure 9

ARES voltage (amplitude and phase) modulation simulated for HER in SuperKEKB.

Figure 10

SCC voltage (amplitude and phase) modulation simulated for HER in SuperKEKB.

Figure 11

Phase modulation of the vector sum of ARES and SCC voltage simulated for HER.

Figure 12

Plot of the phase difference between LER and HER (red solid $\mathrm{line}=\mathrm{\Delta }{\varphi }_{\mathrm{HER}}-\mathrm{\Delta }{\varphi }_{\mathrm{LER}}$). The right side is zoomed in around the gap.

Figure 13

Phase difference between LER and HER (red solid line) for a HER gap delay of 200 ns. The phase difference at the leading part of the train is reduced to 2.4 degrees for the collision.

Figure 14

Phase difference for a 3% gap with HER gap delay. The phase difference at the leading part of the train is almost canceled, while the phase difference of the other part in the train increased to 1.6 degrees.

Figure 15

Illustration of a bunch fill pattern for more effective mitigation. The bunch current at the leading part of the LER train is increased in two steps with a time interval $w_{\mathrm{s}}$ and the bunch current at the first step by $b_{\mathrm{s}}$. The gap lengths are ${\mathrm{g}}_L$ and ${\mathrm{g}}_H$ for LER and HER, respectively, and the HER gap is delayed by $d_g$.

Figure 16

Simulation result of phase difference for the best case of the fill pattern shown in Fig. 15. The gap length of both rings is 2% (200 ns), the current height at the initial step of the LER leading part ($b_s$) is half of the nominal current, the length of the initial step ($w_s$) is 140 ns and the delay of the HER gap ($d_g$) is 160 ns.