Simulation, measurement, and mitigation of beam instability caused by the kicker impedance in the 3-GeV rapid cycling synchrotron at the Japan Proton Accelerator Research Complex

The transverse impedance of eight extraction pulsed kicker magnets is a strong beam instability source in the 3-GeV rapid cycling synchrotron (RCS) at the Japan Proton Accelerator Research Complex. Significant beam instability occurs even at half of the designed 1 MW beam power when the chromaticity ($\xi$) is fully corrected for the entire acceleration cycle by using ac sextupole (SX) fields. However, if $\xi$ is fully corrected only at the injection energy by using dc SX fields, the beam is stable. In order to study realistic beam instability scenarios, including the effect of space charge and to determine practical measures to accomplish 1 MW beam power, we enhance the orbit particle tracking code to incorporate all realistic time-dependent machine parameters, including the time dependence of the impedance itself. The beam stability properties beyond 0.5 MW beam power are found to be very sensitive to a number of parameters in both simulations and measurements. In order to stabilize a beam at 1 MW beam power, two practical measures based on detailed and systematic simulation studies are determined, namely, (i) proper manipulation of the betatron tunes during acceleration and (ii) reduction of the dc SX field to reduce the $\xi$ correction even at injection. The simulation results are well reproduced by measurements, and, as a consequence, an acceleration to 1 MW beam power is successfully demonstrated. In this paper, details of the orbit simulation and the corresponding experimental results up to 1 MW of beam power are presented. To further increase the RCS beam power, beam stability issues and possible measures beyond 1 MW beam power are also considered.

Figure 1

Schematic view of 3-GeV RCS at J-PARC. The eight pulsed kicker magnets (KMs) placed in the second straight (extraction) section are used for beam extraction. The extracted beam is delivered simultaneously to the MLF and MR. The transverse impedance of the KMs is a strong source of beam instability in the RCS.

Figure 2

Layout of the RCS extraction straight section. A total of eight pulsed kicker magnets is used for the beam extraction. The first three are placed upstream of a horizontally focusing quadrupole magnet (QFL), while the other five are placed downstream of the QFL. The transverse impedance of the kicker magnets is the dominant source of beam instability in the RCS.

Figure 3

Real (left) and imaginary (right) parts of theoretically given transverse impedances of a KM in the RCS [5]. The left and right plots show the real and the imaginary parts of the impedance, respectively. The impedance of a relativistic beam is seen to be much higher than that of a nonrelativistic beam. The expanded view of the impedances at the lower frequency region are shown in the lower plots.

Figure 4

Sinusoidal $B$ field pattern of bending magnets, the corresponding kinetic energy of the beam, and the change in the synchronous phase as functions of time. Time-dependent changes in many parameters, including error sources, and kicker impedances are implemented in the present orbit simulations.

Figure 5

The rf voltages used for RCS beam acceleration. The $V_2$ is applied until 5 ms from the beam injection, while it is kept 80% of $V_1$ for the first 1 ms, in order control the charge density of the beam and reduce the effect of space charge at a lower beam energy.

Figure 6

Simulated longitudinal phase space distributions and their projections onto the longitudinal axis of the circulating beam at the end of injection obtained without (left) and with (right) longitudinal injection painting.

Figure 7

Simulated and measured results of beam survival with strong and weak space charge controlled by rf patterns and longitudinal injection painting for beam power of 0.375 MW. The space-charge-induced beam loss is as high as 3% when applying only $V_1$, but it can be well mitigated by adding $V_2$ and applying longitudinal injection painting. The time structure of beam intensity loss in the simulation is shown to be consistent with the measurement results.

Figure 8

Betatron tune footprints at the end of injection obtained in the simulation by using single (left) and dual (right) rf voltages for a beam power of 0.375 MW. The solid black lines are the integer and half integer resonances at ${\nu }_{x,y}=6$ and ${\nu }_{x,y}=6.5$, respectively.

Figure 9

Twiss parameters (${\beta }_x$ and ${\beta }_y$) in the extraction kicker region. The impedance node in the simulation is placed at the average ${\beta }_x$, as shown by the red arrow.

Figure 10

SX field strength factor and chromaticity ${\xi }_x$ as functions of the beam acceleration time in the RCS. The situation is the same for ${\xi }_y$.

Figure 11

Beam centroid motion and instability growth due to the transverse impedance of extraction kicker magnets, as obtained in the simulation at a beam power of 0.5 MW. The values of $E_{\mathrm{inj}}$ in the left and the right figures are 0.181 and 0.4 GeV, respectively. Beam instability occurs only when $\xi$ is fully corrected for the entire acceleration period, but no beam instability occurs if $\xi$ is fully corrected only at the injection energy.

Figure 12

Measured results of the beam centroid evolution at 0.5 MW beam power. The experimental results agree well with those obtained in the simulations (Fig. 11).

Figure 13

Simulated (left) and measured (right) results of beam intensity versus tune ${\nu }_x$, obtained from FFTs of turn-by-turn beam positions for 1000 turns at the middle of the acceleration cycle of 10 ms.

Figure 14

Simulated (left) and measured (right) results of beam instability suppression by the effect of strong space charge (peaky bunch) for 0.375 MW beam power. The beam tends to be stable (green) when the space charge effect is strengthened by turning off the second harmonic rf voltage (apply $V_1$ only) and by not performing longitudinal injection painting.

Figure 15

Simulation results of beam instability growth dependence on the transverse injection painting emittances for 0.375 MW beam power and applying only $V_1$. In this particular condition with strong space charge effect, the Landau damping effect is quite significant, resulting in no remarkable difference on the beam stability condition within the present variation of transverse beam emittance.

Figure 16

Simulation results of beam instability growth dependence on the vacuum chamber radius $\rho$. The indirect space charge effect is reduced by an increase of $\rho$, and the beam tends to destabilize with increasing $\rho$.

Figure 17

Estimated $\mathrm{\Delta }{\nu }_{\mathrm{coh}}$ as a function of time for three different vacuum chamber radii for a beam power of 0.375 MW. The synchrotron tune ${\nu }_s$ is also shown by the black line. The injection and extraction energies are 0.181 and 3 GeV, respectively.

Figure 18

Simulation results of betatron frequency spectra for choices of the vacuum chamber radius, representing a horizontal betatron tune shift at around 14 ms of the acceleration time.

Figure 19

Manipulation of tune ${\nu }_x$ to suppress beam instability at beam power of 1 MW. The ${\nu }_x$ at injection is typically set to 6.45, but it has to be manipulated as a function of time in order to stabilize the beam. The ${\nu }_x$ without any manipulation corresponds to the line denoted by (a).

Figure 20

Simulated (top) and measured (bottom) results of beam instability growth at a beam power of 0.75 MW. The beam instability, which occurs without any tune manipulation, can be well mitigated by applying a proper tune manipulation.

Figure 21

Demonstration of beam instability suppression in the simulation (green) as well as in measurement (blue) by using a narrower momentum spread $\mathrm{\Delta }p/p=0.08\%$ (rms) in the injected beam.

Figure 22

Simulated (left) and measured (right) results of bunching factor $B_f$ with rms injected $\mathrm{\Delta }p/p$ of 0.18% and 0.08% as shown by the red and green lines, respectively.

Figure 23

Simulated (left) and measured (right) results of beam instability dependence on ${\nu }_x$ manipulations [Figs. 19], for 1 MW beam power, when only a quarter of the full chromaticity correction at injection by using dc $\times 0.25$ field was applied. With a very severe beam instability at 1 MW, the simulation results show the necessity of a proper choice of ${\nu }_x$ manipulations in order to suppress the beam instability. Simulated and experimental results were found to be consistent in all cases.

Figure 24

Simulated results of beam instability suppression at 1 MW obtained by reducing the degree of chromaticity correction. In addition to the proper manipulation of ${\nu }_x$ (see Fig. 19), no more than a quarter of the full $\xi$ correction at injection and almost no correction at extraction can be applied to stabilize the designed beam power of 1 MW.

Figure 25

Measured beam instability mitigation at a beam power of 1 MW by reducing the degree of chromaticity correction using the same patterns as those applied in the simulations (Fig. 24). Similar to the simulation results, the designed 1 MW beam acceleration was accomplished by keeping $\xi$ as close as possible to the natural value with SX dc $\times 0.25$ or SX off.

Figure 26

Transverse ${\epsilon }_{\mathrm{rms}}$ of the circulating beam at the extraction energy obtained in the simulation as a function of the degree of chromaticity correction controlled by a SX dc field. Disregarding KM impedances, which are not included in these results, fully corrected $\xi$ at the injection energy leads to the minimum beam emittances extracted from the RCS.

Figure 27

Simulated results of beam centroid growth for beam powers of 1 (black line), 1.2 (blue line), and 1.5 MW (green line) employing reduced KM impedances by nearly a half. Beam powers beyond 1 MW can also be stabilized even with fully corrected $\xi$ at the injection energy by using the SX dc $\times 1$ field.