Suppression of eddy-current effects in beam injection using a pulsed sextupole magnet with a new ceramic chamber

At the Photon Factory storage ring (PF ring) of the High Energy Accelerator Research Organization (KEK), a pulsed sextupole magnet (PSM) has been used for top-up injection for the first time. Following its successful operation at the KEK, this new injection scheme was expanded to one with a nonlinear kicker in BESSY II and was then applied at UVSOR and Aichi SR in Japan. Also, the PSM system in the PF ring was improved by introducing a rectangular shape for the magnet’s bore to strengthen the magnetic field. However, this upgraded PSM was not implemented for user operation because it induced a horizontal oscillation of the stored beam with a maximum amplitude of 5.0 mm. This oscillation was assumed to be caused by eddy currents originating from the uniform inner coating of the ceramic chamber. We, therefore, developed a modified ceramic chamber with a new patterned coating designed to suppress the eddy current–induced magnetic field. The pattern shape was optimized to suppress this magnetic field and, simultaneously, to reduce the resistive wall impedance. A fine-line pattern-coating process, originally developed for a ceramic chamber with an integrated pulsed magnet, was modified for application with the magnet’s chamber of the sextupole. The maximum horizontal oscillation amplitude was suppressed by a factor of 16 by using the new PSM chamber without any issues related to beam instability. Details of the historical background of the upgrading of the PSM system, an investigation of the cause of the abnormal oscillation problem, the development of the new process for coating the ceramic chamber, and the results of the beam-response measurements for the new ceramic chamber installed in the PF ring are reported in this article.

Figure 1

Comparison of injection schemes using a conventional pulsed bump orbit (A) and a pulsed multipole magnet (B). The dynamic aperture is indicated schematically to illustrate the merging of the injection beam into the narrow dynamic aperture.

Figure 2

Photographs of the magnets and ceramic chambers of PSM1 (A-1, A-2) and PSM2 (B-1, B-2).

Figure 3

PSM2 magnetic-field shape at each position in the magnet gap along the horizontal axis with the ceramic chamber. The red arrows show the timing of the kicking of the injected beam. The vertical axes for $x=4\mathrm{mm}$ and $x=0\mathrm{mm}$ are magnified by a factor of 3.

Figure 4

Strength reduction and timing delay as a result of the effects of eddy currents in a pulsed field. The pulse width of the half-sine waveform with the chamber widened from 1.2 to $1.5\mathrm{\mu }\mathrm{s}$ compared with the case without the chamber.

Figure 5

The dependence of the eddy-current magnetic field on the supplied voltage.

Figure 6

Integrated magnetic field distribution for the horizontal axis when the ceramic chamber is inserted into the magnetic bore.

Figure 7

Eddy-current effects of the magnet, as observed without a chamber installed in the bore. The left-hand figure shows the eddy-current signal of the magnet in the absence of the chamber. The right-hand figure shows the eddy-current signal, including eddy currents from the magnet and the chamber coating, in the presence of the chamber. Notably, the pulse width of the eddy-current signal in the absence of the chamber was shortened to $1.6\mathrm{\mu }\mathrm{s}$ from $1.8\mathrm{\mu }\mathrm{s}$ in the presence of the chamber.

Figure 8

Magnet modeling to optimize the parameters of the comb-tooth-shaped coating. The left-hand figure shows the cross-sectional structure of the coil and coating plate. The right-hand figure shows a three-dimensional view of their structure with a uniform coating. The light-blue dots on the $x$-axis and $z$-axis are the magnetic-field measurement points.

Figure 9

Longitudinal slit model used to simulate the comb-tooth shape.

Figure 10

Temporal evolution of the supplied current for six coils.

Figure 11

Horizontal distribution with temporal evolution of the ratio between the vertical magnetic-field strength at each point in the case with a coating and the magnetic field at 15 mm in the case of no coating.

Figure 12

Suppression of the eddy-current magnetic field at the center of the magnet, through which the stored beam passes.

Figure 13

The eddy-current magnetic field is suppressed at an off-center position of the magnet, through which the injection beam passes.

Figure 14

Estimation by gdfidl of the beam heat generation for the pattern-coating shape of an implementation model.

Figure 15

Comb-tooth-patterned coating test using an acryl plate.

Figure 16

Comb-tooth-patterned coating for the PSM2 ceramic chamber using FLiP technology.

Figure 17

Temperature sensors attached to the ceramic chamber surface to monitor the heat generated by the beam heat load.

Figure 18

Schematic view of the lattice configuration from the injection point to PSM2 in the PF ring. BPM013 was used for turn-by-turn oscillation measurements of the stored beam. The blue rectangles represent bending magnets, the red ones represent quadrupole magnets, and the light-blue ones represent undulators.

Figure 19

Oscillation of the stored beam immediately after excitation of the PSM2 with an excitation current of 1000 A. The blue dots indicate the case where the inner surface of the ceramic chamber is fully coated (all coat); the red dots indicate the case where the inner surface is coated by the comb-tooth coating. The left- and right-hand figures show the results of horizontal and vertical beam oscillations, respectively.

Figure 20

Horizontal beam oscillation data for the simulated error kick by an eddy-current magnetic field.

Figure 21

Measured horizontal oscillation of the stored beam using the delayed-timing data sets in beam experiments.