The Leakage Field of the New High-Field Septum Magnets for Fast Extraction in Main Ring of J-PARC

As part of the effort to increase the beam power of the Main Ring (MR) for fast extraction (FX) in J-PARC to 750 kW, five new septum magnets for FX (FX-septa) were installed in the MR in 2022. The most significant goal for the magnets was to achieve an extremely low leakage field in the circulating line. To realize the low leakage field, new pure iron duct-type magnetic shields were mounted in the circulating ducts of the two high-field FX-septa in 2022. In July 2022, we verified that the impact of the leakage field of all of the FX-septa on the 3-GeV circulating beam was below 10% of that of the previous FX-septa. We also measured the leakage field in the circulating ducts of the two high-field FX-septa with new shields in October 2022, and confirmed that the quadrupole field component was reduced to ≈1% of that of the previous high-field FX-septa.


Introduction
The J-PARC Main Ring (MR) is a synchrotron that provides a high-intensity proton beam with an energy of 30 GeV to the neutrino facility (NU) or the hadron facility.The beam operation cycle until summer of 2021 was 2.48 s, and the present maximum beam power for the fast extraction (FX) mode is 515 kW, achieved in 2021 [1].To increase the beam power to a new target of 1.3 MW by 2028, we plan to reduce the operation cycle to 1.16 s and increase the number of particles in the bunches [2].As a first step towards the goal, the MR was upgraded during the long-shutdown from July 2021 to the end of May 2022 to increase the beam power to the original design value of 750 kW for an operating cycle of 1.3 s.The magnets for FX (FXmagnets) in the MR were also upgraded [3,4,5].The FX-magnets, which are used for switching the proton beam direction to the NU or beam abort dump (ABT), consists of five kicker magnets, two low-field septum magnets and four high-field septum magnets (HF-septa).The four HFsepta are conventional type with a typical field strength of ≈1 T, and are called septum magnet 30 (SM30), SM31, SM32 and SM33, in order from upstream (Fig. 1).In the upgrade, the septa were replaced with new septa [6].The beam loss of the low-energy beam around 3 GeV at the injection period and at the beginning of acceleration dominates the total beam loss in the MR because the emittance of the low-energy beam is large.Therefore, the multi-pole component of the leakage field in the circulating line of the FX-septa must be sufficiently small to suppress the beam loss of the beam halo.However, the leakage fields of the previous FX-septa had large quadrupole field components, corresponding to ≈3% of the main quadrupole magnet [7].Hence, the most significant technical goal for the new FX-septa is to achieve an extremely low leakage field, which is negligible compared with the ≈3% contribution in the previous septa.By the end of May 2022, all the FX-septa except one magnet have been upgraded [5].

Reduction of the leakage field of HF-septa
The origin of the largest leakage field of the FX-septa is the opening on the side of the gap of the magnet yoke.To reduce the leakage field, the opening has to be covered by magnetic shields (septum plate).A further significant origin is the end-coils at the beam exit, because they are located very close to the circulating line (end-fringe field).To reduce the end-fringe field, an effective measure is to cover the entire end-coils with magnetic shields (field clamp).In 2019, we confirmed that the end-fringe field of the new SM30 was reduced to ≈10% by using the field clamps [8].The integrated normal quadrupole coefficient (K 1 L = d dx ( B(s)ds) / (Bρ); x is horizontal position, s is longitudinal position, B(s) is magnetic field strength and Bρ is beam rigidity) with a flat bottom (FB) current, which is used to extract the 3-GeV proton beam, was 1.5×10 −4 m −1 .We verified that the end-fringe and K 1 L are small enough for beam operation.
The leakage field of the new SM31 with the field clamps was measured in 2020 [5].The K 1 L with an FB and a flat top (FT) current were 4.8×10 −5 m −1 and 1.0×10 −4 m −1 , respectively, where the FT current is used to extract the 30-GeV proton beam.While the K 1 L were small, we observed a large end-fringe field of ≈170 Gs due to magnetic saturation of the septum plates.Thus, we produced an additional duct-type shield made of pure iron (inner shield) for the new SM31 to reduce the large end-fringe field.We also produced an inner shield for the new SM30 to further reduce the leakage field.The inner shield for the new SM30 has 1 mm thickness and 1.765 m length, and its shape is tapered in the same manner as the circulating duct, with the inner cross section of the entrance and exit being, respectively, 56.8 mm (width)×103.4mm (height) and 85.6 mm×103.4mm.The inner shield for the new SM31 has 3 mm thickness and 1.950 m length, and is also tapered such that the inner cross section of the entrance and exit are, respectively, 82.2 mm×99.4mm and 219.6 mm×99.4mm.The two inner shields were produced and mounted in each circulating duct in March 2022 (Fig. 2).In May 2022, we measured the end-fringe field around the downsteam of the new SM31 where a field strength of ≈170 Gs was observed, and confirmed that the field strength was ≈3 Gs.Therefore, the end-fringe field was reduced to ≈2% of the unshielded end-fringe field [5].

Verification of leakage field by the circulating beam
In June 2022, the first beam test with an operating cycle of 1.36 s after the upgrade of the MR was performed [9].In this beam test, we measured the K 1 L of the new FX-septa by a vertical betatron modulation (∆β y ) of the 3-GeV circulating beam, and compared it with the K 1 L of the previous FX-septa, measured in 2021.∆β y is caused by the leakage field of the FX-septa and is larger than the horizontal betatron modulation because the vertical betatron is tuned (ν y ) closer to the half-integer resonance than the horizontal betatron (ν x ).We applied an optimized current to the septa to extract the 3-GeV proton beam.Fig. 3 shows the ∆β y dependence on the longitudinal position, measured with the previous (left) and new (right) FX-septa.The figure indicates that a large ∆β y was generated by the previous FX-septa and K 1 L was −2.3×10 −3 m −1 .On the other hand, no significant ∆β y was generated by the new FX-septa, and an upper limit on K 1 L of −1.5×10 −4 m −1 was obtained.We verified that the impact of the leakage field of the new FX-septa on the 3-GeV circulating beam was below 10% of that of the previous septa.Hence, the new FX-septa with an extremely low leakage field is very useful for the high-intensity beam because it is expected to suppress the beam loss of the beam halo.The effect of the leakage field of the previous FX-septa had been compensated by using three trim coils in the quadrupole magnets, located just upstream and downstream of the FX-septa.However, going forward, these trim coils can be used to compensate the error field of the quadrupole magnets.

Measurement of leakage field
In October 2022, with the inner shields mounted, we measured the time-dependent longitudinal distribution of the vertical leakage field in the circulating ducts of the new SM30 and SM31 along several straight tracks: on the center of the beam-line (center track), parallel to the beam direction, ±13.4 mm from the center track in the horizontal direction (13-mm tracks), and ±26.1 mm from the center track (26-mm tracks).The 26-mm tracks were only for the new SM31 because the horizontal aperture of the new SM30 is not wide enough for measurement.The applied current shape applied FB currents of 535 A and 471 A to the new SM30 and 31, respectively, and FT currents of 3,843 A and 3,960 A (Fig. 4).The repetition cycle was 1.36 s, which is the same as that of the beam test in summer 2022.We used a Hall probe and a 16-bit analog-to-digital converter for recording the waveform of the magnetic field.Fig. 5 (top) shows the longitudinal distribution of the leakage field along the +13-mm track with a current of 0 A. A significant magnetic field structure was found over the entire area in spite of there being no current applied.We presumed that there is a residual field of the magnet yokes.The field integral along the track was ≈0.2 Gs•m, which corresponds to a bending angle of ≈0.002 mrad for the 3-GeV proton beam.Thus, the impact of this dipole field is sufficiently small.Second, we confirmed that the field strength of the leakage field with an FB current was almost the same as the residual field (Fig. 5 (middle)).This indicates that the contribution of the excited field by an FB current is much smaller than the residual field.Finally, we observed a significant excited field with an FT current, though the strength was sufficiently small (Fig. 5 (bottom)) especially, the end-fringe field of the SM31 was reduced to a few % by using the inner shield.A peak with a strength of ±4 Gs around s = 2.3 m on the 26-mm tracks was observed because there is a non-shielding space of 43 mm between the inner shields of the new SM30 and SM31, as seen in Fig. 2. Fig. 6 shows the time dependence of the K 1 L. The value for the FB current was (−1.1±5.8)×10−5 m −1 , where the errors represent the systematic uncertainties estimated from the variation of the field strength with a current of 0 A along the horizontal direction at the outside of the entrance of the new SM30 and exit of the new SM31.The variations were respectively ±0.05 Gs and ±0.02 Gs.The maximum value was ≈2×10 −5 m −1 , which is extremely small.The K 1 L of the new SM30 with an FB current was (−1.6±4.1)×10−5 m −1 , which is an order of magnitude smaller than that without the inner shield.The K 1 L of the new SM31 with FB and FT currents were respectively (+2.4±1.9)×10−5 m −1 and (+6.5±2.4)×10−6 m −1 , both smaller than that without the inner shield, with that for an FT current reduced to ≈5.4%.In comparison, the K 1 L with an FB current of the previous SM30 and SM31 were of the order of 10 −3 m −1 .Thus, we verified that the quadrupole field components of the new septa were reduced to below ≈1% of the previous septa.

Summary
We are working on upgrading the MR in J-PARC to increase the beam power, and have completed installation of three new high-field septa for FX by the end of May 2022.To realize an extremely low leakage field in the circulating line of the new SM30 and SM31, we mounted field clamps and inner shields.The impact of the leakage field on the 3-GeV circulating beam was measured in July 2022, and we confirmed that the associated modulation of the beta function by the leakage field was reduced by more than an order of magnitude.We also measured the

Figure 1 .
Figure 1.Layout and photographs of the previous and the new high-field FX-septa.

Figure 2 .
Figure 2. Illustration of the beam ducts and magnet yokes of the new SM30 and SM31.The inner shields were mounted in the circulating ducts.

Figure 3 .
Figure 3. Vertical betatron modulation generated by the leakage field of the previous FX-septa (left) and the new FX-septa (right).The dots are data and the line is a fit to the data.

14thFigure 5 .
Figure 5. Longitudinal distribution of the leakage field in the circulating duct with an applied current of 0 A (top), FB current (middle) and FT current (bottom).

Figure 6 .
Figure 6.Time dependence of the integrated normal quadrupole coefficient, K 1 L.