1 S. Enomoto KEK Mar. 22th, 2017 WP3 meetingMFM -MBXFS01b- S. Enomoto KEK Mar. 22th, 2017 WP3 meeting

2 Menus DC loop Z scan MFM at the magnet center 0 A → 12.2 A → 0ATransfer Function Current dependence of multipole components Z scan Long and Short rotating coils 688 A, 1 kA, 2kA, … 12 kA Field distribution along the magnet. Field integral 50, 100, 688, 1k, 2k, … 7k, 7.5k, 8k, …, 11.5 k, k, 12.0k, 12.1k, 12.2kA Z scan By long coil 688, 1k, 2k, … , 10 kA, 11 kA, 12 kA

3 Remark Magnetic Field Measurement was done after quench training.No quench (1 min) 1.9 K SSL No quench (1 hr) 1.9 K Ultimate (13 kA) 1.9 K Nominal (12 kA) Training of MBXFS01b Nominal current after two quenches Ultimate current after 5 quenches Current holding: 13 kA for 1 min, 12 kA for 1hour. Magnetic Field Measurement was done after quench training. A trouble in the power supply was occurred during Z-Scan by the short rotating Coils at 12 kA. → Z-Scan by short coils will be carried out in 2nd test cycle. The 0.8 mm-thick shims were inserted to the MP to increase coil pre-stress. →It is expected that multipole components are affected. The purpose of this MFM mainly to confirm the effect of the iron saturation above 6 kA and the influence of coil end. The MFM results in this report were corrected with taking into account the feed down effects.

4 Setup Vertical test stand at KEK Y Rotating coils Coil-C θ X Coil-B-15mm -48mm -18mm 15mm X Coil-B 18mm 48mm Coil-A ω Coil A: dipole Coil A – Coil B: dipole bucking Coil C: spare “Warm” bore Size of coils made of PCB Long: 350 mm x 30 mm Short: 80 mm x 30 mm Number of turns: 20 Long Short Coil-A Coil-B Coil-C 7m long GFRP shaft Anti-cryostat: f141.3 mm (OD) “Warm” bore: f108.3 mm (ID) GN2 flow from the bottom end of the rotating coils to suppress thermal shrinkage of the pipe Long Coils are used for a regular MFM. Small Coils are used for the detailed study of the field at the coil ends.

5 Data Acquisition DiagramMetro Lab PDI 5025 “Main” Coil (Coil A) Data Acquisition V・dt FFT Main Harmonic (B1) Metro Lab PDI 5025 SUM Data Acquisition V・dt FFT Other Harmonics Other Coil (Coil B) Analog Bucking (Coil A –Coil B) Trigger (Encoder) 𝜱 𝑴𝒂𝒊𝒏 = 𝒏=𝟏 ∞ 𝑵𝑳 𝑩 𝒓𝒆𝒇 𝒏 𝑹 𝒓𝒆𝒇 𝒏−𝟏 × 𝟏𝟎 −𝟒 𝒓 𝟐 𝒏 − 𝒓 𝟏 𝒏 𝒃 𝒏 𝐜𝐨𝐬𝐧 𝜽 + 𝒂 𝒏 𝐬𝐢𝐧 𝒏𝜽 HEIDENHAIN RON285 Agilent DMM 3458A Mag. Current (DCCT) Multi-meter [V] 𝜱 𝑩𝒖𝒄𝒌𝒊𝒏𝒈 = 𝒏=𝟏 ∞ 𝑵𝑳 𝑩 𝒓𝒆𝒇 𝒏 𝑹 𝒓𝒆𝒇 𝒏−𝟏 × 𝟏𝟎 −𝟒 ( 𝒓 𝟐 𝒏 − 𝒓 𝟏 𝒏 )−( 𝒓 𝟒 𝒏 − (−𝒓 𝟑 ) 𝒏 ) 𝒃 𝒏 𝐜𝐨𝐬 𝒏𝜽 + 𝒂 𝒏 𝐬𝐢𝐧 𝒏𝜽 Sony PL20 Z position Magnescale [m]

6 Methodology in Vert. MeasurementAmplitude determined by rotating coil geometry. Area of each coil turn is calculated and summed. Not calibrated by a reference magnet. The gain of Integrator is adjusted by the first rotation. Signal measurements are averaged over 5 rotations Phase adjustment DC loop: a1 may be zero at the magnet center. z-scan: a1 is averaged to be zero over 5 measurements (~1050mm) around the magnet center.

7 Transfer Function MBXFS01bRref in all of ROXIE calculations was taken to be 50 mm. ROXIE 3D: Calculated as an average B1 over z = ±175 mm Magnet exhibited saturation at currents greater than 5-6 kA. Measurements are consistent with the ROXIE 3D calculation.

8 b3 at Coil center MBXFS01b Above 6kA,𝑏 𝑛 𝑧=0,𝐼 = 𝐵 𝑛 (𝑧=0,𝐼) 𝐵 1 (𝑧=0,𝐼) × 10 4 Above 6kA, The influence of iron yoke saturation is well reproduced, but the mismatch still exists. →Next page, the figure w/ offset cancellation is shown. There is a difference between ramp up and down at b3. (Hysteresis curve) Note: ROXIE 3D model is not completed. The coil block geometry is given by approximation.

9 b3 after offset cancellationMBXFS01b reproduces the previous result (MBXFS01). Influence of iron saturation is not large than the ROXIE calculation.

10 b5 and b7 MBXFS01b MBXFS01b Above 6kA,𝑏 𝑛 𝑧=0,𝐼 = 𝐵 𝑛 (𝑧=0,𝐼) 𝐵 1 (𝑧=0,𝐼) × 10 4 MBXFS01b MBXFS01b Above 6kA, Measurements are consistent with the ROXIE 3D calculation. Hysteresis cannot be seen.

11 DC Loop: Other Harmonics at Magnet Center𝑏 𝑛 𝐼,𝑧=0 = 𝐵 𝑛 (𝐼,𝑧=0) 𝐵 1 (𝐼,𝑧=0) × 10 4 Un-allowed multipole components are less than with respect to the dipole field.

12 Z-Scan at 12kA Normal B1, b3, b5 and b7←RE LE→ ←RE LE→ Allowed multipoles (bn: odd): ROXIE3D calculations generally agree with the measurement. The detailed field distributions at the coil end will be measured by the short probe coils. LE→ ←RE LE→ ←RE 𝑏 𝑛 𝑧,𝐼=12𝑘𝐴 = 𝐵 𝑛 (𝑧,𝐼=12𝑘𝐴) 𝐵 1 (𝑧=0,𝐼=12𝑘𝐴) × 10 4

13 Z-Scan 12kA Skew Un-allowed multipole (an: odd):Good agreement is observed between ROXIE-3D and the coil asymmetry model including layer jump for LE. However, large offset for a1. In RE, the skew components may indicate additional tilt of pole angle in comparison with the design. (a1~2.6 mrad) LE→ LE→ ←RE ←RE LE→ ←RE LE→ ←RE 𝑎 𝑛 𝑧,𝐼=12𝑘𝐴 = 𝐴 𝑛 (𝑧,𝐼=12𝑘𝐴) 𝐵 1 (𝑧=0,𝐼=12𝑘𝐴) × 10 4

14 Z-Scan : Current Dependence, B1 by long coilLE→ Integral region: ~ mm kA kA (ROXIE 3D) (MBXFS01b / MBXFS01 / ROXIE 3D) 8.53 / 8.54 / kA

15 Z-Scan : Current Dependence, b3 by long coilROXIE Z-Scan : Current Dependence, b3 by long coil 𝑏 3 𝑧, 𝐼 𝑛 = 𝐵 3 (𝑧, 𝐼 𝑛 ) 𝐵 1 (𝑧=0, 𝐼 𝑛 ) × 10 4 MBXFS01b ←RE LE→ 12kA 11kA 10kA 9kA 8kA 7kA 6kA 5kA 4KA 3kA 2kA 1kA 0.688kA Influence of coil end on b3 was observed in the straight section .

16 Summary Plan to MFM (2nd operation cycle. 19 Mar. – 7 Apr.)Magnetic field measurement of the 2nd 2-m long D1 model magnet (MBXFS01b) was performed at the vertical test stand at KEK. The following items were measured in the 1st operational cycle DC loop at the coil center ( up to 12.2kA) Z scan by long rotating coil ( ~12 kA) Generally, good agreement is observed between the measurement and ROXIE. It was confirmed that field quality at the coil center was strongly influenced by the coil ends even in the 2-m model. Comparison with ROXIE 3D result is necessary. Cause of the offset and large difference between the measurement and ROXIE calculation in b3 has not been understood yet. Plan to MFM (2nd operation cycle. 19 Mar. – 7 Apr.) Z-Scan by small probe coils at 1 ~ 12 kA. Time dependence at injection current 688A.

17 Backup

18 Feed Down effect Normal bn MBXFS01b: Δ𝑢=2.05mm, Δ𝑣=-0.6mm Y’ YMagnet Frame Measurement Frame X X’ Y Y’ Δx Δy Feed down effect 𝒂 𝒑 = 𝒂 𝒑 + 𝒑 𝒓 𝟎 ( 𝒂 𝒑+𝟏 D𝒙- 𝒃 𝒑+𝟏 D𝒚) +~~~ 𝒃 𝒑 = 𝒃 𝒑 + 𝒑 𝒓 𝟎 ( 𝒃 𝒑+𝟏 D𝒙+ 𝒂 𝒑+𝟏 D𝒚)+~~~ MBXFS01b: Δ𝑢=2.05mm, Δ𝑣=-0.6mm

19 Skew an MBXFS01b: Δ𝑢=2.05mm, Δ𝑣=-0.6mm

20 12kA B1~b6 Large Coil Meas. FD corr. Δ𝑢=2.05mm, Δ𝑣=-0.6mm

21 b7~b12 Large Coil Meas. FD corr. Δ𝑢=2.05mm, Δ𝑣=-0.6mm

22 a1~a6 Large Coil Meas. FD corr. Δ𝑢=2.05mm, Δ𝑣=-0.6mm

23 a7~a12 Large Coil Meas. FD corr. Δ𝑢=2.05mm, Δ𝑣=-0.6mm