1. ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators Yasuhiro Watanabe (J-PARC / JAEA) Tracking between bending and quadrupole families in J-PARC RCS

2. To MR or MLF (3GeV) From Linac (400MeV) Layout Blue: Bending Magnet Red: Quadrupole Magnet Circumference348.3 m Injection energy400MeV Extraction energy3.0 GeV Output power1.0 MW Repetition rate25 Hz No. of Bending Magnets24 (1 family) Quadrupole Magnets60 (7 families) Sextupole Magnets18 (3 families) Collection Magnets52 Design parameters J-PARC RCS (Rapid Cycling Synchrotron) 40ms(25Hz) AC DC Magnet current waveform ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators

3. High-precision field tracking control for many magnet families using resonant circuits ・ Main magnet system in J-PARC RCS challenges high-precision tracking control between bending and seven quadrupole families using resonant circuits. ・ Tracking error sources are mainly nonlinear characteristics because it is different for each type of magnet. Nonlinear characteristics in magnet (1) Eddy current effects ・ Eddy current effects produce delay field ・ To reduce eddy current loop at the coil and the core Coil : Development of the stranded conductor Core : Slit at core edge ・ To correct the delay field (2) Magnetic saturation ・ Magnetic saturation produces harmonic field ・ Harmonic field correction using harmonic current control ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators

4. Resonant circuits for rapid-cycling magnet Resonant frequency Additional circuits Choke ・ Harmonic current control requires large capacity of power supply ・ Design policy ： Magnetic saturation ＜ 1% Freq.Impedance [Ω]Ratio 125 Hz2.041 250 Hz11958.2 375 Hz19796.5 4100 Hz270133 Estimated Q value : 60 ～ 100 Frequency [Hz] Impedance [Ω] Equivalent circuit Magnet Capacitor Q value Frequency characteristics 25Hz ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators Q=100 AC resistance

5. Bending magnet Design parameters Coil (Stranded conductor : 30mm×30mm)Slit at the Core edge Picture Gap height [mm]210 Core length [mm]2770 Injection field [T]0.42 Extraction field [T]1.1 Min. current [A]418 Max. current [A]2561 Weight [t]39 SUS pipe (Water channel) Wire Insulation (polyimide impregnated) Aluminum wire ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators Slit

6. Quadrupole Magnet Design parameters Type of MagnetQMA QMBQMCQMD Number of magnets33312 Bore diameter [mm]290330 410 Core length [mm]700900500900 Injection field [T/m]0.670.470.650.47 Extraction field [T/m]4.843.374.673.36 Minimum Current[A]182165228249 Maximum Current[A]131211781640 1818 Coil (Stranded conductor : 20mm×20mm)Slit at the Core edge Picture (Type QMD) ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators Slit

7. Resonant circuit of the bending magnets AC Power (3.8MW) DC Power (4.5MW) Magnet_24 Capacitor Choke Magnet_0 (Monitor only) Magnet_1 Magnet_2 Magnet_3 ・ ・ ChokeCapacitor 1 2 25 ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators

8. Resonant circuit of the quadrupole magnet (1) Power supply FamilyQFNQDNQFXQDXQFLQDLQFM Type of magnetQMA QMCQMAQMD QMB Number of magnets12 9663 Magnet inductance[mH]48.4 26.748.436.3 49.1 DC current [A]667687858620942955620 AC current (peak value)[Ap]401413515372566573372 Voltage to ground [kVp]4.04.22.95.44.2 1.8 Choke transformer[mH]96.8 56.8145.272.6 48 Resonant capacitor [uF]837 14725581116 1689 Power rating(average)[MW]0.740.780.840.490.700.710.20 ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators

9. Resonant circuit of the quadrupole magnet (2) Power Supply (DC+AC) Choke Capacitor Mag_1Mag_2 Mag_3Mag_4Mag_5Mag_6 Mag_11Mag_12 QFN, QDN(Magnet: Type QMA), QFX(Magnet: Type QMC) ChokeCapacitor 1263 ・ ・ ・ ・ ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators

10. Resonant circuit of the quadrupole magnet (3) QDX (Magnet: Type QMA) QFL, QDL (Magnet: Type QMD) QFM (Magnet: Type QMB) Mag_1Mag_2Mag_3 Mag_1Mag_2 Mag_3Mag_4Mag_5Mag_6 Mag_1Mag_2 Mag_3 Mag_4Mag_5 Mag_6 Mag_7Mag_8 Mag_9 Power Supply (DC+AC) Power Supply (DC+AC) Power Supply (DC+AC) Choke Capacitor ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators

11. Dynamic filed measurement of the bending magnet Long-flip coil 4100mm Coil width: 10mm ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators X-Y Stage

12. Measurement results with harmonic field correction (BM) Time [s] Magnet current [A] Dipole BL [Tm] FFT resultsMeasurement results ・ From 2 nd (50Hz), to 5 th (120Hz) component → Harmonic filed correction using harmonic current adjustment could reduce harmonic amplitude less than 0.01%. ・ Over 6 th (150 Hz) component → No harmonic field correction because the harmonic amplitude in the dipole filed is less than 0.01% ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators 400 MeV→3 GeV

13. Saturation problem of the bending magnet Design Measured Max. field 1.1 T → 1.15 T Max. current 2556A → 2703 A Saturation 1% → 2.8 % Q value 100 → 180 2.8% Saturation characteristics 0.15% BM tracking error BM tracking error [%] Time [ms] ・ BM tracking error was calculated from the RF frequency pattern. ・ Harmonic component ｓ caused by magnetic saturation appear. ・ BM power supply cannot correct harmonic field to pure sinusoidal because of shortage of power supply capacity.

14. Dynamic filed measurement of the quadrupole magnet Harmonic coil system Length: 2100mm Diameter: 270mm Stepping Motor Rotary encoder ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators

15. Magnet current [A] Quadrupole GL [T] Time [s] FFT results Measurement results ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators Measurement results with harmonic field correction (QMA) ・ From 2 nd (50Hz) to 5 th (120Hz) component → Harmonic filed correction using harmonic current adjustment could reduce harmonic amplitude less than 0.01%. ・ Over 6 th (150 Hz) component → No harmonic field correction because the harmonic amplitude in the dipole filed is less than 0.01%

16. Required harmonic current in case of harmonic field correction Amplitude of harmonic current [A] Fundamental amplitude in magnet current[A] Phase of harmonic current [rad] 50Hz 75Hz 100Hz 50Hz 75Hz 100Hz amplitude phase ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators Fundamental amplitude in magnet current[A]

17. Measurement of eddy current effects ・ Phase delay is proportional to amplitude of fundamental current. ・ Phase delay is inversely proportional to core length because eddy current effect mainly occurs at the core edge. QMC QMA QMB QMD Core length : 500mm Core length : 700mm Core length : 900mm Phase delay [rad] (50 us) (30 us) ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators Fundamental amplitude in magnet current[A]

18. Block diagram of QM power supply control Harmonic current control to reduce harmonic component of the magnetic field Phase delay collection caused by eddy current effect GLdc GLac GLdc Magnet current Reference field value ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators

19. Tune variation and estimation of QM tracking error 0.4% QM tracking error Before correction Measured Tune Horizontal Vertical QM tracking error [%] Time [ms] Measured Tune 0.03 ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators ・ To reduce the tune variation during acceleration, we tried the harmonic correction for the QM field pattern ・ The QM field pattern was adjusted so as to fit the BM field pattern 。

20. Harmonic correction for the QM field pattern Vertical Time [ms] ― Measured tunes (No correction) ― Measured tunes (W/ 1 st cor.) ― Measured tunes (W/ 1 st & 2 nd harmonic cor.) ・・・ calculated tunes (W/ 1 st & 2 nd harmonic cor.) Tracking error x B  Measured Tune Horizontal Time [ms] Measured Tune Fitting function f(t) =p(1) x sin(1 xωt)+p(2) x sin(2 xωt) +p(3) x sin(3 xωt)+p(4) x sin(4 xωt) p(1)= 0.275E-01 p(2)=-0.661E-02 p(3)=-0.201E-02 p(4)= 0.896E-03 QM correction pattern ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators After correction

21. Tune variation in case of user operation Time (ms) Tune Horizontal Vertical ー measurement ー calculation (A) (B) (A) (B) To avoid the resonance cross ( =0.5), the tune is now adjusted to (B) by reducing the top of the QFM (-6%) and QDL(-1%) field patterns with DC and fundamental (25Hz) amplitude and phase manipulation. (A) W/o manipulation (B) W/ manipulation ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators

22. Summery ・ Recent high-intensity proton synchrotron has many quadrupole magnet families for the purpose of flexible beam operation. ・ In J-PARC RCS, main magnet system consists of bending and seven quadrupole families excited from resonant circuits. ・ Eddy current effects from 25 Hz excitation was reduced and corrected. ・ The harmonic field correction using field measurement data was imperfection because of saturation problem of the bending magnet. ・ The harmonic field correction using measured tune data has been successfully demonstrated reduction of the tune variation during acceleration. ・ In case of present user operation (500 kW), the harmonic field correction was not used because the serious beam loss didn’t occurred. ・ The harmonic field correction will be useful method for high intensity operation (1 MW). ICFA mini-Workshop on Beam Commissioning for High Intensity Accelerators

23. Separated DC and ACCombined DC and AC Principle circuit Number of PS 21 Peak power of PS Small Pdc= Vdc×Idc Pac= Vac×Iac Large P=(Vdc + Vac) × (Idc + Iac) DC+AC DC AC JPARC-RCSBMPSQMPS Power feeding method for resonant circuit

24. Measurement results (Quadrupole magnet : Type QMA) GLdc[T]GLac[T] Idc[A]Iac[A] DC compnentAC component

25. water pipe (SUS) Hollow conductor (Conventional coil) Copper Water cannel Stranded conductor Wire Insulation (polyimide impregnated) Aluminum wire AC Flux Eddy current loop → Large Eddy current loop → small Development of special coil to reduce eddy current effects