1. Harmonic Injection for Magnets of RCS Shouyan Xu AP Group, CSNS 2015-06-09

2. Page 散裂中子源进展汇报 June 11, 2016 2 Outline  Magnetic Tracking Error of RCS  The Way to Perform the Harmonic Injection  Test at CSNS/RCS B/Q  Application at CSNS/RCS  Summary

3. Page 散裂中子源进展汇报 June 11, 2016 3 Magnetic Tracking Error of RCS Resonant Network Structure

4. Page 散裂中子源进展汇报 June 11, 2016 4 Magnetic Tracking Error of RCS DipoleQua-aQua-bQua-cQua-d 25Hz-Amp11111 50Hz-Amp3.73E-3 4.26E-37.89E-036.34E-031.02E-02 75Hz-Amp1.20E-3 0.97E-32.18E-032.14E-034.44E-03 100Hz-Amp3.83E-4 1.92E-45.44E-044.20E-041.42E-03 125Hz-Amp1.52E-4 1.15E-42.64E-041.77E-046.28E-04 25Hz-Pha (°)00000 50Hz-Pha (°)80.55 83.47103.38138.82140.11 75Hz-Pha (°)76.75 105.20114.85144.67139.91 100Hz-Pha (°)74.50 133.50123.32150.22139.10 125Hz-Pha (°)72.63 87.96100.42138.06128.35

5. Page 散裂中子源进展汇报 June 11, 2016 5 Magnetic Tracking Error of RCS It’s necessary to compensate the magnetic field to reduce the magnetic field tracking errors

6. Page 散裂中子源进展汇报 June 11, 2016 6 The Way to Perform the Harmonic Injection Inject higher frequency current harmonics to compensate the magnetic field DipoleQua-aQua-bQua-cQua-d 25Hz-Amp11111 50Hz-Amp3.73E-3 4.26E-37.89E-036.34E-031.02E-02 75Hz-Amp1.20E-3 0.97E-32.18E-032.14E-034.44E-03 100Hz-Amp3.83E-4 1.92E-45.44E-044.20E-041.42E-03 125Hz-Amp1.52E-4 1.15E-42.64E-041.77E-046.28E-04 Inject higher frequency current harmonics to magnets Reduce higher frequency magnetic field harmonics to zero; The higher frequency magnetic field harmonics of B/Q are compensated to the same. What current harmonics should be injected into magnets?

7. Page 散裂中子源进展汇报 June 11, 2016 7 The Way to Perform the Harmonic Injection  The method based on the magnetic field harmonic analysis  The method based on the transfer function

8. Page 散裂中子源进展汇报 June 11, 2016 8 The Way to Perform the Harmonic Injection The method based on the magnetic field harmonic analysis Based on the field measurement, the high order harmonic field can be obtained by FFT. A higher harmonic current with the same frequency, reversal phase and proper amplitude is injected, and the higher order harmonic field can be compensated.

9. Page 散裂中子源进展汇报 June 11, 2016 9 The Way to Perform the Harmonic Injection The method based on the transfer function Transfer function between the current and magnetic field during one cycling period Current/Magnetic field variation with time during one cycling period

10. Page 散裂中子源进展汇报 June 11, 2016 10 The Way to Perform the Harmonic Injection G=F G (t) I? I=F 1 (G) Upward I=F 2 (G) Downward I=F I (t) The method based on the transfer function

11. Page 散裂中子源进展汇报 June 11, 2016 11 The Way to Perform the Harmonic Injection I=F I (t) G? I=F 1 (G) Upward I=F 2 (G) Downward The method based on the transfer function G=F G (t)

12. Page 散裂中子源进展汇报 June 11, 2016 12 Test at CSNS/RCS Magnets No- Harmonic Injection Dipole Curve 25Hz-Amp1111 50Hz-Amp 4.26E-3 3.73E-3 4.49E-053.62E-03 75Hz-Amp 0.97E-3 1.20E-3 3.01E-051.12E-03 100Hz-Amp 1.92E-4 3.83E-4 1.26E-053.40E-04 125Hz-Amp 1.15E-4 1.52E-4 1.53E-051.40E-04 25Hz-Pha (°)0000 50Hz-Pha (°) 83.47 80.55 -8.0981.65 75Hz-Pha (°) 105.20 76.75 0.8371.78 100Hz-Pha (°) 133.50 74.50 38.0770.83 125Hz-Pha (°) 87.96 72.63 15.8965.37 The method based on the transfer function G=F G (t) can be any type of curve Standard Curve Dipole Curve

13. Page 散裂中子源进展汇报 June 11, 2016 13 Test at CSNS/RCS Magnets By using method based on the transfer function, evaluate the magnetic field curve corresponding to the given current curve. 50Hz- Amp(A)/Phase(°) 75Hz- Amp(A)/Phase(°) 100Hz- Amp(A)/Phase(°) 125Hz- Amp(A)/Phase(°) 4.27/10.412.75/8.501.28/6.070.67/-3.50 50Hz- Amp/Phase(°) 75Hz- Amp/Phase(°) 100Hz- Amp/Phase(°) 125Hz- Amp/Phase(°) Evaluated results4.58E-4/169.31.74E-4/-171.10.68E-4/-173.00.18E-4/-118.3 Measured results4.62E-4/160.91.74E-4/-178.00.88E-4/-168.30.22E-4/-145.6 25Hz-Amp=1, phase=0 25Hz-Amp=877A, phase=0

14. Page 散裂中子源进展汇报 June 11, 2016 14 The method based on the transfer function The method based on the transfer function:  The transfer function can be quickly measured  The magnetic field can be compensated to any type of curve  One can “arbitrarily” change the tune during a RCS cycle  One can evaluate the magnetic field curve corresponding to the given current curve

15. Page 散裂中子源进展汇报 June 11, 2016 15 Application at CSNS/RCS DipoleQua-aQua-bQua-cQua-d 25Hz-Amp11111 50Hz-Amp3.73E-3 4.26E-37.89E-036.34E-031.02E-02 75Hz-Amp1.20E-3 0.97E-32.18E-032.14E-034.44E-03 100Hz-Amp3.83E-4 1.92E-45.44E-044.20E-041.42E-03 125Hz-Amp1.52E-4 1.15E-42.64E-041.77E-046.28E-04 25Hz-Phase(°)00000 50Hz-Phase(°)80.55 83.47103.38138.82140.11 75Hz-Phase(°)76.75 105.20114.85144.67139.91 100Hz-Phase(°)74.50 133.50123.32150.22139.10 125Hz-Phase(°)72.63 87.96100.42138.06128.35 No-Harmonic Injection, the higher frequency magnetic field harmonics of dipole and quadrupoles.

16. Page 散裂中子源进展汇报 June 11, 2016 16 Application at CSNS/RCS No-Harmonic Injection, Magnetic field tracking errors between dipole and quadrupoles. Tune Shift Induced by Magnetic Tracking Errors

17. Page 散裂中子源进展汇报 June 11, 2016 17 Application at CSNS/RCS Perform the harmonic injection by using new method which is based on the transfer function between current and magnetic field. Both the dipole and quadrupole magnetic field curve is compensated to standard curve. DipoleQua-aQua-b 25Hz-Amp111 50Hz-Amp 6.48E-054.49E-056.44E-05 75Hz-Amp 3.23E-053.01E-054.30E-05 100Hz-Amp 7.86E-061.26E-053.16E-06 125Hz-Amp 5.93E-061.53E-052.15E-05 DipoleQua-aQua-b 25Hz-Amp111 50Hz-Amp3.73E-34.26E-37.89E-03 75Hz-Amp1.20E-30.97E-32.18E-03 100Hz-Amp3.83E-41.92E-45.44E-04 125Hz-Amp1.52E-41.15E-42.64E-04 No-Harmonic Injection With-Harmonic Injection, All the higher frequency magnetic field harmonics are compensated to almost zero.

18. Page 散裂中子源进展汇报 June 11, 2016 18 Application at CSNS/RCS Both the dipole and quadrupole magnetic field curve is compensated to standard curve. No-Harmonic InjectionWith-Harmonic Injection Deviation from Standard Curve During One Cycling Period

19. Page 散裂中子源进展汇报 June 11, 2016 19 Application at CSNS/RCS Both the dipole and quadrupole magnetic field curve is compensated to standard curve. No-Harmonic InjectionWith-Harmonic Injection Magnetic Field Tracking Errors During One Cycling Period

20. Page 散裂中子源进展汇报 June 11, 2016 20 Application at CSNS/RCS Perform the harmonic injection by using new method which is based on the transfer function between current and magnetic field. No harmonic injection for dipole, quadrupole magnetic field curve is compensated to dipole curve. DipoleQua-a No-Injection Qua-b No-Injection Qua-a With-Injection Qua-b With-Injection 25Hz-Amp11111 50Hz-Amp3.73E-3 4.26E-37.89E-033.62E-033.59E-03 75Hz-Amp1.20E-3 0.97E-32.18E-031.12E-031.09E-03 100Hz-Amp3.83E-4 1.92E-45.44E-043.40E-043.14E-04 125Hz-Amp1.52E-4 1.15E-42.64E-041.40E-041.32E-04 25Hz-Phase(°)00000 50Hz-Phase(°)80.55 83.47103.3881.6578.76 75Hz-Phase(°)76.75 105.20114.8571.7871.52 100Hz-Phase(°)74.50 133.50123.3270.8361.06 125Hz-Phase(°)72.63 87.96100.4265.3758.17

21. Page 散裂中子源进展汇报 June 11, 2016 21 Application at CSNS/RCS No harmonic injection for dipole, quadrupole magnetic field curve is compensated to dipole curve. No-Harmonic InjectionWith-Harmonic Injection Magnetic Field Tracking Errors During One Cycling Period

22. Page 散裂中子源进展汇报 June 11, 2016 22 Application at CSNS/RCS Differences for the same type of dipole/quadrupole DipoleQuadrupole-a During machine commissioning, the injection harmonics may be changed according to magnetic field measurement. The method based on the transfer function can be used to evaluate the magnetic field curve corresponding to the given injection harmonics.

23. Page 散裂中子源进展汇报 June 11, 2016 23 Application at CSNS/RCS 50Hz- Amp(A)/Phase(°) 75Hz- Amp(A)/Phase(°) 100Hz- Amp(A)/Phase(°) 125Hz- Amp(A)/Phase(°) 4.19/9.42.64/8.11.24/5.10.66/-4.1 4.2/8.72.64/8.41.22/5.30.65/-3.8 4.22/9.22.64/8.71.22/6.50.64/-3.3 4.24/9.42.6/8.71.2/5.80.64/-3.0 4.27/9.22.7/8.71.27/6.60.66/-3.1 4.33/9.02.74/8.31.28/5.80.68/-3.4 4.34/8.82.77/8.31.28/5.80.66/-3.5 4.43/9.02.74/8.81.26/6.60.65/-2.6 4.47/8.52.71/8.21.23/5.40.65/-3.5 4.47/8.92.72/8.41.24/5.50.65/-3.6 4.57/8.52.76/7.91.24/5.10.64/-4.3 4.58/8.42.76/7.71.27/5.20.67/-4.3 Injection Harmonics for Different Dipoles 4.36/8.92.70/8.31.25/5.70.65/-3.5

24. Page 散裂中子源进展汇报 June 11, 2016 24 Application at CSNS/RCS 50Hz- Amp(A)/Phase(°) 75Hz- Amp(A)/Phase(°) 100Hz- Amp(A)/Phase(°) 125Hz- Amp(A)/Phase(°) 4.27/10.412.75/8.501.28/6.070.67/-3.50 50Hz- Amp/Phase(°) 75Hz- Amp/Phase(°) 100Hz- Amp/Phase(°) 125Hz- Amp/Phase(°) Evaluated results4.58E-4/169.31.74E-4/-171.10.68E-4/-173.00.18E-4/-118.3 Measured results4.62E-4/160.91.74E-4/-178.00.88E-4/-168.30.22E-4/-145.6 Injection Harmonics Evaluate the magnetic field curve corresponding to the given injection current harmonics.

25. Page 散裂中子源进展汇报 June 11, 2016 25 Application at CSNS/RCS Space charge tune shift varies with beam energy and bunch factor during acceleration, and beam may be close to serious resonance lines. The tune shift induced by magnetic tracking errors can be controlled by harmonic injection for dipoles and quadrupoles. The beam can be moved from serious resonance lines.

26. Page 散裂中子源进展汇报 June 11, 2016 26 Summary  A new method to perform harmonic injection for RCS magnets is tried at CSNS/RCS B/Q, and the new method is based on the transfer function between the current and magnetic field.  The magnetic tracking errors between dipoles and quadrupoles can be reduced obviously by using the new method.  The new method based on transfer function is more useful than the method based on the magnetic harmonic analysis: the magnetic field curve can be compensated to any type of curve; one can “arbitrarily” change the tune during a RCS cycle; one can evaluate the magnetic field harmonics for any given injection current harmonics.

27. Thanks! 27