SLAC Magnetic Measurements Date: 04-03-1995 Time: 12:26:33 Magnet Name (Serial #): 177 Bar Code Number: 229 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl Run Number: 1 Comment: Standardization Currents (A): 500.0 10.0 350.0 10.0 350.0 10.0 350.0 10.0 Test Currents (A): 10.0 25.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 300.0 250.0 200.0 150.0 100.0 50.0 25.0 10.0 Harmonics Measurements Date: 04-03-1995 Time: 13:13:43 Magnet Name: 177 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00317 +- 4.403701E-04 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00030 0.00000 97.80 0.05 1.9761 0.0025 2 0.01497 0.00000 45.00 0.00 100.0000 0.0000 3 0.00001 0.00000 19.01 0.47 0.0794 0.0029 4 0.00001 0.00000 -32.94 0.61 0.0402 0.0022 5 0.00001 0.00000 17.23 0.35 0.0543 0.0018 6 0.00003 0.00000 15.17 0.12 0.2135 0.0022 7 0.00000 0.00000 -7.07 19.56 0.0021 0.0006 8 0.00000 0.00000 -8.52 0.69 0.0069 0.0011 9 0.00001 0.00000 -8.76 0.15 0.0557 0.0006 10 0.00004 0.00000 -9.05 0.05 0.2974 0.0026 11 0.00000 0.00000 -0.70 10.89 0.0017 0.0007 12 0.00000 0.00000 -7.64 0.40 0.0123 0.0054 13 0.00001 0.00000 -6.29 0.15 0.0733 0.0053 14 0.00004 0.00000 -6.41 0.04 0.2581 0.0010 15 0.00000 0.00000 -4.68 6.26 0.0067 0.0017 16 0.00000 0.00000 2.24 8.16 0.0078 0.0028 The magnetic center is at X = -874.5 +- 1.2 microns Y = 119.8 +- 0.8 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 04-03-1995 Time: 13:19:48 Magnet Name: 177 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10681 +- 3.465737E-04 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00069 0.00000 99.24 0.06 1.9644 0.0030 2 0.03504 0.00001 45.00 0.00 100.0000 0.0000 3 0.00001 0.00000 -3.25 0.60 0.0381 0.0022 4 0.00002 0.00000 -32.97 0.47 0.0469 0.0026 5 0.00002 0.00000 16.72 0.34 0.0480 0.0025 6 0.00008 0.00000 15.09 0.02 0.2190 0.0013 7 0.00000 0.00000 15.37 3.15 0.0040 0.0012 8 0.00000 0.00000 -18.07 1.10 0.0101 0.0017 9 0.00002 0.00000 -9.00 0.24 0.0551 0.0005 10 0.00010 0.00000 -9.03 0.05 0.2986 0.0022 11 0.00000 0.00000 0.81 11.87 0.0022 0.0006 12 0.00001 0.00000 -5.23 1.38 0.0157 0.0023 13 0.00003 0.00000 -6.44 0.08 0.0742 0.0010 14 0.00009 0.00000 -6.41 0.04 0.2574 0.0023 15 0.00000 0.00000 -0.64 2.95 0.0060 0.0031 16 0.00000 0.00000 -2.74 4.08 0.0070 0.0041 The magnetic center is at X = -866.0 +- 1.2 microns Y = 140.8 +- 0.9 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 04-03-1995 Time: 13:26:00 Magnet Name: 177 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06902 +- 4.852469E-04 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00137 0.00000 99.76 0.05 1.9800 0.0012 2 0.06895 0.00001 45.00 0.00 100.0000 0.0000 3 0.00003 0.00000 -10.62 0.49 0.0421 0.0019 4 0.00003 0.00000 -31.12 0.83 0.0453 0.0014 5 0.00003 0.00000 17.17 0.49 0.0479 0.0021 6 0.00015 0.00000 15.12 0.09 0.2185 0.0013 7 0.00000 0.00000 12.78 1.93 0.0051 0.0006 8 0.00000 0.00000 -9.12 2.41 0.0063 0.0009 9 0.00004 0.00000 -8.97 0.11 0.0550 0.0012 10 0.00021 0.00000 -9.02 0.02 0.2981 0.0018 11 0.00000 0.00000 -6.25 13.13 0.0041 0.0014 12 0.00001 0.00000 -5.38 1.33 0.0143 0.0029 13 0.00005 0.00000 -6.28 0.09 0.0728 0.0033 14 0.00017 0.00000 -6.41 0.05 0.2527 0.0017 15 0.00000 0.00000 0.45 8.96 0.0072 0.0021 16 0.00001 0.00000 6.35 1.62 0.0089 0.0060 The magnetic center is at X = -871.6 +- 0.6 microns Y = 150.0 +- 0.8 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 04-03-1995 Time: 13:32:15 Magnet Name: 177 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0643 +- 1.018474E-03 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00275 0.00000 99.85 0.07 2.0016 0.0015 2 0.13755 0.00002 45.00 0.00 100.0000 0.0000 3 0.00006 0.00000 -12.47 0.27 0.0408 0.0007 4 0.00006 0.00000 -31.17 0.68 0.0456 0.0020 5 0.00007 0.00000 16.94 0.44 0.0484 0.0017 6 0.00030 0.00000 15.17 0.04 0.2193 0.0008 7 0.00001 0.00000 12.74 1.39 0.0045 0.0012 8 0.00001 0.00000 -9.78 0.52 0.0070 0.0015 9 0.00008 0.00000 -8.88 0.16 0.0555 0.0023 10 0.00042 0.00000 -9.05 0.02 0.3028 0.0025 11 0.00000 0.00000 -2.23 13.00 0.0023 0.0007 12 0.00002 0.00001 -8.02 0.45 0.0152 0.0044 13 0.00010 0.00000 -6.49 0.14 0.0728 0.0023 14 0.00035 0.00000 -6.43 0.03 0.2559 0.0017 15 0.00000 0.00000 -3.65 5.39 0.0035 0.0015 16 0.00001 0.00000 -1.24 4.35 0.0051 0.0018 The magnetic center is at X = -880.9 +- 0.8 microns Y = 152.9 +- 1.0 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 04-03-1995 Time: 13:38:30 Magnet Name: 177 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0792 +- 3.601203E-04 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00415 0.00000 99.43 0.03 2.0151 0.0019 2 0.20583 0.00006 44.98 0.00 100.0000 0.0000 3 0.00007 0.00000 -12.19 0.63 0.0358 0.0015 4 0.00009 0.00000 -31.14 0.74 0.0442 0.0014 5 0.00010 0.00000 16.74 0.52 0.0466 0.0023 6 0.00043 0.00000 15.16 0.14 0.2088 0.0013 7 0.00001 0.00000 12.49 2.58 0.0049 0.0013 8 0.00002 0.00000 -9.04 0.38 0.0080 0.0019 9 0.00012 0.00000 -8.94 0.15 0.0569 0.0011 10 0.00063 0.00000 -9.01 0.02 0.3048 0.0008 11 0.00001 0.00000 -6.74 6.89 0.0037 0.0009 12 0.00003 0.00001 -8.11 1.19 0.0141 0.0034 13 0.00015 0.00001 -6.44 0.10 0.0742 0.0041 14 0.00053 0.00001 -6.48 0.03 0.2556 0.0027 15 0.00001 0.00000 -0.01 4.97 0.0040 0.0019 16 0.00001 0.00000 -2.45 7.96 0.0030 0.0014 The magnetic center is at X = -887.9 +- 1.0 microns Y = 147.5 +- 0.6 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 04-03-1995 Time: 13:44:45 Magnet Name: 177 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3283 +- 1.199393E-03 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00555 0.00001 99.37 0.06 2.0312 0.0021 2 0.27346 0.00004 44.97 0.00 100.0000 0.0000 3 0.00010 0.00000 -10.01 1.08 0.0356 0.0013 4 0.00015 0.00000 -34.30 0.57 0.0551 0.0012 5 0.00012 0.00001 16.78 0.65 0.0442 0.0021 6 0.00055 0.00000 15.19 0.06 0.2019 0.0013 7 0.00001 0.00000 14.88 5.21 0.0022 0.0015 8 0.00003 0.00000 -4.36 0.73 0.0126 0.0004 9 0.00016 0.00000 -8.90 0.18 0.0573 0.0014 10 0.00084 0.00000 -9.04 0.05 0.3059 0.0006 11 0.00000 0.00000 1.94 10.37 0.0017 0.0005 12 0.00005 0.00001 -6.46 1.43 0.0177 0.0020 13 0.00021 0.00000 -6.24 0.08 0.0757 0.0013 14 0.00070 0.00001 -6.41 0.05 0.2563 0.0019 15 0.00002 0.00000 7.32 2.49 0.0059 0.0004 16 0.00002 0.00001 -5.52 9.41 0.0086 0.0036 The magnetic center is at X = -895.1 +- 1.0 microns Y = 147.7 +- 1.0 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 04-03-1995 Time: 13:51:02 Magnet Name: 177 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4297 +- 5.461815E-04 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00693 0.00001 98.83 0.01 2.0507 0.0018 2 0.33816 0.00009 44.97 0.00 100.0000 0.0000 3 0.00008 0.00001 -4.44 0.87 0.0238 0.0016 4 0.00017 0.00001 -33.65 0.51 0.0489 0.0031 5 0.00014 0.00000 15.95 0.62 0.0414 0.0013 6 0.00060 0.00000 15.13 0.10 0.1779 0.0010 7 0.00001 0.00000 11.40 5.37 0.0032 0.0006 8 0.00002 0.00000 -16.33 1.26 0.0072 0.0007 9 0.00020 0.00000 -9.26 0.14 0.0591 0.0014 10 0.00105 0.00001 -9.06 0.00 0.3093 0.0023 11 0.00001 0.00000 -8.94 5.76 0.0028 0.0008 12 0.00005 0.00001 -4.89 1.02 0.0145 0.0034 13 0.00025 0.00001 -6.59 0.12 0.0752 0.0028 14 0.00086 0.00001 -6.47 0.05 0.2544 0.0016 15 0.00002 0.00000 -0.41 3.17 0.0068 0.0013 16 0.00003 0.00001 1.22 7.61 0.0088 0.0039 The magnetic center is at X = -905.1 +- 1.0 microns Y = 140.7 +- 0.2 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 04-03-1995 Time: 13:57:19 Magnet Name: 177 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4144 +- 3.67797E-04 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00795 0.00001 97.89 0.06 2.0371 0.0019 2 0.39010 0.00003 44.97 0.00 100.0000 0.0000 3 0.00005 0.00001 -23.92 1.71 0.0127 0.0025 4 0.00018 0.00001 -32.23 0.52 0.0457 0.0015 5 0.00014 0.00001 15.22 0.88 0.0357 0.0019 6 0.00050 0.00000 15.20 0.10 0.1272 0.0006 7 0.00001 0.00000 8.72 3.66 0.0033 0.0011 8 0.00003 0.00000 -14.94 0.69 0.0077 0.0010 9 0.00024 0.00001 -8.89 0.08 0.0613 0.0016 10 0.00125 0.00001 -9.02 0.03 0.3192 0.0037 11 0.00001 0.00000 0.62 14.76 0.0029 0.0012 12 0.00006 0.00002 -5.46 1.62 0.0150 0.0042 13 0.00028 0.00000 -6.45 0.08 0.0729 0.0010 14 0.00100 0.00001 -6.46 0.05 0.2552 0.0022 15 0.00001 0.00001 -0.74 5.74 0.0031 0.0017 16 0.00002 0.00001 2.68 5.13 0.0052 0.0022 The magnetic center is at X = -901.3 +- 0.9 microns Y = 124.9 +- 0.9 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 04-03-1995 Time: 14:03:35 Magnet Name: 177 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4194 +- 9.710634E-04 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00866 0.00001 97.44 0.03 2.0314 0.0015 2 0.42645 0.00005 44.97 0.00 100.0000 0.0000 3 0.00007 0.00001 -37.24 1.23 0.0162 0.0027 4 0.00019 0.00001 -32.33 0.61 0.0445 0.0019 5 0.00013 0.00001 13.79 0.78 0.0313 0.0030 6 0.00030 0.00001 15.25 0.12 0.0699 0.0018 7 0.00002 0.00000 11.57 2.78 0.0042 0.0004 8 0.00003 0.00000 -12.81 0.79 0.0078 0.0006 9 0.00027 0.00000 -9.16 0.07 0.0623 0.0004 10 0.00141 0.00002 -9.04 0.05 0.3298 0.0036 11 0.00001 0.00000 1.07 11.29 0.0028 0.0007 12 0.00005 0.00002 -7.19 3.31 0.0116 0.0050 13 0.00030 0.00001 -6.36 0.09 0.0711 0.0017 14 0.00108 0.00001 -6.47 0.06 0.2531 0.0023 15 0.00002 0.00001 0.48 2.83 0.0038 0.0022 16 0.00002 0.00001 0.39 3.45 0.0036 0.0019 The magnetic center is at X = -899.7 +- 0.8 microns Y = 117.5 +- 0.5 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N SUMMARY OF THE CALCULATIONS AND CONVENTIONS USED Calculation Of GL: V2 = Nturns * velocity * B2 * L = Nturns * Rcoil * ang_freq * GL * Rcoil = Nturns * Rcoil^2 * ang_freq * GL GL = V2 / (Nturns * Rcoil^2 * ang_freq) Calculation Of The Harmonics: Magnitude, harmonic n: Vn = Nturns * velocity * Bn * L = Nturns * Rcoil * ang_freq * (BLn) BLn = Vn / (Nturns * Rcoil * ang_freq) Rn = BLn / BL2 = Vn / V2 Phase, harmonic n: At the coil radius, the radial field as a function of angle is, BLn(th) = BLn * cos(n*(th - THspole)) The coil voltage Vn(th) = Nturns * velocity * BLn(th) Vn(th)= Nturns * Rcoil * ang_freq * BLn * cos(n*(th - THspole)) The FFT gives Vn and PhiVn in the formula Vn(i) = Vn * cos(n*2pi*i/N + PhiVn) So, Nturns * Rcoil * ang_freq * BLn = Vn -n * THspole = PhiVn Or, BLn = Vn / (Nturns * Rcoil * ang_freq) THspole = -PhiVn / n Calculation Of The Magnetic Center: In the quadrupole's frame, Bx' = G * y', By' = G * x'. In the coil's frame (unprimed frame) the magnetic center is at (x0, y0). In the coil's frame, Bx = G * (y - y0), By = G * (x - x0). This gives the magnetic center in terms of the measured dipole field. x0 = - By / G, y0 = - Bx / G In terms of the measured integrated strengths, Xcenter = - (1/GL) * BL1 * sin(THspole1) Ycenter = - (1/GL) * BL1 * cos(THspole1)