SLAC Magnetic Measurements Date: 03-28-1995 Time: 13:17:16 Magnet Name (Serial #): 172 Bar Code Number: 281 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: bmd 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: 03-28-1995 Time: 14:04:47 Magnet Name: 172 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00302 +- 4.042092E-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 0.00020 0.00000 88.74 0.28 1.3142 0.0035 2 0.01492 0.00000 44.98 0.00 100.0000 0.0000 3 0.00001 0.00000 28.30 49.89 0.0434 0.0056 4 0.00001 0.00000 22.10 0.73 0.0375 0.0018 5 0.00000 0.00000 12.21 1.61 0.0284 0.0035 6 0.00003 0.00000 15.12 0.11 0.2212 0.0024 7 0.00000 0.00000 3.29 1.84 0.0069 0.0012 8 0.00000 0.00000 -0.64 21.34 0.0049 0.0007 9 0.00001 0.00000 -8.89 0.21 0.0338 0.0018 10 0.00004 0.00000 -9.23 0.04 0.2979 0.0026 11 0.00000 0.00000 4.77 10.74 0.0032 0.0016 12 0.00000 0.00000 -8.03 9.84 0.0080 0.0029 13 0.00001 0.00000 -6.35 0.13 0.0487 0.0019 14 0.00004 0.00000 -6.44 0.02 0.2610 0.0038 15 0.00000 0.00000 0.76 9.44 0.0088 0.0057 16 0.00000 0.00000 4.34 2.24 0.0067 0.0014 The magnetic center is at X = -586.8 +- 1.6 microns Y = -12.9 +- 2.8 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: 03-28-1995 Time: 14:10:52 Magnet Name: 172 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10704 +- 5.515256E-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 0.00052 0.00000 95.97 0.19 1.4780 0.0032 2 0.03497 0.00001 44.98 0.00 100.0000 0.0000 3 0.00001 0.00000 18.70 2.37 0.0425 0.0051 4 0.00001 0.00000 25.02 1.05 0.0342 0.0019 5 0.00001 0.00000 13.23 0.89 0.0284 0.0031 6 0.00008 0.00000 15.24 0.08 0.2246 0.0020 7 0.00000 0.00000 3.55 3.65 0.0045 0.0010 8 0.00000 0.00000 21.38 0.91 0.0119 0.0012 9 0.00001 0.00000 -8.68 0.35 0.0365 0.0024 10 0.00011 0.00000 -9.18 0.04 0.3008 0.0041 11 0.00000 0.00000 1.49 11.03 0.0021 0.0008 12 0.00000 0.00000 -1.02 5.90 0.0053 0.0011 13 0.00002 0.00000 -6.32 0.11 0.0481 0.0028 14 0.00009 0.00000 -6.42 0.06 0.2586 0.0011 15 0.00000 0.00000 -6.81 2.07 0.0062 0.0021 16 0.00000 0.00000 2.11 2.34 0.0082 0.0007 The magnetic center is at X = -656.6 +- 1.4 microns Y = 68.7 +- 2.2 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: 03-28-1995 Time: 14:17:04 Magnet Name: 172 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06871 +- 1.554717E-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 0.00105 0.00000 97.66 0.15 1.5256 0.0032 2 0.06883 0.00001 44.98 0.00 100.0000 0.0000 3 0.00004 0.00000 16.88 1.25 0.0537 0.0040 4 0.00002 0.00000 21.99 1.38 0.0323 0.0021 5 0.00002 0.00000 15.43 0.55 0.0283 0.0012 6 0.00016 0.00000 15.16 0.10 0.2260 0.0020 7 0.00000 0.00000 -0.80 8.42 0.0024 0.0005 8 0.00000 0.00000 11.18 16.01 0.0038 0.0016 9 0.00002 0.00000 -8.95 0.26 0.0360 0.0011 10 0.00021 0.00000 -9.15 0.03 0.3030 0.0021 11 0.00000 0.00000 10.88 3.63 0.0023 0.0005 12 0.00001 0.00000 -5.79 11.81 0.0073 0.0037 13 0.00003 0.00000 -6.29 0.11 0.0495 0.0013 14 0.00018 0.00000 -6.42 0.03 0.2583 0.0020 15 0.00000 0.00000 -10.52 0.60 0.0070 0.0023 16 0.00000 0.00000 5.41 3.60 0.0071 0.0004 The magnetic center is at X = -675.4 +- 1.4 microns Y = 90.8 +- 1.8 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: 03-28-1995 Time: 14:23:19 Magnet Name: 172 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0632 +- 2.57711E-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 0.00212 0.00000 97.91 0.17 1.5419 0.0033 2 0.13730 0.00001 44.98 0.00 100.0000 0.0000 3 0.00007 0.00000 15.90 1.49 0.0505 0.0020 4 0.00004 0.00000 22.34 0.85 0.0319 0.0020 5 0.00004 0.00000 15.47 0.24 0.0280 0.0016 6 0.00031 0.00000 15.16 0.09 0.2255 0.0015 7 0.00000 0.00000 3.51 10.11 0.0022 0.0013 8 0.00000 0.00000 -5.66 15.44 0.0024 0.0020 9 0.00005 0.00000 -8.50 0.32 0.0356 0.0010 10 0.00042 0.00000 -9.18 0.09 0.3040 0.0020 11 0.00000 0.00000 10.94 1.62 0.0036 0.0019 12 0.00001 0.00001 1.44 12.16 0.0106 0.0043 13 0.00007 0.00000 -6.46 0.14 0.0494 0.0022 14 0.00036 0.00000 -6.42 0.07 0.2602 0.0008 15 0.00001 0.00000 -9.05 0.63 0.0070 0.0027 16 0.00001 0.00001 0.27 1.18 0.0083 0.0038 The magnetic center is at X = -682.2 +- 1.5 microns Y = 94.7 +- 2.1 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: 03-28-1995 Time: 14:29:34 Magnet Name: 172 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0765 +- 7.008254E-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 0.00318 0.00001 98.17 0.13 1.5448 0.0042 2 0.20557 0.00002 44.96 0.00 100.0000 0.0000 3 0.00011 0.00001 14.28 0.61 0.0551 0.0045 4 0.00006 0.00000 20.95 0.73 0.0303 0.0022 5 0.00006 0.00000 14.72 0.34 0.0282 0.0022 6 0.00044 0.00000 15.18 0.06 0.2159 0.0021 7 0.00001 0.00000 8.81 4.41 0.0044 0.0016 8 0.00001 0.00000 -10.24 16.01 0.0040 0.0008 9 0.00007 0.00000 -8.76 0.07 0.0362 0.0018 10 0.00063 0.00000 -9.22 0.03 0.3048 0.0013 11 0.00001 0.00000 3.76 8.73 0.0033 0.0009 12 0.00002 0.00000 0.62 13.99 0.0112 0.0023 13 0.00010 0.00001 -6.36 0.26 0.0489 0.0033 14 0.00053 0.00001 -6.43 0.05 0.2582 0.0035 15 0.00002 0.00001 -9.42 1.43 0.0077 0.0041 16 0.00001 0.00000 5.17 1.89 0.0056 0.0020 The magnetic center is at X = -683.0 +- 1.9 microns Y = 98.1 +- 1.6 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: 03-28-1995 Time: 14:35:49 Magnet Name: 172 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3258 +- 4.992446E-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 0.00421 0.00000 97.99 0.28 1.5407 0.0018 2 0.27323 0.00003 44.96 0.00 100.0000 0.0000 3 0.00013 0.00001 14.26 2.16 0.0486 0.0024 4 0.00008 0.00001 28.84 1.23 0.0311 0.0026 5 0.00007 0.00000 15.10 0.75 0.0263 0.0007 6 0.00057 0.00000 15.25 0.04 0.2102 0.0014 7 0.00001 0.00000 -3.06 10.65 0.0023 0.0009 8 0.00002 0.00000 0.40 2.23 0.0061 0.0008 9 0.00010 0.00001 -8.73 0.19 0.0373 0.0023 10 0.00084 0.00001 -9.18 0.05 0.3073 0.0024 11 0.00001 0.00000 9.71 5.63 0.0024 0.0014 12 0.00002 0.00001 6.93 11.17 0.0083 0.0047 13 0.00013 0.00000 -6.36 0.15 0.0464 0.0017 14 0.00071 0.00001 -6.49 0.03 0.2609 0.0027 15 0.00002 0.00001 -4.38 8.49 0.0072 0.0034 16 0.00002 0.00000 7.80 2.79 0.0069 0.0013 The magnetic center is at X = -681.5 +- 0.9 microns Y = 95.6 +- 3.3 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: 03-28-1995 Time: 14:42:05 Magnet Name: 172 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.429 +- 5.530127E-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 0.00523 0.00001 97.66 0.26 1.5466 0.0026 2 0.33822 0.00004 44.96 0.00 100.0000 0.0000 3 0.00017 0.00001 16.61 1.88 0.0513 0.0027 4 0.00010 0.00001 26.64 1.38 0.0288 0.0020 5 0.00008 0.00000 14.64 0.41 0.0233 0.0013 6 0.00063 0.00000 15.17 0.06 0.1869 0.0015 7 0.00001 0.00000 0.49 11.12 0.0026 0.0007 8 0.00003 0.00000 -11.27 18.10 0.0102 0.0013 9 0.00013 0.00000 -9.23 0.21 0.0373 0.0012 10 0.00106 0.00001 -9.20 0.03 0.3139 0.0023 11 0.00001 0.00000 9.67 1.81 0.0017 0.0006 12 0.00001 0.00001 -7.22 4.45 0.0042 0.0031 13 0.00016 0.00001 -6.40 0.17 0.0475 0.0021 14 0.00087 0.00001 -6.45 0.04 0.2581 0.0017 15 0.00003 0.00001 -3.95 9.12 0.0083 0.0028 16 0.00002 0.00001 6.77 2.45 0.0070 0.0028 The magnetic center is at X = -684.6 +- 1.3 microns Y = 92.1 +- 3.1 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: 03-28-1995 Time: 14:48:21 Magnet Name: 172 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4139 +- 1.003606E-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 0.00601 0.00001 96.82 0.08 1.5392 0.0022 2 0.39014 0.00004 44.96 0.00 100.0000 0.0000 3 0.00016 0.00001 20.53 0.95 0.0415 0.0024 4 0.00010 0.00001 25.13 1.01 0.0268 0.0024 5 0.00007 0.00001 13.13 0.59 0.0191 0.0013 6 0.00052 0.00000 15.29 0.14 0.1336 0.0012 7 0.00001 0.00000 0.19 4.87 0.0022 0.0011 8 0.00004 0.00000 0.06 21.48 0.0103 0.0013 9 0.00015 0.00000 -8.65 0.14 0.0389 0.0010 10 0.00126 0.00000 -9.20 0.04 0.3230 0.0011 11 0.00002 0.00000 13.70 0.92 0.0041 0.0007 12 0.00002 0.00001 -11.80 1.31 0.0058 0.0038 13 0.00019 0.00000 -6.37 0.17 0.0479 0.0012 14 0.00101 0.00001 -6.43 0.05 0.2590 0.0023 15 0.00004 0.00001 -4.10 9.33 0.0090 0.0035 16 0.00004 0.00002 4.21 3.89 0.0105 0.0041 The magnetic center is at X = -682.6 +- 1.0 microns Y = 81.6 +- 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: 03-28-1995 Time: 14:54:36 Magnet Name: 172 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4214 +- 7.306714E-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 0.00656 0.00001 96.84 0.14 1.5390 0.0032 2 0.42650 0.00006 44.96 0.00 100.0000 0.0000 3 0.00018 0.00003 20.63 0.98 0.0413 0.0060 4 0.00011 0.00001 23.34 1.00 0.0257 0.0021 5 0.00007 0.00001 10.39 1.05 0.0167 0.0013 6 0.00033 0.00001 15.53 0.11 0.0778 0.0018 7 0.00001 0.00001 -0.12 4.56 0.0031 0.0014 8 0.00003 0.00001 -11.12 18.33 0.0079 0.0025 9 0.00017 0.00000 -8.54 0.10 0.0404 0.0008 10 0.00142 0.00001 -9.21 0.05 0.3323 0.0032 11 0.00001 0.00000 -1.00 10.93 0.0015 0.0010 12 0.00004 0.00001 -6.01 10.61 0.0100 0.0027 13 0.00020 0.00001 -6.37 0.14 0.0458 0.0016 14 0.00109 0.00001 -6.44 0.04 0.2558 0.0033 15 0.00004 0.00001 -9.95 0.70 0.0094 0.0020 16 0.00004 0.00001 0.02 1.31 0.0105 0.0031 The magnetic center is at X = -682.5 +- 1.4 microns Y = 81.8 +- 1.6 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 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)