SLAC Magnetic Measurements Date: 04-19-1995 Time: 09:01:43 Magnet Name (Serial #): 150 Bar Code Number: 481 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl Run Number: 2 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: 04-19-1995 Time: 09:48:59 Magnet Name: 150 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00019 +- 5.096825E-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 0.00006 0.00000 -132.52 0.88 0.4003 0.0037 2 0.01481 0.00000 44.99 0.00 100.0000 0.0000 3 0.00002 0.00000 22.84 0.42 0.1268 0.0026 4 0.00000 0.00000 22.26 0.97 0.0295 0.0023 5 0.00000 0.00000 16.38 1.79 0.0199 0.0021 6 0.00003 0.00000 15.14 0.10 0.2128 0.0025 7 0.00000 0.00000 13.92 0.76 0.0073 0.0015 8 0.00000 0.00000 14.87 2.01 0.0027 0.0008 9 0.00000 0.00000 5.11 0.47 0.0127 0.0012 10 0.00004 0.00000 -9.09 0.04 0.2989 0.0010 11 0.00000 0.00000 6.87 4.72 0.0018 0.0010 12 0.00000 0.00000 6.41 11.84 0.0053 0.0008 13 0.00000 0.00000 2.68 0.89 0.0142 0.0029 14 0.00004 0.00000 -6.45 0.02 0.2589 0.0020 15 0.00000 0.00000 -6.77 2.46 0.0052 0.0019 16 0.00000 0.00000 2.37 7.17 0.0079 0.0028 The magnetic center is at X = 131.8 +- 2.2 microns Y = 120.8 +- 2.3 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: 04-19-1995 Time: 09:55:05 Magnet Name: 150 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10239 +- 7.248264E-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 0.00013 0.00000 -149.03 0.41 0.3775 0.0038 2 0.03489 0.00000 44.98 0.00 100.0000 0.0000 3 0.00004 0.00000 23.13 0.31 0.1194 0.0021 4 0.00001 0.00000 26.09 1.05 0.0271 0.0017 5 0.00001 0.00000 16.99 1.36 0.0209 0.0018 6 0.00008 0.00000 15.19 0.07 0.2176 0.0017 7 0.00000 0.00000 12.27 1.08 0.0071 0.0007 8 0.00000 0.00000 21.01 0.45 0.0101 0.0010 9 0.00001 0.00000 5.73 0.47 0.0146 0.0005 10 0.00011 0.00000 -9.08 0.01 0.3012 0.0019 11 0.00000 0.00000 2.89 5.12 0.0026 0.0006 12 0.00000 0.00000 3.11 3.08 0.0037 0.0010 13 0.00000 0.00000 2.16 0.64 0.0131 0.0048 14 0.00009 0.00000 -6.45 0.02 0.2575 0.0017 15 0.00000 0.00000 -7.29 2.51 0.0056 0.0022 16 0.00000 0.00000 5.32 1.55 0.0046 0.0020 The magnetic center is at X = 86.8 +- 1.3 microns Y = 144.6 +- 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: 04-19-1995 Time: 10:01:17 Magnet Name: 150 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.06689 +- 4.753586E-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 0.00026 0.00000 -155.76 0.63 0.3816 0.0055 2 0.06878 0.00001 44.98 0.00 100.0000 0.0000 3 0.00008 0.00000 23.24 0.94 0.1198 0.0045 4 0.00002 0.00000 22.43 1.68 0.0241 0.0030 5 0.00001 0.00000 16.26 1.51 0.0210 0.0020 6 0.00015 0.00000 15.20 0.10 0.2171 0.0013 7 0.00001 0.00000 11.07 1.17 0.0077 0.0014 8 0.00000 0.00000 16.55 0.86 0.0033 0.0007 9 0.00001 0.00000 4.79 0.70 0.0128 0.0021 10 0.00021 0.00000 -9.07 0.02 0.3025 0.0017 11 0.00000 0.00000 3.64 2.28 0.0028 0.0010 12 0.00000 0.00000 1.31 10.89 0.0036 0.0008 13 0.00001 0.00000 3.71 0.20 0.0163 0.0038 14 0.00017 0.00000 -6.48 0.02 0.2539 0.0006 15 0.00001 0.00000 -6.91 1.58 0.0112 0.0026 16 0.00000 0.00000 6.48 3.19 0.0063 0.0013 The magnetic center is at X = 70.0 +- 2.0 microns Y = 155.4 +- 2.4 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: 04-19-1995 Time: 10:07:34 Magnet Name: 150 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0646 +- 7.236874E-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 0.00053 0.00001 -160.04 0.50 0.3836 0.0055 2 0.13724 0.00004 44.99 0.00 100.0000 0.0000 3 0.00017 0.00000 23.36 0.75 0.1211 0.0035 4 0.00003 0.00000 22.70 1.21 0.0243 0.0023 5 0.00003 0.00001 16.21 1.20 0.0196 0.0038 6 0.00030 0.00000 15.20 0.04 0.2169 0.0015 7 0.00001 0.00000 10.12 1.99 0.0058 0.0013 8 0.00000 0.00000 12.89 1.10 0.0024 0.0009 9 0.00002 0.00000 4.69 0.66 0.0125 0.0010 10 0.00042 0.00000 -9.06 0.04 0.3042 0.0011 11 0.00000 0.00000 1.84 5.19 0.0017 0.0002 12 0.00000 0.00000 0.37 11.40 0.0027 0.0014 13 0.00002 0.00000 2.81 0.93 0.0117 0.0029 14 0.00035 0.00000 -6.45 0.02 0.2544 0.0020 15 0.00001 0.00000 -5.82 0.58 0.0050 0.0014 16 0.00001 0.00000 6.86 0.81 0.0081 0.0009 The magnetic center is at X = 58.5 +- 1.6 microns Y = 161.0 +- 2.4 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: 04-19-1995 Time: 10:13:50 Magnet Name: 150 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0825 +- 5.196396E-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 0.00080 0.00001 -161.95 0.45 0.3883 0.0055 2 0.20545 0.00003 44.96 0.00 100.0000 0.0000 3 0.00026 0.00001 23.29 0.39 0.1246 0.0043 4 0.00005 0.00000 22.89 1.96 0.0242 0.0015 5 0.00004 0.00000 17.02 1.80 0.0185 0.0021 6 0.00043 0.00000 15.23 0.05 0.2090 0.0011 7 0.00001 0.00000 7.89 2.55 0.0064 0.0013 8 0.00000 0.00000 3.73 12.87 0.0017 0.0008 9 0.00003 0.00000 5.63 0.77 0.0131 0.0012 10 0.00063 0.00000 -9.10 0.04 0.3074 0.0007 11 0.00001 0.00000 8.84 3.93 0.0026 0.0006 12 0.00002 0.00000 7.11 12.20 0.0092 0.0016 13 0.00003 0.00001 2.48 1.08 0.0129 0.0026 14 0.00052 0.00000 -6.45 0.01 0.2552 0.0013 15 0.00002 0.00001 -5.55 1.32 0.0099 0.0041 16 0.00001 0.00001 7.11 1.66 0.0071 0.0027 The magnetic center is at X = 53.7 +- 1.5 microns Y = 164.9 +- 2.4 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: 04-19-1995 Time: 10:20:06 Magnet Name: 150 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3308 +- 6.040727E-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 0.00106 0.00002 -162.69 0.61 0.3883 0.0068 2 0.27312 0.00002 44.96 0.00 100.0000 0.0000 3 0.00035 0.00001 23.09 0.99 0.1265 0.0026 4 0.00008 0.00000 31.58 1.06 0.0301 0.0011 5 0.00005 0.00001 16.77 1.67 0.0181 0.0026 6 0.00055 0.00001 15.20 0.12 0.2008 0.0022 7 0.00002 0.00000 11.94 0.72 0.0057 0.0005 8 0.00002 0.00000 1.17 1.05 0.0066 0.0008 9 0.00004 0.00001 5.61 0.90 0.0132 0.0023 10 0.00085 0.00001 -9.09 0.03 0.3108 0.0023 11 0.00001 0.00000 5.82 4.21 0.0024 0.0010 12 0.00001 0.00000 2.69 11.38 0.0035 0.0010 13 0.00005 0.00001 2.32 0.76 0.0166 0.0024 14 0.00069 0.00000 -6.48 0.02 0.2544 0.0012 15 0.00003 0.00001 -8.48 1.20 0.0095 0.0037 16 0.00002 0.00001 8.85 0.82 0.0081 0.0026 The magnetic center is at X = 51.6 +- 2.0 microns Y = 165.6 +- 3.0 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: 04-19-1995 Time: 10:26:22 Magnet Name: 150 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4352 +- 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 0.00127 0.00002 -164.14 0.56 0.3748 0.0051 2 0.33800 0.00010 44.96 0.00 100.0000 0.0000 3 0.00044 0.00001 23.94 0.55 0.1298 0.0044 4 0.00009 0.00001 28.53 0.91 0.0267 0.0027 5 0.00006 0.00001 17.30 0.70 0.0182 0.0022 6 0.00060 0.00001 15.21 0.08 0.1782 0.0019 7 0.00002 0.00000 8.90 2.59 0.0046 0.0013 8 0.00002 0.00000 20.99 0.82 0.0052 0.0008 9 0.00005 0.00000 5.30 0.66 0.0137 0.0010 10 0.00106 0.00000 -9.10 0.02 0.3128 0.0012 11 0.00001 0.00000 0.61 5.17 0.0018 0.0005 12 0.00001 0.00000 2.78 1.36 0.0027 0.0012 13 0.00005 0.00001 2.80 0.51 0.0142 0.0041 14 0.00087 0.00000 -6.46 0.01 0.2560 0.0010 15 0.00002 0.00002 -7.43 0.90 0.0073 0.0046 16 0.00003 0.00001 8.65 1.34 0.0078 0.0030 The magnetic center is at X = 45.7 +- 1.7 microns Y = 161.0 +- 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: 04-19-1995 Time: 10:32:38 Magnet Name: 150 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4232 +- 3.674803E-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 0.00144 0.00002 -164.12 0.66 0.3705 0.0051 2 0.38956 0.00009 44.96 0.00 100.0000 0.0000 3 0.00050 0.00001 24.23 0.77 0.1295 0.0036 4 0.00010 0.00001 25.85 0.99 0.0251 0.0023 5 0.00007 0.00001 16.52 0.82 0.0187 0.0021 6 0.00049 0.00001 15.26 0.10 0.1265 0.0020 7 0.00002 0.00001 10.06 1.58 0.0047 0.0013 8 0.00003 0.00001 10.51 18.84 0.0073 0.0013 9 0.00005 0.00000 5.59 0.70 0.0133 0.0004 10 0.00126 0.00001 -9.11 0.01 0.3226 0.0015 11 0.00001 0.00000 0.96 8.87 0.0020 0.0008 12 0.00001 0.00000 2.78 3.60 0.0028 0.0007 13 0.00006 0.00000 2.52 0.79 0.0161 0.0010 14 0.00100 0.00001 -6.46 0.03 0.2562 0.0021 15 0.00002 0.00000 -7.38 1.19 0.0061 0.0013 16 0.00003 0.00001 2.09 1.86 0.0084 0.0029 The magnetic center is at X = 45.3 +- 1.9 microns Y = 159.2 +- 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: 04-19-1995 Time: 10:38:55 Magnet Name: 150 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4323 +- 1.36291E-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 0.00156 0.00002 -164.09 0.57 0.3669 0.0049 2 0.42570 0.00004 44.96 0.00 100.0000 0.0000 3 0.00055 0.00001 24.36 0.74 0.1281 0.0029 4 0.00010 0.00001 26.33 1.60 0.0238 0.0020 5 0.00009 0.00001 15.16 0.97 0.0201 0.0016 6 0.00029 0.00000 15.64 0.24 0.0691 0.0010 7 0.00002 0.00000 8.71 2.60 0.0049 0.0010 8 0.00002 0.00000 -0.53 21.04 0.0053 0.0011 9 0.00006 0.00000 5.75 0.40 0.0142 0.0005 10 0.00143 0.00000 -9.12 0.01 0.3348 0.0007 11 0.00001 0.00000 2.42 7.94 0.0029 0.0010 12 0.00003 0.00000 -4.88 11.02 0.0059 0.0006 13 0.00006 0.00000 3.61 0.64 0.0146 0.0012 14 0.00108 0.00001 -6.50 0.01 0.2542 0.0024 15 0.00004 0.00001 -6.71 0.76 0.0092 0.0020 16 0.00005 0.00001 1.85 0.61 0.0113 0.0018 The magnetic center is at X = 44.9 +- 1.7 microns Y = 157.6 +- 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 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)