SLAC Magnetic Measurements Date: 02-28-1995 Time: 07:50:30 Magnet Name (Serial #): 197 Bar Code Number: 602 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: 02-28-1995 Time: 08:37:40 Magnet Name: 197 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.996796 +- 9.048221E-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 0.00008 0.00000 -6.38 0.13 0.5351 0.0031 2 0.01486 0.00000 -44.96 0.00 100.0000 0.0000 3 0.00001 0.00000 38.36 0.68 0.0700 0.0024 4 0.00000 0.00000 20.26 1.58 0.0206 0.0023 5 0.00000 0.00000 -24.84 2.21 0.0046 0.0017 6 0.00003 0.00000 -14.73 0.10 0.2222 0.0022 7 0.00000 0.00000 -13.26 1.31 0.0087 0.0009 8 0.00000 0.00000 13.93 1.16 0.0060 0.0012 9 0.00000 0.00000 19.48 0.40 0.0094 0.0014 10 0.00004 0.00000 9.06 0.02 0.2977 0.0009 11 0.00000 0.00000 4.48 4.50 0.0028 0.0008 12 0.00000 0.00000 8.99 1.58 0.0048 0.0018 13 0.00000 0.00000 12.17 0.72 0.0122 0.0011 14 0.00004 0.00000 6.56 0.05 0.2562 0.0030 15 0.00000 0.00000 -2.94 8.07 0.0047 0.0034 16 0.00000 0.00000 -0.69 5.45 0.0050 0.0013 The magnetic center is at X = -26.6 +- 0.6 microns Y = 237.5 +- 1.4 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 ^ | S N --> x N S Date: 02-28-1995 Time: 08:43:45 Magnet Name: 197 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.09736 +- 8.783838E-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 0.00016 0.00000 -15.63 0.32 0.4461 0.0008 2 0.03492 0.00000 -44.96 0.00 100.0000 0.0000 3 0.00001 0.00000 -33.28 0.98 0.0293 0.0031 4 0.00001 0.00000 25.05 1.35 0.0253 0.0018 5 0.00000 0.00000 -21.46 1.31 0.0121 0.0022 6 0.00008 0.00000 -14.82 0.04 0.2249 0.0012 7 0.00000 0.00000 -16.77 2.42 0.0039 0.0006 8 0.00000 0.00000 20.83 0.73 0.0107 0.0026 9 0.00000 0.00000 17.79 0.97 0.0086 0.0009 10 0.00010 0.00000 9.07 0.01 0.3002 0.0016 11 0.00000 0.00000 6.75 2.11 0.0028 0.0004 12 0.00000 0.00000 5.60 2.75 0.0046 0.0015 13 0.00000 0.00000 12.39 0.56 0.0113 0.0005 14 0.00009 0.00000 6.48 0.02 0.2560 0.0031 15 0.00000 0.00000 0.33 7.07 0.0050 0.0019 16 0.00000 0.00000 -0.78 0.33 0.0087 0.0015 The magnetic center is at X = -53.7 +- 1.1 microns Y = 191.9 +- 0.4 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 ^ | S N --> x N S Date: 02-28-1995 Time: 08:49:56 Magnet Name: 197 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.05978 +- 4.885569E-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 0.00029 0.00000 -17.54 0.25 0.4165 0.0041 2 0.06878 0.00001 -44.96 0.00 100.0000 0.0000 3 0.00004 0.00000 -29.20 1.37 0.0530 0.0019 4 0.00002 0.00000 21.68 0.61 0.0267 0.0009 5 0.00001 0.00000 -22.32 0.89 0.0137 0.0019 6 0.00016 0.00000 -14.82 0.04 0.2264 0.0010 7 0.00000 0.00000 -22.29 0.52 0.0032 0.0006 8 0.00000 0.00000 16.39 3.18 0.0045 0.0017 9 0.00001 0.00000 17.70 0.54 0.0105 0.0008 10 0.00021 0.00000 9.07 0.02 0.3008 0.0027 11 0.00000 0.00000 -3.58 12.34 0.0020 0.0012 12 0.00000 0.00000 11.44 1.63 0.0046 0.0013 13 0.00001 0.00000 11.41 0.30 0.0125 0.0011 14 0.00017 0.00000 6.49 0.04 0.2536 0.0010 15 0.00000 0.00000 -1.61 9.47 0.0027 0.0015 16 0.00000 0.00000 2.42 2.30 0.0026 0.0008 The magnetic center is at X = -56.1 +- 1.0 microns Y = 177.4 +- 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 ^ | S N --> x N S Date: 02-28-1995 Time: 08:56:11 Magnet Name: 197 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0511 +- 6.674957E-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 0.00055 0.00001 -15.67 0.36 0.3977 0.0040 2 0.13723 0.00002 -44.96 0.00 100.0000 0.0000 3 0.00008 0.00000 -28.45 0.96 0.0549 0.0004 4 0.00004 0.00000 20.87 1.11 0.0281 0.0008 5 0.00002 0.00000 -21.14 0.95 0.0131 0.0022 6 0.00031 0.00000 -14.75 0.04 0.2264 0.0005 7 0.00000 0.00000 -9.79 18.40 0.0027 0.0008 8 0.00001 0.00000 16.79 3.06 0.0046 0.0015 9 0.00001 0.00000 17.07 0.34 0.0100 0.0011 10 0.00042 0.00000 9.07 0.02 0.3028 0.0028 11 0.00000 0.00000 2.44 4.36 0.0025 0.0005 12 0.00001 0.00000 9.47 2.40 0.0056 0.0026 13 0.00002 0.00000 12.39 0.26 0.0115 0.0011 14 0.00035 0.00000 6.51 0.03 0.2561 0.0026 15 0.00001 0.00000 2.68 7.44 0.0050 0.0030 16 0.00001 0.00000 0.74 7.14 0.0045 0.0018 The magnetic center is at X = -48.0 +- 1.2 microns Y = 171.0 +- 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 ^ | S N --> x N S Date: 02-28-1995 Time: 09:02:25 Magnet Name: 197 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0621 +- 4.136089E-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 -15.24 0.34 0.3873 0.0041 2 0.20536 0.00003 -44.98 0.00 100.0000 0.0000 3 0.00011 0.00000 -27.45 0.91 0.0559 0.0020 4 0.00006 0.00000 19.72 0.70 0.0275 0.0023 5 0.00002 0.00001 -22.19 1.45 0.0118 0.0025 6 0.00044 0.00000 -14.75 0.05 0.2159 0.0022 7 0.00001 0.00000 -22.56 4.64 0.0035 0.0021 8 0.00001 0.00000 16.73 2.30 0.0051 0.0017 9 0.00002 0.00000 18.02 0.88 0.0110 0.0015 10 0.00063 0.00000 9.03 0.02 0.3062 0.0016 11 0.00000 0.00000 4.16 2.34 0.0020 0.0015 12 0.00002 0.00000 4.68 11.39 0.0078 0.0023 13 0.00002 0.00000 12.44 1.02 0.0105 0.0019 14 0.00052 0.00000 6.47 0.02 0.2538 0.0008 15 0.00001 0.00000 6.64 2.93 0.0043 0.0011 16 0.00001 0.00000 -5.86 2.62 0.0037 0.0023 The magnetic center is at X = -45.5 +- 1.1 microns Y = 166.9 +- 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 ^ | S N --> x N S Date: 02-28-1995 Time: 09:08:38 Magnet Name: 197 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3018 +- 3.6125E-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 0.00103 0.00001 -17.64 0.27 0.3773 0.0027 2 0.27305 0.00005 -44.98 0.00 100.0000 0.0000 3 0.00017 0.00001 -25.53 0.68 0.0615 0.0040 4 0.00008 0.00000 27.85 0.80 0.0302 0.0016 5 0.00004 0.00001 -21.03 1.25 0.0130 0.0031 6 0.00057 0.00001 -14.76 0.06 0.2105 0.0024 7 0.00001 0.00000 12.30 20.42 0.0025 0.0007 8 0.00001 0.00000 4.76 1.53 0.0051 0.0013 9 0.00003 0.00000 15.75 0.43 0.0098 0.0017 10 0.00084 0.00001 9.02 0.01 0.3081 0.0021 11 0.00001 0.00000 3.71 3.22 0.0022 0.0006 12 0.00001 0.00001 8.68 1.49 0.0052 0.0024 13 0.00003 0.00001 12.57 0.66 0.0116 0.0019 14 0.00069 0.00000 6.50 0.03 0.2517 0.0009 15 0.00001 0.00000 -1.97 7.57 0.0050 0.0017 16 0.00001 0.00000 3.02 7.21 0.0045 0.0012 The magnetic center is at X = -51.1 +- 0.8 microns Y = 160.6 +- 1.2 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 ^ | S N --> x N S Date: 02-28-1995 Time: 09:14:54 Magnet Name: 197 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.3985 +- 8.342596E-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 0.00123 0.00001 -21.60 0.45 0.3651 0.0034 2 0.33804 0.00009 -44.98 0.00 100.0000 0.0000 3 0.00025 0.00001 -23.54 0.50 0.0750 0.0028 4 0.00010 0.00000 24.82 1.25 0.0285 0.0008 5 0.00005 0.00000 -22.97 2.13 0.0143 0.0012 6 0.00063 0.00001 -14.73 0.04 0.1874 0.0017 7 0.00001 0.00000 21.59 1.44 0.0031 0.0009 8 0.00004 0.00001 9.04 18.04 0.0123 0.0020 9 0.00004 0.00001 16.69 1.03 0.0114 0.0016 10 0.00106 0.00001 9.04 0.02 0.3122 0.0028 11 0.00001 0.00000 6.93 3.17 0.0030 0.0008 12 0.00003 0.00001 3.66 1.53 0.0086 0.0018 13 0.00004 0.00001 12.37 0.60 0.0117 0.0017 14 0.00086 0.00001 6.50 0.06 0.2541 0.0019 15 0.00002 0.00001 3.19 8.85 0.0056 0.0020 16 0.00001 0.00001 -1.35 6.15 0.0044 0.0038 The magnetic center is at X = -60.0 +- 1.3 microns Y = 151.6 +- 1.5 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 ^ | S N --> x N S Date: 02-28-1995 Time: 09:21:07 Magnet Name: 197 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3813 +- 6.388678E-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 0.00130 0.00002 -18.53 0.34 0.3331 0.0039 2 0.39000 0.00006 -44.98 0.00 100.0000 0.0000 3 0.00026 0.00001 -18.76 0.72 0.0679 0.0038 4 0.00011 0.00001 21.48 0.97 0.0272 0.0027 5 0.00005 0.00001 -24.65 2.20 0.0141 0.0018 6 0.00052 0.00001 -14.64 0.13 0.1338 0.0014 7 0.00002 0.00000 -1.36 23.12 0.0050 0.0011 8 0.00004 0.00001 19.02 1.33 0.0097 0.0015 9 0.00004 0.00000 16.38 0.46 0.0099 0.0011 10 0.00126 0.00000 9.01 0.02 0.3223 0.0007 11 0.00001 0.00001 5.72 3.01 0.0026 0.0014 12 0.00002 0.00001 7.05 1.60 0.0048 0.0014 13 0.00005 0.00000 12.37 0.48 0.0122 0.0009 14 0.00100 0.00001 6.48 0.01 0.2571 0.0014 15 0.00002 0.00001 -0.40 6.39 0.0046 0.0020 16 0.00002 0.00001 0.41 1.19 0.0058 0.0022 The magnetic center is at X = -47.3 +- 1.0 microns Y = 141.1 +- 1.7 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 ^ | S N --> x N S Date: 02-28-1995 Time: 09:27:22 Magnet Name: 197 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3837 +- 8.121633E-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 0.00135 0.00001 -15.47 0.76 0.3162 0.0012 2 0.42637 0.00005 -44.98 0.00 100.0000 0.0000 3 0.00027 0.00001 -15.77 0.63 0.0639 0.0022 4 0.00011 0.00001 22.59 1.06 0.0265 0.0013 5 0.00006 0.00001 -24.92 1.40 0.0136 0.0016 6 0.00034 0.00001 -14.22 0.05 0.0789 0.0017 7 0.00002 0.00001 -0.41 25.22 0.0047 0.0012 8 0.00004 0.00001 18.67 0.46 0.0083 0.0013 9 0.00004 0.00000 17.13 0.38 0.0095 0.0006 10 0.00142 0.00001 9.03 0.04 0.3330 0.0012 11 0.00002 0.00001 5.52 2.31 0.0035 0.0012 12 0.00002 0.00001 10.11 1.88 0.0044 0.0013 13 0.00004 0.00001 12.05 0.71 0.0099 0.0025 14 0.00108 0.00001 6.43 0.04 0.2544 0.0015 15 0.00003 0.00001 2.09 7.59 0.0063 0.0025 16 0.00003 0.00001 -0.33 0.88 0.0067 0.0025 The magnetic center is at X = -37.7 +- 1.8 microns Y = 136.1 +- 0.7 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 ^ | S N --> x N S 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)