SLAC Magnetic Measurements Date: 04-14-1995 Time: 11:48:39 Magnet Name (Serial #): 171 Bar Code Number: 526 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: 04-14-1995 Time: 12:35:56 Magnet Name: 171 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00237 +- 4.865359E-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 0.00009 0.00000 -113.70 0.21 0.6107 0.0008 2 0.01493 0.00000 45.04 0.00 100.0000 0.0000 3 0.00001 0.00000 0.67 0.36 0.0952 0.0014 4 0.00000 0.00000 25.36 1.05 0.0294 0.0033 5 0.00000 0.00000 13.26 2.33 0.0113 0.0020 6 0.00003 0.00000 15.08 0.02 0.2152 0.0022 7 0.00000 0.00000 15.73 1.00 0.0145 0.0016 8 0.00000 0.00000 19.16 0.59 0.0042 0.0012 9 0.00000 0.00000 6.72 0.55 0.0155 0.0012 10 0.00004 0.00000 -9.01 0.01 0.2994 0.0023 11 0.00000 0.00000 -4.01 7.83 0.0017 0.0007 12 0.00000 0.00000 5.77 11.00 0.0041 0.0016 13 0.00000 0.00000 2.43 1.01 0.0116 0.0021 14 0.00004 0.00000 -6.40 0.02 0.2580 0.0014 15 0.00000 0.00000 -2.73 8.52 0.0086 0.0036 16 0.00000 0.00000 -0.42 5.75 0.0053 0.0045 The magnetic center is at X = 249.8 +- 0.5 microns Y = 109.7 +- 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: 04-14-1995 Time: 12:42:02 Magnet Name: 171 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10537 +- 2.15581E-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 -124.71 0.34 0.3808 0.0022 2 0.03493 0.00000 45.04 0.00 100.0000 0.0000 3 0.00003 0.00000 20.34 0.29 0.0846 0.0005 4 0.00001 0.00000 29.84 1.14 0.0279 0.0022 5 0.00001 0.00000 11.99 1.36 0.0165 0.0024 6 0.00008 0.00000 15.12 0.03 0.2200 0.0015 7 0.00000 0.00000 14.62 1.64 0.0081 0.0011 8 0.00000 0.00000 20.71 0.50 0.0125 0.0014 9 0.00000 0.00000 6.26 0.42 0.0131 0.0013 10 0.00010 0.00000 -9.03 0.02 0.3002 0.0014 11 0.00000 0.00000 -0.50 2.98 0.0021 0.0010 12 0.00000 0.00000 2.36 1.28 0.0062 0.0012 13 0.00000 0.00000 3.24 0.91 0.0136 0.0028 14 0.00009 0.00000 -6.43 0.04 0.2563 0.0020 15 0.00000 0.00000 -8.51 1.09 0.0110 0.0010 16 0.00000 0.00000 0.25 6.95 0.0035 0.0023 The magnetic center is at X = 139.8 +- 1.0 microns Y = 96.8 +- 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: 04-14-1995 Time: 12:48:13 Magnet Name: 171 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06934 +- 5.884812E-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 0.00023 0.00000 -132.04 0.43 0.3389 0.0017 2 0.06877 0.00001 45.04 0.00 100.0000 0.0000 3 0.00006 0.00000 22.52 0.45 0.0921 0.0025 4 0.00002 0.00000 28.07 1.27 0.0239 0.0016 5 0.00001 0.00000 13.09 2.25 0.0193 0.0031 6 0.00015 0.00000 15.09 0.03 0.2190 0.0007 7 0.00001 0.00000 11.86 0.93 0.0079 0.0011 8 0.00000 0.00000 18.02 2.28 0.0053 0.0007 9 0.00001 0.00000 6.00 0.76 0.0146 0.0004 10 0.00021 0.00000 -9.00 0.03 0.3007 0.0013 11 0.00000 0.00000 -2.00 1.50 0.0021 0.0006 12 0.00000 0.00000 1.81 9.85 0.0045 0.0010 13 0.00001 0.00000 3.17 0.79 0.0164 0.0018 14 0.00018 0.00000 -6.41 0.04 0.2545 0.0035 15 0.00001 0.00000 -8.70 0.68 0.0105 0.0032 16 0.00000 0.00000 5.48 3.41 0.0028 0.0010 The magnetic center is at X = 112.4 +- 1.0 microns Y = 101.4 +- 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: 04-14-1995 Time: 12:54:28 Magnet Name: 171 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0658 +- 2.566075E-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 0.00046 0.00000 -135.61 0.13 0.3331 0.0012 2 0.13723 0.00002 45.04 0.00 100.0000 0.0000 3 0.00012 0.00000 23.07 0.57 0.0910 0.0008 4 0.00003 0.00000 27.93 0.96 0.0220 0.0023 5 0.00002 0.00000 12.22 1.85 0.0169 0.0023 6 0.00030 0.00000 15.14 0.07 0.2199 0.0024 7 0.00001 0.00000 12.14 1.28 0.0064 0.0021 8 0.00000 0.00000 16.74 1.97 0.0035 0.0003 9 0.00002 0.00000 6.25 0.57 0.0136 0.0017 10 0.00042 0.00000 -8.99 0.04 0.3039 0.0023 11 0.00000 0.00000 -1.49 8.35 0.0027 0.0010 12 0.00000 0.00000 -0.21 8.25 0.0030 0.0016 13 0.00002 0.00000 3.37 0.33 0.0155 0.0023 14 0.00035 0.00000 -6.38 0.03 0.2548 0.0017 15 0.00002 0.00000 -8.14 0.88 0.0124 0.0012 16 0.00001 0.00001 5.07 1.68 0.0070 0.0036 The magnetic center is at X = 104.1 +- 0.5 microns Y = 106.3 +- 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 Date: 04-14-1995 Time: 13:00:44 Magnet Name: 171 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0826 +- 4.504574E-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 0.00068 0.00000 -136.18 0.07 0.3306 0.0019 2 0.20538 0.00003 45.01 0.00 100.0000 0.0000 3 0.00018 0.00000 23.07 0.71 0.0878 0.0015 4 0.00005 0.00000 26.91 1.44 0.0233 0.0023 5 0.00004 0.00000 13.60 1.72 0.0174 0.0020 6 0.00043 0.00001 15.09 0.08 0.2100 0.0026 7 0.00002 0.00001 11.05 2.16 0.0085 0.0033 8 0.00001 0.00000 8.09 17.57 0.0047 0.0005 9 0.00003 0.00000 6.83 0.92 0.0140 0.0008 10 0.00063 0.00000 -9.02 0.02 0.3076 0.0004 11 0.00001 0.00000 -2.24 4.91 0.0033 0.0007 12 0.00001 0.00000 0.60 12.02 0.0056 0.0020 13 0.00003 0.00000 3.17 0.72 0.0167 0.0011 14 0.00052 0.00001 -6.40 0.05 0.2529 0.0031 15 0.00003 0.00000 -8.59 0.96 0.0137 0.0020 16 0.00001 0.00000 4.48 7.72 0.0055 0.0020 The magnetic center is at X = 102.2 +- 0.6 microns Y = 106.5 +- 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: 04-14-1995 Time: 13:07:00 Magnet Name: 171 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3306 +- 9.099473E-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 0.00090 0.00000 -137.67 0.15 0.3296 0.0015 2 0.27304 0.00003 45.01 0.00 100.0000 0.0000 3 0.00025 0.00001 23.32 0.23 0.0930 0.0022 4 0.00009 0.00000 33.98 0.89 0.0318 0.0015 5 0.00004 0.00001 11.58 1.85 0.0162 0.0021 6 0.00055 0.00001 15.11 0.10 0.2027 0.0020 7 0.00002 0.00000 10.63 2.09 0.0089 0.0017 8 0.00001 0.00000 4.22 1.64 0.0047 0.0018 9 0.00004 0.00001 5.90 0.91 0.0144 0.0019 10 0.00084 0.00000 -9.01 0.01 0.3080 0.0016 11 0.00000 0.00000 1.20 5.40 0.0014 0.0007 12 0.00001 0.00001 6.03 5.19 0.0036 0.0023 13 0.00004 0.00001 3.01 0.86 0.0155 0.0019 14 0.00070 0.00000 -6.42 0.06 0.2566 0.0010 15 0.00004 0.00001 -8.92 0.29 0.0141 0.0033 16 0.00001 0.00001 6.50 3.12 0.0044 0.0022 The magnetic center is at X = 99.1 +- 0.5 microns Y = 108.8 +- 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 Date: 04-14-1995 Time: 13:13:17 Magnet Name: 171 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4357 +- 8.794346E-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 0.00109 0.00001 -139.82 0.12 0.3221 0.0020 2 0.33802 0.00004 45.01 0.00 100.0000 0.0000 3 0.00034 0.00000 23.63 0.41 0.1003 0.0012 4 0.00010 0.00001 30.91 1.11 0.0304 0.0021 5 0.00006 0.00001 13.42 1.01 0.0183 0.0024 6 0.00061 0.00001 15.07 0.09 0.1797 0.0025 7 0.00003 0.00001 10.98 1.99 0.0081 0.0024 8 0.00003 0.00000 20.37 0.62 0.0084 0.0007 9 0.00005 0.00001 6.52 0.82 0.0154 0.0015 10 0.00106 0.00001 -9.04 0.02 0.3127 0.0023 11 0.00001 0.00000 -3.44 7.85 0.0020 0.0002 12 0.00002 0.00000 0.85 1.50 0.0045 0.0011 13 0.00005 0.00001 2.86 0.86 0.0136 0.0016 14 0.00086 0.00000 -6.46 0.03 0.2538 0.0013 15 0.00004 0.00001 -8.98 1.76 0.0106 0.0024 16 0.00002 0.00001 -1.91 8.50 0.0064 0.0016 The magnetic center is at X = 92.8 +- 0.6 microns Y = 109.9 +- 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 ^ | N S --> x S N Date: 04-14-1995 Time: 13:19:34 Magnet Name: 171 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4237 +- 1.024159E-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 0.00135 0.00000 -139.97 0.29 0.3469 0.0009 2 0.39014 0.00003 45.01 0.00 100.0000 0.0000 3 0.00036 0.00001 21.03 0.46 0.0930 0.0017 4 0.00011 0.00001 28.54 0.91 0.0283 0.0025 5 0.00007 0.00000 12.19 0.59 0.0171 0.0007 6 0.00050 0.00001 15.31 0.13 0.1271 0.0016 7 0.00002 0.00000 12.28 3.64 0.0056 0.0011 8 0.00004 0.00001 20.96 0.96 0.0095 0.0014 9 0.00005 0.00000 5.99 1.00 0.0138 0.0002 10 0.00125 0.00000 -9.05 0.02 0.3212 0.0011 11 0.00001 0.00000 -3.39 3.52 0.0019 0.0003 12 0.00002 0.00001 4.43 5.28 0.0039 0.0014 13 0.00005 0.00001 2.84 0.63 0.0126 0.0029 14 0.00100 0.00001 -6.45 0.02 0.2567 0.0019 15 0.00004 0.00000 -9.12 0.67 0.0101 0.0011 16 0.00003 0.00002 1.71 1.04 0.0073 0.0053 The magnetic center is at X = 99.7 +- 0.7 microns Y = 118.6 +- 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: 04-14-1995 Time: 13:25:51 Magnet Name: 171 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4301 +- 8.399267E-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 0.00155 0.00000 -139.46 0.17 0.3638 0.0008 2 0.42663 0.00003 45.01 0.00 100.0000 0.0000 3 0.00038 0.00001 19.45 0.45 0.0880 0.0012 4 0.00013 0.00001 29.68 1.28 0.0301 0.0017 5 0.00007 0.00001 12.55 1.06 0.0158 0.0017 6 0.00029 0.00000 15.50 0.26 0.0690 0.0007 7 0.00003 0.00000 13.36 0.96 0.0078 0.0010 8 0.00003 0.00000 20.83 1.23 0.0070 0.0008 9 0.00007 0.00001 6.00 0.22 0.0163 0.0017 10 0.00142 0.00000 -9.04 0.02 0.3325 0.0007 11 0.00001 0.00000 -6.53 11.14 0.0016 0.0009 12 0.00002 0.00000 0.83 11.51 0.0041 0.0009 13 0.00006 0.00001 2.80 1.27 0.0136 0.0013 14 0.00108 0.00001 -6.44 0.04 0.2529 0.0023 15 0.00003 0.00001 -5.39 8.63 0.0076 0.0016 16 0.00003 0.00001 1.78 1.06 0.0079 0.0020 The magnetic center is at X = 105.6 +- 0.4 microns Y = 123.5 +- 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 ^ | 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)