SLAC Magnetic Measurements Date: 03-09-1995 Time: 11:17:08 Magnet Name (Serial #): 191 Bar Code Number: 586 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: 03-09-1995 Time: 12:37:05 Magnet Name: 191 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00291 +- 2.391622E-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 0.00005 0.00000 -134.77 0.12 0.3341 0.0025 2 0.01487 0.00000 44.95 0.00 100.0000 0.0000 3 0.00002 0.00000 33.21 0.20 0.1059 0.0027 4 0.00000 0.00000 35.08 3.10 0.0088 0.0013 5 0.00000 0.00000 21.11 1.47 0.0141 0.0020 6 0.00003 0.00000 15.26 0.06 0.2173 0.0027 7 0.00000 0.00000 13.28 18.47 0.0033 0.0010 8 0.00000 0.00000 -9.01 3.29 0.0034 0.0013 9 0.00000 0.00000 0.21 1.06 0.0075 0.0016 10 0.00005 0.00000 -9.05 0.04 0.3030 0.0033 11 0.00000 0.00000 -7.60 3.58 0.0019 0.0011 12 0.00000 0.00000 1.53 1.27 0.0072 0.0021 13 0.00000 0.00000 0.71 0.42 0.0148 0.0037 14 0.00004 0.00000 -6.41 0.05 0.2535 0.0028 15 0.00000 0.00000 -3.38 2.12 0.0062 0.0032 16 0.00000 0.00000 2.46 0.93 0.0059 0.0017 The magnetic center is at X = 105.9 +- 0.8 microns Y = 105.1 +- 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: 03-09-1995 Time: 12:43:14 Magnet Name: 191 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10389 +- 2.084231E-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 0.00010 0.00000 -143.61 0.08 0.2811 0.0019 2 0.03499 0.00001 44.95 0.00 100.0000 0.0000 3 0.00003 0.00000 40.44 0.23 0.0969 0.0012 4 0.00001 0.00000 20.91 37.93 0.0213 0.0029 5 0.00000 0.00000 18.96 1.49 0.0132 0.0021 6 0.00008 0.00000 15.24 0.08 0.2182 0.0016 7 0.00000 0.00000 16.87 2.53 0.0019 0.0008 8 0.00000 0.00000 -3.68 1.89 0.0044 0.0011 9 0.00000 0.00000 -0.27 0.83 0.0073 0.0010 10 0.00011 0.00000 -9.03 0.02 0.3017 0.0017 11 0.00000 0.00000 -0.95 11.69 0.0022 0.0003 12 0.00000 0.00000 -1.61 2.33 0.0051 0.0030 13 0.00001 0.00000 1.63 0.33 0.0149 0.0014 14 0.00009 0.00000 -6.50 0.06 0.2557 0.0023 15 0.00000 0.00000 -0.75 1.19 0.0069 0.0016 16 0.00000 0.00000 6.23 0.51 0.0043 0.0007 The magnetic center is at X = 74.5 +- 0.5 microns Y = 101.1 +- 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 ^ | N S --> x S N Date: 03-09-1995 Time: 12:49:28 Magnet Name: 191 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.0657 +- 4.217743E-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 0.00019 0.00000 -150.32 0.28 0.2747 0.0014 2 0.06896 0.00003 44.95 0.00 100.0000 0.0000 3 0.00007 0.00000 41.62 0.46 0.0955 0.0010 4 0.00001 0.00000 -1.02 43.82 0.0119 0.0027 5 0.00001 0.00000 17.22 3.21 0.0116 0.0026 6 0.00015 0.00000 15.22 0.03 0.2193 0.0018 7 0.00000 0.00000 -6.75 16.66 0.0017 0.0010 8 0.00000 0.00000 -4.78 0.97 0.0050 0.0008 9 0.00000 0.00000 0.34 0.92 0.0068 0.0017 10 0.00021 0.00000 -9.04 0.04 0.3021 0.0012 11 0.00000 0.00000 -10.97 0.65 0.0028 0.0011 12 0.00000 0.00000 3.06 3.53 0.0066 0.0021 13 0.00001 0.00000 1.43 1.02 0.0166 0.0012 14 0.00017 0.00000 -6.48 0.05 0.2505 0.0061 15 0.00000 0.00000 2.01 4.80 0.0069 0.0039 16 0.00000 0.00000 -0.95 3.58 0.0064 0.0027 The magnetic center is at X = 60.8 +- 0.6 microns Y = 106.6 +- 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: 03-09-1995 Time: 12:55:47 Magnet Name: 191 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0577 +- 9.863408E-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 0.00037 0.00000 -155.71 0.27 0.2725 0.0009 2 0.13758 0.00004 44.95 0.00 100.0000 0.0000 3 0.00013 0.00000 42.68 0.22 0.0961 0.0020 4 0.00002 0.00000 22.27 37.33 0.0112 0.0020 5 0.00001 0.00000 18.59 3.33 0.0103 0.0008 6 0.00030 0.00000 15.25 0.10 0.2188 0.0017 7 0.00000 0.00000 -6.42 14.88 0.0013 0.0005 8 0.00001 0.00000 -9.13 2.91 0.0045 0.0007 9 0.00001 0.00000 0.04 0.90 0.0078 0.0013 10 0.00042 0.00000 -9.06 0.04 0.3025 0.0018 11 0.00000 0.00000 -10.65 3.22 0.0021 0.0008 12 0.00001 0.00000 0.26 2.45 0.0054 0.0030 13 0.00002 0.00000 1.37 0.51 0.0135 0.0030 14 0.00035 0.00001 -6.43 0.06 0.2535 0.0043 15 0.00001 0.00000 -1.38 3.97 0.0065 0.0029 16 0.00001 0.00000 3.09 3.15 0.0060 0.0006 The magnetic center is at X = 50.1 +- 0.6 microns Y = 110.9 +- 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 ^ | N S --> x S N Date: 03-09-1995 Time: 13:02:05 Magnet Name: 191 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0686 +- 3.43577E-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 0.00058 0.00000 -157.63 0.55 0.2810 0.0016 2 0.20596 0.00006 44.93 0.00 100.0000 0.0000 3 0.00019 0.00000 41.77 0.37 0.0927 0.0024 4 0.00002 0.00000 2.46 42.54 0.0089 0.0022 5 0.00002 0.00000 20.29 1.05 0.0105 0.0014 6 0.00044 0.00000 15.26 0.11 0.2119 0.0017 7 0.00001 0.00000 -8.55 9.79 0.0026 0.0012 8 0.00001 0.00000 -4.88 2.68 0.0055 0.0013 9 0.00002 0.00000 -0.57 0.67 0.0078 0.0011 10 0.00062 0.00000 -9.07 0.01 0.3017 0.0012 11 0.00001 0.00000 -8.61 1.34 0.0039 0.0011 12 0.00001 0.00001 3.91 1.80 0.0059 0.0029 13 0.00003 0.00000 1.03 1.14 0.0142 0.0009 14 0.00052 0.00000 -6.38 0.09 0.2523 0.0016 15 0.00001 0.00000 -1.15 1.60 0.0033 0.0019 16 0.00001 0.00000 2.35 1.45 0.0054 0.0022 The magnetic center is at X = 47.8 +- 1.1 microns Y = 116.1 +- 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: 03-09-1995 Time: 13:08:23 Magnet Name: 191 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3122 +- 2.434243E-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 0.00078 0.00000 -156.90 0.15 0.2835 0.0010 2 0.27374 0.00007 44.93 0.00 100.0000 0.0000 3 0.00025 0.00000 41.55 0.67 0.0902 0.0010 4 0.00003 0.00001 -38.27 4.10 0.0119 0.0025 5 0.00003 0.00001 19.05 2.05 0.0108 0.0022 6 0.00055 0.00000 15.22 0.05 0.2011 0.0010 7 0.00000 0.00000 4.63 13.55 0.0015 0.0004 8 0.00002 0.00000 -6.93 0.68 0.0055 0.0016 9 0.00002 0.00000 0.90 1.71 0.0058 0.0006 10 0.00085 0.00001 -9.05 0.02 0.3101 0.0021 11 0.00001 0.00000 -11.88 1.40 0.0031 0.0012 12 0.00002 0.00001 0.40 1.66 0.0075 0.0031 13 0.00004 0.00001 1.02 0.52 0.0148 0.0019 14 0.00070 0.00000 -6.43 0.04 0.2549 0.0007 15 0.00002 0.00000 -2.13 2.27 0.0060 0.0011 16 0.00002 0.00001 0.91 1.12 0.0059 0.0031 The magnetic center is at X = 49.7 +- 0.4 microns Y = 116.5 +- 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 Date: 03-09-1995 Time: 13:14:41 Magnet Name: 191 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4107 +- 9.082825E-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 0.00096 0.00001 -153.27 0.22 0.2845 0.0026 2 0.33890 0.00004 44.93 0.00 100.0000 0.0000 3 0.00027 0.00001 44.33 0.40 0.0796 0.0043 4 0.00009 0.00001 -41.36 0.71 0.0271 0.0026 5 0.00002 0.00001 16.18 3.18 0.0072 0.0021 6 0.00058 0.00001 15.30 0.10 0.1725 0.0017 7 0.00001 0.00000 -13.88 3.98 0.0029 0.0008 8 0.00003 0.00000 -5.50 0.73 0.0078 0.0012 9 0.00003 0.00000 -0.61 1.01 0.0088 0.0011 10 0.00107 0.00000 -9.08 0.04 0.3144 0.0010 11 0.00001 0.00000 -7.70 5.22 0.0024 0.0014 12 0.00003 0.00001 -1.76 4.25 0.0076 0.0034 13 0.00006 0.00001 0.34 0.55 0.0165 0.0027 14 0.00084 0.00001 -6.45 0.10 0.2484 0.0038 15 0.00003 0.00001 -1.58 2.31 0.0078 0.0026 16 0.00001 0.00001 4.29 8.87 0.0036 0.0023 The magnetic center is at X = 57.2 +- 0.7 microns Y = 113.5 +- 1.1 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: 03-09-1995 Time: 13:21:00 Magnet Name: 191 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3941 +- 2.252933E-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 0.00124 0.00001 -148.59 0.30 0.3181 0.0022 2 0.39094 0.00007 44.93 0.00 100.0000 0.0000 3 0.00023 0.00001 46.39 0.52 0.0581 0.0022 4 0.00008 0.00001 -39.08 1.51 0.0196 0.0025 5 0.00002 0.00001 18.97 2.45 0.0056 0.0022 6 0.00050 0.00001 15.35 0.13 0.1287 0.0017 7 0.00001 0.00000 0.03 14.03 0.0021 0.0010 8 0.00003 0.00000 -18.07 1.81 0.0071 0.0013 9 0.00003 0.00000 0.30 0.29 0.0083 0.0008 10 0.00126 0.00000 -9.07 0.02 0.3235 0.0008 11 0.00001 0.00000 -7.37 8.88 0.0025 0.0005 12 0.00004 0.00001 -1.87 2.53 0.0112 0.0029 13 0.00006 0.00001 1.23 1.12 0.0165 0.0028 14 0.00098 0.00002 -6.48 0.04 0.2517 0.0056 15 0.00002 0.00001 -1.97 3.43 0.0061 0.0017 16 0.00001 0.00001 1.89 3.75 0.0037 0.0014 The magnetic center is at X = 74.1 +- 0.8 microns Y = 121.3 +- 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: 03-09-1995 Time: 13:27:19 Magnet Name: 191 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3984 +- 1.297087E-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 0.00145 0.00002 -146.76 0.66 0.3385 0.0037 2 0.42721 0.00008 44.93 0.00 100.0000 0.0000 3 0.00019 0.00001 46.33 1.42 0.0442 0.0033 4 0.00008 0.00001 -35.23 1.78 0.0197 0.0023 5 0.00002 0.00001 17.54 1.15 0.0056 0.0019 6 0.00031 0.00000 15.87 0.16 0.0718 0.0007 7 0.00001 0.00000 -9.58 5.63 0.0019 0.0009 8 0.00003 0.00000 -17.72 0.82 0.0066 0.0009 9 0.00003 0.00001 0.88 0.55 0.0079 0.0013 10 0.00142 0.00001 -9.07 0.01 0.3329 0.0015 11 0.00001 0.00000 -10.51 4.14 0.0022 0.0012 12 0.00004 0.00001 0.56 1.87 0.0104 0.0030 13 0.00007 0.00001 1.65 0.35 0.0159 0.0016 14 0.00105 0.00001 -6.48 0.06 0.2457 0.0032 15 0.00002 0.00001 3.12 1.69 0.0055 0.0028 16 0.00004 0.00000 0.32 0.66 0.0095 0.0005 The magnetic center is at X = 82.9 +- 1.7 microns Y = 126.5 +- 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 ^ | 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)