SLAC Magnetic Measurements Date: 03-21-1995 Time: 11:10:51 Magnet Name (Serial #): 115 Bar Code Number: 425 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: 03-21-1995 Time: 11:59:23 Magnet Name: 115 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00069 +- 4.647225E-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 0.00003 0.00000 -85.62 1.85 0.1768 0.0041 2 0.01491 0.00000 44.90 0.00 100.0000 0.0000 3 0.00001 0.00000 41.84 1.87 0.0560 0.0045 4 0.00000 0.00000 1.59 39.61 0.0068 0.0036 5 0.00000 0.00000 10.24 2.24 0.0145 0.0020 6 0.00003 0.00000 15.09 0.08 0.2166 0.0020 7 0.00000 0.00000 14.06 3.79 0.0037 0.0011 8 0.00000 0.00000 1.21 12.67 0.0019 0.0010 9 0.00000 0.00000 -10.88 3.99 0.0032 0.0015 10 0.00004 0.00000 -9.08 0.01 0.3010 0.0013 11 0.00000 0.00000 3.55 8.03 0.0036 0.0008 12 0.00000 0.00000 -10.05 2.09 0.0033 0.0015 13 0.00000 0.00000 -3.27 2.70 0.0087 0.0030 14 0.00004 0.00000 -6.50 0.02 0.2542 0.0007 15 0.00000 0.00000 -0.31 1.48 0.0086 0.0019 16 0.00000 0.00000 2.68 8.10 0.0045 0.0013 The magnetic center is at X = 78.7 +- 1.8 microns Y = -6.0 +- 2.6 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: 03-21-1995 Time: 12:05:29 Magnet Name: 115 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10151 +- 3.591568E-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 -167.62 1.42 0.1329 0.0082 2 0.03496 0.00001 44.90 0.00 100.0000 0.0000 3 0.00002 0.00000 26.72 1.94 0.0652 0.0029 4 0.00000 0.00000 -41.59 1.60 0.0133 0.0022 5 0.00001 0.00000 14.70 1.72 0.0149 0.0021 6 0.00008 0.00000 15.01 0.05 0.2243 0.0022 7 0.00000 0.00000 0.16 22.18 0.0040 0.0008 8 0.00000 0.00000 -10.34 17.75 0.0085 0.0007 9 0.00000 0.00000 -3.65 4.81 0.0048 0.0013 10 0.00011 0.00000 -9.15 0.06 0.3015 0.0012 11 0.00000 0.00000 -0.08 7.29 0.0014 0.0007 12 0.00000 0.00000 -3.19 3.36 0.0060 0.0029 13 0.00000 0.00000 -2.02 4.97 0.0072 0.0027 14 0.00009 0.00000 -6.51 0.02 0.2552 0.0015 15 0.00000 0.00000 -2.28 4.78 0.0078 0.0036 16 0.00000 0.00000 0.33 5.42 0.0061 0.0009 The magnetic center is at X = 12.7 +- 1.6 microns Y = 58.0 +- 3.6 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: 03-21-1995 Time: 12:11:40 Magnet Name: 115 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.0639 +- 2.742407E-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 0.00011 0.00000 175.71 1.68 0.1648 0.0053 2 0.06883 0.00002 44.90 0.00 100.0000 0.0000 3 0.00005 0.00000 25.32 1.16 0.0675 0.0052 4 0.00001 0.00000 -38.56 3.78 0.0079 0.0020 5 0.00001 0.00000 15.70 1.03 0.0160 0.0019 6 0.00015 0.00000 15.02 0.08 0.2224 0.0018 7 0.00000 0.00000 -2.26 22.53 0.0058 0.0012 8 0.00000 0.00000 -9.58 2.89 0.0025 0.0011 9 0.00000 0.00000 3.03 8.21 0.0036 0.0017 10 0.00021 0.00000 -9.11 0.01 0.3036 0.0014 11 0.00000 0.00000 5.05 5.58 0.0023 0.0008 12 0.00000 0.00000 -10.01 2.45 0.0042 0.0023 13 0.00001 0.00000 -2.21 2.51 0.0082 0.0034 14 0.00017 0.00000 -6.53 0.02 0.2527 0.0012 15 0.00001 0.00000 -0.28 3.89 0.0080 0.0044 16 0.00001 0.00000 -0.41 8.93 0.0110 0.0024 The magnetic center is at X = -5.5 +- 2.2 microns Y = 73.4 +- 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: 03-21-1995 Time: 12:17:56 Magnet Name: 115 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0575 +- 4.323249E-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 0.00025 0.00000 170.24 1.57 0.1803 0.0034 2 0.13732 0.00003 44.90 0.00 100.0000 0.0000 3 0.00009 0.00001 24.54 1.19 0.0648 0.0043 4 0.00001 0.00000 -36.55 3.56 0.0080 0.0019 5 0.00002 0.00000 15.60 0.92 0.0161 0.0025 6 0.00031 0.00000 15.04 0.03 0.2238 0.0019 7 0.00001 0.00000 10.37 20.42 0.0049 0.0014 8 0.00000 0.00000 -11.16 2.61 0.0023 0.0004 9 0.00001 0.00000 -5.48 3.15 0.0043 0.0017 10 0.00042 0.00000 -9.13 0.01 0.3048 0.0012 11 0.00000 0.00000 -0.17 6.89 0.0017 0.0005 12 0.00001 0.00000 -11.24 1.05 0.0052 0.0012 13 0.00001 0.00001 -3.13 1.42 0.0095 0.0047 14 0.00035 0.00000 -6.53 0.02 0.2545 0.0013 15 0.00001 0.00000 2.54 3.16 0.0083 0.0018 16 0.00001 0.00000 6.78 4.90 0.0059 0.0007 The magnetic center is at X = -13.7 +- 2.2 microns Y = 79.4 +- 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: 03-21-1995 Time: 12:24:11 Magnet Name: 115 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0693 +- 2.954852E-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 0.00036 0.00002 166.91 1.45 0.1758 0.0093 2 0.20544 0.00002 44.87 0.00 100.0000 0.0000 3 0.00013 0.00001 25.18 1.79 0.0632 0.0037 4 0.00001 0.00000 -14.17 34.32 0.0064 0.0013 5 0.00003 0.00000 17.03 1.25 0.0163 0.0016 6 0.00044 0.00000 15.01 0.04 0.2149 0.0011 7 0.00001 0.00000 -2.12 22.60 0.0055 0.0006 8 0.00001 0.00000 -12.31 4.32 0.0027 0.0014 9 0.00001 0.00000 -9.13 3.63 0.0038 0.0016 10 0.00063 0.00000 -9.15 0.02 0.3059 0.0010 11 0.00001 0.00000 0.41 5.55 0.0034 0.0024 12 0.00001 0.00000 -13.19 1.11 0.0057 0.0004 13 0.00002 0.00001 1.57 2.31 0.0084 0.0041 14 0.00052 0.00000 -6.55 0.03 0.2516 0.0015 15 0.00002 0.00000 -5.08 3.47 0.0076 0.0023 16 0.00001 0.00001 4.45 6.99 0.0055 0.0036 The magnetic center is at X = -17.8 +- 2.2 microns Y = 76.5 +- 4.1 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: 03-21-1995 Time: 12:30:25 Magnet Name: 115 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.312 +- 1.461383E-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 0.00046 0.00002 165.65 1.21 0.1702 0.0076 2 0.27296 0.00008 44.87 0.00 100.0000 0.0000 3 0.00017 0.00001 25.20 1.75 0.0622 0.0047 4 0.00006 0.00001 -41.13 1.08 0.0222 0.0023 5 0.00004 0.00001 16.82 0.79 0.0145 0.0027 6 0.00056 0.00000 15.02 0.05 0.2067 0.0011 7 0.00001 0.00000 12.06 20.14 0.0047 0.0011 8 0.00002 0.00000 -1.76 1.38 0.0085 0.0008 9 0.00001 0.00001 -5.08 2.82 0.0036 0.0019 10 0.00085 0.00000 -9.14 0.02 0.3106 0.0007 11 0.00001 0.00000 4.82 3.07 0.0036 0.0018 12 0.00002 0.00000 -11.08 2.07 0.0057 0.0008 13 0.00002 0.00000 -1.93 5.95 0.0077 0.0018 14 0.00069 0.00000 -6.52 0.04 0.2528 0.0014 15 0.00003 0.00001 -2.62 1.68 0.0094 0.0045 16 0.00002 0.00001 -4.37 8.30 0.0081 0.0040 The magnetic center is at X = -18.8 +- 1.8 microns Y = 73.7 +- 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: 03-21-1995 Time: 12:36:41 Magnet Name: 115 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4031 +- 1.114202E-02 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 0.00059 0.00002 162.97 1.24 0.1745 0.0049 2 0.33781 0.00008 44.87 0.00 100.0000 0.0000 3 0.00023 0.00001 24.92 0.95 0.0681 0.0042 4 0.00005 0.00001 -40.17 2.28 0.0155 0.0034 5 0.00005 0.00001 17.21 1.61 0.0135 0.0017 6 0.00062 0.00001 15.12 0.08 0.1840 0.0018 7 0.00002 0.00000 0.59 21.13 0.0051 0.0010 8 0.00002 0.00000 -19.30 1.71 0.0048 0.0011 9 0.00002 0.00000 -6.27 4.81 0.0045 0.0011 10 0.00106 0.00000 -9.13 0.02 0.3146 0.0007 11 0.00001 0.00000 0.28 1.28 0.0024 0.0014 12 0.00003 0.00001 -2.86 1.32 0.0087 0.0021 13 0.00001 0.00001 3.16 3.56 0.0044 0.0034 14 0.00085 0.00000 -6.57 0.02 0.2507 0.0007 15 0.00003 0.00001 -2.63 2.16 0.0101 0.0026 16 0.00003 0.00001 5.08 8.63 0.0091 0.0036 The magnetic center is at X = -22.8 +- 1.7 microns Y = 74.5 +- 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: 03-21-1995 Time: 12:42:57 Magnet Name: 115 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.397 +- 1.561922E-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 0.00084 0.00003 161.93 1.08 0.2156 0.0071 2 0.39003 0.00006 44.87 0.00 100.0000 0.0000 3 0.00031 0.00002 19.71 1.21 0.0803 0.0039 4 0.00004 0.00001 -37.61 2.07 0.0106 0.0026 5 0.00005 0.00000 18.08 1.68 0.0117 0.0006 6 0.00051 0.00000 15.24 0.13 0.1304 0.0012 7 0.00002 0.00001 -10.51 20.54 0.0056 0.0018 8 0.00002 0.00000 -10.71 18.96 0.0060 0.0003 9 0.00001 0.00001 -4.83 3.11 0.0038 0.0027 10 0.00126 0.00000 -9.10 0.03 0.3241 0.0011 11 0.00001 0.00000 -4.62 6.46 0.0019 0.0009 12 0.00002 0.00001 -4.11 4.29 0.0058 0.0024 13 0.00003 0.00001 -3.48 1.23 0.0072 0.0017 14 0.00099 0.00001 -6.52 0.02 0.2538 0.0014 15 0.00003 0.00001 0.51 2.40 0.0065 0.0024 16 0.00001 0.00001 -0.78 7.79 0.0036 0.0026 The magnetic center is at X = -29.9 +- 2.0 microns Y = 91.5 +- 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: 03-21-1995 Time: 12:49:13 Magnet Name: 115 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.399 +- 2.112667E-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 0.00098 0.00003 161.31 1.32 0.2297 0.0061 2 0.42665 0.00004 44.87 0.00 100.0000 0.0000 3 0.00038 0.00002 19.14 0.99 0.0883 0.0038 4 0.00005 0.00001 -37.80 3.14 0.0109 0.0017 5 0.00005 0.00001 19.17 1.95 0.0125 0.0025 6 0.00031 0.00001 15.53 0.22 0.0720 0.0015 7 0.00003 0.00000 -23.16 1.59 0.0072 0.0011 8 0.00002 0.00000 -8.34 17.81 0.0041 0.0011 9 0.00001 0.00000 -0.93 5.44 0.0026 0.0011 10 0.00142 0.00001 -9.14 0.03 0.3337 0.0012 11 0.00001 0.00001 -2.14 4.93 0.0033 0.0018 12 0.00002 0.00001 -8.72 6.71 0.0044 0.0016 13 0.00005 0.00001 -0.60 2.47 0.0107 0.0030 14 0.00107 0.00000 -6.51 0.03 0.2502 0.0002 15 0.00003 0.00001 -4.16 3.21 0.0064 0.0024 16 0.00002 0.00001 0.37 3.36 0.0052 0.0026 The magnetic center is at X = -32.9 +- 2.4 microns Y = 97.2 +- 2.7 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)