SLAC Magnetic Measurements Date: 03-27-1995 Time: 13:28:30 Magnet Name (Serial #): 137 Bar Code Number: 242 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: bmd 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: 03-27-1995 Time: 14:15:35 Magnet Name: 137 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00037 +- 2.729429E-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 0.00004 0.00000 -168.25 0.90 0.2814 0.0042 2 0.01492 0.00000 44.99 0.00 100.0000 0.0000 3 0.00002 0.00000 -7.97 0.81 0.1032 0.0037 4 0.00000 0.00000 5.82 3.72 0.0098 0.0027 5 0.00000 0.00000 8.58 1.37 0.0140 0.0017 6 0.00003 0.00000 15.01 0.10 0.2206 0.0011 7 0.00000 0.00000 15.75 4.00 0.0035 0.0012 8 0.00000 0.00000 -7.51 12.32 0.0035 0.0012 9 0.00000 0.00000 -3.14 1.20 0.0059 0.0015 10 0.00005 0.00000 -9.09 0.03 0.3020 0.0014 11 0.00000 0.00000 -11.92 2.42 0.0018 0.0008 12 0.00000 0.00000 -11.15 2.74 0.0045 0.0029 13 0.00000 0.00000 -4.35 0.97 0.0101 0.0028 14 0.00004 0.00000 -6.47 0.02 0.2636 0.0020 15 0.00000 0.00000 -7.94 1.99 0.0071 0.0019 16 0.00000 0.00000 2.09 3.66 0.0047 0.0018 The magnetic center is at X = 25.6 +- 2.0 microns Y = 123.0 +- 1.9 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: 03-27-1995 Time: 14:21:40 Magnet Name: 137 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10085 +- 2.819539E-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 157.21 0.92 0.2844 0.0055 2 0.03500 0.00000 44.99 0.00 100.0000 0.0000 3 0.00002 0.00000 -4.71 1.86 0.0621 0.0036 4 0.00000 0.00000 -8.12 8.90 0.0057 0.0028 5 0.00001 0.00000 7.28 2.39 0.0179 0.0024 6 0.00008 0.00000 15.00 0.08 0.2203 0.0016 7 0.00000 0.00000 8.45 1.44 0.0039 0.0014 8 0.00000 0.00000 -20.36 1.19 0.0076 0.0015 9 0.00000 0.00000 -3.95 0.87 0.0062 0.0013 10 0.00011 0.00000 -9.05 0.01 0.3003 0.0019 11 0.00000 0.00000 -4.80 9.74 0.0017 0.0014 12 0.00000 0.00000 -1.64 3.26 0.0054 0.0017 13 0.00000 0.00000 -3.31 0.44 0.0121 0.0016 14 0.00009 0.00000 -6.43 0.02 0.2652 0.0040 15 0.00000 0.00000 -7.91 1.53 0.0103 0.0051 16 0.00000 0.00000 -0.13 2.82 0.0081 0.0021 The magnetic center is at X = -49.2 +- 2.1 microns Y = 117.1 +- 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: 03-27-1995 Time: 14:27:51 Magnet Name: 137 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.0642 +- 3.370669E-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 148.32 0.70 0.3330 0.0054 2 0.06890 0.00001 44.99 0.00 100.0000 0.0000 3 0.00004 0.00001 -0.55 0.81 0.0557 0.0073 4 0.00001 0.00000 -9.97 2.77 0.0086 0.0027 5 0.00001 0.00000 8.93 2.33 0.0188 0.0027 6 0.00015 0.00000 14.98 0.12 0.2207 0.0019 7 0.00000 0.00000 6.18 11.87 0.0030 0.0012 8 0.00000 0.00000 -6.93 9.95 0.0027 0.0007 9 0.00000 0.00000 -2.04 3.11 0.0052 0.0012 10 0.00021 0.00000 -9.10 0.05 0.3039 0.0019 11 0.00000 0.00000 -9.22 2.72 0.0018 0.0006 12 0.00000 0.00000 -11.65 1.46 0.0047 0.0018 13 0.00001 0.00000 -3.50 1.42 0.0118 0.0027 14 0.00018 0.00000 -6.44 0.03 0.2574 0.0021 15 0.00001 0.00000 -7.36 2.12 0.0091 0.0048 16 0.00000 0.00000 0.91 7.20 0.0034 0.0027 The magnetic center is at X = -78.1 +- 2.0 microns Y = 126.6 +- 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: 03-27-1995 Time: 14:34:06 Magnet Name: 137 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0591 +- 5.697707E-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 0.00050 0.00000 145.66 0.48 0.3613 0.0018 2 0.13745 0.00002 44.99 0.00 100.0000 0.0000 3 0.00008 0.00000 1.26 0.16 0.0555 0.0027 4 0.00002 0.00000 -9.88 2.51 0.0118 0.0025 5 0.00002 0.00000 9.07 1.32 0.0174 0.0020 6 0.00031 0.00000 14.97 0.07 0.2224 0.0015 7 0.00000 0.00000 8.91 15.69 0.0020 0.0008 8 0.00000 0.00000 -3.25 6.66 0.0020 0.0008 9 0.00001 0.00000 -3.54 0.76 0.0052 0.0021 10 0.00042 0.00000 -9.05 0.06 0.3031 0.0013 11 0.00000 0.00000 -4.58 6.81 0.0025 0.0011 12 0.00001 0.00000 3.94 10.94 0.0041 0.0028 13 0.00001 0.00000 -4.17 1.56 0.0105 0.0012 14 0.00036 0.00000 -6.45 0.05 0.2597 0.0011 15 0.00001 0.00000 -7.14 0.89 0.0103 0.0022 16 0.00001 0.00000 0.84 2.88 0.0045 0.0015 The magnetic center is at X = -91.0 +- 1.2 microns Y = 133.3 +- 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: 03-27-1995 Time: 14:40:21 Magnet Name: 137 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0735 +- 7.124809E-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 0.00076 0.00001 144.69 0.39 0.3690 0.0046 2 0.20568 0.00002 44.97 0.00 100.0000 0.0000 3 0.00012 0.00001 1.16 1.38 0.0573 0.0038 4 0.00002 0.00000 -11.76 1.40 0.0120 0.0023 5 0.00004 0.00000 9.51 0.64 0.0184 0.0009 6 0.00044 0.00000 15.01 0.12 0.2121 0.0020 7 0.00001 0.00000 -3.78 13.63 0.0025 0.0003 8 0.00001 0.00000 8.21 13.19 0.0028 0.0008 9 0.00001 0.00000 -4.64 1.98 0.0059 0.0024 10 0.00063 0.00000 -9.13 0.02 0.3079 0.0016 11 0.00001 0.00000 1.84 10.30 0.0029 0.0014 12 0.00002 0.00001 -6.16 12.05 0.0093 0.0049 13 0.00002 0.00001 -3.85 0.60 0.0109 0.0025 14 0.00053 0.00001 -6.47 0.05 0.2592 0.0046 15 0.00002 0.00001 -6.41 2.79 0.0079 0.0034 16 0.00001 0.00000 4.44 6.50 0.0039 0.0017 The magnetic center is at X = -95.3 +- 1.5 microns Y = 134.5 +- 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 ^ | N S --> x S N Date: 03-27-1995 Time: 14:46:36 Magnet Name: 137 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3181 +- 1.358032E-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 0.00105 0.00000 142.07 0.49 0.3826 0.0004 2 0.27336 0.00003 44.97 0.00 100.0000 0.0000 3 0.00015 0.00000 5.41 0.46 0.0564 0.0018 4 0.00003 0.00001 -33.89 2.61 0.0102 0.0031 5 0.00006 0.00001 8.64 1.22 0.0203 0.0023 6 0.00056 0.00000 15.01 0.04 0.2035 0.0007 7 0.00001 0.00000 -9.46 18.68 0.0023 0.0012 8 0.00002 0.00000 -2.02 1.02 0.0076 0.0016 9 0.00001 0.00001 -2.36 3.62 0.0046 0.0019 10 0.00085 0.00001 -9.14 0.05 0.3115 0.0032 11 0.00001 0.00000 3.26 5.57 0.0036 0.0017 12 0.00002 0.00001 -7.08 7.99 0.0079 0.0027 13 0.00003 0.00001 -3.81 2.47 0.0093 0.0029 14 0.00071 0.00001 -6.44 0.04 0.2583 0.0022 15 0.00003 0.00001 -8.82 0.69 0.0108 0.0045 16 0.00002 0.00000 3.85 0.72 0.0077 0.0006 The magnetic center is at X = -105.1 +- 1.2 microns Y = 134.8 +- 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: 03-27-1995 Time: 14:52:51 Magnet Name: 137 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4189 +- 4.124815E-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 139.96 0.54 0.3857 0.0049 2 0.33826 0.00009 44.97 0.00 100.0000 0.0000 3 0.00018 0.00002 6.85 1.86 0.0543 0.0062 4 0.00003 0.00001 -23.12 5.67 0.0079 0.0029 5 0.00007 0.00001 7.95 1.17 0.0209 0.0028 6 0.00060 0.00001 15.09 0.14 0.1776 0.0022 7 0.00001 0.00000 -17.05 3.69 0.0022 0.0007 8 0.00002 0.00001 -9.78 18.33 0.0064 0.0026 9 0.00002 0.00000 -4.01 1.22 0.0047 0.0013 10 0.00107 0.00001 -9.10 0.02 0.3149 0.0016 11 0.00001 0.00000 5.20 12.23 0.0032 0.0012 12 0.00004 0.00001 -3.73 0.59 0.0104 0.0017 13 0.00003 0.00000 -4.07 1.66 0.0100 0.0004 14 0.00087 0.00001 -6.49 0.06 0.2585 0.0027 15 0.00003 0.00001 -6.98 0.82 0.0099 0.0031 16 0.00002 0.00001 4.69 3.36 0.0056 0.0035 The magnetic center is at X = -110.8 +- 1.9 microns Y = 131.9 +- 2.0 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: 03-27-1995 Time: 14:59:07 Magnet Name: 137 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.405 +- 7.194321E-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 0.00150 0.00003 141.92 0.63 0.3845 0.0065 2 0.39011 0.00007 44.97 0.00 100.0000 0.0000 3 0.00021 0.00002 4.69 1.78 0.0550 0.0063 4 0.00003 0.00001 -12.03 2.99 0.0090 0.0026 5 0.00008 0.00001 7.82 1.25 0.0203 0.0015 6 0.00049 0.00001 15.21 0.22 0.1248 0.0027 7 0.00001 0.00000 -3.69 13.03 0.0023 0.0008 8 0.00003 0.00001 1.35 20.05 0.0077 0.0027 9 0.00003 0.00001 -4.63 2.34 0.0076 0.0022 10 0.00127 0.00001 -9.07 0.08 0.3260 0.0022 11 0.00002 0.00001 -9.00 10.26 0.0046 0.0025 12 0.00003 0.00000 -5.80 3.65 0.0088 0.0005 13 0.00006 0.00001 -4.19 0.86 0.0143 0.0025 14 0.00101 0.00002 -6.51 0.06 0.2598 0.0043 15 0.00003 0.00001 0.48 6.09 0.0079 0.0026 16 0.00004 0.00000 1.25 2.32 0.0095 0.0008 The magnetic center is at X = -105.9 +- 2.3 microns Y = 135.2 +- 2.5 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: 03-27-1995 Time: 15:05:24 Magnet Name: 137 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4102 +- 6.201905E-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 0.00166 0.00002 143.84 0.83 0.3899 0.0045 2 0.42666 0.00006 44.97 0.00 100.0000 0.0000 3 0.00025 0.00002 2.78 1.84 0.0593 0.0050 4 0.00003 0.00001 -12.67 4.40 0.0078 0.0018 5 0.00008 0.00000 8.26 1.02 0.0194 0.0009 6 0.00029 0.00000 15.47 0.27 0.0675 0.0010 7 0.00001 0.00001 8.96 12.28 0.0025 0.0015 8 0.00003 0.00000 -20.62 0.70 0.0064 0.0006 9 0.00002 0.00000 -5.64 2.45 0.0049 0.0009 10 0.00144 0.00000 -9.12 0.04 0.3369 0.0009 11 0.00001 0.00000 8.04 11.63 0.0028 0.0009 12 0.00004 0.00001 -11.24 0.73 0.0091 0.0017 13 0.00004 0.00001 -4.05 0.81 0.0103 0.0024 14 0.00110 0.00001 -6.45 0.03 0.2569 0.0024 15 0.00006 0.00001 -5.77 2.28 0.0134 0.0014 16 0.00005 0.00000 2.46 0.78 0.0117 0.0011 The magnetic center is at X = -102.7 +- 2.4 microns Y = 140.6 +- 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 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)