SLAC Magnetic Measurements Date: 03-16-1995 Time: 14:12:52 Magnet Name (Serial #): 148 Bar Code Number: 594 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: 03-16-1995 Time: 15:00:11 Magnet Name: 148 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00531 +- 8.099733E-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 0.00007 0.00000 -124.33 0.25 0.4862 0.0012 2 0.01485 0.00001 44.90 0.00 100.0000 0.0000 3 0.00001 0.00000 20.80 3.95 0.0340 0.0013 4 0.00000 0.00000 25.02 2.50 0.0331 0.0063 5 0.00000 0.00000 15.68 2.02 0.0263 0.0040 6 0.00003 0.00000 15.12 0.22 0.2098 0.0023 7 0.00000 0.00000 12.16 1.29 0.0068 0.0021 8 0.00000 0.00000 7.52 12.09 0.0020 0.0007 9 0.00000 0.00000 3.69 1.03 0.0105 0.0008 10 0.00005 0.00000 -9.17 0.05 0.3035 0.0012 11 0.00000 0.00000 14.92 0.96 0.0050 0.0018 12 0.00000 0.00000 -4.53 1.48 0.0032 0.0018 13 0.00000 0.00000 2.16 0.51 0.0123 0.0013 14 0.00004 0.00000 -6.55 0.03 0.2586 0.0034 15 0.00000 0.00000 3.85 6.47 0.0051 0.0028 16 0.00000 0.00000 0.52 1.05 0.0085 0.0020 The magnetic center is at X = 179.3 +- 0.7 microns Y = 122.5 +- 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: 03-16-1995 Time: 15:06:21 Magnet Name: 148 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.11036 +- 2.500864E-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 0.00015 0.00000 -142.14 0.17 0.4323 0.0011 2 0.03495 0.00001 44.90 0.00 100.0000 0.0000 3 0.00002 0.00000 21.01 0.71 0.0543 0.0021 4 0.00001 0.00000 30.41 2.25 0.0287 0.0016 5 0.00001 0.00000 15.29 0.83 0.0253 0.0006 6 0.00007 0.00000 15.04 0.13 0.2125 0.0013 7 0.00000 0.00000 10.76 1.43 0.0065 0.0012 8 0.00000 0.00000 -0.05 1.52 0.0044 0.0013 9 0.00000 0.00000 3.86 0.47 0.0105 0.0016 10 0.00011 0.00000 -9.13 0.03 0.3052 0.0016 11 0.00000 0.00000 15.04 0.63 0.0063 0.0004 12 0.00000 0.00000 -2.22 1.97 0.0070 0.0032 13 0.00000 0.00000 1.77 0.55 0.0128 0.0014 14 0.00009 0.00000 -6.54 0.06 0.2576 0.0035 15 0.00000 0.00000 4.19 1.89 0.0068 0.0044 16 0.00000 0.00000 0.72 3.52 0.0033 0.0018 The magnetic center is at X = 118.5 +- 0.6 microns Y = 152.5 +- 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: 03-16-1995 Time: 15:12:36 Magnet Name: 148 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.07061 +- 7.722218E-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 -148.75 0.22 0.4237 0.0007 2 0.06884 0.00003 44.90 0.00 100.0000 0.0000 3 0.00004 0.00000 22.09 0.45 0.0589 0.0016 4 0.00002 0.00000 23.89 0.91 0.0233 0.0041 5 0.00002 0.00000 14.51 0.58 0.0246 0.0008 6 0.00015 0.00000 15.03 0.06 0.2162 0.0007 7 0.00000 0.00000 9.87 1.51 0.0058 0.0010 8 0.00000 0.00000 0.59 4.80 0.0027 0.0015 9 0.00001 0.00000 3.02 0.52 0.0090 0.0013 10 0.00021 0.00000 -9.10 0.03 0.3039 0.0008 11 0.00000 0.00000 14.86 0.30 0.0044 0.0006 12 0.00000 0.00000 -5.08 2.30 0.0055 0.0023 13 0.00001 0.00000 1.54 0.08 0.0132 0.0015 14 0.00018 0.00000 -6.54 0.06 0.2557 0.0028 15 0.00000 0.00000 5.20 9.90 0.0071 0.0047 16 0.00001 0.00000 0.55 1.01 0.0084 0.0009 The magnetic center is at X = 98.2 +- 0.6 microns Y = 161.8 +- 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: 03-16-1995 Time: 15:18:55 Magnet Name: 148 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0625 +- 2.99472E-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 -152.47 0.18 0.4217 0.0005 2 0.13741 0.00005 44.90 0.00 100.0000 0.0000 3 0.00008 0.00000 22.79 0.34 0.0610 0.0004 4 0.00003 0.00000 23.69 1.71 0.0221 0.0023 5 0.00004 0.00000 14.46 0.45 0.0261 0.0011 6 0.00030 0.00000 15.05 0.04 0.2154 0.0017 7 0.00001 0.00000 9.56 2.20 0.0067 0.0006 8 0.00000 0.00000 5.92 5.31 0.0023 0.0008 9 0.00002 0.00000 3.78 0.98 0.0109 0.0014 10 0.00042 0.00000 -9.13 0.04 0.3060 0.0023 11 0.00001 0.00000 7.01 12.70 0.0047 0.0009 12 0.00001 0.00000 -6.82 4.97 0.0041 0.0006 13 0.00002 0.00000 1.51 0.35 0.0126 0.0018 14 0.00035 0.00001 -6.61 0.08 0.2525 0.0040 15 0.00001 0.00000 0.73 8.32 0.0052 0.0027 16 0.00002 0.00000 1.00 0.45 0.0117 0.0021 The magnetic center is at X = 87.1 +- 0.5 microns Y = 167.0 +- 0.3 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: 03-16-1995 Time: 15:25:15 Magnet Name: 148 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.074 +- 2.934095E-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 0.00087 0.00000 -153.21 0.22 0.4220 0.0006 2 0.20565 0.00008 44.88 0.00 100.0000 0.0000 3 0.00013 0.00000 23.30 0.28 0.0620 0.0014 4 0.00004 0.00000 20.57 1.10 0.0192 0.0016 5 0.00006 0.00001 14.67 0.92 0.0269 0.0028 6 0.00043 0.00000 15.04 0.10 0.2086 0.0012 7 0.00001 0.00000 8.27 1.15 0.0069 0.0009 8 0.00000 0.00000 3.97 3.99 0.0024 0.0007 9 0.00002 0.00000 4.08 0.88 0.0100 0.0010 10 0.00062 0.00000 -9.15 0.03 0.3039 0.0009 11 0.00001 0.00000 14.56 0.97 0.0055 0.0008 12 0.00001 0.00000 -5.38 11.71 0.0049 0.0020 13 0.00003 0.00001 1.71 0.77 0.0132 0.0026 14 0.00053 0.00001 -6.61 0.06 0.2592 0.0028 15 0.00001 0.00001 2.11 9.37 0.0064 0.0027 16 0.00003 0.00000 1.58 0.50 0.0128 0.0019 The magnetic center is at X = 84.9 +- 0.6 microns Y = 168.3 +- 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: 03-16-1995 Time: 15:31:33 Magnet Name: 148 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3235 +- 1.274429E-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 0.00114 0.00001 -153.13 0.21 0.4186 0.0021 2 0.27325 0.00018 44.88 0.00 100.0000 0.0000 3 0.00016 0.00001 23.37 0.60 0.0604 0.0033 4 0.00006 0.00001 22.62 1.54 0.0205 0.0032 5 0.00007 0.00001 14.89 0.92 0.0256 0.0020 6 0.00054 0.00000 15.06 0.07 0.1984 0.0005 7 0.00002 0.00000 10.94 3.59 0.0062 0.0009 8 0.00001 0.00000 3.12 3.79 0.0036 0.0013 9 0.00003 0.00000 4.57 1.08 0.0105 0.0008 10 0.00085 0.00000 -9.15 0.02 0.3106 0.0013 11 0.00002 0.00000 13.81 1.81 0.0058 0.0017 12 0.00001 0.00000 -4.22 10.15 0.0034 0.0013 13 0.00003 0.00000 1.70 0.64 0.0121 0.0006 14 0.00071 0.00000 -6.68 0.05 0.2585 0.0016 15 0.00002 0.00001 -1.44 9.49 0.0075 0.0027 16 0.00002 0.00001 2.61 1.30 0.0073 0.0019 The magnetic center is at X = 84.5 +- 0.7 microns Y = 166.8 +- 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: 03-16-1995 Time: 15:37:54 Magnet Name: 148 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4228 +- 8.559215E-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 0.00139 0.00001 -152.58 0.17 0.4106 0.0017 2 0.33848 0.00010 44.88 0.00 100.0000 0.0000 3 0.00020 0.00001 24.32 0.82 0.0583 0.0025 4 0.00008 0.00000 30.60 0.82 0.0241 0.0013 5 0.00008 0.00001 15.17 0.98 0.0249 0.0023 6 0.00059 0.00001 15.03 0.10 0.1729 0.0015 7 0.00002 0.00000 10.86 3.64 0.0051 0.0012 8 0.00002 0.00000 0.63 1.18 0.0060 0.0010 9 0.00004 0.00000 4.49 0.84 0.0115 0.0010 10 0.00106 0.00000 -9.16 0.02 0.3141 0.0009 11 0.00002 0.00000 13.38 1.67 0.0064 0.0002 12 0.00002 0.00001 -3.61 2.68 0.0065 0.0027 13 0.00005 0.00000 1.47 0.47 0.0139 0.0011 14 0.00087 0.00001 -6.58 0.04 0.2569 0.0015 15 0.00002 0.00001 -2.83 7.73 0.0047 0.0022 16 0.00002 0.00001 5.45 1.67 0.0061 0.0021 The magnetic center is at X = 84.5 +- 0.6 microns Y = 162.8 +- 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: 03-16-1995 Time: 15:44:15 Magnet Name: 148 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4055 +- 1.441612E-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 0.00169 0.00001 -153.03 0.10 0.4333 0.0014 2 0.39046 0.00014 44.88 0.00 100.0000 0.0000 3 0.00023 0.00001 21.51 0.95 0.0581 0.0013 4 0.00008 0.00000 27.01 0.64 0.0206 0.0009 5 0.00010 0.00001 14.48 0.65 0.0248 0.0014 6 0.00050 0.00001 15.25 0.14 0.1277 0.0018 7 0.00003 0.00001 9.12 1.28 0.0070 0.0014 8 0.00001 0.00000 3.36 18.59 0.0034 0.0012 9 0.00005 0.00000 3.54 0.84 0.0116 0.0008 10 0.00126 0.00000 -9.15 0.03 0.3235 0.0011 11 0.00002 0.00000 12.94 0.86 0.0059 0.0012 12 0.00003 0.00001 -3.23 1.49 0.0076 0.0020 13 0.00005 0.00000 2.04 0.58 0.0132 0.0013 14 0.00099 0.00000 -6.68 0.07 0.2548 0.0009 15 0.00003 0.00002 0.39 11.05 0.0089 0.0048 16 0.00003 0.00001 4.17 0.99 0.0080 0.0017 The magnetic center is at X = 87.8 +- 0.4 microns Y = 172.5 +- 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: 03-16-1995 Time: 15:50:36 Magnet Name: 148 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4088 +- 1.139312E-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 0.00190 0.00000 -153.01 0.20 0.4444 0.0010 2 0.42697 0.00012 44.88 0.00 100.0000 0.0000 3 0.00026 0.00000 19.62 0.54 0.0617 0.0007 4 0.00008 0.00001 25.42 2.77 0.0192 0.0027 5 0.00011 0.00001 14.75 0.54 0.0259 0.0012 6 0.00030 0.00000 15.45 0.07 0.0711 0.0011 7 0.00002 0.00001 9.65 1.10 0.0058 0.0016 8 0.00003 0.00000 -10.49 17.71 0.0059 0.0007 9 0.00005 0.00001 4.24 0.60 0.0119 0.0023 10 0.00144 0.00001 -9.15 0.02 0.3365 0.0013 11 0.00003 0.00001 6.62 12.81 0.0059 0.0019 12 0.00003 0.00001 -3.44 0.51 0.0080 0.0023 13 0.00005 0.00001 1.21 0.51 0.0121 0.0018 14 0.00108 0.00001 -6.61 0.09 0.2538 0.0026 15 0.00003 0.00001 3.55 4.61 0.0070 0.0030 16 0.00006 0.00001 0.70 1.02 0.0149 0.0016 The magnetic center is at X = 90.1 +- 0.7 microns Y = 176.9 +- 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 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)