SLAC Magnetic Measurements Date: 01-17-1996 Time: 15:11:58 Magnet Name (Serial #): 439 Bar Code Number: 439 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: dan Run Number: 1 Comment: none 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: 01-17-1996 Time: 15:59:46 Magnet Name: 439 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00709 +- 8.115424E-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 -105.74 0.45 0.3012 0.0003 2 0.01492 0.00000 -45.08 0.00 100.0000 0.0000 3 0.00002 0.00000 49.14 0.40 0.1121 0.0024 4 0.00002 0.00000 25.46 0.43 0.1018 0.0013 5 0.00001 0.00000 21.36 0.47 0.0529 0.0014 6 0.00003 0.00000 -13.64 0.06 0.1801 0.0005 7 0.00000 0.00000 0.64 0.19 0.0296 0.0014 8 0.00000 0.00000 -2.56 0.49 0.0269 0.0007 9 0.00000 0.00000 -6.81 0.12 0.0232 0.0009 10 0.00004 0.00000 9.05 0.03 0.2848 0.0006 11 0.00000 0.00000 -14.89 0.41 0.0107 0.0015 12 0.00000 0.00000 13.12 0.36 0.0132 0.0011 13 0.00000 0.00000 6.58 1.07 0.0140 0.0020 14 0.00004 0.00000 6.35 0.03 0.2648 0.0009 15 0.00000 0.00000 3.91 1.46 0.0129 0.0026 16 0.00000 0.00000 1.95 1.32 0.0048 0.0033 The magnetic center is at X = -129.5 +- 0.3 microns Y = -36.5 +- 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 ^ | S N --> x N S Date: 01-17-1996 Time: 16:05:51 Magnet Name: 439 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.1187 +- 1.94734E-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 0.00010 0.00000 -124.22 0.31 0.2906 0.0015 2 0.03492 0.00001 -45.08 0.00 100.0000 0.0000 3 0.00003 0.00000 53.06 0.37 0.0838 0.0010 4 0.00004 0.00000 25.79 0.28 0.1119 0.0011 5 0.00002 0.00000 21.39 0.62 0.0518 0.0032 6 0.00006 0.00000 -13.66 0.04 0.1845 0.0010 7 0.00001 0.00000 1.19 0.43 0.0313 0.0015 8 0.00001 0.00000 -3.37 0.22 0.0194 0.0005 9 0.00001 0.00000 -6.91 0.21 0.0245 0.0012 10 0.00010 0.00000 9.04 0.03 0.2842 0.0003 11 0.00000 0.00000 -13.76 0.52 0.0131 0.0013 12 0.00000 0.00000 11.43 1.27 0.0082 0.0005 13 0.00000 0.00000 7.18 0.43 0.0130 0.0025 14 0.00009 0.00000 6.35 0.06 0.2658 0.0021 15 0.00000 0.00000 3.19 1.63 0.0131 0.0036 16 0.00000 0.00000 0.92 1.95 0.0107 0.0018 The magnetic center is at X = -107.3 +- 0.7 microns Y = -73.0 +- 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 ^ | S N --> x N S Date: 01-17-1996 Time: 16:12:02 Magnet Name: 439 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.09961 +- 1.096155E-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 0.00020 0.00000 -131.44 0.20 0.2881 0.0009 2 0.06883 0.00001 -45.08 0.00 100.0000 0.0000 3 0.00005 0.00000 53.79 0.63 0.0793 0.0011 4 0.00008 0.00000 25.01 0.15 0.1134 0.0017 5 0.00004 0.00000 21.11 0.36 0.0534 0.0028 6 0.00013 0.00000 -13.58 0.06 0.1831 0.0012 7 0.00002 0.00000 1.80 0.30 0.0313 0.0005 8 0.00002 0.00000 -2.48 0.27 0.0270 0.0009 9 0.00002 0.00000 -6.30 0.40 0.0240 0.0014 10 0.00020 0.00000 9.05 0.01 0.2866 0.0016 11 0.00001 0.00000 -14.14 0.45 0.0141 0.0013 12 0.00001 0.00000 13.49 0.41 0.0124 0.0022 13 0.00001 0.00000 6.79 0.68 0.0154 0.0011 14 0.00018 0.00000 6.36 0.03 0.2594 0.0033 15 0.00001 0.00000 3.14 0.65 0.0091 0.0017 16 0.00000 0.00000 1.75 1.50 0.0028 0.0009 The magnetic center is at X = -96.5 +- 0.4 microns Y = -85.2 +- 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 ^ | S N --> x N S Date: 01-17-1996 Time: 16:18:19 Magnet Name: 439 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.133 +- 5.642556E-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 0.00039 0.00000 -137.94 0.40 0.2859 0.0011 2 0.13734 0.00001 -45.08 0.00 100.0000 0.0000 3 0.00011 0.00000 51.82 0.85 0.0782 0.0014 4 0.00016 0.00000 25.01 0.35 0.1170 0.0024 5 0.00008 0.00000 21.05 0.39 0.0557 0.0034 6 0.00025 0.00000 -13.53 0.05 0.1828 0.0007 7 0.00004 0.00000 1.91 0.52 0.0320 0.0007 8 0.00004 0.00000 -2.18 0.11 0.0287 0.0007 9 0.00003 0.00000 -6.65 0.42 0.0241 0.0010 10 0.00039 0.00000 9.03 0.03 0.2869 0.0008 11 0.00002 0.00000 -14.06 0.90 0.0143 0.0013 12 0.00002 0.00000 12.78 0.47 0.0148 0.0005 13 0.00002 0.00000 7.63 1.07 0.0151 0.0027 14 0.00036 0.00000 6.34 0.07 0.2602 0.0015 15 0.00002 0.00000 2.69 0.65 0.0138 0.0019 16 0.00001 0.00000 0.54 0.68 0.0101 0.0017 The magnetic center is at X = -85.5 +- 0.7 microns Y = -94.8 +- 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 ^ | S N --> x N S Date: 01-17-1996 Time: 16:24:34 Magnet Name: 439 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.1821 +- 3.837517E-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 0.00060 0.00000 -142.54 0.46 0.2926 0.0008 2 0.20545 0.00005 -45.11 0.00 100.0000 0.0000 3 0.00017 0.00000 50.91 0.67 0.0816 0.0004 4 0.00024 0.00000 24.89 0.19 0.1155 0.0012 5 0.00012 0.00001 20.59 0.48 0.0576 0.0030 6 0.00036 0.00000 -13.34 0.05 0.1741 0.0016 7 0.00007 0.00000 1.72 0.33 0.0325 0.0012 8 0.00006 0.00000 -2.32 0.22 0.0290 0.0010 9 0.00005 0.00000 -6.43 0.14 0.0262 0.0022 10 0.00059 0.00000 9.01 0.02 0.2891 0.0008 11 0.00003 0.00000 -14.01 0.46 0.0128 0.0009 12 0.00003 0.00000 14.12 0.30 0.0163 0.0016 13 0.00003 0.00001 8.90 0.63 0.0134 0.0031 14 0.00054 0.00000 6.34 0.05 0.2628 0.0017 15 0.00003 0.00000 2.61 1.25 0.0148 0.0018 16 0.00002 0.00000 3.10 0.74 0.0075 0.0020 The magnetic center is at X = -79.5 +- 0.9 microns Y = -103.8 +- 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 ^ | S N --> x N S Date: 01-17-1996 Time: 16:30:49 Magnet Name: 439 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.4635 +- 7.916944E-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 0.00001 -147.21 0.57 0.2871 0.0020 2 0.27287 0.00005 -45.11 0.00 100.0000 0.0000 3 0.00023 0.00001 48.32 0.66 0.0842 0.0027 4 0.00032 0.00001 26.75 0.07 0.1165 0.0026 5 0.00016 0.00001 20.77 0.55 0.0577 0.0029 6 0.00045 0.00000 -13.29 0.04 0.1651 0.0009 7 0.00009 0.00000 1.73 0.37 0.0327 0.0009 8 0.00010 0.00000 -1.91 0.32 0.0373 0.0014 9 0.00007 0.00000 -6.54 0.26 0.0274 0.0006 10 0.00079 0.00000 9.03 0.02 0.2906 0.0012 11 0.00004 0.00001 -13.72 0.24 0.0146 0.0026 12 0.00004 0.00001 13.49 0.63 0.0129 0.0019 13 0.00004 0.00001 7.48 0.87 0.0144 0.0023 14 0.00072 0.00000 6.38 0.03 0.2651 0.0016 15 0.00003 0.00001 3.66 1.09 0.0118 0.0024 16 0.00001 0.00001 -1.68 6.49 0.0054 0.0027 The magnetic center is at X = -69.4 +- 1.2 microns Y = -107.8 +- 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 ^ | S N --> x N S Date: 01-17-1996 Time: 16:37:05 Magnet Name: 439 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.5954 +- 5.502693E-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 0.00094 0.00000 -153.02 0.25 0.2781 0.0013 2 0.33732 0.00002 -45.11 0.00 100.0000 0.0000 3 0.00031 0.00001 46.39 0.65 0.0909 0.0041 4 0.00038 0.00001 26.01 0.33 0.1133 0.0018 5 0.00020 0.00001 20.27 0.67 0.0584 0.0023 6 0.00048 0.00000 -12.89 0.02 0.1432 0.0013 7 0.00012 0.00000 1.68 0.36 0.0346 0.0009 8 0.00009 0.00000 -2.59 0.21 0.0253 0.0010 9 0.00009 0.00001 -6.67 0.11 0.0259 0.0015 10 0.00100 0.00001 9.02 0.01 0.2956 0.0020 11 0.00005 0.00000 -13.92 0.71 0.0145 0.0010 12 0.00003 0.00001 12.00 0.74 0.0078 0.0020 13 0.00004 0.00000 7.87 0.48 0.0132 0.0009 14 0.00088 0.00001 6.36 0.03 0.2612 0.0018 15 0.00005 0.00001 3.37 0.55 0.0144 0.0039 16 0.00002 0.00000 5.61 2.94 0.0050 0.0011 The magnetic center is at X = -56.4 +- 0.5 microns Y = -110.7 +- 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 ^ | S N --> x N S Date: 01-17-1996 Time: 16:43:22 Magnet Name: 439 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.6072 +- 8.09579E-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 0.00112 0.00001 -151.51 0.22 0.2870 0.0014 2 0.38904 0.00010 -45.11 0.00 100.0000 0.0000 3 0.00032 0.00001 47.30 0.51 0.0833 0.0029 4 0.00042 0.00001 25.33 0.24 0.1084 0.0022 5 0.00022 0.00001 19.74 0.58 0.0578 0.0019 6 0.00036 0.00000 -11.69 0.13 0.0919 0.0007 7 0.00013 0.00000 1.87 0.13 0.0345 0.0011 8 0.00010 0.00000 -2.79 0.19 0.0249 0.0004 9 0.00010 0.00000 -6.67 0.25 0.0269 0.0010 10 0.00119 0.00000 9.01 0.02 0.3055 0.0012 11 0.00006 0.00000 -14.16 0.30 0.0151 0.0012 12 0.00004 0.00000 13.24 0.45 0.0102 0.0013 13 0.00006 0.00000 7.23 0.75 0.0145 0.0006 14 0.00103 0.00001 6.36 0.03 0.2638 0.0020 15 0.00004 0.00001 2.54 0.93 0.0114 0.0014 16 0.00004 0.00001 0.44 1.12 0.0106 0.0015 The magnetic center is at X = -61.1 +- 0.5 microns Y = -112.7 +- 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 ^ | S N --> x N S Date: 01-17-1996 Time: 16:49:38 Magnet Name: 439 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.6375 +- 6.147228E-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 0.00000 -150.49 0.29 0.2919 0.0011 2 0.42512 0.00007 -45.11 0.00 100.0000 0.0000 3 0.00034 0.00000 47.76 0.17 0.0795 0.0009 4 0.00046 0.00001 25.35 0.28 0.1088 0.0024 5 0.00024 0.00001 19.94 0.77 0.0571 0.0016 6 0.00019 0.00001 -7.04 0.26 0.0440 0.0012 7 0.00014 0.00001 1.85 0.33 0.0338 0.0015 8 0.00012 0.00000 -2.62 0.09 0.0279 0.0009 9 0.00012 0.00000 -6.41 0.17 0.0278 0.0010 10 0.00134 0.00000 9.00 0.03 0.3145 0.0006 11 0.00007 0.00000 -13.79 0.29 0.0154 0.0011 12 0.00006 0.00001 13.89 0.70 0.0135 0.0019 13 0.00006 0.00001 7.95 0.23 0.0150 0.0024 14 0.00111 0.00001 6.37 0.04 0.2603 0.0018 15 0.00007 0.00002 2.68 0.55 0.0158 0.0056 16 0.00005 0.00001 1.00 0.68 0.0114 0.0032 The magnetic center is at X = -64.2 +- 0.6 microns Y = -113.5 +- 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 ^ | S N --> x N S 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)