SLAC Magnetic Measurements Date: 02-12-1998 Time: 11:16:19 Project: SLC Magnet Type: QUAD Magnet Name (Serial #): SRTLSKEW Bar Code Number: NONE Test Stand: 1 Measurement System: SQ1 Operator: tss Run Number: 1 Comment: Gl vs I, + terminal is to the right, - terminal is up looking from the leadend looking from the encoder. Standardization Currents 3 cycles, -4 to 4 to -4 A Test Currents -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Harmonics Measurements Date: 02-12-1998 Time: 11:26:16 Magnet Name: SRTLSKEW Run Number: 1 FIELD HARMONICS Harmonics at Rcoil = .007874 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00012 0.00000 -158.75 0.04 4.9823 0.0072 2 0.00246 0.00000 88.01 0.01 100.0000 0.1862 3 0.00000 0.00000 47.28 2.66 0.1460 0.0093 4 0.00000 0.00000 16.12 2.36 0.0501 0.0110 5 0.00000 0.00000 14.74 3.55 0.0235 0.0031 6 0.00000 0.00000 -24.54 3.49 0.0213 0.0083 7 0.00000 0.00000 14.48 9.52 0.0125 0.0052 8 0.00000 0.00000 -11.76 13.13 0.0113 0.0084 9 0.00000 0.00000 -7.92 7.01 0.0096 0.0058 10 0.00000 0.00000 14.38 18.24 0.0083 0.0024 11 0.00000 0.00000 7.08 1.48 0.0251 0.0058 12 0.00000 0.00000 1.97 15.70 0.0198 0.0051 13 0.00000 0.00000 -11.32 27.69 0.0099 0.0033 14 0.00000 0.00000 12.17 5.39 0.0111 0.0038 15 0.00000 0.00000 -10.83 7.75 0.0165 0.0039 16 0.00000 0.00000 9.48 6.53 0.0176 0.0101 17 0.00000 0.00000 -3.52 4.01 0.0300 0.0110 18 0.00000 0.00000 -0.01 9.87 0.0240 0.0081 19 0.00000 0.00000 8.87 8.20 0.0712 0.0188 20 0.00000 0.00000 4.46 16.18 0.0217 0.0091 View from the lead end of the magnet: y ^ | S N N --> x S The magnetic center is at X = 142.2 +- 0.3 microns Y = 365.6 +- 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. Date: 02-12-1998 Time: 11:33:11 Magnet Name: SRTLSKEW Run Number: 1 FIELD HARMONICS Harmonics at Rcoil = .007874 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00009 0.00000 -159.32 0.06 4.8877 0.0074 2 0.00186 0.00000 88.04 0.03 100.0000 0.1663 3 0.00000 0.00000 49.16 1.46 0.1650 0.0275 4 0.00000 0.00000 16.10 2.44 0.0429 0.0034 5 0.00000 0.00000 9.90 3.84 0.0274 0.0111 6 0.00000 0.00000 -22.25 1.30 0.0249 0.0062 7 0.00000 0.00000 12.81 3.89 0.0153 0.0017 8 0.00000 0.00000 -14.96 3.92 0.0172 0.0021 9 0.00000 0.00000 0.15 9.97 0.0115 0.0043 10 0.00000 0.00000 -7.86 8.93 0.0115 0.0060 11 0.00000 0.00000 5.60 4.87 0.0199 0.0096 12 0.00000 0.00000 1.78 8.54 0.0255 0.0070 13 0.00000 0.00000 3.55 18.59 0.0097 0.0041 14 0.00000 0.00000 -9.27 5.41 0.0101 0.0049 15 0.00000 0.00000 5.40 24.00 0.0248 0.0103 16 0.00000 0.00000 -0.43 22.50 0.0180 0.0114 17 0.00000 0.00000 5.95 6.60 0.0268 0.0088 18 0.00000 0.00000 6.74 8.76 0.0247 0.0082 19 0.00000 0.00000 5.26 18.95 0.0775 0.0057 20 0.00000 0.00000 -7.62 4.70 0.0232 0.0116 View from the lead end of the magnet: y ^ | S N N --> x S The magnetic center is at X = 135.9 +- 0.4 microns Y = 360.1 +- 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. Date: 02-12-1998 Time: 11:40:06 Magnet Name: SRTLSKEW Run Number: 1 FIELD HARMONICS Harmonics at Rcoil = .007874 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00006 0.00000 -160.44 0.02 4.6992 0.0063 2 0.00125 0.00000 88.01 0.03 100.0000 0.0902 3 0.00000 0.00000 44.67 2.23 0.1598 0.0087 4 0.00000 0.00000 15.16 2.35 0.0465 0.0111 5 0.00000 0.00000 7.97 1.21 0.0322 0.0032 6 0.00000 0.00000 -22.93 2.11 0.0221 0.0071 7 0.00000 0.00000 18.06 1.16 0.0260 0.0054 8 0.00000 0.00000 11.40 13.05 0.0143 0.0110 9 0.00000 0.00000 -15.98 1.93 0.0135 0.0068 10 0.00000 0.00000 14.67 3.84 0.0160 0.0016 11 0.00000 0.00000 0.89 5.77 0.0221 0.0071 12 0.00000 0.00000 -9.96 2.30 0.0342 0.0080 13 0.00000 0.00000 0.60 1.78 0.0111 0.0042 14 0.00000 0.00000 1.54 5.83 0.0088 0.0041 15 0.00000 0.00000 -1.15 11.66 0.0279 0.0204 16 0.00000 0.00000 -4.29 3.32 0.0243 0.0046 17 0.00000 0.00000 -7.16 5.34 0.0270 0.0068 18 0.00000 0.00000 5.66 4.06 0.0263 0.0069 19 0.00000 0.00000 2.24 2.69 0.0624 0.0351 20 0.00000 0.00000 -8.36 2.19 0.0382 0.0052 View from the lead end of the magnet: y ^ | S N N --> x S The magnetic center is at X = 123.9 +- 0.2 microns Y = 348.7 +- 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. Date: 02-12-1998 Time: 11:47:01 Magnet Name: SRTLSKEW Run Number: 1 FIELD HARMONICS Harmonics at Rcoil = .007874 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00003 0.00000 -164.26 0.08 4.1259 0.0029 2 0.00062 0.00000 87.96 0.03 100.0000 0.0391 3 0.00000 0.00000 39.07 1.94 0.1290 0.0371 4 0.00000 0.00000 12.17 2.22 0.0575 0.0191 5 0.00000 0.00000 6.47 6.32 0.0316 0.0104 6 0.00000 0.00000 -24.39 2.69 0.0315 0.0167 7 0.00000 0.00000 21.26 45.16 0.0357 0.0042 8 0.00000 0.00000 -11.84 12.93 0.0557 0.0181 9 0.00000 0.00000 1.91 7.52 0.0199 0.0116 10 0.00000 0.00000 -1.42 9.97 0.0455 0.0103 11 0.00000 0.00000 2.53 2.73 0.0830 0.0274 12 0.00000 0.00000 3.92 20.55 0.0672 0.0134 13 0.00000 0.00000 -12.72 4.21 0.0243 0.0167 14 0.00000 0.00000 11.03 4.71 0.0118 0.0041 15 0.00000 0.00000 -10.44 1.54 0.0749 0.0176 16 0.00000 0.00000 -8.51 4.92 0.0179 0.0101 17 0.00000 0.00000 4.89 6.36 0.0370 0.0175 18 0.00000 0.00000 4.08 14.88 0.0356 0.0133 19 0.00000 0.00000 -2.65 4.99 0.1120 0.0103 20 0.00000 0.00000 4.75 5.73 0.0340 0.0073 View from the lead end of the magnet: y ^ | S N N --> x S The magnetic center is at X = 88.1 +- 0.5 microns Y = 312.7 +- 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. Date: 02-12-1998 Time: 11:51:29 Magnet Name: SRTLSKEW Run Number: 1 FIELD HARMONICS Harmonics at Rcoil = .007874 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00001 0.00000 -175.71 0.41 3.0642 0.0244 2 0.00031 0.00000 87.95 0.04 100.0000 0.0626 3 0.00000 0.00000 33.23 23.75 0.1002 0.0421 4 0.00000 0.00000 27.25 20.34 0.0619 0.0279 5 0.00000 0.00000 28.12 15.50 0.0663 0.0157 6 0.00000 0.00000 27.47 8.75 0.0430 0.0176 7 0.00000 0.00000 -16.55 17.18 0.0759 0.0226 8 0.00000 0.00000 12.81 4.89 0.0783 0.0412 9 0.00000 0.00000 -1.21 6.56 0.0549 0.0129 10 0.00000 0.00000 -15.38 8.49 0.0693 0.0093 11 0.00000 0.00000 4.60 9.76 0.1536 0.0362 12 0.00000 0.00000 -3.71 5.33 0.1584 0.0282 13 0.00000 0.00000 -7.05 6.94 0.0481 0.0185 14 0.00000 0.00000 -10.03 19.04 0.0270 0.0048 15 0.00000 0.00000 -6.98 5.69 0.1007 0.0311 16 0.00000 0.00000 -1.80 9.26 0.0218 0.0099 17 0.00000 0.00000 2.82 14.70 0.0433 0.0236 18 0.00000 0.00000 -0.28 4.01 0.0278 0.0138 19 0.00000 0.00000 3.79 3.64 0.1775 0.0539 20 0.00000 0.00000 -2.23 5.85 0.0602 0.0169 View from the lead end of the magnet: y ^ | S N N --> x S The magnetic center is at X = 18.1 +- 1.7 microns Y = 240.6 +- 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. Date: 02-12-1998 Time: 11:55:55 Magnet Name: SRTLSKEW Run Number: 1 FIELD HARMONICS Magnet Current, Imag = .0076015 +- 2.091038E-05 A Harmonics at Rcoil = .007874 m Nmain = 1 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00001 0.00000 43.34 0.16 100.0000 0.4515 2 0.00000 0.00000 7.16 1.56 14.4596 0.7172 3 0.00000 0.00000 -21.49 1.81 8.6473 0.7044 4 0.00000 0.00000 -39.18 18.85 1.9774 1.4742 5 0.00000 0.00000 28.87 4.90 1.6553 0.9734 6 0.00000 0.00000 -20.33 7.69 1.6435 0.2592 7 0.00000 0.00000 11.41 2.75 1.9566 0.2191 8 0.00000 0.00000 6.47 9.54 3.3941 0.8714 9 0.00000 0.00000 15.13 9.17 2.1229 0.3896 10 0.00000 0.00000 14.03 7.30 2.4358 1.4834 11 0.00000 0.00000 -8.54 9.54 3.7964 0.3790 12 0.00000 0.00000 -11.66 3.91 4.0979 0.4552 13 0.00000 0.00000 8.08 10.50 1.6857 1.1510 14 0.00000 0.00000 6.79 15.60 0.7771 0.1444 15 0.00000 0.00000 7.25 24.00 4.5437 0.3943 16 0.00000 0.00000 -0.45 2.23 1.0370 0.4930 17 0.00000 0.00000 -3.53 2.20 1.0017 0.1801 18 0.00000 0.00000 1.81 4.19 1.1256 0.5614 19 0.00000 0.00000 -7.89 8.11 7.3277 1.0174 20 0.00000 0.00000 6.83 10.30 1.8442 0.6862 View from the lead end of the magnet: y ^ | N S N S --> x N S The magnetic center is at X = %-37373.0 +- 1856.9 microns Y = %-39605.8 +- 1967.1 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. Date: 02-12-1998 Time: 12:00:23 Magnet Name: SRTLSKEW Run Number: 1 FIELD HARMONICS Magnet Current, Imag = .513599 +- 2.175906E-05 A Harmonics at Rcoil = .007874 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00002 0.00000 29.03 0.09 7.7503 0.0178 2 0.00031 0.00000 -2.01 0.03 100.0000 0.0969 3 0.00000 0.00000 -15.30 1.07 0.4194 0.0575 4 0.00000 0.00000 -32.83 5.44 0.0628 0.0108 5 0.00000 0.00000 25.73 3.13 0.0541 0.0279 6 0.00000 0.00000 6.44 2.89 0.0365 0.0153 7 0.00000 0.00000 -16.07 8.98 0.0911 0.0181 8 0.00000 0.00000 -3.65 13.78 0.1021 0.0182 9 0.00000 0.00000 17.33 6.93 0.0430 0.0280 10 0.00000 0.00000 6.67 5.94 0.0794 0.0199 11 0.00000 0.00000 -9.04 2.91 0.1381 0.0652 12 0.00000 0.00000 -12.29 9.37 0.1524 0.0327 13 0.00000 0.00000 9.65 3.19 0.0551 0.0283 14 0.00000 0.00000 -6.17 3.35 0.0241 0.0073 15 0.00000 0.00000 7.00 1.52 0.1245 0.0283 16 0.00000 0.00000 2.55 4.65 0.0281 0.0115 17 0.00000 0.00000 -1.41 1.66 0.0434 0.0173 18 0.00000 0.00000 -7.11 12.08 0.0380 0.0099 19 0.00000 0.00000 -2.24 4.21 0.2117 0.0523 20 0.00000 0.00000 -3.79 4.34 0.0419 0.0291 View from the lead end of the magnet: y ^ | N S S --> x N The magnetic center is at X = 296.1 +- 1.1 microns Y = 533.6 +- 1.3 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. Date: 02-12-1998 Time: 12:04:53 Magnet Name: SRTLSKEW Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 1.020648 +- 2.004852E-05 A Harmonics at Rcoil = .007874 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00004 0.00000 26.27 0.05 6.4898 0.0060 2 0.00063 0.00000 -1.98 0.02 100.0000 0.0301 3 0.00000 0.00000 -17.42 1.52 0.3622 0.0236 4 0.00000 0.00000 -31.82 3.31 0.0925 0.0075 5 0.00000 0.00000 -35.06 10.49 0.0331 0.0152 6 0.00000 0.00000 3.22 2.66 0.0318 0.0043 7 0.00000 0.00000 17.38 12.87 0.0342 0.0167 8 0.00000 0.00000 21.57 45.00 0.0388 0.0097 9 0.00000 0.00000 3.51 5.01 0.0192 0.0031 10 0.00000 0.00000 -9.76 18.30 0.0366 0.0147 11 0.00000 0.00000 -4.58 2.13 0.0605 0.0283 12 0.00000 0.00000 -1.27 10.73 0.0663 0.0167 13 0.00000 0.00000 12.76 2.51 0.0418 0.0120 14 0.00000 0.00000 11.72 4.37 0.0130 0.0038 15 0.00000 0.00000 8.04 1.38 0.0619 0.0185 16 0.00000 0.00000 9.39 12.52 0.0359 0.0096 17 0.00000 0.00000 5.21 7.44 0.0304 0.0023 18 0.00000 0.00000 7.92 7.38 0.0210 0.0218 19 0.00000 0.00000 -2.25 8.19 0.0808 0.0397 20 0.00000 0.00000 3.72 18.00 0.0466 0.0197 View from the lead end of the magnet: y ^ | N S S --> x N The magnetic center is at X = 226.1 +- 0.5 microns Y = 458.2 +- 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. Date: 02-12-1998 Time: 12:11:48 Magnet Name: SRTLSKEW Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 2.033837 +- 3.364533E-05 A Harmonics at Rcoil = .007874 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00007 0.00000 24.21 0.06 5.8974 0.0071 2 0.00126 0.00000 -2.07 0.01 100.0000 0.1156 3 0.00000 0.00000 -15.82 1.18 0.2299 0.0241 4 0.00000 0.00000 -29.33 4.27 0.0475 0.0129 5 0.00000 0.00000 27.19 1.41 0.0256 0.0097 6 0.00000 0.00000 4.55 1.72 0.0279 0.0042 7 0.00000 0.00000 -20.40 4.89 0.0259 0.0056 8 0.00000 0.00000 -20.74 9.93 0.0244 0.0081 9 0.00000 0.00000 3.41 20.69 0.0167 0.0066 10 0.00000 0.00000 -8.92 32.03 0.0219 0.0091 11 0.00000 0.00000 -10.96 11.14 0.0429 0.0144 12 0.00000 0.00000 -10.01 30.00 0.0326 0.0032 13 0.00000 0.00000 -9.85 6.49 0.0148 0.0111 14 0.00000 0.00000 6.01 10.71 0.0111 0.0069 15 0.00000 0.00000 6.47 7.00 0.0387 0.0112 16 0.00000 0.00000 5.29 3.91 0.0249 0.0057 17 0.00000 0.00000 -8.52 4.40 0.0227 0.0139 18 0.00000 0.00000 -6.94 10.96 0.0212 0.0117 19 0.00000 0.00000 8.63 6.76 0.1067 0.0212 20 0.00000 0.00000 -0.83 5.07 0.0242 0.0099 View from the lead end of the magnet: y ^ | N S S --> x N The magnetic center is at X = 190.4 +- 0.5 microns Y = 423.5 +- 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. Date: 02-12-1998 Time: 12:18:44 Magnet Name: SRTLSKEW Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 3.046735 +- 1.119806E-05 A Harmonics at Rcoil = .007874 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00011 0.00000 23.44 0.01 5.7151 0.0053 2 0.00188 0.00000 -2.00 0.04 100.0000 0.0526 3 0.00000 0.00000 -18.74 0.72 0.2444 0.0370 4 0.00000 0.00000 -27.32 3.22 0.0778 0.0180 5 0.00000 0.00000 -31.88 7.75 0.0232 0.0060 6 0.00000 0.00000 8.44 1.32 0.0173 0.0039 7 0.00000 0.00000 -15.94 3.27 0.0246 0.0072 8 0.00000 0.00000 -19.11 7.31 0.0162 0.0088 9 0.00000 0.00000 9.77 10.75 0.0111 0.0040 10 0.00000 0.00000 -11.20 6.07 0.0172 0.0098 11 0.00000 0.00000 15.63 7.69 0.0294 0.0115 12 0.00000 0.00000 9.71 6.90 0.0215 0.0045 13 0.00000 0.00000 -7.70 4.50 0.0227 0.0082 14 0.00000 0.00000 1.71 11.65 0.0100 0.0056 15 0.00000 0.00000 1.47 1.86 0.0369 0.0209 16 0.00000 0.00000 -2.63 2.18 0.0286 0.0117 17 0.00000 0.00000 -7.07 7.77 0.0177 0.0019 18 0.00000 0.00000 9.41 2.90 0.0204 0.0098 19 0.00000 0.00000 4.90 2.16 0.0660 0.0040 20 0.00000 0.00000 -6.39 1.81 0.0376 0.0054 View from the lead end of the magnet: y ^ | N S S --> x N The magnetic center is at X = 179.0 +- 0.2 microns Y = 412.9 +- 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. Date: 02-12-1998 Time: 12:25:40 Magnet Name: SRTLSKEW Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 4.060762 +- 2.58956E-05 A Harmonics at Rcoil = .007874 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00014 0.00000 22.89 0.03 5.5965 0.0037 2 0.00252 0.00000 -2.03 0.02 100.0000 0.0399 3 0.00001 0.00000 -18.10 1.16 0.2576 0.0074 4 0.00000 0.00000 -30.03 1.71 0.0690 0.0111 5 0.00000 0.00000 -35.34 2.86 0.0197 0.0027 6 0.00000 0.00000 6.07 2.38 0.0277 0.0067 7 0.00000 0.00000 -17.57 6.72 0.0107 0.0016 8 0.00000 0.00000 21.91 26.58 0.0109 0.0062 9 0.00000 0.00000 15.55 10.46 0.0095 0.0055 10 0.00000 0.00000 -3.47 10.05 0.0111 0.0024 11 0.00000 0.00000 1.36 14.93 0.0188 0.0070 12 0.00000 0.00000 7.15 30.00 0.0164 0.0075 13 0.00000 0.00000 -13.40 9.22 0.0166 0.0111 14 0.00000 0.00000 -11.60 2.76 0.0093 0.0032 15 0.00000 0.00000 -8.96 4.27 0.0313 0.0080 16 0.00000 0.00000 8.61 3.72 0.0295 0.0064 17 0.00000 0.00000 1.46 2.39 0.0137 0.0068 18 0.00000 0.00000 5.20 10.27 0.0191 0.0179 19 0.00000 0.00000 -4.20 2.87 0.0677 0.0238 20 0.00000 0.00000 3.24 4.95 0.0397 0.0138 View from the lead end of the magnet: y ^ | N S S --> x N The magnetic center is at X = 171.4 +- 0.2 microns Y = 406.0 +- 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. 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) For a double coil (for coil bowing correction), V2 = [(Nturns * Rcoil^2)1 + (Nturns * Rcoil^2)2] * ang_freq * GL GL = [(Nturns * Rcoil^2)1 + (Nturns * Rcoil^2)2]^(-1) * (V2 / ang_freq) Let CoilConst = [(Nturns * Rcoil^2)1 + (Nturns * Rcoil^2)2]^(-1) GL = CoilConst * V2 / 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)