SLAC Magnetic Measurements Date: 09-11-1996 Time: 14:23:32 Project: PEP2HER Magnet Type: SKEWQUAD Magnet Name (Serial #): 2903 Bar Code Number: 2903 Test Stand: IR8 Measurement System: COIL Operator: dan Run Number: 1 Comment: north pole on top Saturation Current The current was initially run to 50 A. Standardization Currents 3 cycles, 0 to 10 to 0 A Test Currents 1.0 2.0 3.0 4.0 5.0 6.0 8.0 10.0 Harmonics Measurements Date: 09-11-1996 Time: 14:38:50 Magnet Name: 2903 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = .9923853 +- 4.677625E-05 A Harmonics at Rcoil = .0446722 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00004 0.00000 -67.42 0.01 14.9317 0.0044 2 0.00029 0.00000 -0.21 0.00 100.0000 0.0356 3 0.00000 0.00000 -0.88 0.18 0.1533 0.0015 4 0.00000 0.00000 -16.81 17.58 0.0345 0.0105 5 0.00000 0.00000 -14.15 25.78 0.3416 0.0153 6 0.00000 0.00000 9.99 19.98 0.3226 0.0394 7 0.00000 0.00000 14.46 5.36 0.6816 0.0239 8 0.00000 0.00000 -3.03 4.42 0.1306 0.0071 9 0.00000 0.00000 -12.02 5.70 0.0235 0.0055 10 0.00000 0.00000 -13.12 3.37 0.0108 0.0047 11 0.00000 0.00000 5.37 3.65 0.0137 0.0040 12 0.00000 0.00000 -6.06 12.08 0.0160 0.0059 13 0.00000 0.00000 -3.03 6.97 0.0116 0.0055 14 0.00000 0.00000 2.36 8.60 0.0106 0.0069 15 0.00000 0.00000 0.95 8.96 0.0122 0.0070 The magnetic center is at X = -6158.9 +- 1.9 microns Y = 2561.5 +- 1.7 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: 09-11-1996 Time: 14:43:38 Magnet Name: 2903 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 1.989304 +- 2.351318E-05 A Harmonics at Rcoil = .0446722 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00004 0.00000 -68.48 0.05 8.4760 0.0040 2 0.00052 0.00000 -0.23 0.00 100.0000 0.0070 3 0.00000 0.00000 -1.15 0.85 0.1067 0.0078 4 0.00000 0.00000 -2.89 34.41 0.0347 0.0040 5 0.00000 0.00000 16.74 12.44 0.1828 0.0062 6 0.00000 0.00000 4.59 7.25 0.2781 0.0723 7 0.00000 0.00000 -1.93 9.12 0.3477 0.0178 8 0.00000 0.00000 5.07 14.87 0.0704 0.0024 9 0.00000 0.00000 -3.96 13.04 0.0155 0.0028 10 0.00000 0.00000 -2.27 11.61 0.0071 0.0042 11 0.00000 0.00000 8.06 4.46 0.0092 0.0035 12 0.00000 0.00000 -4.14 10.08 0.0071 0.0013 13 0.00000 0.00000 4.73 6.14 0.0054 0.0028 14 0.00000 0.00000 -5.28 7.06 0.0152 0.0047 15 0.00000 0.00000 -0.53 9.27 0.0128 0.0054 The magnetic center is at X = -3522.4 +- 2.0 microns Y = 1389.1 +- 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 ^ | S N --> x N S Date: 09-11-1996 Time: 14:48:26 Magnet Name: 2903 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 2.99133 +- 3.197432E-05 A Harmonics at Rcoil = .0446722 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00004 0.00000 -69.66 0.03 5.8789 0.0026 2 0.00074 0.00000 -0.24 0.00 100.0000 0.0155 3 0.00000 0.00000 -0.43 1.61 0.0760 0.0042 4 0.00000 0.00000 -6.76 25.17 0.0153 0.0051 5 0.00000 0.00000 12.09 22.17 0.1254 0.0054 6 0.00000 0.00000 1.06 10.15 0.1518 0.0520 7 0.00000 0.00000 7.48 15.19 0.2385 0.0132 8 0.00000 0.00000 2.06 9.21 0.0481 0.0022 9 0.00000 0.00000 -5.06 8.64 0.0137 0.0018 10 0.00000 0.00000 -7.35 9.40 0.0050 0.0040 11 0.00000 0.00000 5.37 4.48 0.0079 0.0036 12 0.00000 0.00000 -0.68 8.18 0.0077 0.0035 13 0.00000 0.00000 0.97 5.60 0.0080 0.0017 14 0.00000 0.00000 4.95 2.60 0.0113 0.0089 15 0.00000 0.00000 0.14 8.80 0.0100 0.0053 The magnetic center is at X = -2462.5 +- 1.2 microns Y = 912.8 +- 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. View from the non-lead end of the magnet: y ^ | S N --> x N S Date: 09-11-1996 Time: 14:53:12 Magnet Name: 2903 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 4.005332 +- 1.076805E-04 A Harmonics at Rcoil = .0446722 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00004 0.00000 -70.89 0.01 4.4846 0.0016 2 0.00097 0.00000 -0.25 0.00 100.0000 0.0209 3 0.00000 0.00000 0.24 1.06 0.0670 0.0007 4 0.00000 0.00000 -5.78 36.12 0.0148 0.0048 5 0.00000 0.00000 7.78 11.58 0.0963 0.0074 6 0.00000 0.00000 -0.15 4.41 0.2191 0.0328 7 0.00000 0.00000 -7.82 8.39 0.1894 0.0039 8 0.00000 0.00000 -0.05 16.35 0.0382 0.0031 9 0.00000 0.00000 12.09 4.37 0.0108 0.0018 10 0.00000 0.00000 -7.93 2.17 0.0046 0.0006 11 0.00000 0.00000 8.21 1.67 0.0076 0.0022 12 0.00000 0.00000 -8.16 2.82 0.0103 0.0033 13 0.00000 0.00000 6.68 1.27 0.0163 0.0053 14 0.00000 0.00000 -2.34 7.73 0.0065 0.0037 15 0.00000 0.00000 -3.65 6.60 0.0067 0.0020 The magnetic center is at X = -1892.9 +- 0.7 microns Y = 656.0 +- 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 Date: 09-11-1996 Time: 14:57:58 Magnet Name: 2903 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 4.997584 +- 2.537114E-05 A Harmonics at Rcoil = .0446722 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00004 0.00000 -72.14 0.04 3.6414 0.0025 2 0.00120 0.00000 -0.25 0.00 100.0000 0.0092 3 0.00000 0.00000 1.04 0.89 0.0594 0.0034 4 0.00000 0.00000 -12.24 30.71 0.0107 0.0050 5 0.00000 0.00000 5.25 12.40 0.0752 0.0053 6 0.00000 0.00000 -1.06 4.07 0.1883 0.0295 7 0.00000 0.00000 -9.86 9.80 0.1407 0.0153 8 0.00000 0.00000 -1.50 15.71 0.0274 0.0016 9 0.00000 0.00000 9.20 6.46 0.0076 0.0021 10 0.00000 0.00000 -10.47 4.28 0.0047 0.0021 11 0.00000 0.00000 6.37 2.83 0.0063 0.0027 12 0.00000 0.00000 -9.72 1.35 0.0054 0.0023 13 0.00000 0.00000 1.68 6.89 0.0068 0.0055 14 0.00000 0.00000 -2.48 4.54 0.0110 0.0058 15 0.00000 0.00000 -8.85 2.43 0.0141 0.0032 The magnetic center is at X = -1548.3 +- 1.1 microns Y = 498.9 +- 1.2 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 ^ | S N --> x N S Date: 09-11-1996 Time: 15:02:43 Magnet Name: 2903 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 6.003247 +- 1.024728E-04 A Harmonics at Rcoil = .0446722 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00004 0.00000 -73.40 0.08 3.0569 0.0023 2 0.00143 0.00000 -0.25 0.00 100.0000 0.0146 3 0.00000 0.00000 2.81 1.31 0.0533 0.0052 4 0.00000 0.00000 -6.41 29.71 0.0127 0.0048 5 0.00000 0.00000 -0.67 25.16 0.0591 0.0028 6 0.00000 0.00000 1.65 3.96 0.1239 0.0455 7 0.00000 0.00000 11.18 11.01 0.1132 0.0123 8 0.00000 0.00000 -6.32 9.48 0.0258 0.0032 9 0.00000 0.00000 6.53 13.11 0.0037 0.0021 10 0.00000 0.00000 -1.83 11.52 0.0068 0.0012 11 0.00000 0.00000 7.43 1.48 0.0050 0.0019 12 0.00000 0.00000 -1.89 7.40 0.0064 0.0019 13 0.00000 0.00000 9.12 2.78 0.0060 0.0028 14 0.00000 0.00000 3.07 5.62 0.0119 0.0078 15 0.00000 0.00000 -1.71 8.84 0.0167 0.0056 The magnetic center is at X = -1308.7 +- 1.1 microns Y = 390.1 +- 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 ^ | S N --> x N S Date: 09-11-1996 Time: 15:07:31 Magnet Name: 2903 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 8.003854 +- 7.243061E-05 A Harmonics at Rcoil = .0446722 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00004 0.00000 -76.03 0.07 2.3252 0.0033 2 0.00189 0.00000 -0.28 0.00 100.0000 0.0225 3 0.00000 0.00000 5.38 0.72 0.0440 0.0031 4 0.00000 0.00000 -21.41 7.85 0.0127 0.0065 5 0.00000 0.00000 1.45 21.76 0.0498 0.0072 6 0.00000 0.00000 -0.56 3.07 0.1290 0.0381 7 0.00000 0.00000 11.80 12.92 0.0906 0.0138 8 0.00000 0.00000 -4.92 10.39 0.0188 0.0036 9 0.00000 0.00000 10.70 5.36 0.0056 0.0029 10 0.00000 0.00000 -7.52 3.79 0.0057 0.0025 11 0.00000 0.00000 5.78 2.08 0.0079 0.0014 12 0.00000 0.00000 -9.76 2.55 0.0082 0.0008 13 0.00000 0.00000 4.82 0.88 0.0139 0.0043 14 0.00000 0.00000 -0.92 11.57 0.0117 0.0017 15 0.00000 0.00000 -8.65 1.34 0.0110 0.0075 The magnetic center is at X = -1008.0 +- 1.5 microns Y = 250.7 +- 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. View from the non-lead end of the magnet: y ^ | S N --> x N S Date: 09-11-1996 Time: 15:12:18 Magnet Name: 2903 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.993841 +- 5.546705E-05 A Harmonics at Rcoil = .0446722 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00004 0.00000 -78.72 0.04 1.8914 0.0015 2 0.00235 0.00000 -0.28 0.00 100.0000 0.0059 3 0.00000 0.00000 6.49 0.75 0.0418 0.0034 4 0.00000 0.00000 -22.07 8.68 0.0083 0.0030 5 0.00000 0.00000 3.50 19.64 0.0428 0.0087 6 0.00000 0.00000 -1.19 2.45 0.1369 0.0283 7 0.00000 0.00000 -11.73 14.90 0.0793 0.0096 8 0.00000 0.00000 6.45 10.06 0.0159 0.0034 9 0.00000 0.00000 0.73 8.13 0.0060 0.0014 10 0.00000 0.00000 -13.35 1.91 0.0054 0.0013 11 0.00000 0.00000 7.72 1.90 0.0075 0.0014 12 0.00000 0.00000 -4.03 10.33 0.0079 0.0014 13 0.00000 0.00000 6.68 5.62 0.0094 0.0092 14 0.00000 0.00000 2.23 9.41 0.0105 0.0024 15 0.00000 0.00000 -0.07 9.81 0.0096 0.0061 The magnetic center is at X = -828.6 +- 0.7 microns Y = 165.3 +- 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 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), GL = ( (1 / Nturns * Rcoil^2)1 + (1 / Nturns * Rcoil^2)2 ) * (V2 / ang_freq) Let CoilConst = ( (1 / Nturns * Rcoil^2)1 + (1 / Nturns * Rcoil^2)2 ) 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)