SLAC Magnetic Measurements Date: 09-12-1996 Time: 07:37:34 Project: PEP2HER Magnet Type: SKEWQUAD Magnet Name (Serial #): 2904 Bar Code Number: 2904 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: 09-12-1996 Time: 07:52:54 Magnet Name: 2904 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = .9932706 +- 4.328694E-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 -70.54 0.01 13.9179 0.0078 2 0.00030 0.00000 -0.20 0.00 100.0000 0.0382 3 0.00000 0.00000 -43.20 0.88 0.1042 0.0101 4 0.00000 0.00000 21.71 6.39 0.1350 0.0215 5 0.00000 0.00000 -7.82 9.06 0.3648 0.0045 6 0.00000 0.00000 -12.16 7.41 0.4373 0.0752 7 0.00000 0.00000 -7.57 17.18 0.7332 0.0159 8 0.00000 0.00000 13.70 6.12 0.1035 0.0108 9 0.00000 0.00000 -11.50 2.95 0.0144 0.0069 10 0.00000 0.00000 -11.55 2.95 0.0112 0.0034 11 0.00000 0.00000 1.79 12.61 0.0106 0.0070 12 0.00000 0.00000 0.41 9.35 0.0099 0.0057 13 0.00000 0.00000 -2.76 8.28 0.0106 0.0060 14 0.00000 0.00000 1.54 8.09 0.0182 0.0121 15 0.00000 0.00000 -6.86 4.05 0.0161 0.0047 The magnetic center is at X = -5862.3 +- 3.3 microns Y = 2071.3 +- 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: 09-12-1996 Time: 07:57:42 Magnet Name: 2904 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 1.991623 +- 1.762303E-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 -70.30 0.03 7.9745 0.0041 2 0.00052 0.00000 -0.22 0.00 100.0000 0.0194 3 0.00000 0.00000 -33.49 2.14 0.0421 0.0069 4 0.00000 0.00000 21.89 10.90 0.0657 0.0106 5 0.00000 0.00000 -6.52 13.11 0.2105 0.0093 6 0.00000 0.00000 -10.04 8.61 0.2545 0.0824 7 0.00000 0.00000 6.07 17.85 0.4264 0.0147 8 0.00000 0.00000 2.83 12.59 0.0574 0.0025 9 0.00000 0.00000 -4.15 7.12 0.0124 0.0020 10 0.00000 0.00000 -1.13 11.71 0.0058 0.0027 11 0.00000 0.00000 6.52 8.73 0.0071 0.0014 12 0.00000 0.00000 -5.11 4.99 0.0077 0.0033 13 0.00000 0.00000 7.38 2.26 0.0095 0.0040 14 0.00000 0.00000 7.68 7.69 0.0191 0.0062 15 0.00000 0.00000 -3.92 7.03 0.0103 0.0035 The magnetic center is at X = -3353.9 +- 1.9 microns Y = 1200.8 +- 2.1 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. View from the non-lead end of the magnet: y ^ | S N --> x N S Date: 09-12-1996 Time: 08:02:31 Magnet Name: 2904 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 2.992682 +- 3.102489E-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 -70.09 0.03 5.5343 0.0018 2 0.00074 0.00000 -0.23 0.00 100.0000 0.0251 3 0.00000 0.00000 -19.92 2.11 0.0279 0.0057 4 0.00000 0.00000 7.79 30.42 0.0378 0.0067 5 0.00000 0.00000 4.38 17.86 0.1618 0.0060 6 0.00000 0.00000 -2.97 9.79 0.2161 0.0627 7 0.00000 0.00000 1.38 14.92 0.3174 0.0036 8 0.00000 0.00000 -1.59 11.64 0.0470 0.0020 9 0.00000 0.00000 2.95 7.59 0.0078 0.0014 10 0.00000 0.00000 -0.61 5.10 0.0041 0.0008 11 0.00000 0.00000 0.44 9.21 0.0046 0.0017 12 0.00000 0.00000 -1.01 4.94 0.0050 0.0030 13 0.00000 0.00000 1.46 9.20 0.0045 0.0019 14 0.00000 0.00000 1.14 9.05 0.0248 0.0053 15 0.00000 0.00000 2.86 5.42 0.0069 0.0033 The magnetic center is at X = -2324.5 +- 0.9 microns Y = 841.9 +- 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: 09-12-1996 Time: 08:07:16 Magnet Name: 2904 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 4.006966 +- 3.221122E-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 -70.00 0.04 4.2115 0.0020 2 0.00097 0.00000 -0.23 0.00 100.0000 0.0175 3 0.00000 0.00000 -12.00 1.43 0.0262 0.0004 4 0.00000 0.00000 -3.65 20.53 0.0208 0.0034 5 0.00000 0.00000 -7.21 16.63 0.1257 0.0045 6 0.00000 0.00000 -7.29 7.30 0.1444 0.0560 7 0.00000 0.00000 5.80 19.43 0.2486 0.0053 8 0.00000 0.00000 1.97 9.17 0.0386 0.0024 9 0.00000 0.00000 -0.64 9.53 0.0074 0.0008 10 0.00000 0.00000 -1.64 7.87 0.0045 0.0020 11 0.00000 0.00000 2.93 7.13 0.0028 0.0014 12 0.00000 0.00000 -6.03 6.88 0.0044 0.0015 13 0.00000 0.00000 1.71 6.73 0.0097 0.0010 14 0.00000 0.00000 2.05 8.76 0.0178 0.0034 15 0.00000 0.00000 -0.54 8.85 0.0092 0.0051 The magnetic center is at X = -1767.9 +- 1.0 microns Y = 643.5 +- 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: 09-12-1996 Time: 08:12:02 Magnet Name: 2904 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 4.99861 +- 5.338287E-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 -69.88 0.03 3.4001 0.0015 2 0.00120 0.00000 -0.24 0.00 100.0000 0.0198 3 0.00000 0.00000 -4.69 1.66 0.0280 0.0019 4 0.00000 0.00000 -9.99 19.20 0.0227 0.0042 5 0.00000 0.00000 7.17 21.65 0.0944 0.0072 6 0.00000 0.00000 -0.91 8.18 0.1385 0.0306 7 0.00000 0.00000 3.07 17.65 0.2022 0.0059 8 0.00000 0.00000 -0.24 9.06 0.0316 0.0045 9 0.00000 0.00000 5.59 11.33 0.0065 0.0024 10 0.00000 0.00000 -1.00 4.59 0.0028 0.0011 11 0.00000 0.00000 0.68 8.71 0.0030 0.0013 12 0.00000 0.00000 -2.23 5.37 0.0051 0.0028 13 0.00000 0.00000 6.23 6.17 0.0026 0.0005 14 0.00000 0.00000 1.38 9.22 0.0224 0.0089 15 0.00000 0.00000 -0.13 7.11 0.0059 0.0030 The magnetic center is at X = -1426.2 +- 0.7 microns Y = 522.5 +- 0.8 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: 09-12-1996 Time: 08:16:47 Magnet Name: 2904 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 6.004756 +- 6.977482E-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 -69.82 0.05 2.8427 0.0007 2 0.00142 0.00000 -0.24 0.00 100.0000 0.0181 3 0.00000 0.00000 -0.96 2.36 0.0313 0.0014 4 0.00000 0.00000 -9.14 23.80 0.0149 0.0062 5 0.00000 0.00000 7.20 14.54 0.0871 0.0084 6 0.00000 0.00000 -0.48 4.98 0.1836 0.0156 7 0.00000 0.00000 -8.86 10.82 0.1647 0.0032 8 0.00000 0.00000 -0.46 13.12 0.0236 0.0016 9 0.00000 0.00000 5.82 3.83 0.0055 0.0036 10 0.00000 0.00000 3.30 7.77 0.0037 0.0018 11 0.00000 0.00000 1.94 9.08 0.0045 0.0022 12 0.00000 0.00000 -1.80 7.26 0.0033 0.0015 13 0.00000 0.00000 3.43 5.96 0.0063 0.0045 14 0.00000 0.00000 -5.06 7.08 0.0219 0.0073 15 0.00000 0.00000 -1.34 8.57 0.0148 0.0052 The magnetic center is at X = -1191.9 +- 0.5 microns Y = 438.1 +- 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: 09-12-1996 Time: 08:21:35 Magnet Name: 2904 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 8.004647 +- 5.25517E-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 0.05 2.1300 0.0020 2 0.00188 0.00000 -0.27 0.00 100.0000 0.0220 3 0.00000 0.00000 2.79 1.88 0.0354 0.0013 4 0.00000 0.00000 -9.17 21.29 0.0163 0.0082 5 0.00000 0.00000 -6.15 18.38 0.0628 0.0073 6 0.00000 0.00000 -0.77 2.93 0.1319 0.0597 7 0.00000 0.00000 6.22 14.30 0.1229 0.0050 8 0.00000 0.00000 1.82 11.01 0.0213 0.0009 9 0.00000 0.00000 -3.58 9.27 0.0039 0.0016 10 0.00000 0.00000 -1.89 12.17 0.0024 0.0016 11 0.00000 0.00000 -3.13 9.03 0.0024 0.0027 12 0.00000 0.00000 -6.15 3.27 0.0031 0.0012 13 0.00000 0.00000 0.16 10.82 0.0026 0.0008 14 0.00000 0.00000 -5.45 5.93 0.0104 0.0042 15 0.00000 0.00000 -1.15 10.50 0.0103 0.0049 The magnetic center is at X = -892.2 +- 0.9 microns Y = 330.8 +- 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 ^ | S N --> x N S Date: 09-12-1996 Time: 08:26:23 Magnet Name: 2904 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.995112 +- 7.735351E-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 -69.56 0.04 1.7014 0.0013 2 0.00233 0.00000 -0.27 0.00 100.0000 0.0102 3 0.00000 0.00000 4.62 0.96 0.0382 0.0021 4 0.00000 0.00000 -15.82 6.25 0.0116 0.0039 5 0.00000 0.00000 -11.42 7.88 0.0578 0.0042 6 0.00000 0.00000 -3.24 1.12 0.1321 0.0348 7 0.00000 0.00000 -10.30 17.66 0.0997 0.0028 8 0.00000 0.00000 9.70 5.91 0.0163 0.0023 9 0.00000 0.00000 -7.92 6.38 0.0032 0.0021 10 0.00000 0.00000 3.61 12.19 0.0027 0.0019 11 0.00000 0.00000 8.07 3.00 0.0031 0.0015 12 0.00000 0.00000 2.01 10.63 0.0028 0.0006 13 0.00000 0.00000 6.91 4.27 0.0039 0.0025 14 0.00000 0.00000 -2.56 9.26 0.0125 0.0034 15 0.00000 0.00000 -3.29 8.98 0.0147 0.0057 The magnetic center is at X = -712.2 +- 0.6 microns Y = 265.4 +- 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) 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)