SLAC Magnetic Measurements Date: 09-11-1996 Time: 12:18:19 Project: PEP2HER Magnet Type: SKEWQUAD Magnet Name (Serial #): 2902 Bar Code Number: 2902 Test Stand: IR8 Measurement System: COIL Operator: dan Run Number: 1 Comment: south 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: 12:33:36 Magnet Name: 2902 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = .9922729 +- 6.821891E-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 -75.24 0.01 15.3528 0.0050 2 0.00029 0.00000 89.73 0.00 100.0000 0.0170 3 0.00000 0.00000 37.17 0.54 0.2180 0.0090 4 0.00000 0.00000 13.93 29.98 0.0489 0.0063 5 0.00000 0.00000 15.22 13.70 0.2319 0.0272 6 0.00000 0.00000 5.84 14.33 0.2192 0.0570 7 0.00000 0.00000 -3.31 9.65 0.3631 0.0502 8 0.00000 0.00000 -8.43 12.19 0.0917 0.0065 9 0.00000 0.00000 5.83 13.13 0.0272 0.0049 10 0.00000 0.00000 0.22 8.29 0.0117 0.0024 11 0.00000 0.00000 -10.73 2.99 0.0130 0.0066 12 0.00000 0.00000 6.99 7.65 0.0154 0.0071 13 0.00000 0.00000 -5.30 4.05 0.0077 0.0049 14 0.00000 0.00000 -0.07 9.95 0.0127 0.0062 15 0.00000 0.00000 -2.99 3.42 0.0124 0.0064 The magnetic center is at X = 6632.0 +- 2.2 microns Y = -1747.9 +- 1.5 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: 09-11-1996 Time: 12:38:24 Magnet Name: 2902 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 1.989745 +- 3.765816E-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 -76.64 0.03 8.4785 0.0032 2 0.00051 0.00000 89.75 0.00 100.0000 0.0213 3 0.00000 0.00000 38.22 0.83 0.1017 0.0087 4 0.00000 0.00000 35.34 5.96 0.0219 0.0086 5 0.00000 0.00000 -7.42 21.10 0.1106 0.0193 6 0.00000 0.00000 -13.33 20.99 0.1967 0.0505 7 0.00000 0.00000 7.61 16.23 0.2201 0.0185 8 0.00000 0.00000 0.82 9.96 0.0536 0.0024 9 0.00000 0.00000 -5.99 8.89 0.0138 0.0031 10 0.00000 0.00000 -0.40 10.06 0.0062 0.0027 11 0.00000 0.00000 -3.75 9.09 0.0078 0.0022 12 0.00000 0.00000 3.05 9.38 0.0103 0.0020 13 0.00000 0.00000 4.52 6.38 0.0085 0.0047 14 0.00000 0.00000 7.58 5.86 0.0081 0.0048 15 0.00000 0.00000 -0.02 1.66 0.0072 0.0050 The magnetic center is at X = 3685.1 +- 1.4 microns Y = -874.9 +- 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. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 09-11-1996 Time: 12:43:12 Magnet Name: 2902 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 2.990805 +- 4.984959E-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 -78.22 0.05 5.7535 0.0019 2 0.00074 0.00000 89.76 0.00 100.0000 0.0285 3 0.00000 0.00000 36.25 1.61 0.0607 0.0026 4 0.00000 0.00000 13.65 32.14 0.0207 0.0111 5 0.00000 0.00000 -9.18 25.22 0.0830 0.0126 6 0.00000 0.00000 14.55 21.48 0.1469 0.0681 7 0.00000 0.00000 4.77 10.97 0.1370 0.0118 8 0.00000 0.00000 -1.11 13.19 0.0356 0.0025 9 0.00000 0.00000 2.58 12.28 0.0086 0.0018 10 0.00000 0.00000 -1.88 9.93 0.0039 0.0023 11 0.00000 0.00000 4.80 9.03 0.0089 0.0013 12 0.00000 0.00000 -4.85 7.82 0.0073 0.0049 13 0.00000 0.00000 -0.81 8.78 0.0095 0.0022 14 0.00000 0.00000 -7.00 4.65 0.0200 0.0112 15 0.00000 0.00000 4.43 4.05 0.0068 0.0024 The magnetic center is at X = 2516.1 +- 0.9 microns Y = -524.8 +- 2.0 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 ^ | N S --> x S N Date: 09-11-1996 Time: 12:47:57 Magnet Name: 2902 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 4.005569 +- 2.573375E-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 -80.01 0.05 4.2951 0.0021 2 0.00097 0.00000 89.76 0.00 100.0000 0.0096 3 0.00000 0.00000 36.46 1.07 0.0340 0.0019 4 0.00000 0.00000 28.88 5.14 0.0183 0.0010 5 0.00000 0.00000 -20.20 5.08 0.0565 0.0092 6 0.00000 0.00000 -27.03 1.24 0.1742 0.0150 7 0.00000 0.00000 1.12 23.05 0.1100 0.0044 8 0.00000 0.00000 7.30 3.11 0.0247 0.0023 9 0.00000 0.00000 -2.00 1.66 0.0043 0.0017 10 0.00000 0.00000 8.08 2.65 0.0055 0.0012 11 0.00000 0.00000 -3.52 8.88 0.0043 0.0007 12 0.00000 0.00000 0.77 6.66 0.0078 0.0036 13 0.00000 0.00000 1.84 4.10 0.0047 0.0012 14 0.00000 0.00000 -4.67 4.62 0.0127 0.0066 15 0.00000 0.00000 -5.03 2.51 0.0080 0.0047 The magnetic center is at X = 1889.6 +- 1.0 microns Y = -332.9 +- 1.5 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: 09-11-1996 Time: 12:52:43 Magnet Name: 2902 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 4.997375 +- 8.057031E-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 -81.96 0.03 3.4197 0.0016 2 0.00119 0.00000 89.76 0.00 100.0000 0.0078 3 0.00000 0.00000 29.46 3.79 0.0216 0.0038 4 0.00000 0.00000 30.43 3.28 0.0225 0.0031 5 0.00000 0.00000 5.22 15.87 0.0395 0.0199 6 0.00000 0.00000 -14.15 22.99 0.1106 0.0271 7 0.00000 0.00000 -12.36 8.76 0.0788 0.0059 8 0.00000 0.00000 5.75 14.71 0.0208 0.0025 9 0.00000 0.00000 1.54 13.56 0.0058 0.0023 10 0.00000 0.00000 9.22 4.99 0.0047 0.0015 11 0.00000 0.00000 -7.87 8.94 0.0030 0.0012 12 0.00000 0.00000 0.51 10.32 0.0065 0.0019 13 0.00000 0.00000 4.39 4.31 0.0046 0.0024 14 0.00000 0.00000 2.87 9.38 0.0310 0.0096 15 0.00000 0.00000 -1.18 1.09 0.0073 0.0049 The magnetic center is at X = 1512.6 +- 0.7 microns Y = -213.7 +- 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 ^ | N S --> x S N Date: 09-11-1996 Time: 12:57:28 Magnet Name: 2902 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 6.003866 +- 5.88918E-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 -84.08 0.05 2.8184 0.0004 2 0.00142 0.00000 89.77 0.00 100.0000 0.0036 3 0.00000 0.00000 30.90 2.10 0.0178 0.0032 4 0.00000 0.00000 27.24 4.47 0.0216 0.0054 5 0.00000 0.00000 15.32 12.37 0.0237 0.0185 6 0.00000 0.00000 -14.63 23.95 0.1159 0.0165 7 0.00000 0.00000 -8.56 8.38 0.0603 0.0052 8 0.00000 0.00000 10.08 12.66 0.0136 0.0032 9 0.00000 0.00000 4.03 12.37 0.0061 0.0016 10 0.00000 0.00000 -0.26 14.49 0.0027 0.0011 11 0.00000 0.00000 3.40 12.69 0.0038 0.0014 12 0.00000 0.00000 -1.82 10.06 0.0039 0.0023 13 0.00000 0.00000 0.02 9.65 0.0077 0.0036 14 0.00000 0.00000 -1.26 6.71 0.0127 0.0085 15 0.00000 0.00000 -0.62 3.09 0.0122 0.0038 The magnetic center is at X = 1252.3 +- 0.2 microns Y = -129.8 +- 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 ^ | N S --> x S N Date: 09-11-1996 Time: 13:02:15 Magnet Name: 2902 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 8.003394 +- 5.926416E-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 -88.47 0.08 2.0749 0.0017 2 0.00188 0.00000 89.74 0.00 100.0000 0.0276 3 0.00000 0.00000 26.15 5.31 0.0091 0.0016 4 0.00000 0.00000 28.47 1.87 0.0224 0.0024 5 0.00000 0.00000 -2.65 30.50 0.0410 0.0151 6 0.00000 0.00000 -0.22 29.00 0.1466 0.0290 7 0.00000 0.00000 1.79 16.25 0.0560 0.0110 8 0.00000 0.00000 -5.99 8.88 0.0127 0.0043 9 0.00000 0.00000 -10.74 7.68 0.0043 0.0022 10 0.00000 0.00000 12.90 2.38 0.0024 0.0007 11 0.00000 0.00000 3.76 11.86 0.0024 0.0008 12 0.00000 0.00000 -0.13 8.70 0.0066 0.0027 13 0.00000 0.00000 1.17 9.78 0.0070 0.0021 14 0.00000 0.00000 3.66 6.70 0.0151 0.0065 15 0.00000 0.00000 -1.27 3.85 0.0096 0.0045 The magnetic center is at X = 926.6 +- 0.7 microns Y = -24.8 +- 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 ^ | N S --> x S N Date: 09-11-1996 Time: 13:07:03 Magnet Name: 2902 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.994084 +- 7.554672E-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 -93.43 0.12 1.6431 0.0023 2 0.00234 0.00000 89.74 0.00 100.0000 0.0151 3 0.00000 0.00000 25.67 9.78 0.0086 0.0021 4 0.00000 0.00000 25.93 1.59 0.0213 0.0018 5 0.00000 0.00000 -11.39 25.55 0.0220 0.0158 6 0.00000 0.00000 0.52 28.53 0.1391 0.0057 7 0.00000 0.00000 -4.25 15.60 0.0346 0.0055 8 0.00000 0.00000 1.93 9.22 0.0098 0.0017 9 0.00000 0.00000 -1.16 14.85 0.0046 0.0023 10 0.00000 0.00000 2.49 4.28 0.0036 0.0018 11 0.00000 0.00000 -11.68 2.32 0.0034 0.0017 12 0.00000 0.00000 -0.27 9.01 0.0043 0.0019 13 0.00000 0.00000 3.07 9.01 0.0054 0.0020 14 0.00000 0.00000 -4.52 5.60 0.0164 0.0056 15 0.00000 0.00000 -1.17 2.66 0.0123 0.0048 The magnetic center is at X = 732.7 +- 1.0 microns Y = 43.9 +- 1.5 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) 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)