SLAC Magnetic Measurements Date: 04-11-1995 Time: 09:35:51 Magnet Name (Serial #): 136 Bar Code Number: 386 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl Run Number: 1 Comment: 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: 04-11-1995 Time: 10:22:59 Magnet Name: 136 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00677 +- 3.080612E-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 0.00002 0.00000 152.07 1.16 0.1401 0.0024 2 0.01489 0.00000 44.97 0.00 100.0000 0.0000 3 0.00002 0.00000 29.01 0.22 0.1157 0.0028 4 0.00000 0.00000 18.23 1.51 0.0235 0.0023 5 0.00000 0.00000 11.73 0.41 0.0248 0.0024 6 0.00003 0.00000 15.18 0.08 0.2245 0.0015 7 0.00000 0.00000 11.12 1.48 0.0096 0.0013 8 0.00000 0.00000 6.70 16.68 0.0029 0.0014 9 0.00000 0.00000 2.37 2.13 0.0049 0.0010 10 0.00004 0.00000 -9.15 0.02 0.3021 0.0019 11 0.00000 0.00000 -3.36 12.40 0.0017 0.0007 12 0.00000 0.00000 7.34 12.13 0.0087 0.0022 13 0.00000 0.00000 -3.00 1.90 0.0146 0.0033 14 0.00004 0.00000 -6.41 0.03 0.2598 0.0019 15 0.00000 0.00000 -3.31 9.07 0.0089 0.0033 16 0.00000 0.00000 4.46 1.12 0.0088 0.0036 The magnetic center is at X = -29.3 +- 1.2 microns Y = 55.3 +- 1.1 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 ^ | N S --> x S N Date: 04-11-1995 Time: 10:29:05 Magnet Name: 136 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.11156 +- 8.369616E-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 0.00010 0.00000 146.90 0.79 0.2784 0.0027 2 0.03498 0.00001 44.96 0.00 100.0000 0.0000 3 0.00004 0.00000 23.56 0.57 0.1069 0.0035 4 0.00001 0.00000 20.34 0.70 0.0212 0.0019 5 0.00001 0.00000 11.48 0.39 0.0216 0.0013 6 0.00008 0.00000 15.21 0.06 0.2260 0.0007 7 0.00000 0.00000 11.63 1.88 0.0120 0.0007 8 0.00000 0.00000 21.59 0.40 0.0106 0.0019 9 0.00000 0.00000 1.07 3.36 0.0060 0.0016 10 0.00011 0.00000 -9.15 0.03 0.3007 0.0013 11 0.00000 0.00000 -2.27 8.42 0.0027 0.0019 12 0.00000 0.00000 -3.89 9.84 0.0020 0.0008 13 0.00000 0.00000 -1.34 2.12 0.0103 0.0047 14 0.00009 0.00000 -6.43 0.02 0.2580 0.0022 15 0.00000 0.00000 -6.10 0.58 0.0097 0.0054 16 0.00000 0.00000 3.74 1.32 0.0066 0.0009 The magnetic center is at X = -67.9 +- 1.6 microns Y = 104.2 +- 1.4 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 ^ | N S --> x S N Date: 04-11-1995 Time: 10:35:16 Magnet Name: 136 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.07528 +- 3.815556E-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 0.00022 0.00000 145.38 0.43 0.3246 0.0043 2 0.06889 0.00001 44.96 0.00 100.0000 0.0000 3 0.00007 0.00000 21.89 0.52 0.1027 0.0020 4 0.00001 0.00000 16.42 1.18 0.0211 0.0016 5 0.00001 0.00000 11.83 1.28 0.0210 0.0019 6 0.00016 0.00000 15.20 0.07 0.2252 0.0016 7 0.00001 0.00000 11.36 1.08 0.0107 0.0009 8 0.00000 0.00000 16.08 5.75 0.0018 0.0006 9 0.00000 0.00000 1.75 1.01 0.0054 0.0012 10 0.00021 0.00000 -9.15 0.02 0.3007 0.0022 11 0.00000 0.00000 0.42 7.06 0.0022 0.0005 12 0.00001 0.00000 5.63 11.82 0.0074 0.0022 13 0.00001 0.00000 -2.87 1.26 0.0103 0.0043 14 0.00018 0.00000 -6.45 0.05 0.2567 0.0016 15 0.00001 0.00000 -7.36 1.18 0.0096 0.0024 16 0.00000 0.00000 6.61 1.65 0.0069 0.0033 The magnetic center is at X = -82.4 +- 1.4 microns Y = 119.3 +- 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 ^ | N S --> x S N Date: 04-11-1995 Time: 10:41:32 Magnet Name: 136 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0688 +- 1.403684E-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 0.00048 0.00001 144.14 0.33 0.3466 0.0043 2 0.13745 0.00002 44.96 0.00 100.0000 0.0000 3 0.00014 0.00000 21.50 0.33 0.1034 0.0030 4 0.00003 0.00000 17.44 1.42 0.0208 0.0012 5 0.00003 0.00000 12.20 1.18 0.0207 0.0014 6 0.00031 0.00000 15.21 0.06 0.2255 0.0018 7 0.00001 0.00000 11.79 1.33 0.0102 0.0007 8 0.00000 0.00000 4.60 15.23 0.0021 0.0012 9 0.00001 0.00000 2.52 1.43 0.0055 0.0012 10 0.00042 0.00000 -9.12 0.01 0.3054 0.0020 11 0.00000 0.00000 4.55 5.90 0.0014 0.0005 12 0.00001 0.00000 -1.02 13.84 0.0077 0.0015 13 0.00001 0.00000 -2.85 1.56 0.0092 0.0023 14 0.00035 0.00000 -6.44 0.02 0.2576 0.0020 15 0.00001 0.00000 -7.14 1.05 0.0107 0.0023 16 0.00001 0.00001 4.09 1.58 0.0102 0.0041 The magnetic center is at X = -90.7 +- 1.3 microns Y = 125.5 +- 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 ^ | N S --> x S N Date: 04-11-1995 Time: 10:47:47 Magnet Name: 136 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0832 +- 1.469109E-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 0.00073 0.00001 145.68 0.28 0.3526 0.0025 2 0.20567 0.00003 44.94 0.00 100.0000 0.0000 3 0.00021 0.00001 19.99 0.16 0.1007 0.0034 4 0.00004 0.00000 16.28 1.72 0.0209 0.0020 5 0.00004 0.00000 11.89 1.54 0.0201 0.0017 6 0.00045 0.00000 15.26 0.04 0.2166 0.0018 7 0.00002 0.00000 12.26 1.45 0.0089 0.0021 8 0.00000 0.00000 0.23 18.43 0.0012 0.0007 9 0.00001 0.00000 1.33 2.35 0.0062 0.0015 10 0.00063 0.00000 -9.20 0.04 0.3074 0.0015 11 0.00001 0.00000 6.74 4.75 0.0028 0.0010 12 0.00002 0.00000 13.97 0.60 0.0089 0.0019 13 0.00002 0.00001 -2.14 0.57 0.0085 0.0026 14 0.00053 0.00000 -6.48 0.04 0.2563 0.0011 15 0.00002 0.00001 -7.55 1.35 0.0121 0.0029 16 0.00002 0.00000 5.27 2.15 0.0107 0.0002 The magnetic center is at X = -88.8 +- 0.9 microns Y = 130.1 +- 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 ^ | N S --> x S N Date: 04-11-1995 Time: 10:54:03 Magnet Name: 136 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3361 +- 4.898285E-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 0.00097 0.00001 144.04 0.18 0.3557 0.0025 2 0.27338 0.00004 44.94 0.00 100.0000 0.0000 3 0.00028 0.00001 20.38 0.27 0.1006 0.0024 4 0.00005 0.00001 27.88 1.73 0.0180 0.0021 5 0.00005 0.00001 12.19 1.64 0.0196 0.0025 6 0.00057 0.00001 15.21 0.07 0.2076 0.0019 7 0.00003 0.00001 12.48 1.26 0.0103 0.0019 8 0.00001 0.00000 1.33 1.63 0.0054 0.0010 9 0.00002 0.00000 1.52 0.69 0.0069 0.0015 10 0.00085 0.00000 -9.17 0.03 0.3094 0.0016 11 0.00001 0.00000 -0.94 8.39 0.0029 0.0009 12 0.00002 0.00000 -5.97 11.62 0.0069 0.0012 13 0.00004 0.00001 -2.19 0.74 0.0143 0.0029 14 0.00071 0.00000 -6.46 0.02 0.2581 0.0016 15 0.00003 0.00001 -7.89 0.84 0.0112 0.0028 16 0.00002 0.00001 4.28 4.91 0.0072 0.0036 The magnetic center is at X = -93.3 +- 0.8 microns Y = 128.6 +- 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: 04-11-1995 Time: 11:00:20 Magnet Name: 136 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4416 +- 4.294882E-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 0.00120 0.00001 144.02 0.53 0.3549 0.0029 2 0.33829 0.00002 44.94 0.00 100.0000 0.0000 3 0.00035 0.00001 20.15 0.39 0.1035 0.0020 4 0.00005 0.00001 22.36 1.52 0.0155 0.0027 5 0.00007 0.00001 11.89 0.70 0.0194 0.0027 6 0.00063 0.00001 15.31 0.10 0.1850 0.0018 7 0.00004 0.00000 11.12 1.55 0.0115 0.0014 8 0.00002 0.00001 0.01 21.44 0.0059 0.0023 9 0.00002 0.00001 3.28 1.60 0.0061 0.0019 10 0.00105 0.00000 -9.16 0.00 0.3106 0.0005 11 0.00001 0.00000 5.80 2.19 0.0039 0.0006 12 0.00001 0.00001 3.43 7.20 0.0037 0.0015 13 0.00004 0.00001 -1.55 2.38 0.0114 0.0028 14 0.00087 0.00001 -6.46 0.01 0.2562 0.0023 15 0.00004 0.00002 -7.32 2.33 0.0114 0.0057 16 0.00002 0.00000 8.67 0.68 0.0063 0.0008 The magnetic center is at X = -93.1 +- 1.4 microns Y = 128.3 +- 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: 04-11-1995 Time: 11:06:37 Magnet Name: 136 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4255 +- 1.100115E-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 0.00127 0.00001 138.47 0.27 0.3254 0.0019 2 0.38993 0.00003 44.94 0.00 100.0000 0.0000 3 0.00037 0.00001 24.60 0.51 0.0958 0.0029 4 0.00005 0.00001 16.28 1.25 0.0137 0.0024 5 0.00008 0.00001 10.92 1.28 0.0196 0.0027 6 0.00051 0.00000 15.40 0.12 0.1310 0.0009 7 0.00004 0.00000 10.95 1.68 0.0097 0.0012 8 0.00003 0.00000 10.17 18.44 0.0073 0.0004 9 0.00002 0.00000 2.72 1.97 0.0052 0.0010 10 0.00126 0.00001 -9.13 0.03 0.3225 0.0015 11 0.00001 0.00000 -2.11 2.81 0.0021 0.0012 12 0.00002 0.00000 -0.57 13.49 0.0050 0.0011 13 0.00005 0.00001 -1.36 1.56 0.0130 0.0028 14 0.00101 0.00001 -6.46 0.03 0.2589 0.0025 15 0.00004 0.00002 -3.74 8.56 0.0098 0.0041 16 0.00004 0.00002 3.48 0.84 0.0105 0.0050 The magnetic center is at X = -96.4 +- 0.8 microns Y = 108.8 +- 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: 04-11-1995 Time: 11:12:53 Magnet Name: 136 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4328 +- 7.739982E-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 0.00131 0.00000 134.85 0.51 0.3062 0.0010 2 0.42628 0.00013 44.94 0.00 100.0000 0.0000 3 0.00039 0.00000 27.63 0.84 0.0908 0.0005 4 0.00005 0.00001 16.97 2.88 0.0113 0.0013 5 0.00009 0.00001 10.33 1.58 0.0211 0.0017 6 0.00031 0.00001 15.62 0.24 0.0725 0.0016 7 0.00004 0.00000 10.18 0.90 0.0094 0.0009 8 0.00002 0.00000 10.64 18.11 0.0051 0.0009 9 0.00002 0.00001 1.29 1.98 0.0051 0.0013 10 0.00142 0.00001 -9.17 0.04 0.3320 0.0013 11 0.00001 0.00000 3.38 7.23 0.0023 0.0009 12 0.00004 0.00001 0.06 14.43 0.0085 0.0018 13 0.00004 0.00001 -2.44 2.19 0.0101 0.0019 14 0.00109 0.00001 -6.43 0.02 0.2547 0.0025 15 0.00006 0.00002 -6.49 1.23 0.0131 0.0038 16 0.00005 0.00003 2.48 1.70 0.0109 0.0059 The magnetic center is at X = -97.0 +- 0.9 microns Y = 96.5 +- 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 ^ | 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) 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)