SLAC Magnetic Measurements Date: 04-18-1995 Time: 06:18:54 Magnet Name (Serial #): 191 Bar Code Number: 586 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl Run Number: 2 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: 04-18-1995 Time: 07:06:09 Magnet Name: 191 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00113 +- 6.326021E-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 0.00005 0.00000 -144.35 0.30 0.3318 0.0041 2 0.01486 0.00000 45.03 0.00 100.0000 0.0000 3 0.00002 0.00000 25.81 0.79 0.1037 0.0023 4 0.00000 0.00000 34.12 3.49 0.0069 0.0027 5 0.00000 0.00000 14.70 2.32 0.0141 0.0030 6 0.00003 0.00000 15.25 0.08 0.2161 0.0012 7 0.00000 0.00000 13.44 3.07 0.0034 0.0005 8 0.00000 0.00000 -9.53 5.28 0.0019 0.0008 9 0.00000 0.00000 3.43 0.27 0.0105 0.0016 10 0.00004 0.00000 -9.00 0.04 0.2954 0.0005 11 0.00000 0.00000 -9.03 5.22 0.0014 0.0006 12 0.00000 0.00000 -2.33 6.08 0.0033 0.0011 13 0.00000 0.00000 0.80 0.48 0.0110 0.0044 14 0.00004 0.00000 -6.41 0.02 0.2566 0.0020 15 0.00000 0.00000 -6.86 2.21 0.0069 0.0033 16 0.00000 0.00000 1.94 7.53 0.0041 0.0021 The magnetic center is at X = 86.4 +- 1.2 microns Y = 120.4 +- 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: 04-18-1995 Time: 07:12:14 Magnet Name: 191 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10298 +- 9.390181E-05 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 -152.82 0.98 0.2858 0.0030 2 0.03496 0.00001 45.03 0.00 100.0000 0.0000 3 0.00003 0.00000 33.89 0.70 0.0763 0.0010 4 0.00000 0.00000 21.80 38.46 0.0132 0.0013 5 0.00000 0.00000 12.10 3.75 0.0125 0.0015 6 0.00008 0.00000 15.25 0.09 0.2180 0.0007 7 0.00000 0.00000 8.07 1.39 0.0040 0.0008 8 0.00000 0.00000 -9.83 18.70 0.0073 0.0003 9 0.00000 0.00000 3.13 1.14 0.0090 0.0012 10 0.00010 0.00000 -9.02 0.03 0.2984 0.0004 11 0.00000 0.00000 -5.39 9.08 0.0030 0.0011 12 0.00000 0.00000 -0.27 1.69 0.0090 0.0018 13 0.00000 0.00000 1.99 1.50 0.0106 0.0033 14 0.00009 0.00000 -6.45 0.02 0.2560 0.0013 15 0.00000 0.00000 -5.99 1.50 0.0104 0.0022 16 0.00000 0.00000 5.91 1.75 0.0046 0.0029 The magnetic center is at X = 58.3 +- 2.0 microns Y = 113.6 +- 1.6 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 ^ | N S --> x S N Date: 04-18-1995 Time: 07:18:26 Magnet Name: 191 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.06697 +- 4.172824E-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 0.00020 0.00000 -160.34 0.64 0.2837 0.0024 2 0.06889 0.00003 45.03 0.00 100.0000 0.0000 3 0.00005 0.00000 35.27 0.85 0.0770 0.0032 4 0.00000 0.00000 -21.10 38.03 0.0072 0.0023 5 0.00001 0.00000 12.05 0.66 0.0123 0.0032 6 0.00015 0.00000 15.28 0.05 0.2180 0.0011 7 0.00000 0.00000 6.64 2.15 0.0046 0.0010 8 0.00000 0.00000 -5.69 1.84 0.0027 0.0005 9 0.00001 0.00000 2.63 0.47 0.0091 0.0014 10 0.00021 0.00000 -8.99 0.02 0.2985 0.0019 11 0.00000 0.00000 -10.14 1.83 0.0030 0.0016 12 0.00000 0.00000 2.63 8.32 0.0026 0.0022 13 0.00001 0.00000 0.92 1.02 0.0109 0.0035 14 0.00017 0.00000 -6.41 0.06 0.2535 0.0016 15 0.00000 0.00000 -2.30 8.33 0.0065 0.0022 16 0.00000 0.00000 1.50 7.20 0.0046 0.0031 The magnetic center is at X = 42.6 +- 1.4 microns Y = 119.3 +- 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: 04-18-1995 Time: 07:24:42 Magnet Name: 191 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0647 +- 2.277665E-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 0.00040 0.00001 -164.77 0.51 0.2918 0.0067 2 0.13741 0.00001 45.03 0.00 100.0000 0.0000 3 0.00010 0.00001 35.37 0.98 0.0742 0.0050 4 0.00001 0.00000 -38.43 2.94 0.0082 0.0016 5 0.00001 0.00000 11.85 0.33 0.0109 0.0033 6 0.00030 0.00000 15.28 0.00 0.2178 0.0012 7 0.00000 0.00000 7.65 3.81 0.0034 0.0012 8 0.00000 0.00000 -3.75 1.98 0.0036 0.0007 9 0.00001 0.00000 2.32 0.97 0.0087 0.0010 10 0.00041 0.00000 -8.97 0.02 0.3007 0.0012 11 0.00000 0.00000 -7.45 2.17 0.0020 0.0008 12 0.00000 0.00000 0.49 8.11 0.0026 0.0011 13 0.00002 0.00000 2.07 0.57 0.0150 0.0004 14 0.00035 0.00000 -6.41 0.02 0.2546 0.0034 15 0.00002 0.00000 -7.39 0.44 0.0122 0.0016 16 0.00001 0.00000 3.07 2.91 0.0084 0.0020 The magnetic center is at X = 34.2 +- 1.4 microns Y = 125.8 +- 2.9 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: 04-18-1995 Time: 07:30:57 Magnet Name: 191 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0807 +- 4.611841E-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 0.00062 0.00000 -166.51 0.70 0.3000 0.0015 2 0.20570 0.00002 45.00 0.00 100.0000 0.0000 3 0.00015 0.00001 34.86 1.09 0.0748 0.0043 4 0.00002 0.00000 -37.73 4.31 0.0075 0.0024 5 0.00002 0.00000 10.54 1.96 0.0101 0.0010 6 0.00043 0.00000 15.26 0.04 0.2070 0.0010 7 0.00001 0.00000 3.65 2.10 0.0047 0.0004 8 0.00001 0.00000 -3.44 2.76 0.0035 0.0008 9 0.00002 0.00000 2.31 0.77 0.0105 0.0008 10 0.00063 0.00000 -9.02 0.03 0.3045 0.0017 11 0.00000 0.00000 1.84 6.61 0.0022 0.0010 12 0.00001 0.00000 -6.31 10.93 0.0051 0.0020 13 0.00003 0.00001 1.67 1.53 0.0128 0.0049 14 0.00052 0.00000 -6.43 0.02 0.2548 0.0005 15 0.00002 0.00000 -7.98 2.29 0.0074 0.0021 16 0.00001 0.00001 -1.26 7.25 0.0059 0.0028 The magnetic center is at X = 31.3 +- 1.6 microns Y = 130.3 +- 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: 04-18-1995 Time: 07:37:13 Magnet Name: 191 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3279 +- 4.034211E-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 0.00082 0.00001 -165.84 0.91 0.2984 0.0031 2 0.27355 0.00006 45.00 0.00 100.0000 0.0000 3 0.00020 0.00001 35.50 1.40 0.0729 0.0029 4 0.00007 0.00000 -41.80 1.42 0.0238 0.0011 5 0.00003 0.00000 11.33 2.91 0.0108 0.0004 6 0.00054 0.00000 15.29 0.06 0.1976 0.0008 7 0.00001 0.00000 3.90 3.44 0.0039 0.0007 8 0.00003 0.00000 -1.30 0.45 0.0107 0.0008 9 0.00003 0.00000 2.09 1.47 0.0094 0.0013 10 0.00084 0.00001 -9.01 0.01 0.3079 0.0019 11 0.00001 0.00000 0.58 10.20 0.0019 0.0006 12 0.00001 0.00000 -9.76 1.22 0.0023 0.0010 13 0.00004 0.00001 1.89 1.78 0.0147 0.0019 14 0.00070 0.00001 -6.39 0.02 0.2556 0.0021 15 0.00003 0.00001 -7.03 0.82 0.0099 0.0033 16 0.00002 0.00001 0.76 7.07 0.0068 0.0021 The magnetic center is at X = 32.6 +- 2.1 microns Y = 129.3 +- 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: 04-18-1995 Time: 07:43:29 Magnet Name: 191 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.431 +- 3.494562E-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 0.00101 0.00002 -162.57 0.32 0.2993 0.0062 2 0.33855 0.00006 45.00 0.00 100.0000 0.0000 3 0.00021 0.00001 36.60 0.87 0.0620 0.0030 4 0.00006 0.00000 -38.05 2.08 0.0191 0.0008 5 0.00003 0.00000 10.73 3.52 0.0097 0.0014 6 0.00059 0.00000 15.25 0.12 0.1750 0.0008 7 0.00001 0.00000 1.19 1.92 0.0040 0.0012 8 0.00001 0.00000 -15.19 1.20 0.0042 0.0011 9 0.00003 0.00000 1.22 0.83 0.0094 0.0008 10 0.00105 0.00000 -9.03 0.02 0.3104 0.0006 11 0.00001 0.00000 -1.75 7.70 0.0015 0.0009 12 0.00003 0.00000 -1.70 1.31 0.0090 0.0014 13 0.00004 0.00000 1.84 1.37 0.0132 0.0014 14 0.00085 0.00001 -6.47 0.04 0.2511 0.0023 15 0.00002 0.00000 -6.72 1.44 0.0072 0.0012 16 0.00002 0.00000 3.35 7.61 0.0061 0.0006 The magnetic center is at X = 40.0 +- 1.1 microns Y = 127.5 +- 2.7 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: 04-18-1995 Time: 07:49:45 Magnet Name: 191 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4203 +- 7.903699E-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 0.00002 -157.10 0.50 0.3344 0.0052 2 0.39055 0.00003 45.00 0.00 100.0000 0.0000 3 0.00014 0.00002 33.75 1.73 0.0350 0.0041 4 0.00006 0.00001 -33.52 1.70 0.0164 0.0019 5 0.00003 0.00001 8.52 1.74 0.0074 0.0030 6 0.00048 0.00000 15.31 0.03 0.1220 0.0009 7 0.00002 0.00000 4.61 1.50 0.0039 0.0006 8 0.00002 0.00000 -16.91 1.31 0.0046 0.0005 9 0.00004 0.00001 2.71 0.99 0.0102 0.0016 10 0.00125 0.00001 -9.01 0.02 0.3199 0.0014 11 0.00001 0.00000 -3.35 11.03 0.0016 0.0008 12 0.00002 0.00001 -3.10 3.56 0.0042 0.0014 13 0.00005 0.00001 1.91 1.16 0.0135 0.0038 14 0.00100 0.00001 -6.42 0.03 0.2551 0.0020 15 0.00004 0.00001 -7.29 0.62 0.0106 0.0020 16 0.00004 0.00002 0.50 2.21 0.0094 0.0056 The magnetic center is at X = 58.1 +- 1.5 microns Y = 137.6 +- 2.2 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 ^ | N S --> x S N Date: 04-18-1995 Time: 07:56:02 Magnet Name: 191 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4285 +- 4.531629E-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 0.00148 0.00001 -154.81 0.64 0.3470 0.0035 2 0.42711 0.00006 45.00 0.00 100.0000 0.0000 3 0.00011 0.00001 31.44 2.80 0.0265 0.0031 4 0.00007 0.00000 -33.57 2.34 0.0166 0.0010 5 0.00003 0.00001 5.77 2.66 0.0075 0.0025 6 0.00027 0.00000 15.72 0.17 0.0638 0.0002 7 0.00002 0.00000 4.24 2.39 0.0039 0.0010 8 0.00001 0.00000 -10.94 1.38 0.0031 0.0009 9 0.00005 0.00001 2.91 0.51 0.0114 0.0013 10 0.00141 0.00001 -9.01 0.02 0.3295 0.0015 11 0.00001 0.00000 -11.29 4.12 0.0016 0.0006 12 0.00001 0.00001 -1.24 12.02 0.0029 0.0018 13 0.00006 0.00001 0.52 1.21 0.0132 0.0019 14 0.00109 0.00001 -6.41 0.03 0.2542 0.0031 15 0.00002 0.00001 -5.53 2.65 0.0051 0.0020 16 0.00003 0.00001 1.17 2.61 0.0079 0.0025 The magnetic center is at X = 66.0 +- 1.7 microns Y = 140.3 +- 1.6 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 ^ | 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)