SLAC Magnetic Measurements Date: 04-17-1995 Time: 11:54:53 Magnet Name (Serial #): 164 Bar Code Number: 514 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: 04-17-1995 Time: 12:42:01 Magnet Name: 164 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 9.999775 +- 5.529747E-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 0.00007 0.00000 -127.25 0.23 0.4826 0.0022 2 0.01494 0.00000 45.03 0.00 100.0000 0.0000 3 0.00001 0.00000 6.11 0.32 0.0937 0.0042 4 0.00000 0.00000 25.91 2.25 0.0158 0.0020 5 0.00000 0.00000 21.53 1.16 0.0137 0.0022 6 0.00003 0.00000 14.98 0.06 0.2166 0.0024 7 0.00000 0.00000 13.55 0.40 0.0105 0.0008 8 0.00000 0.00000 0.04 21.66 0.0067 0.0008 9 0.00000 0.00000 5.31 1.02 0.0126 0.0009 10 0.00004 0.00000 -9.00 0.02 0.2979 0.0015 11 0.00000 0.00000 1.86 2.05 0.0026 0.0011 12 0.00000 0.00000 12.04 1.91 0.0070 0.0019 13 0.00000 0.00000 2.69 1.85 0.0137 0.0041 14 0.00004 0.00000 -6.31 0.03 0.2604 0.0017 15 0.00000 0.00000 -6.04 1.31 0.0112 0.0027 16 0.00000 0.00000 7.04 1.72 0.0069 0.0021 The magnetic center is at X = 171.6 +- 1.0 microns Y = 130.5 +- 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 Date: 04-17-1995 Time: 12:48:07 Magnet Name: 164 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10193 +- 8.325276E-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 0.00012 0.00000 -149.12 0.26 0.3354 0.0031 2 0.03498 0.00000 45.03 0.00 100.0000 0.0000 3 0.00003 0.00000 18.74 0.59 0.0986 0.0011 4 0.00001 0.00000 31.56 1.46 0.0165 0.0018 5 0.00001 0.00000 19.18 1.67 0.0173 0.0014 6 0.00008 0.00000 15.02 0.11 0.2201 0.0016 7 0.00000 0.00000 10.46 2.13 0.0075 0.0026 8 0.00000 0.00000 11.16 19.25 0.0142 0.0008 9 0.00000 0.00000 5.30 0.86 0.0110 0.0009 10 0.00010 0.00000 -9.02 0.01 0.2981 0.0011 11 0.00000 0.00000 -0.11 8.36 0.0031 0.0007 12 0.00000 0.00000 1.76 6.80 0.0045 0.0013 13 0.00000 0.00000 1.91 1.17 0.0139 0.0033 14 0.00009 0.00000 -6.34 0.03 0.2611 0.0031 15 0.00000 0.00000 -8.66 1.67 0.0104 0.0037 16 0.00000 0.00000 5.81 3.61 0.0040 0.0016 The magnetic center is at X = 76.9 +- 0.9 microns Y = 128.6 +- 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 ^ | N S --> x S N Date: 04-17-1995 Time: 12:54:18 Magnet Name: 164 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.06608 +- 3.787756E-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 -158.60 0.51 0.3250 0.0020 2 0.06884 0.00001 45.03 0.00 100.0000 0.0000 3 0.00007 0.00000 20.48 0.32 0.1030 0.0020 4 0.00001 0.00000 29.16 2.59 0.0111 0.0016 5 0.00001 0.00000 16.98 0.78 0.0163 0.0010 6 0.00015 0.00000 15.02 0.06 0.2206 0.0022 7 0.00000 0.00000 9.45 1.41 0.0070 0.0008 8 0.00000 0.00000 21.19 0.65 0.0058 0.0006 9 0.00001 0.00000 4.66 0.63 0.0098 0.0020 10 0.00021 0.00000 -8.99 0.03 0.3007 0.0004 11 0.00000 0.00000 -1.47 1.64 0.0028 0.0013 12 0.00000 0.00000 0.40 12.29 0.0048 0.0007 13 0.00001 0.00000 2.31 1.47 0.0130 0.0020 14 0.00018 0.00000 -6.32 0.04 0.2552 0.0023 15 0.00001 0.00000 -6.74 0.15 0.0129 0.0030 16 0.00000 0.00000 1.96 7.73 0.0068 0.0007 The magnetic center is at X = 53.0 +- 1.3 microns Y = 135.1 +- 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: 04-17-1995 Time: 13:00:34 Magnet Name: 164 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0634 +- 1.009245E-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 0.00046 0.00000 -163.69 0.31 0.3318 0.0012 2 0.13730 0.00002 45.03 0.00 100.0000 0.0000 3 0.00015 0.00000 20.11 0.26 0.1070 0.0015 4 0.00001 0.00000 29.67 2.77 0.0103 0.0013 5 0.00002 0.00000 17.95 1.13 0.0153 0.0010 6 0.00030 0.00000 14.99 0.05 0.2221 0.0011 7 0.00001 0.00000 9.52 1.16 0.0069 0.0013 8 0.00001 0.00000 0.68 21.22 0.0047 0.0010 9 0.00001 0.00000 5.24 1.20 0.0096 0.0011 10 0.00042 0.00000 -9.00 0.03 0.3031 0.0025 11 0.00000 0.00000 0.13 3.16 0.0031 0.0008 12 0.00000 0.00000 3.52 10.79 0.0030 0.0011 13 0.00002 0.00000 2.45 1.11 0.0139 0.0021 14 0.00035 0.00000 -6.30 0.04 0.2581 0.0011 15 0.00001 0.00001 -6.83 1.69 0.0105 0.0038 16 0.00000 0.00000 -1.98 5.24 0.0016 0.0004 The magnetic center is at X = 41.6 +- 0.8 microns Y = 142.2 +- 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 ^ | N S --> x S N Date: 04-17-1995 Time: 13:06:48 Magnet Name: 164 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0824 +- 9.880582E-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 0.00068 0.00001 -166.12 0.05 0.3325 0.0033 2 0.20549 0.00001 45.00 0.00 100.0000 0.0000 3 0.00023 0.00001 20.38 0.35 0.1107 0.0026 4 0.00002 0.00001 28.43 3.72 0.0106 0.0024 5 0.00003 0.00000 19.47 1.44 0.0158 0.0018 6 0.00044 0.00000 14.94 0.03 0.2126 0.0015 7 0.00001 0.00000 8.49 0.64 0.0066 0.0010 8 0.00001 0.00000 10.40 18.48 0.0061 0.0006 9 0.00002 0.00000 5.35 1.07 0.0094 0.0009 10 0.00063 0.00000 -9.02 0.03 0.3052 0.0006 11 0.00001 0.00000 1.78 3.03 0.0030 0.0009 12 0.00001 0.00000 6.22 11.99 0.0062 0.0009 13 0.00003 0.00001 2.56 0.83 0.0137 0.0027 14 0.00053 0.00001 -6.36 0.02 0.2583 0.0027 15 0.00002 0.00001 -7.58 1.53 0.0111 0.0031 16 0.00002 0.00000 3.13 8.02 0.0078 0.0012 The magnetic center is at X = 35.6 +- 0.4 microns Y = 144.2 +- 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: 04-17-1995 Time: 13:13:03 Magnet Name: 164 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3293 +- 1.50208E-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 0.00089 0.00001 -168.49 0.45 0.3267 0.0021 2 0.27316 0.00003 45.00 0.00 100.0000 0.0000 3 0.00031 0.00001 21.10 0.38 0.1144 0.0022 4 0.00005 0.00000 38.36 2.27 0.0197 0.0007 5 0.00004 0.00000 17.69 1.34 0.0161 0.0012 6 0.00056 0.00000 14.93 0.10 0.2037 0.0002 7 0.00002 0.00000 8.88 1.15 0.0059 0.0012 8 0.00001 0.00000 2.84 3.03 0.0035 0.0007 9 0.00003 0.00000 4.72 0.75 0.0118 0.0016 10 0.00083 0.00000 -9.00 0.03 0.3056 0.0008 11 0.00001 0.00000 -6.01 6.18 0.0019 0.0012 12 0.00001 0.00000 1.93 10.61 0.0045 0.0013 13 0.00003 0.00000 2.08 0.45 0.0122 0.0017 14 0.00071 0.00001 -6.36 0.04 0.2602 0.0026 15 0.00002 0.00001 -6.54 1.82 0.0065 0.0032 16 0.00002 0.00001 3.40 8.37 0.0084 0.0044 The magnetic center is at X = 29.1 +- 1.2 microns Y = 143.0 +- 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: 04-17-1995 Time: 13:19:20 Magnet Name: 164 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4339 +- 1.054845E-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 0.00104 0.00000 -170.17 0.07 0.3087 0.0011 2 0.33795 0.00007 45.00 0.00 100.0000 0.0000 3 0.00039 0.00000 22.51 0.25 0.1164 0.0008 4 0.00005 0.00001 34.64 2.67 0.0134 0.0018 5 0.00005 0.00001 17.65 1.56 0.0139 0.0028 6 0.00061 0.00000 14.97 0.05 0.1812 0.0014 7 0.00002 0.00000 6.84 3.23 0.0070 0.0010 8 0.00003 0.00000 10.61 18.83 0.0100 0.0008 9 0.00004 0.00000 5.28 0.62 0.0109 0.0010 10 0.00104 0.00000 -9.01 0.04 0.3081 0.0011 11 0.00001 0.00000 -0.42 2.71 0.0040 0.0010 12 0.00001 0.00001 5.76 3.48 0.0040 0.0021 13 0.00004 0.00001 2.70 1.19 0.0107 0.0020 14 0.00087 0.00001 -6.30 0.05 0.2580 0.0038 15 0.00003 0.00001 -5.40 2.56 0.0094 0.0032 16 0.00002 0.00001 4.15 7.92 0.0064 0.0027 The magnetic center is at X = 23.5 +- 0.2 microns Y = 135.9 +- 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 ^ | N S --> x S N Date: 04-17-1995 Time: 13:25:35 Magnet Name: 164 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4218 +- 1.192628E-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 0.00108 0.00001 -166.40 0.31 0.2778 0.0013 2 0.38987 0.00003 45.00 0.00 100.0000 0.0000 3 0.00040 0.00000 25.16 0.35 0.1016 0.0004 4 0.00004 0.00001 30.04 3.11 0.0092 0.0015 5 0.00006 0.00001 15.62 1.74 0.0144 0.0025 6 0.00050 0.00000 14.90 0.07 0.1281 0.0008 7 0.00002 0.00001 5.30 0.69 0.0064 0.0015 8 0.00005 0.00000 10.98 19.25 0.0120 0.0012 9 0.00003 0.00001 5.58 1.19 0.0090 0.0013 10 0.00124 0.00001 -9.03 0.02 0.3190 0.0021 11 0.00001 0.00001 0.79 4.45 0.0021 0.0013 12 0.00002 0.00001 1.81 10.02 0.0049 0.0016 13 0.00005 0.00001 1.90 1.88 0.0131 0.0022 14 0.00102 0.00001 -6.35 0.05 0.2612 0.0025 15 0.00003 0.00001 -3.81 4.06 0.0078 0.0032 16 0.00003 0.00001 1.58 1.74 0.0072 0.0026 The magnetic center is at X = 29.2 +- 0.7 microns Y = 120.6 +- 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 ^ | N S --> x S N Date: 04-17-1995 Time: 13:31:51 Magnet Name: 164 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4298 +- 9.101711E-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 0.00110 0.00001 -163.59 0.27 0.2590 0.0012 2 0.42617 0.00008 45.00 0.00 100.0000 0.0000 3 0.00041 0.00000 27.08 0.53 0.0958 0.0006 4 0.00004 0.00001 30.65 2.67 0.0103 0.0022 5 0.00006 0.00001 13.63 2.24 0.0147 0.0021 6 0.00030 0.00000 14.86 0.14 0.0709 0.0011 7 0.00003 0.00001 4.90 0.43 0.0079 0.0014 8 0.00004 0.00001 0.02 21.72 0.0099 0.0014 9 0.00004 0.00000 5.49 0.89 0.0098 0.0009 10 0.00141 0.00001 -9.02 0.02 0.3300 0.0012 11 0.00001 0.00001 3.82 6.89 0.0024 0.0017 12 0.00002 0.00001 0.28 12.99 0.0044 0.0022 13 0.00006 0.00001 2.17 1.56 0.0130 0.0026 14 0.00110 0.00001 -6.33 0.05 0.2572 0.0017 15 0.00004 0.00001 -6.82 1.36 0.0099 0.0034 16 0.00003 0.00001 1.17 3.05 0.0069 0.0022 The magnetic center is at X = 32.7 +- 0.5 microns Y = 111.0 +- 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 ^ | 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)