SLAC Magnetic Measurements Date: 02-27-1995 Time: 13:41:30 Magnet Name (Serial #): 103 Bar Code Number: 454 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: bmd 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: 02-27-1995 Time: 14:28:41 Magnet Name: 103 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00132 +- 2.908464E-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 0.00004 0.00000 -155.85 0.17 0.2853 0.0016 2 0.01485 0.00000 45.00 0.00 100.0000 0.0000 3 0.00001 0.00000 32.27 0.37 0.0597 0.0021 4 0.00000 0.00000 32.70 4.09 0.0096 0.0014 5 0.00000 0.00000 16.88 1.23 0.0151 0.0012 6 0.00003 0.00000 15.18 0.07 0.2195 0.0009 7 0.00000 0.00000 10.73 3.89 0.0025 0.0003 8 0.00000 0.00000 -7.21 17.11 0.0031 0.0007 9 0.00000 0.00000 -2.25 0.50 0.0111 0.0018 10 0.00004 0.00000 -8.97 0.04 0.3027 0.0013 11 0.00000 0.00000 -2.41 8.47 0.0031 0.0004 12 0.00000 0.00000 -5.01 3.03 0.0026 0.0007 13 0.00000 0.00000 -1.55 0.66 0.0154 0.0019 14 0.00004 0.00000 -6.41 0.02 0.2560 0.0014 15 0.00000 0.00000 0.77 7.35 0.0042 0.0023 16 0.00000 0.00000 4.27 6.81 0.0032 0.0010 The magnetic center is at X = 52.1 +- 0.4 microns Y = 116.3 +- 0.7 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: 02-27-1995 Time: 14:34:46 Magnet Name: 103 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10084 +- 1.061624E-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 0.00011 0.00000 -174.81 0.17 0.3205 0.0030 2 0.03502 0.00000 44.99 0.00 100.0000 0.0000 3 0.00002 0.00000 33.93 1.01 0.0485 0.0010 4 0.00000 0.00000 42.30 1.89 0.0112 0.0018 5 0.00001 0.00000 15.48 0.72 0.0173 0.0017 6 0.00008 0.00000 15.19 0.10 0.2228 0.0008 7 0.00000 0.00000 12.93 2.54 0.0034 0.0011 8 0.00000 0.00000 -21.36 0.88 0.0123 0.0011 9 0.00000 0.00000 -1.60 0.96 0.0116 0.0023 10 0.00011 0.00000 -8.98 0.02 0.3040 0.0017 11 0.00000 0.00000 -5.73 5.31 0.0034 0.0014 12 0.00000 0.00000 -3.59 1.75 0.0062 0.0026 13 0.00001 0.00000 -1.63 0.41 0.0150 0.0012 14 0.00009 0.00000 -6.40 0.03 0.2553 0.0008 15 0.00000 0.00000 -2.19 5.05 0.0055 0.0024 16 0.00000 0.00000 1.57 3.00 0.0075 0.0026 The magnetic center is at X = 13.0 +- 0.4 microns Y = 142.6 +- 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: 02-27-1995 Time: 14:40:56 Magnet Name: 103 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.06169 +- 7.10479E-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 0.00024 0.00000 178.70 0.17 0.3426 0.0011 2 0.06901 0.00001 44.99 0.00 100.0000 0.0000 3 0.00003 0.00000 33.26 0.60 0.0478 0.0010 4 0.00000 0.00000 -20.52 37.08 0.0072 0.0021 5 0.00001 0.00000 15.81 2.06 0.0166 0.0016 6 0.00015 0.00000 15.09 0.06 0.2243 0.0023 7 0.00000 0.00000 14.49 1.44 0.0042 0.0011 8 0.00000 0.00000 0.31 20.35 0.0046 0.0013 9 0.00001 0.00000 -1.72 0.75 0.0112 0.0006 10 0.00021 0.00000 -8.99 0.03 0.3019 0.0025 11 0.00000 0.00000 0.80 7.31 0.0016 0.0001 12 0.00000 0.00000 -7.89 3.48 0.0033 0.0017 13 0.00001 0.00000 -0.76 0.58 0.0141 0.0037 14 0.00017 0.00000 -6.43 0.02 0.2519 0.0005 15 0.00000 0.00000 -1.43 5.99 0.0065 0.0021 16 0.00000 0.00000 -4.92 8.50 0.0041 0.0011 The magnetic center is at X = -3.5 +- 0.5 microns Y = 153.0 +- 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 Date: 02-27-1995 Time: 14:47:10 Magnet Name: 103 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0522 +- 5.094871E-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 0.00049 0.00000 176.00 0.17 0.3549 0.0011 2 0.13774 0.00003 44.99 0.00 100.0000 0.0000 3 0.00006 0.00000 33.29 0.91 0.0454 0.0017 4 0.00001 0.00000 -38.69 3.54 0.0064 0.0018 5 0.00002 0.00000 15.35 2.03 0.0164 0.0018 6 0.00031 0.00000 15.11 0.04 0.2253 0.0018 7 0.00000 0.00000 12.87 1.41 0.0034 0.0006 8 0.00000 0.00000 -8.04 16.84 0.0027 0.0008 9 0.00002 0.00000 -2.11 0.45 0.0110 0.0010 10 0.00042 0.00000 -9.00 0.06 0.3041 0.0015 11 0.00000 0.00000 4.96 12.52 0.0024 0.0015 12 0.00001 0.00000 -12.61 2.68 0.0044 0.0016 13 0.00002 0.00000 -1.56 0.48 0.0139 0.0023 14 0.00035 0.00000 -6.42 0.05 0.2545 0.0020 15 0.00001 0.00000 -0.43 5.90 0.0055 0.0023 16 0.00001 0.00000 -3.68 4.92 0.0039 0.0020 The magnetic center is at X = -11.0 +- 0.5 microns Y = 158.1 +- 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: 02-27-1995 Time: 14:53:24 Magnet Name: 103 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0624 +- 7.350794E-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 0.00074 0.00001 176.23 0.05 0.3571 0.0027 2 0.20612 0.00002 44.97 0.00 100.0000 0.0000 3 0.00009 0.00000 33.83 1.20 0.0418 0.0017 4 0.00001 0.00000 -17.38 31.43 0.0054 0.0021 5 0.00004 0.00000 15.75 0.96 0.0174 0.0017 6 0.00045 0.00000 15.12 0.03 0.2175 0.0023 7 0.00001 0.00000 13.57 1.88 0.0034 0.0021 8 0.00001 0.00000 -8.32 15.91 0.0027 0.0006 9 0.00002 0.00000 -1.80 0.93 0.0100 0.0016 10 0.00064 0.00000 -9.02 0.01 0.3082 0.0009 11 0.00000 0.00000 -6.34 4.33 0.0021 0.0014 12 0.00001 0.00000 -4.55 10.48 0.0036 0.0016 13 0.00003 0.00000 -1.03 0.84 0.0166 0.0016 14 0.00052 0.00000 -6.41 0.04 0.2536 0.0017 15 0.00001 0.00000 0.27 5.54 0.0044 0.0016 16 0.00001 0.00001 3.24 7.91 0.0051 0.0026 The magnetic center is at X = -10.5 +- 0.2 microns Y = 159.2 +- 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: 02-27-1995 Time: 14:59:38 Magnet Name: 103 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3017 +- 9.004625E-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 0.00099 0.00000 176.93 0.36 0.3619 0.0013 2 0.27405 0.00002 44.97 0.00 100.0000 0.0000 3 0.00011 0.00001 32.54 1.33 0.0417 0.0027 4 0.00005 0.00001 -21.32 37.38 0.0178 0.0020 5 0.00005 0.00000 15.67 1.39 0.0181 0.0016 6 0.00057 0.00000 15.15 0.03 0.2084 0.0016 7 0.00001 0.00000 13.12 3.72 0.0047 0.0008 8 0.00001 0.00000 -0.89 3.97 0.0041 0.0009 9 0.00003 0.00000 -2.26 0.71 0.0093 0.0011 10 0.00085 0.00000 -9.03 0.01 0.3099 0.0015 11 0.00001 0.00000 1.73 9.31 0.0020 0.0011 12 0.00001 0.00000 -7.21 5.84 0.0024 0.0008 13 0.00003 0.00001 -0.91 0.74 0.0126 0.0027 14 0.00069 0.00000 -6.44 0.02 0.2533 0.0017 15 0.00001 0.00000 -9.38 1.58 0.0044 0.0009 16 0.00002 0.00001 -0.60 9.51 0.0084 0.0020 The magnetic center is at X = -8.6 +- 1.0 microns Y = 161.4 +- 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: 02-27-1995 Time: 15:05:52 Magnet Name: 103 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.3991 +- 2.360234E-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 0.00126 0.00001 175.98 0.42 0.3704 0.0029 2 0.33928 0.00008 44.97 0.00 100.0000 0.0000 3 0.00014 0.00001 31.01 0.99 0.0426 0.0016 4 0.00004 0.00001 -19.61 37.06 0.0125 0.0018 5 0.00006 0.00000 15.33 0.46 0.0167 0.0013 6 0.00062 0.00001 15.14 0.03 0.1829 0.0024 7 0.00001 0.00000 14.86 4.42 0.0036 0.0015 8 0.00004 0.00000 -0.27 22.00 0.0122 0.0012 9 0.00004 0.00001 -1.65 0.60 0.0119 0.0021 10 0.00107 0.00001 -9.04 0.04 0.3143 0.0019 11 0.00001 0.00000 10.60 3.86 0.0027 0.0012 12 0.00003 0.00001 -2.02 2.03 0.0081 0.0016 13 0.00005 0.00001 -1.68 0.43 0.0152 0.0019 14 0.00086 0.00001 -6.46 0.01 0.2549 0.0023 15 0.00002 0.00000 -1.93 5.41 0.0052 0.0010 16 0.00002 0.00001 2.65 8.03 0.0058 0.0024 The magnetic center is at X = -11.6 +- 1.2 microns Y = 165.0 +- 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: 02-27-1995 Time: 15:12:06 Magnet Name: 103 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.3802 +- 3.753166E-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 0.00153 0.00001 175.50 0.43 0.3913 0.0029 2 0.39121 0.00004 44.97 0.00 100.0000 0.0000 3 0.00018 0.00001 25.77 0.58 0.0464 0.0038 4 0.00002 0.00001 -37.80 4.50 0.0060 0.0015 5 0.00007 0.00001 14.45 1.36 0.0170 0.0013 6 0.00050 0.00000 15.27 0.12 0.1285 0.0005 7 0.00002 0.00001 13.97 2.98 0.0039 0.0014 8 0.00004 0.00001 -0.13 21.74 0.0093 0.0022 9 0.00005 0.00001 -1.99 0.56 0.0124 0.0015 10 0.00127 0.00001 -9.05 0.02 0.3250 0.0020 11 0.00001 0.00000 -8.24 7.54 0.0014 0.0009 12 0.00002 0.00001 -7.59 0.69 0.0042 0.0014 13 0.00006 0.00001 -0.77 0.86 0.0147 0.0018 14 0.00099 0.00000 -6.47 0.03 0.2534 0.0012 15 0.00002 0.00001 1.92 6.55 0.0059 0.0029 16 0.00002 0.00001 -2.86 3.70 0.0049 0.0024 The magnetic center is at X = -13.7 +- 1.3 microns Y = 174.2 +- 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: 02-27-1995 Time: 15:18:20 Magnet Name: 103 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.3838 +- 9.365218E-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 0.00170 0.00001 175.93 0.26 0.3965 0.0019 2 0.42755 0.00008 44.97 0.00 100.0000 0.0000 3 0.00021 0.00001 22.25 0.64 0.0492 0.0027 4 0.00003 0.00001 -39.97 4.65 0.0059 0.0021 5 0.00007 0.00001 13.25 1.69 0.0166 0.0019 6 0.00030 0.00001 15.56 0.04 0.0709 0.0025 7 0.00002 0.00001 8.13 16.41 0.0043 0.0013 8 0.00003 0.00001 -0.03 22.39 0.0081 0.0020 9 0.00005 0.00000 -1.85 0.23 0.0116 0.0009 10 0.00142 0.00001 -9.03 0.02 0.3327 0.0014 11 0.00001 0.00000 2.49 12.21 0.0019 0.0011 12 0.00002 0.00001 -10.09 1.96 0.0052 0.0019 13 0.00006 0.00001 -1.21 0.54 0.0133 0.0022 14 0.00108 0.00000 -6.48 0.06 0.2527 0.0010 15 0.00001 0.00001 -3.35 5.42 0.0031 0.0017 16 0.00003 0.00001 1.39 2.45 0.0074 0.0025 The magnetic center is at X = -12.6 +- 0.8 microns Y = 176.6 +- 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 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)