SLAC Magnetic Measurements Date: 03-08-1995 Time: 10:14:45 Magnet Name (Serial #): 124 Bar Code Number: 398 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: bmd 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: 03-08-1995 Time: 11:02:20 Magnet Name: 124 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.998915 +- 4.708508E-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 0.00003 0.00000 -84.88 0.50 0.2153 0.0005 2 0.01487 0.00000 44.97 0.00 100.0000 0.0000 3 0.00001 0.00000 53.82 0.54 0.0651 0.0026 4 0.00000 0.00000 30.93 2.12 0.0134 0.0025 5 0.00000 0.00000 -26.95 8.24 0.0081 0.0040 6 0.00003 0.00000 15.08 0.17 0.2224 0.0049 7 0.00000 0.00000 -5.04 12.23 0.0082 0.0010 8 0.00000 0.00000 -6.40 13.64 0.0114 0.0020 9 0.00000 0.00000 -6.65 7.89 0.0059 0.0032 10 0.00004 0.00000 -9.09 0.05 0.2980 0.0016 11 0.00000 0.00000 -2.87 3.14 0.0033 0.0005 12 0.00000 0.00000 -3.17 7.29 0.0068 0.0036 13 0.00000 0.00000 -1.16 1.37 0.0069 0.0004 14 0.00004 0.00000 -6.51 0.04 0.2590 0.0036 15 0.00000 0.00000 -1.22 6.32 0.0039 0.0021 16 0.00000 0.00000 -1.14 5.37 0.0100 0.0008 The magnetic center is at X = 95.8 +- 0.2 microns Y = -8.6 +- 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 Date: 03-08-1995 Time: 11:08:24 Magnet Name: 124 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.09944 +- 5.325407E-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 0.00003 0.00000 -159.25 1.11 0.0846 0.0015 2 0.03497 0.00001 44.96 0.00 100.0000 0.0000 3 0.00003 0.00000 41.93 0.25 0.0738 0.0016 4 0.00001 0.00000 37.71 1.82 0.0153 0.0019 5 0.00000 0.00000 16.69 29.51 0.0065 0.0018 6 0.00008 0.00000 15.11 0.05 0.2245 0.0013 7 0.00000 0.00000 -11.58 9.45 0.0047 0.0007 8 0.00000 0.00000 -0.30 20.57 0.0124 0.0033 9 0.00000 0.00000 0.90 6.18 0.0046 0.0020 10 0.00011 0.00000 -9.06 0.05 0.3011 0.0019 11 0.00000 0.00000 -6.57 4.76 0.0040 0.0008 12 0.00000 0.00000 -0.27 4.12 0.0060 0.0020 13 0.00000 0.00000 -0.98 1.81 0.0059 0.0018 14 0.00009 0.00000 -6.47 0.02 0.2551 0.0036 15 0.00000 0.00000 -5.29 2.30 0.0043 0.0008 16 0.00000 0.00000 0.60 1.92 0.0109 0.0049 The magnetic center is at X = 13.4 +- 0.7 microns Y = 35.3 +- 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: 03-08-1995 Time: 11:14:35 Magnet Name: 124 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06041 +- 1.950818E-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 0.00008 0.00000 165.04 0.36 0.1113 0.0017 2 0.06888 0.00000 44.96 0.00 100.0000 0.0000 3 0.00006 0.00000 39.70 0.32 0.0828 0.0017 4 0.00001 0.00000 36.35 3.14 0.0114 0.0016 5 0.00000 0.00000 -0.51 33.53 0.0070 0.0023 6 0.00016 0.00000 15.12 0.06 0.2291 0.0021 7 0.00000 0.00000 -9.84 8.31 0.0030 0.0007 8 0.00000 0.00000 -1.97 16.63 0.0022 0.0008 9 0.00000 0.00000 -1.92 1.68 0.0059 0.0025 10 0.00021 0.00000 -9.00 0.04 0.3004 0.0024 11 0.00000 0.00000 -4.06 2.01 0.0028 0.0009 12 0.00000 0.00000 -3.14 7.33 0.0064 0.0032 13 0.00000 0.00000 -1.48 1.84 0.0071 0.0014 14 0.00018 0.00000 -6.48 0.04 0.2545 0.0035 15 0.00000 0.00000 -1.62 7.73 0.0036 0.0018 16 0.00001 0.00000 -4.31 5.34 0.0074 0.0025 The magnetic center is at X = -12.8 +- 0.4 microns Y = 48.0 +- 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: 03-08-1995 Time: 11:20:51 Magnet Name: 124 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0518 +- 8.514469E-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 0.00017 0.00000 155.75 0.58 0.1229 0.0020 2 0.13744 0.00001 44.96 0.00 100.0000 0.0000 3 0.00012 0.00000 40.09 0.51 0.0838 0.0007 4 0.00002 0.00000 36.52 3.33 0.0115 0.0020 5 0.00001 0.00000 16.40 29.34 0.0062 0.0006 6 0.00031 0.00000 15.09 0.06 0.2284 0.0013 7 0.00000 0.00000 -6.49 8.25 0.0024 0.0006 8 0.00000 0.00000 8.05 9.38 0.0021 0.0006 9 0.00001 0.00000 -3.16 1.30 0.0053 0.0012 10 0.00041 0.00000 -9.00 0.02 0.3008 0.0014 11 0.00000 0.00000 2.17 8.19 0.0033 0.0016 12 0.00001 0.00000 4.38 5.04 0.0047 0.0013 13 0.00001 0.00000 -2.45 1.74 0.0060 0.0007 14 0.00035 0.00001 -6.46 0.11 0.2566 0.0051 15 0.00001 0.00000 4.65 6.50 0.0043 0.0013 16 0.00001 0.00000 0.61 5.54 0.0073 0.0009 The magnetic center is at X = -22.5 +- 0.6 microns Y = 50.0 +- 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: 03-08-1995 Time: 11:27:05 Magnet Name: 124 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0634 +- 1.121495E-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 0.00025 0.00000 148.39 0.38 0.1220 0.0013 2 0.20577 0.00003 44.94 0.00 100.0000 0.0000 3 0.00017 0.00000 39.86 0.38 0.0850 0.0007 4 0.00002 0.00000 34.65 5.13 0.0100 0.0020 5 0.00001 0.00000 32.38 2.07 0.0064 0.0009 6 0.00045 0.00000 15.11 0.04 0.2201 0.0012 7 0.00000 0.00000 0.04 10.59 0.0023 0.0011 8 0.00001 0.00000 -1.00 19.24 0.0034 0.0008 9 0.00001 0.00000 -2.33 1.47 0.0046 0.0003 10 0.00063 0.00000 -9.03 0.05 0.3072 0.0019 11 0.00000 0.00000 -2.94 7.02 0.0023 0.0008 12 0.00001 0.00000 -8.35 4.34 0.0068 0.0014 13 0.00001 0.00000 -1.50 1.99 0.0060 0.0002 14 0.00052 0.00000 -6.51 0.08 0.2548 0.0021 15 0.00001 0.00000 0.89 5.06 0.0040 0.0013 16 0.00001 0.00001 -1.65 8.10 0.0046 0.0027 The magnetic center is at X = -28.6 +- 0.4 microns Y = 46.4 +- 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: 03-08-1995 Time: 11:33:19 Magnet Name: 124 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3053 +- 5.775205E-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 0.00035 0.00000 144.38 0.68 0.1285 0.0013 2 0.27355 0.00004 44.94 0.00 100.0000 0.0000 3 0.00024 0.00001 39.07 0.53 0.0873 0.0020 4 0.00006 0.00000 41.52 1.75 0.0228 0.0016 5 0.00002 0.00000 30.90 1.72 0.0075 0.0007 6 0.00059 0.00000 15.11 0.04 0.2150 0.0006 7 0.00001 0.00000 -11.72 3.30 0.0026 0.0010 8 0.00002 0.00000 2.10 2.11 0.0067 0.0015 9 0.00002 0.00000 -1.47 1.92 0.0055 0.0018 10 0.00084 0.00000 -9.05 0.03 0.3067 0.0010 11 0.00001 0.00000 -3.70 6.34 0.0020 0.0011 12 0.00002 0.00000 -10.11 4.04 0.0086 0.0011 13 0.00002 0.00001 -0.96 0.31 0.0058 0.0033 14 0.00069 0.00001 -6.50 0.07 0.2513 0.0021 15 0.00001 0.00000 -6.30 1.75 0.0053 0.0016 16 0.00002 0.00001 -1.95 8.21 0.0084 0.0045 The magnetic center is at X = -33.4 +- 0.6 microns Y = 46.7 +- 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: 03-08-1995 Time: 11:39:34 Magnet Name: 124 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.403 +- 1.163226E-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 0.00047 0.00000 143.08 0.30 0.1381 0.0007 2 0.33849 0.00002 44.94 0.00 100.0000 0.0000 3 0.00029 0.00001 38.40 0.31 0.0869 0.0019 4 0.00006 0.00001 40.26 2.33 0.0171 0.0024 5 0.00002 0.00001 29.88 2.97 0.0068 0.0017 6 0.00064 0.00000 15.15 0.07 0.1889 0.0014 7 0.00001 0.00000 -9.81 5.28 0.0026 0.0012 8 0.00004 0.00001 22.01 0.36 0.0115 0.0021 9 0.00001 0.00001 -2.56 2.49 0.0042 0.0029 10 0.00105 0.00000 -9.05 0.03 0.3109 0.0014 11 0.00001 0.00000 -2.75 7.86 0.0019 0.0001 12 0.00003 0.00001 -2.75 4.11 0.0078 0.0036 13 0.00003 0.00000 -0.97 1.53 0.0089 0.0015 14 0.00086 0.00001 -6.51 0.06 0.2527 0.0018 15 0.00002 0.00001 5.21 4.33 0.0046 0.0027 16 0.00002 0.00001 2.22 5.39 0.0054 0.0030 The magnetic center is at X = -37.0 +- 0.3 microns Y = 49.3 +- 0.3 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: 03-08-1995 Time: 11:45:49 Magnet Name: 124 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3864 +- 1.110752E-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 0.00050 0.00001 152.92 1.02 0.1285 0.0017 2 0.39033 0.00004 44.94 0.00 100.0000 0.0000 3 0.00029 0.00001 39.83 0.38 0.0740 0.0019 4 0.00004 0.00001 37.31 4.24 0.0096 0.0018 5 0.00002 0.00000 15.53 26.82 0.0049 0.0010 6 0.00053 0.00000 15.23 0.06 0.1362 0.0008 7 0.00001 0.00000 -13.32 4.24 0.0026 0.0003 8 0.00003 0.00000 20.88 1.24 0.0078 0.0011 9 0.00002 0.00000 -3.23 0.37 0.0052 0.0007 10 0.00126 0.00001 -9.06 0.03 0.3220 0.0018 11 0.00001 0.00000 -4.96 12.31 0.0023 0.0005 12 0.00003 0.00001 -7.97 5.13 0.0073 0.0028 13 0.00003 0.00001 -2.65 1.27 0.0070 0.0025 14 0.00099 0.00001 -6.53 0.09 0.2540 0.0021 15 0.00002 0.00001 -5.40 3.70 0.0049 0.0023 16 0.00003 0.00002 1.51 0.87 0.0078 0.0050 The magnetic center is at X = -26.1 +- 1.0 microns Y = 51.1 +- 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: 03-08-1995 Time: 11:52:04 Magnet Name: 124 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3887 +- 1.123466E-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 0.00053 0.00000 161.66 0.34 0.1248 0.0005 2 0.42678 0.00009 44.93 0.00 100.0000 0.0000 3 0.00026 0.00000 39.59 0.79 0.0619 0.0009 4 0.00004 0.00001 39.45 3.08 0.0090 0.0026 5 0.00002 0.00000 -0.55 30.97 0.0056 0.0008 6 0.00034 0.00000 15.36 0.29 0.0791 0.0004 7 0.00001 0.00000 -13.69 6.17 0.0024 0.0008 8 0.00003 0.00000 10.37 18.95 0.0076 0.0009 9 0.00002 0.00001 -2.39 2.05 0.0043 0.0028 10 0.00141 0.00000 -9.02 0.03 0.3314 0.0012 11 0.00001 0.00001 -0.71 4.82 0.0021 0.0014 12 0.00002 0.00001 -7.56 8.01 0.0054 0.0016 13 0.00003 0.00001 -0.64 1.31 0.0059 0.0014 14 0.00108 0.00001 -6.48 0.05 0.2521 0.0026 15 0.00003 0.00001 2.18 7.89 0.0070 0.0016 16 0.00004 0.00001 0.25 0.86 0.0090 0.0021 The magnetic center is at X = -17.5 +- 0.3 microns Y = 52.9 +- 0.2 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 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)