SLAC Magnetic Measurements Date: 03-14-1995 Time: 07:35:28 Magnet Name (Serial #): 151 Bar Code Number: 378 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: 03-14-1995 Time: 08:23:34 Magnet Name: 151 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00095 +- 4.734565E-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 0.00001 0.00000 -20.46 0.63 0.0830 0.0021 2 0.01490 0.00001 44.96 0.00 100.0000 0.0000 3 0.00001 0.00000 48.01 0.38 0.0949 0.0018 4 0.00000 0.00000 -29.10 1.79 0.0154 0.0031 5 0.00000 0.00000 19.74 1.47 0.0110 0.0006 6 0.00003 0.00000 15.15 0.06 0.2215 0.0018 7 0.00000 0.00000 -6.34 14.33 0.0026 0.0015 8 0.00000 0.00000 -8.54 5.49 0.0041 0.0007 9 0.00000 0.00000 -6.07 1.75 0.0061 0.0019 10 0.00004 0.00000 -9.07 0.05 0.3016 0.0014 11 0.00000 0.00000 -7.61 1.58 0.0031 0.0005 12 0.00000 0.00000 -4.82 6.53 0.0028 0.0011 13 0.00000 0.00000 -3.89 1.04 0.0081 0.0014 14 0.00004 0.00000 -6.43 0.02 0.2572 0.0029 15 0.00000 0.00000 2.47 7.14 0.0080 0.0037 16 0.00000 0.00000 2.40 4.91 0.0039 0.0026 The magnetic center is at X = 13.0 +- 0.5 microns Y = -34.7 +- 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: 03-14-1995 Time: 08:29:44 Magnet Name: 151 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10258 +- 1.515142E-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 123.22 1.06 0.0748 0.0017 2 0.03501 0.00002 44.96 0.00 100.0000 0.0000 3 0.00002 0.00000 47.03 0.90 0.0644 0.0015 4 0.00001 0.00000 -38.24 1.57 0.0271 0.0016 5 0.00000 0.00000 19.50 1.32 0.0098 0.0032 6 0.00008 0.00000 15.19 0.13 0.2183 0.0075 7 0.00000 0.00000 6.02 12.10 0.0017 0.0017 8 0.00000 0.00000 -3.46 1.96 0.0060 0.0013 9 0.00000 0.00000 -4.98 0.34 0.0088 0.0011 10 0.00011 0.00000 -9.08 0.03 0.3043 0.0054 11 0.00000 0.00000 -11.19 1.05 0.0026 0.0012 12 0.00000 0.00000 -1.84 3.00 0.0057 0.0023 13 0.00000 0.00000 -2.98 0.50 0.0096 0.0021 14 0.00009 0.00000 -6.46 0.05 0.2585 0.0027 15 0.00000 0.00000 4.07 7.39 0.0079 0.0032 16 0.00000 0.00000 5.11 8.17 0.0046 0.0019 The magnetic center is at X = -28.0 +- 0.7 microns Y = 18.3 +- 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: 03-14-1995 Time: 08:35:58 Magnet Name: 151 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06529 +- 9.978551E-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 0.00009 0.00000 126.39 0.97 0.1302 0.0012 2 0.06893 0.00002 44.96 0.00 100.0000 0.0000 3 0.00004 0.00000 45.86 0.93 0.0596 0.0019 4 0.00001 0.00000 -31.44 1.81 0.0171 0.0015 5 0.00001 0.00000 22.82 2.66 0.0099 0.0008 6 0.00015 0.00000 15.09 0.07 0.2235 0.0011 7 0.00000 0.00000 -15.39 5.26 0.0021 0.0009 8 0.00000 0.00000 -4.92 1.45 0.0034 0.0005 9 0.00001 0.00000 -5.67 0.82 0.0079 0.0007 10 0.00021 0.00000 -9.07 0.04 0.3002 0.0011 11 0.00000 0.00000 -10.47 0.79 0.0039 0.0004 12 0.00000 0.00000 3.90 4.60 0.0033 0.0013 13 0.00001 0.00000 -3.32 0.44 0.0083 0.0014 14 0.00018 0.00000 -6.46 0.03 0.2571 0.0030 15 0.00000 0.00000 -3.28 2.14 0.0060 0.0026 16 0.00000 0.00000 -0.59 4.35 0.0042 0.0013 The magnetic center is at X = -46.8 +- 0.7 microns Y = 34.5 +- 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: 03-14-1995 Time: 08:42:19 Magnet Name: 151 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0577 +- 8.644562E-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 126.14 0.26 0.1565 0.0021 2 0.13753 0.00005 44.96 0.00 100.0000 0.0000 3 0.00008 0.00000 45.10 0.54 0.0584 0.0019 4 0.00003 0.00000 -30.33 0.81 0.0198 0.0014 5 0.00001 0.00000 20.38 1.58 0.0101 0.0018 6 0.00031 0.00000 15.10 0.05 0.2238 0.0008 7 0.00000 0.00000 -0.58 16.91 0.0019 0.0008 8 0.00000 0.00000 -10.45 1.41 0.0031 0.0005 9 0.00001 0.00000 -5.37 0.48 0.0070 0.0012 10 0.00042 0.00000 -9.09 0.03 0.3022 0.0010 11 0.00000 0.00000 -8.89 1.46 0.0035 0.0006 12 0.00000 0.00000 4.51 8.01 0.0027 0.0013 13 0.00001 0.00000 -2.71 0.42 0.0103 0.0010 14 0.00035 0.00000 -6.43 0.04 0.2555 0.0018 15 0.00001 0.00000 0.94 7.75 0.0067 0.0008 16 0.00000 0.00000 2.80 4.33 0.0030 0.0014 The magnetic center is at X = -56.4 +- 0.8 microns Y = 41.2 +- 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: 03-14-1995 Time: 08:48:38 Magnet Name: 151 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0695 +- 8.763183E-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 0.00034 0.00000 128.26 0.54 0.1638 0.0013 2 0.20570 0.00007 44.94 0.00 100.0000 0.0000 3 0.00011 0.00001 44.66 0.26 0.0527 0.0029 4 0.00004 0.00000 -29.52 1.27 0.0194 0.0017 5 0.00002 0.00000 21.02 3.14 0.0099 0.0018 6 0.00045 0.00000 15.07 0.08 0.2172 0.0019 7 0.00001 0.00000 -10.96 6.52 0.0025 0.0009 8 0.00001 0.00000 -6.98 2.16 0.0046 0.0019 9 0.00001 0.00000 -4.68 1.40 0.0070 0.0015 10 0.00062 0.00000 -9.09 0.02 0.3008 0.0005 11 0.00001 0.00000 -12.55 1.94 0.0036 0.0019 12 0.00001 0.00000 -6.22 11.78 0.0040 0.0006 13 0.00002 0.00000 -3.53 0.51 0.0086 0.0013 14 0.00054 0.00000 -6.45 0.03 0.2601 0.0014 15 0.00001 0.00001 -1.36 6.58 0.0069 0.0038 16 0.00002 0.00001 1.46 1.38 0.0076 0.0031 The magnetic center is at X = -57.5 +- 0.6 microns Y = 45.3 +- 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: 03-14-1995 Time: 08:54:58 Magnet Name: 151 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3137 +- 5.196396E-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 134.12 0.19 0.1738 0.0024 2 0.27347 0.00006 44.94 0.00 100.0000 0.0000 3 0.00012 0.00001 42.64 0.55 0.0434 0.0031 4 0.00006 0.00001 -30.18 0.91 0.0209 0.0020 5 0.00002 0.00000 23.07 1.67 0.0090 0.0007 6 0.00057 0.00000 15.06 0.05 0.2081 0.0013 7 0.00001 0.00000 -13.58 1.17 0.0028 0.0012 8 0.00002 0.00000 -5.55 0.71 0.0061 0.0002 9 0.00002 0.00000 -4.19 1.05 0.0069 0.0014 10 0.00084 0.00000 -9.10 0.02 0.3068 0.0013 11 0.00001 0.00000 -2.98 11.14 0.0039 0.0009 12 0.00001 0.00000 -0.83 7.58 0.0026 0.0014 13 0.00003 0.00000 -3.96 0.71 0.0098 0.0005 14 0.00070 0.00001 -6.43 0.02 0.2574 0.0029 15 0.00001 0.00001 -4.90 2.63 0.0053 0.0025 16 0.00001 0.00001 5.15 5.91 0.0052 0.0021 The magnetic center is at X = -55.7 +- 0.8 microns Y = 54.0 +- 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: 03-14-1995 Time: 09:01:18 Magnet Name: 151 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.412 +- 4.827062E-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 0.00070 0.00000 147.02 0.64 0.2073 0.0005 2 0.33839 0.00012 44.94 0.00 100.0000 0.0000 3 0.00009 0.00001 30.86 1.82 0.0258 0.0027 4 0.00012 0.00001 -36.05 0.87 0.0342 0.0029 5 0.00003 0.00000 25.24 3.65 0.0088 0.0013 6 0.00061 0.00000 15.10 0.03 0.1812 0.0011 7 0.00001 0.00000 -18.71 3.06 0.0021 0.0006 8 0.00002 0.00000 -5.82 1.91 0.0063 0.0011 9 0.00002 0.00000 -5.05 0.97 0.0072 0.0008 10 0.00106 0.00000 -9.11 0.02 0.3122 0.0011 11 0.00001 0.00000 -11.15 1.45 0.0034 0.0009 12 0.00002 0.00001 -2.21 1.32 0.0056 0.0016 13 0.00004 0.00001 -3.41 0.20 0.0111 0.0025 14 0.00087 0.00001 -6.42 0.04 0.2570 0.0019 15 0.00002 0.00001 -4.94 4.15 0.0060 0.0023 16 0.00002 0.00000 4.64 8.38 0.0051 0.0009 The magnetic center is at X = -50.4 +- 0.9 microns Y = 77.7 +- 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: 03-14-1995 Time: 09:07:38 Magnet Name: 151 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3966 +- 1.510543E-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 0.00111 0.00001 153.53 0.23 0.2842 0.0013 2 0.39034 0.00026 44.94 0.00 100.0000 0.0000 3 0.00021 0.00001 12.87 0.49 0.0540 0.0034 4 0.00011 0.00001 -33.98 0.43 0.0277 0.0014 5 0.00004 0.00001 26.46 1.44 0.0115 0.0032 6 0.00053 0.00000 15.16 0.09 0.1369 0.0012 7 0.00002 0.00001 -20.32 1.74 0.0044 0.0013 8 0.00002 0.00000 -16.05 0.67 0.0052 0.0011 9 0.00004 0.00001 -4.16 0.49 0.0092 0.0013 10 0.00125 0.00000 -9.10 0.01 0.3192 0.0011 11 0.00001 0.00001 -8.02 0.52 0.0035 0.0016 12 0.00003 0.00000 -0.48 1.54 0.0075 0.0007 13 0.00004 0.00000 -2.96 0.34 0.0107 0.0010 14 0.00098 0.00001 -6.45 0.02 0.2523 0.0021 15 0.00002 0.00000 -3.34 5.69 0.0053 0.0004 16 0.00003 0.00001 -0.86 10.09 0.0067 0.0034 The magnetic center is at X = -56.6 +- 0.5 microns Y = 113.7 +- 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: 03-14-1995 Time: 09:13:58 Magnet Name: 151 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4006 +- 1.075718E-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 0.00135 0.00000 155.93 0.30 0.3168 0.0005 2 0.42661 0.00012 44.94 0.00 100.0000 0.0000 3 0.00031 0.00001 10.15 1.06 0.0728 0.0012 4 0.00012 0.00000 -33.28 0.88 0.0272 0.0009 5 0.00005 0.00001 26.42 2.86 0.0121 0.0029 6 0.00034 0.00001 15.32 0.21 0.0801 0.0012 7 0.00003 0.00001 -22.06 1.08 0.0064 0.0017 8 0.00003 0.00000 -17.74 0.42 0.0070 0.0010 9 0.00004 0.00000 -4.94 1.21 0.0092 0.0010 10 0.00141 0.00001 -9.08 0.02 0.3313 0.0017 11 0.00002 0.00001 -9.36 1.32 0.0042 0.0017 12 0.00004 0.00001 -0.01 1.06 0.0083 0.0015 13 0.00004 0.00000 -3.36 0.83 0.0084 0.0010 14 0.00107 0.00001 -6.45 0.06 0.2502 0.0021 15 0.00002 0.00001 -4.26 3.63 0.0051 0.0029 16 0.00004 0.00001 -0.35 2.14 0.0088 0.0013 The magnetic center is at X = -57.7 +- 0.7 microns Y = 129.2 +- 0.4 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 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)