SLAC Magnetic Measurements Date: 03-01-1995 Time: 13:26:40 Magnet Name (Serial #): 159 Bar Code Number: 293 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: 03-01-1995 Time: 14:13:43 Magnet Name: 159 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00116 +- 3.791848E-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 0.00002 0.00000 -12.56 0.23 0.1675 0.0016 2 0.01491 0.00000 28.33 0.00 100.0000 0.0000 3 0.00002 0.00000 -57.25 0.34 0.1007 0.0011 4 0.00000 0.00000 8.50 1.46 0.0229 0.0010 5 0.00000 0.00000 0.22 35.02 0.0124 0.0029 6 0.00003 0.00000 -1.59 0.04 0.2159 0.0025 7 0.00000 0.00000 -2.81 21.31 0.0052 0.0013 8 0.00000 0.00000 -7.21 11.23 0.0028 0.0016 9 0.00000 0.00000 -3.11 0.62 0.0083 0.0017 10 0.00004 0.00000 10.40 0.03 0.2971 0.0014 11 0.00000 0.00000 0.58 10.82 0.0022 0.0011 12 0.00000 0.00000 5.17 11.01 0.0061 0.0011 13 0.00000 0.00000 -6.90 0.60 0.0137 0.0032 14 0.00004 0.00000 2.67 0.02 0.2565 0.0019 15 0.00000 0.00000 -7.28 1.85 0.0068 0.0034 16 0.00000 0.00000 -2.14 5.80 0.0035 0.0025 The magnetic center is at X = 16.3 +- 0.3 microns Y = -73.0 +- 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: 03-01-1995 Time: 14:19:47 Magnet Name: 159 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10212 +- 4.103272E-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 0.00009 0.00000 -56.76 0.72 0.2493 0.0038 2 0.03500 0.00000 28.32 0.00 100.0000 0.0000 3 0.00004 0.00000 -52.07 0.52 0.1220 0.0027 4 0.00001 0.00000 14.65 1.58 0.0181 0.0021 5 0.00001 0.00000 17.70 30.32 0.0166 0.0020 6 0.00008 0.00000 -1.59 0.10 0.2195 0.0020 7 0.00000 0.00000 21.56 1.45 0.0059 0.0009 8 0.00000 0.00000 2.82 1.50 0.0067 0.0008 9 0.00000 0.00000 -3.97 1.15 0.0073 0.0010 10 0.00011 0.00000 10.34 0.02 0.3008 0.0012 11 0.00000 0.00000 -8.81 4.85 0.0014 0.0009 12 0.00000 0.00000 -1.58 13.13 0.0059 0.0009 13 0.00000 0.00000 -7.54 0.64 0.0110 0.0013 14 0.00009 0.00000 2.65 0.03 0.2577 0.0021 15 0.00000 0.00000 -6.24 2.43 0.0064 0.0009 16 0.00000 0.00000 3.14 2.25 0.0052 0.0030 The magnetic center is at X = 93.1 +- 1.6 microns Y = -61.0 +- 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: 03-01-1995 Time: 14:25:58 Magnet Name: 159 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06327 +- 1.090335E-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 0.00020 0.00000 -62.16 0.28 0.2927 0.0020 2 0.06895 0.00001 28.32 0.00 100.0000 0.0000 3 0.00009 0.00000 -51.75 0.48 0.1242 0.0029 4 0.00001 0.00000 12.56 2.80 0.0128 0.0022 5 0.00001 0.00000 -17.91 30.38 0.0168 0.0015 6 0.00015 0.00000 -1.67 0.05 0.2210 0.0016 7 0.00000 0.00000 22.12 0.38 0.0056 0.0011 8 0.00000 0.00000 -8.76 7.17 0.0035 0.0009 9 0.00001 0.00000 -4.30 1.13 0.0075 0.0010 10 0.00021 0.00000 10.34 0.01 0.3016 0.0016 11 0.00000 0.00000 -8.69 2.70 0.0023 0.0008 12 0.00000 0.00000 3.52 4.75 0.0027 0.0014 13 0.00001 0.00000 -7.48 0.10 0.0133 0.0010 14 0.00018 0.00000 2.65 0.04 0.2554 0.0019 15 0.00000 0.00000 -6.83 1.54 0.0058 0.0022 16 0.00000 0.00000 -6.33 1.77 0.0041 0.0024 The magnetic center is at X = 115.6 +- 0.8 microns Y = -61.0 +- 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: 03-01-1995 Time: 14:32:13 Magnet Name: 159 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0538 +- 9.489706E-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 0.00043 0.00001 -63.71 0.60 0.3116 0.0037 2 0.13755 0.00003 28.32 0.00 100.0000 0.0000 3 0.00017 0.00001 -51.36 0.42 0.1206 0.0046 4 0.00002 0.00000 11.03 3.33 0.0126 0.0033 5 0.00002 0.00000 -0.61 34.83 0.0164 0.0010 6 0.00030 0.00000 -1.54 0.04 0.2216 0.0013 7 0.00001 0.00000 22.25 2.70 0.0049 0.0007 8 0.00000 0.00000 -9.41 2.63 0.0036 0.0012 9 0.00001 0.00000 -4.77 0.46 0.0087 0.0004 10 0.00041 0.00000 10.36 0.02 0.3013 0.0016 11 0.00000 0.00000 -2.29 11.43 0.0021 0.0011 12 0.00000 0.00000 -1.22 9.52 0.0028 0.0013 13 0.00002 0.00000 -7.52 0.18 0.0128 0.0010 14 0.00035 0.00000 2.64 0.02 0.2573 0.0023 15 0.00001 0.00001 -5.83 1.23 0.0076 0.0037 16 0.00001 0.00000 4.80 3.47 0.0058 0.0016 The magnetic center is at X = 124.8 +- 1.6 microns Y = -61.6 +- 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: 03-01-1995 Time: 14:38:26 Magnet Name: 159 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.064 +- 6.648526E-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 0.00066 0.00000 -66.07 0.68 0.3221 0.0013 2 0.20587 0.00003 28.30 0.00 100.0000 0.0000 3 0.00026 0.00000 -51.86 0.53 0.1244 0.0022 4 0.00002 0.00000 9.05 3.01 0.0108 0.0012 5 0.00003 0.00000 17.45 30.06 0.0168 0.0019 6 0.00044 0.00000 -1.66 0.08 0.2127 0.0021 7 0.00001 0.00000 20.68 0.91 0.0043 0.0017 8 0.00000 0.00000 2.69 16.28 0.0017 0.0010 9 0.00002 0.00000 -4.17 1.27 0.0080 0.0007 10 0.00063 0.00000 10.30 0.03 0.3038 0.0011 11 0.00001 0.00000 -4.33 11.62 0.0033 0.0008 12 0.00001 0.00000 -0.10 5.07 0.0032 0.0012 13 0.00003 0.00000 -8.01 0.36 0.0123 0.0013 14 0.00053 0.00000 2.61 0.02 0.2565 0.0017 15 0.00002 0.00000 -4.64 0.72 0.0076 0.0015 16 0.00001 0.00001 -4.34 3.67 0.0051 0.0038 The magnetic center is at X = 131.5 +- 0.9 microns Y = -58.4 +- 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: 03-01-1995 Time: 14:44:40 Magnet Name: 159 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3052 +- 7.767758E-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 0.00089 0.00001 -66.32 0.31 0.3256 0.0044 2 0.27366 0.00001 28.30 0.00 100.0000 0.0000 3 0.00034 0.00001 -51.82 0.72 0.1241 0.0034 4 0.00006 0.00000 20.13 1.56 0.0212 0.0016 5 0.00004 0.00001 16.95 30.54 0.0157 0.0025 6 0.00056 0.00000 -1.61 0.07 0.2063 0.0007 7 0.00001 0.00000 22.68 1.19 0.0046 0.0009 8 0.00003 0.00000 -15.20 1.00 0.0106 0.0009 9 0.00002 0.00000 -3.73 0.34 0.0084 0.0007 10 0.00084 0.00000 10.32 0.02 0.3060 0.0010 11 0.00001 0.00000 0.36 13.42 0.0025 0.0013 12 0.00001 0.00001 -8.63 7.56 0.0047 0.0025 13 0.00004 0.00000 -7.89 0.49 0.0141 0.0009 14 0.00070 0.00001 2.61 0.04 0.2571 0.0018 15 0.00002 0.00001 -5.82 1.14 0.0088 0.0034 16 0.00002 0.00000 -0.77 4.82 0.0056 0.0015 The magnetic center is at X = 133.2 +- 1.8 microns Y = -58.4 +- 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: 03-01-1995 Time: 14:50:55 Magnet Name: 159 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4021 +- 1.535386E-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 -64.67 0.48 0.3201 0.0033 2 0.33875 0.00005 28.30 0.00 100.0000 0.0000 3 0.00041 0.00001 -52.60 0.29 0.1196 0.0031 4 0.00006 0.00001 16.83 1.52 0.0188 0.0024 5 0.00005 0.00001 17.69 30.46 0.0159 0.0019 6 0.00062 0.00000 -1.54 0.09 0.1821 0.0011 7 0.00002 0.00000 8.44 18.80 0.0049 0.0006 8 0.00002 0.00000 2.95 1.72 0.0065 0.0012 9 0.00003 0.00000 -2.67 0.59 0.0075 0.0011 10 0.00104 0.00001 10.34 0.02 0.3084 0.0016 11 0.00001 0.00000 -5.88 10.93 0.0023 0.0009 12 0.00003 0.00000 13.41 0.88 0.0087 0.0006 13 0.00004 0.00001 -7.50 0.44 0.0128 0.0020 14 0.00086 0.00001 2.62 0.02 0.2551 0.0028 15 0.00002 0.00001 -4.62 0.87 0.0060 0.0018 16 0.00001 0.00001 -0.05 6.29 0.0040 0.0015 The magnetic center is at X = 129.2 +- 1.4 microns Y = -61.2 +- 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: 03-01-1995 Time: 14:57:09 Magnet Name: 159 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3853 +- 7.912532E-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 0.00124 0.00001 -56.46 0.55 0.3180 0.0018 2 0.39077 0.00005 28.30 0.00 100.0000 0.0000 3 0.00041 0.00001 -56.56 0.49 0.1061 0.0038 4 0.00006 0.00001 12.78 1.81 0.0145 0.0027 5 0.00005 0.00001 17.81 29.60 0.0138 0.0015 6 0.00049 0.00000 -1.56 0.15 0.1266 0.0010 7 0.00003 0.00001 23.09 1.64 0.0067 0.0015 8 0.00001 0.00000 1.95 1.80 0.0035 0.0012 9 0.00003 0.00000 -2.66 0.90 0.0086 0.0012 10 0.00125 0.00001 10.32 0.04 0.3211 0.0019 11 0.00001 0.00000 1.82 12.27 0.0022 0.0007 12 0.00001 0.00000 10.41 1.52 0.0033 0.0006 13 0.00005 0.00001 -7.73 0.54 0.0139 0.0021 14 0.00100 0.00001 2.62 0.03 0.2569 0.0018 15 0.00003 0.00001 -5.41 1.89 0.0068 0.0023 16 0.00002 0.00001 1.48 6.99 0.0046 0.0033 The magnetic center is at X = 118.4 +- 1.0 microns Y = -78.5 +- 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: 03-01-1995 Time: 15:03:24 Magnet Name: 159 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3864 +- 1.038271E-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 0.00138 0.00002 -52.17 0.44 0.3233 0.0045 2 0.42731 0.00005 28.29 0.00 100.0000 0.0000 3 0.00045 0.00002 -59.45 0.35 0.1059 0.0037 4 0.00005 0.00001 13.54 2.17 0.0128 0.0020 5 0.00005 0.00000 -17.72 30.27 0.0116 0.0006 6 0.00029 0.00000 -1.17 0.15 0.0688 0.0011 7 0.00002 0.00000 11.53 21.26 0.0056 0.0011 8 0.00001 0.00000 4.43 2.18 0.0030 0.0011 9 0.00005 0.00001 -3.05 0.36 0.0110 0.0015 10 0.00141 0.00001 10.33 0.04 0.3298 0.0028 11 0.00001 0.00000 -8.47 2.97 0.0024 0.0008 12 0.00001 0.00000 0.71 7.00 0.0018 0.0006 13 0.00005 0.00000 -7.78 1.04 0.0118 0.0010 14 0.00108 0.00001 2.64 0.02 0.2525 0.0019 15 0.00003 0.00001 -4.55 0.70 0.0077 0.0020 16 0.00003 0.00001 0.59 6.68 0.0074 0.0027 The magnetic center is at X = 114.1 +- 1.7 microns Y = -88.6 +- 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 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)