SLAC Magnetic Measurements Date: 03-29-1995 Time: 10:34:31 Magnet Name (Serial #): 173 Bar Code Number: 569 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: 03-29-1995 Time: 11:22:06 Magnet Name: 173 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00119 +- 3.360349E-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 0.00006 0.00000 -105.62 0.58 0.3911 0.0047 2 0.01494 0.00000 45.06 0.00 100.0000 0.0000 3 0.00001 0.00000 23.01 1.09 0.0873 0.0044 4 0.00000 0.00000 20.88 1.20 0.0214 0.0018 5 0.00000 0.00000 9.35 1.49 0.0154 0.0024 6 0.00003 0.00000 15.24 0.10 0.2239 0.0024 7 0.00000 0.00000 8.58 1.77 0.0073 0.0007 8 0.00000 0.00000 7.91 17.54 0.0029 0.0010 9 0.00000 0.00000 6.90 0.52 0.0142 0.0017 10 0.00004 0.00000 -9.03 0.04 0.2990 0.0011 11 0.00000 0.00000 0.11 9.01 0.0016 0.0006 12 0.00000 0.00000 10.79 3.91 0.0054 0.0022 13 0.00000 0.00000 3.48 0.19 0.0129 0.0022 14 0.00004 0.00000 -6.44 0.03 0.2599 0.0009 15 0.00000 0.00000 -10.06 1.11 0.0054 0.0026 16 0.00000 0.00000 4.06 4.44 0.0050 0.0025 The magnetic center is at X = 168.2 +- 2.1 microns Y = 47.0 +- 1.8 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: 03-29-1995 Time: 11:28:12 Magnet Name: 173 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10221 +- 3.867476E-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 -124.58 1.15 0.3498 0.0040 2 0.03501 0.00001 45.06 0.00 100.0000 0.0000 3 0.00003 0.00000 19.18 0.92 0.0866 0.0025 4 0.00001 0.00000 27.04 1.62 0.0165 0.0031 5 0.00001 0.00000 10.50 1.75 0.0161 0.0042 6 0.00008 0.00000 15.19 0.11 0.2266 0.0026 7 0.00000 0.00000 8.86 1.20 0.0063 0.0007 8 0.00000 0.00000 20.89 0.79 0.0098 0.0005 9 0.00001 0.00000 6.84 0.38 0.0144 0.0006 10 0.00010 0.00000 -9.04 0.05 0.2982 0.0021 11 0.00000 0.00000 7.32 7.93 0.0025 0.0005 12 0.00000 0.00000 1.60 2.60 0.0057 0.0024 13 0.00000 0.00000 2.90 0.38 0.0131 0.0013 14 0.00009 0.00000 -6.43 0.03 0.2586 0.0015 15 0.00000 0.00000 -5.30 9.74 0.0087 0.0016 16 0.00000 0.00000 -0.62 1.99 0.0082 0.0015 The magnetic center is at X = 128.6 +- 2.3 microns Y = 88.7 +- 2.8 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: 03-29-1995 Time: 11:34:24 Magnet Name: 173 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06545 +- 2.163811E-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 0.00023 0.00000 -132.28 0.69 0.3374 0.0060 2 0.06888 0.00001 45.06 0.00 100.0000 0.0000 3 0.00006 0.00000 18.96 1.18 0.0871 0.0034 4 0.00001 0.00000 21.25 1.82 0.0123 0.0017 5 0.00001 0.00000 9.40 1.20 0.0151 0.0017 6 0.00016 0.00000 15.18 0.07 0.2261 0.0021 7 0.00000 0.00000 8.06 0.91 0.0069 0.0008 8 0.00000 0.00000 12.77 3.62 0.0025 0.0012 9 0.00001 0.00000 6.12 0.28 0.0132 0.0012 10 0.00021 0.00000 -9.01 0.03 0.2989 0.0013 11 0.00000 0.00000 -4.34 7.94 0.0019 0.0008 12 0.00000 0.00000 4.47 5.80 0.0021 0.0014 13 0.00001 0.00000 3.16 0.92 0.0154 0.0016 14 0.00018 0.00000 -6.43 0.02 0.2550 0.0030 15 0.00001 0.00000 -9.62 1.17 0.0102 0.0032 16 0.00000 0.00000 -0.08 4.60 0.0049 0.0025 The magnetic center is at X = 111.5 +- 2.3 microns Y = 101.4 +- 2.3 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: 03-29-1995 Time: 11:40:39 Magnet Name: 173 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0596 +- 5.869429E-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 0.00047 0.00000 -135.43 0.72 0.3386 0.0033 2 0.13743 0.00002 45.06 0.00 100.0000 0.0000 3 0.00012 0.00001 18.45 0.49 0.0870 0.0041 4 0.00001 0.00000 21.72 3.10 0.0109 0.0017 5 0.00002 0.00000 9.42 1.80 0.0131 0.0025 6 0.00031 0.00000 15.14 0.09 0.2265 0.0009 7 0.00001 0.00000 7.59 2.57 0.0083 0.0017 8 0.00000 0.00000 10.33 6.78 0.0018 0.0005 9 0.00002 0.00000 5.90 0.61 0.0134 0.0007 10 0.00041 0.00000 -8.99 0.05 0.3008 0.0015 11 0.00000 0.00000 2.10 11.09 0.0026 0.0009 12 0.00000 0.00000 2.05 6.21 0.0031 0.0011 13 0.00002 0.00000 2.81 1.10 0.0134 0.0024 14 0.00035 0.00000 -6.40 0.04 0.2572 0.0013 15 0.00001 0.00000 -4.40 8.81 0.0104 0.0031 16 0.00001 0.00000 1.15 6.24 0.0052 0.0019 The magnetic center is at X = 106.1 +- 1.7 microns Y = 107.7 +- 1.7 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: 03-29-1995 Time: 11:46:54 Magnet Name: 173 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0749 +- 5.75754E-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 0.00001 -135.43 1.20 0.3423 0.0054 2 0.20569 0.00004 45.03 0.00 100.0000 0.0000 3 0.00017 0.00001 18.66 1.38 0.0803 0.0051 4 0.00002 0.00001 21.06 3.11 0.0099 0.0030 5 0.00003 0.00000 10.87 0.79 0.0125 0.0021 6 0.00045 0.00000 15.12 0.11 0.2176 0.0017 7 0.00002 0.00000 8.89 0.87 0.0081 0.0012 8 0.00000 0.00000 8.89 13.12 0.0024 0.0014 9 0.00003 0.00000 6.32 0.32 0.0138 0.0018 10 0.00062 0.00000 -9.04 0.01 0.3029 0.0018 11 0.00001 0.00000 -7.21 9.46 0.0030 0.0013 12 0.00001 0.00000 5.89 10.48 0.0050 0.0004 13 0.00003 0.00000 3.00 0.06 0.0125 0.0016 14 0.00052 0.00000 -6.45 0.02 0.2541 0.0024 15 0.00001 0.00001 -4.06 9.44 0.0072 0.0027 16 0.00001 0.00000 5.94 6.26 0.0057 0.0012 The magnetic center is at X = 107.3 +- 2.8 microns Y = 108.9 +- 2.8 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: 03-29-1995 Time: 11:53:09 Magnet Name: 173 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3217 +- 2.629652E-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 0.00094 0.00001 -135.24 0.46 0.3455 0.0050 2 0.27344 0.00002 45.03 0.00 100.0000 0.0000 3 0.00022 0.00000 18.68 1.13 0.0809 0.0012 4 0.00005 0.00001 37.38 1.23 0.0167 0.0026 5 0.00004 0.00001 10.97 1.30 0.0131 0.0022 6 0.00057 0.00000 15.17 0.08 0.2092 0.0008 7 0.00003 0.00001 9.33 0.32 0.0093 0.0027 8 0.00002 0.00000 1.73 1.24 0.0059 0.0004 9 0.00004 0.00000 5.90 0.58 0.0147 0.0006 10 0.00084 0.00000 -9.05 0.04 0.3057 0.0012 11 0.00001 0.00000 8.25 7.20 0.0024 0.0011 12 0.00001 0.00000 7.14 2.53 0.0041 0.0014 13 0.00004 0.00001 3.18 1.06 0.0131 0.0023 14 0.00071 0.00001 -6.46 0.03 0.2589 0.0021 15 0.00002 0.00001 -4.43 9.35 0.0062 0.0027 16 0.00001 0.00000 -1.96 2.70 0.0040 0.0011 The magnetic center is at X = 108.7 +- 1.8 microns Y = 109.6 +- 1.8 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: 03-29-1995 Time: 11:59:26 Magnet Name: 173 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4231 +- 5.75754E-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 0.00122 0.00001 -134.69 0.22 0.3603 0.0041 2 0.33835 0.00006 45.03 0.00 100.0000 0.0000 3 0.00027 0.00001 15.79 0.90 0.0789 0.0021 4 0.00003 0.00001 31.79 3.25 0.0093 0.0019 5 0.00005 0.00000 10.99 1.05 0.0134 0.0010 6 0.00063 0.00001 15.09 0.06 0.1858 0.0015 7 0.00003 0.00000 7.66 0.68 0.0080 0.0010 8 0.00002 0.00000 -0.43 20.65 0.0062 0.0007 9 0.00005 0.00000 6.13 0.27 0.0149 0.0011 10 0.00105 0.00000 -9.03 0.03 0.3094 0.0009 11 0.00001 0.00000 4.14 12.00 0.0022 0.0004 12 0.00002 0.00001 1.94 1.69 0.0066 0.0020 13 0.00005 0.00000 3.67 0.38 0.0153 0.0010 14 0.00087 0.00000 -6.47 0.03 0.2560 0.0008 15 0.00004 0.00001 -10.30 1.08 0.0126 0.0023 16 0.00002 0.00001 3.44 7.25 0.0071 0.0035 The magnetic center is at X = 114.4 +- 1.3 microns Y = 113.2 +- 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: 03-29-1995 Time: 12:05:43 Magnet Name: 173 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4073 +- 3.51615E-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 0.00142 0.00001 -133.50 0.18 0.3633 0.0022 2 0.39025 0.00011 45.03 0.00 100.0000 0.0000 3 0.00030 0.00001 15.59 0.73 0.0780 0.0031 4 0.00003 0.00001 18.33 6.65 0.0069 0.0023 5 0.00006 0.00000 9.48 1.37 0.0156 0.0009 6 0.00051 0.00000 15.12 0.11 0.1316 0.0003 7 0.00004 0.00000 6.99 1.36 0.0095 0.0012 8 0.00002 0.00000 0.49 21.62 0.0061 0.0007 9 0.00006 0.00000 6.07 0.24 0.0155 0.0012 10 0.00125 0.00000 -9.02 0.02 0.3206 0.0007 11 0.00001 0.00001 1.95 8.18 0.0021 0.0014 12 0.00001 0.00000 2.45 1.29 0.0024 0.0011 13 0.00004 0.00001 3.59 1.15 0.0111 0.0015 14 0.00100 0.00001 -6.46 0.07 0.2574 0.0019 15 0.00005 0.00001 -9.75 1.72 0.0120 0.0036 16 0.00003 0.00001 1.05 1.37 0.0074 0.0025 The magnetic center is at X = 117.7 +- 0.8 microns Y = 111.7 +- 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: 03-29-1995 Time: 12:11:58 Magnet Name: 173 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4122 +- 1.49357E-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 0.00152 0.00001 -131.56 0.86 0.3574 0.0034 2 0.42661 0.00007 45.03 0.00 100.0000 0.0000 3 0.00030 0.00002 16.58 1.01 0.0704 0.0050 4 0.00002 0.00001 13.79 7.67 0.0049 0.0012 5 0.00007 0.00001 9.43 1.47 0.0155 0.0015 6 0.00032 0.00001 15.23 0.13 0.0754 0.0014 7 0.00004 0.00000 6.59 0.50 0.0086 0.0004 8 0.00002 0.00000 0.07 20.09 0.0041 0.0009 9 0.00007 0.00001 5.44 0.30 0.0159 0.0016 10 0.00141 0.00001 -9.02 0.03 0.3298 0.0015 11 0.00001 0.00000 -2.77 4.48 0.0022 0.0011 12 0.00001 0.00000 -1.20 8.59 0.0032 0.0009 13 0.00007 0.00000 3.20 0.40 0.0166 0.0006 14 0.00109 0.00001 -6.43 0.07 0.2548 0.0028 15 0.00004 0.00001 -5.35 9.69 0.0100 0.0016 16 0.00004 0.00001 1.28 1.31 0.0083 0.0013 The magnetic center is at X = 119.4 +- 1.9 microns Y = 105.9 +- 2.0 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 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)