SLAC Magnetic Measurements Date: 03-16-1995 Time: 10:20:24 Magnet Name (Serial #): 107 Bar Code Number: 450 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: 03-16-1995 Time: 11:07:38 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00185 +- 3.450921E-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 -105.91 0.10 0.5897 0.0017 2 0.01487 0.00001 44.96 0.00 100.0000 0.0000 3 0.00000 0.00000 20.84 0.97 0.0236 0.0018 4 0.00000 0.00000 4.79 23.27 0.0037 0.0016 5 0.00000 0.00000 11.35 0.37 0.0190 0.0022 6 0.00003 0.00000 14.97 0.06 0.2164 0.0015 7 0.00000 0.00000 11.70 3.40 0.0029 0.0016 8 0.00000 0.00000 -6.92 15.70 0.0031 0.0018 9 0.00000 0.00000 6.47 0.18 0.0112 0.0012 10 0.00005 0.00000 -9.05 0.01 0.3040 0.0025 11 0.00000 0.00000 -5.53 12.48 0.0051 0.0009 12 0.00000 0.00000 -5.74 1.52 0.0034 0.0015 13 0.00000 0.00000 4.25 0.45 0.0125 0.0010 14 0.00004 0.00000 -6.47 0.05 0.2557 0.0017 15 0.00000 0.00000 -5.52 4.87 0.0092 0.0031 16 0.00000 0.00000 2.78 0.59 0.0057 0.0025 The magnetic center is at X = 253.3 +- 0.8 microns Y = 72.2 +- 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: 03-16-1995 Time: 11:13:49 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10183 +- 6.861069E-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 0.00018 0.00000 -117.82 0.32 0.5202 0.0005 2 0.03500 0.00001 44.96 0.00 100.0000 0.0000 3 0.00001 0.00000 11.34 1.97 0.0290 0.0021 4 0.00000 0.00000 -40.29 1.91 0.0122 0.0014 5 0.00001 0.00000 11.89 1.32 0.0180 0.0021 6 0.00008 0.00000 14.98 0.12 0.2208 0.0012 7 0.00000 0.00000 14.61 5.10 0.0032 0.0008 8 0.00000 0.00000 -6.54 3.30 0.0032 0.0013 9 0.00000 0.00000 7.14 1.04 0.0117 0.0007 10 0.00011 0.00000 -9.03 0.02 0.3030 0.0002 11 0.00000 0.00000 -13.79 2.22 0.0046 0.0011 12 0.00000 0.00000 -2.97 1.20 0.0056 0.0011 13 0.00001 0.00000 4.07 0.37 0.0147 0.0013 14 0.00009 0.00000 -6.48 0.03 0.2528 0.0049 15 0.00000 0.00000 1.85 8.81 0.0067 0.0039 16 0.00000 0.00000 4.80 3.83 0.0043 0.0020 The magnetic center is at X = 205.5 +- 0.6 microns Y = 108.5 +- 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: 03-16-1995 Time: 11:20:04 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06431 +- 7.456611E-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 -123.15 0.22 0.4950 0.0020 2 0.06896 0.00005 44.96 0.00 100.0000 0.0000 3 0.00002 0.00000 11.85 0.85 0.0330 0.0016 4 0.00000 0.00000 -21.93 4.78 0.0056 0.0012 5 0.00001 0.00000 13.50 0.51 0.0167 0.0011 6 0.00015 0.00000 15.00 0.08 0.2219 0.0012 7 0.00000 0.00000 8.34 15.13 0.0024 0.0015 8 0.00000 0.00000 -11.67 2.67 0.0015 0.0006 9 0.00001 0.00000 6.93 0.82 0.0122 0.0017 10 0.00021 0.00000 -9.04 0.02 0.3030 0.0012 11 0.00000 0.00000 -6.02 12.76 0.0048 0.0010 12 0.00000 0.00000 -5.03 3.86 0.0053 0.0021 13 0.00001 0.00000 3.91 0.24 0.0140 0.0012 14 0.00018 0.00000 -6.45 0.06 0.2566 0.0043 15 0.00001 0.00000 -0.47 6.78 0.0085 0.0010 16 0.00000 0.00000 2.87 3.78 0.0037 0.0007 The magnetic center is at X = 185.1 +- 0.8 microns Y = 120.9 +- 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: 03-16-1995 Time: 11:26:25 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0577 +- 7.829521E-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 -126.49 0.17 0.4826 0.0012 2 0.13760 0.00004 44.96 0.00 100.0000 0.0000 3 0.00005 0.00000 12.66 0.49 0.0387 0.0023 4 0.00001 0.00000 -22.02 4.09 0.0058 0.0024 5 0.00002 0.00000 13.02 0.59 0.0179 0.0013 6 0.00031 0.00000 15.00 0.05 0.2229 0.0011 7 0.00000 0.00000 15.83 3.60 0.0027 0.0014 8 0.00000 0.00000 -17.58 2.01 0.0023 0.0009 9 0.00002 0.00000 7.40 0.67 0.0119 0.0009 10 0.00042 0.00000 -9.04 0.01 0.3054 0.0005 11 0.00001 0.00000 -13.70 1.56 0.0050 0.0010 12 0.00000 0.00000 -7.78 3.25 0.0023 0.0010 13 0.00002 0.00000 4.14 0.42 0.0139 0.0013 14 0.00035 0.00000 -6.45 0.05 0.2551 0.0019 15 0.00001 0.00000 -2.64 8.55 0.0051 0.0022 16 0.00001 0.00000 3.24 0.67 0.0059 0.0026 The magnetic center is at X = 173.3 +- 0.6 microns Y = 128.2 +- 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: 03-16-1995 Time: 11:32:44 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0685 +- 1.499016E-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 0.00099 0.00000 -127.72 0.07 0.4788 0.0011 2 0.20599 0.00013 44.94 0.00 100.0000 0.0000 3 0.00008 0.00000 13.19 0.54 0.0379 0.0016 4 0.00001 0.00000 -16.77 3.31 0.0047 0.0013 5 0.00004 0.00000 12.89 0.46 0.0185 0.0012 6 0.00044 0.00000 14.98 0.07 0.2141 0.0008 7 0.00001 0.00000 13.11 6.45 0.0031 0.0016 8 0.00001 0.00000 -14.79 3.06 0.0035 0.0009 9 0.00002 0.00000 6.54 0.35 0.0117 0.0009 10 0.00062 0.00000 -9.06 0.02 0.3017 0.0010 11 0.00001 0.00000 -10.30 2.01 0.0045 0.0020 12 0.00001 0.00000 -4.02 9.37 0.0032 0.0008 13 0.00003 0.00000 4.24 0.71 0.0138 0.0011 14 0.00052 0.00000 -6.48 0.06 0.2540 0.0020 15 0.00001 0.00000 -5.76 9.35 0.0071 0.0024 16 0.00003 0.00000 0.47 0.62 0.0126 0.0020 The magnetic center is at X = 169.2 +- 0.4 microns Y = 130.8 +- 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: 03-16-1995 Time: 11:39:04 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3128 +- 1.148978E-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 0.00129 0.00000 -127.35 0.24 0.4728 0.0013 2 0.27381 0.00016 44.94 0.00 100.0000 0.0000 3 0.00010 0.00001 13.07 0.78 0.0361 0.0027 4 0.00002 0.00001 -20.65 4.87 0.0073 0.0026 5 0.00005 0.00000 13.29 0.83 0.0179 0.0004 6 0.00056 0.00000 15.01 0.06 0.2059 0.0011 7 0.00001 0.00001 14.21 3.49 0.0031 0.0020 8 0.00001 0.00000 -7.94 6.83 0.0035 0.0010 9 0.00003 0.00000 6.48 0.15 0.0121 0.0010 10 0.00084 0.00000 -9.06 0.06 0.3084 0.0015 11 0.00001 0.00000 -12.94 1.03 0.0041 0.0005 12 0.00001 0.00000 -7.38 4.72 0.0020 0.0011 13 0.00004 0.00000 4.08 0.87 0.0139 0.0010 14 0.00070 0.00000 -6.50 0.05 0.2566 0.0009 15 0.00002 0.00001 -5.14 8.90 0.0082 0.0030 16 0.00001 0.00001 6.22 2.97 0.0051 0.0021 The magnetic center is at X = 167.9 +- 0.7 microns Y = 128.1 +- 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: 03-16-1995 Time: 11:45:23 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4128 +- 6.232799E-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 0.00160 0.00000 -126.32 0.20 0.4716 0.0006 2 0.33917 0.00006 44.94 0.00 100.0000 0.0000 3 0.00011 0.00000 12.41 0.45 0.0311 0.0014 4 0.00005 0.00001 -40.13 2.11 0.0133 0.0026 5 0.00006 0.00000 13.06 1.02 0.0168 0.0009 6 0.00060 0.00001 14.99 0.17 0.1772 0.0034 7 0.00001 0.00000 11.96 3.20 0.0021 0.0006 8 0.00002 0.00001 -4.06 1.91 0.0050 0.0019 9 0.00004 0.00000 6.67 1.02 0.0130 0.0006 10 0.00107 0.00001 -9.06 0.04 0.3156 0.0016 11 0.00002 0.00000 -7.98 13.77 0.0062 0.0006 12 0.00001 0.00000 -3.14 2.59 0.0035 0.0008 13 0.00005 0.00000 4.09 0.62 0.0146 0.0013 14 0.00085 0.00002 -6.52 0.03 0.2501 0.0054 15 0.00001 0.00000 0.31 9.50 0.0044 0.0014 16 0.00002 0.00001 5.88 2.45 0.0048 0.0031 The magnetic center is at X = 169.7 +- 0.5 microns Y = 124.8 +- 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: 03-16-1995 Time: 11:51:42 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.397 +- 4.685716E-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 0.00185 0.00001 -123.21 0.27 0.4722 0.0015 2 0.39095 0.00011 44.94 0.00 100.0000 0.0000 3 0.00006 0.00001 12.66 1.32 0.0156 0.0019 4 0.00003 0.00001 -36.89 4.66 0.0089 0.0022 5 0.00007 0.00001 12.15 0.98 0.0178 0.0015 6 0.00052 0.00000 15.12 0.14 0.1324 0.0009 7 0.00001 0.00000 11.00 4.61 0.0021 0.0010 8 0.00002 0.00000 -19.62 1.25 0.0063 0.0010 9 0.00005 0.00001 7.12 0.83 0.0125 0.0018 10 0.00127 0.00000 -9.05 0.02 0.3248 0.0007 11 0.00002 0.00000 -13.27 0.78 0.0046 0.0010 12 0.00003 0.00001 -1.62 0.67 0.0086 0.0014 13 0.00005 0.00000 4.30 0.26 0.0126 0.0012 14 0.00099 0.00001 -6.51 0.03 0.2521 0.0022 15 0.00003 0.00001 -5.59 3.73 0.0068 0.0036 16 0.00002 0.00001 6.69 2.47 0.0050 0.0024 The magnetic center is at X = 176.5 +- 0.8 microns Y = 115.5 +- 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: 03-16-1995 Time: 11:58:02 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4012 +- 4.315837E-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 0.00200 0.00000 -121.54 0.20 0.4677 0.0007 2 0.42752 0.00027 44.94 0.00 100.0000 0.0000 3 0.00004 0.00001 15.60 2.99 0.0090 0.0022 4 0.00004 0.00001 -34.56 3.56 0.0090 0.0030 5 0.00009 0.00000 12.06 0.87 0.0200 0.0007 6 0.00032 0.00001 15.14 0.14 0.0749 0.0015 7 0.00001 0.00000 9.76 8.67 0.0024 0.0007 8 0.00004 0.00000 -20.93 0.39 0.0087 0.0010 9 0.00005 0.00000 5.88 0.80 0.0126 0.0009 10 0.00144 0.00001 -9.05 0.01 0.3368 0.0022 11 0.00002 0.00001 -12.99 1.10 0.0046 0.0014 12 0.00003 0.00001 -2.35 0.81 0.0079 0.0019 13 0.00006 0.00001 4.33 0.39 0.0135 0.0013 14 0.00109 0.00002 -6.50 0.05 0.2545 0.0041 15 0.00004 0.00001 -1.51 10.19 0.0094 0.0034 16 0.00005 0.00001 2.81 0.51 0.0114 0.0024 The magnetic center is at X = 178.1 +- 0.5 microns Y = 109.3 +- 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 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)