SLAC Magnetic Measurements Date: 04-04-1995 Time: 09:13:00 Magnet Name (Serial #): 146 Bar Code Number: 538 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: janitor 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: 04-04-1995 Time: 10:00:05 Magnet Name: 146 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00013 +- 5.880881E-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 -113.80 0.46 0.3872 0.0018 2 0.01486 0.00000 45.01 0.00 100.0000 0.0000 3 0.00001 0.00000 -13.17 1.00 0.0395 0.0018 4 0.00001 0.00000 -24.72 0.65 0.0535 0.0011 5 0.00000 0.00000 11.85 3.46 0.0126 0.0016 6 0.00003 0.00000 15.26 0.07 0.2188 0.0015 7 0.00000 0.00000 17.77 1.10 0.0111 0.0014 8 0.00000 0.00000 -12.45 1.67 0.0047 0.0007 9 0.00000 0.00000 0.94 3.17 0.0053 0.0019 10 0.00004 0.00000 -8.96 0.02 0.2965 0.0020 11 0.00000 0.00000 -11.74 4.36 0.0040 0.0026 12 0.00000 0.00000 -1.54 6.47 0.0046 0.0026 13 0.00000 0.00000 -1.18 1.90 0.0076 0.0017 14 0.00004 0.00000 -6.40 0.03 0.2600 0.0017 15 0.00000 0.00000 4.17 4.20 0.0031 0.0011 16 0.00000 0.00000 1.98 8.09 0.0045 0.0036 The magnetic center is at X = 158.2 +- 0.9 microns Y = 69.8 +- 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: 04-04-1995 Time: 10:06:11 Magnet Name: 146 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10089 +- 3.15202E-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 -133.82 0.77 0.2309 0.0019 2 0.03493 0.00001 45.01 0.00 100.0000 0.0000 3 0.00001 0.00000 27.18 2.03 0.0260 0.0016 4 0.00002 0.00000 -26.35 0.48 0.0626 0.0022 5 0.00001 0.00000 14.75 0.72 0.0162 0.0032 6 0.00008 0.00000 15.33 0.07 0.2244 0.0022 7 0.00000 0.00000 19.24 1.78 0.0059 0.0006 8 0.00000 0.00000 -18.54 1.01 0.0095 0.0011 9 0.00000 0.00000 0.75 3.04 0.0055 0.0008 10 0.00010 0.00000 -8.97 0.02 0.2960 0.0017 11 0.00000 0.00000 -8.91 4.97 0.0034 0.0007 12 0.00000 0.00000 -2.88 1.91 0.0090 0.0020 13 0.00000 0.00000 -0.59 2.21 0.0084 0.0013 14 0.00009 0.00000 -6.41 0.04 0.2611 0.0024 15 0.00000 0.00000 2.04 3.66 0.0049 0.0014 16 0.00000 0.00000 -4.53 4.26 0.0058 0.0046 The magnetic center is at X = 74.4 +- 1.1 microns Y = 71.4 +- 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: 04-04-1995 Time: 10:12:22 Magnet Name: 146 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.0646 +- 7.515873E-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 0.00015 0.00000 -147.04 0.55 0.2108 0.0006 2 0.06884 0.00001 45.01 0.00 100.0000 0.0000 3 0.00002 0.00000 30.38 1.36 0.0349 0.0021 4 0.00004 0.00000 -25.27 0.60 0.0645 0.0023 5 0.00001 0.00000 14.63 0.89 0.0164 0.0013 6 0.00015 0.00000 15.27 0.06 0.2240 0.0011 7 0.00000 0.00000 19.84 2.49 0.0060 0.0024 8 0.00000 0.00000 -12.61 0.89 0.0037 0.0009 9 0.00000 0.00000 0.67 2.39 0.0048 0.0014 10 0.00021 0.00000 -8.97 0.04 0.2997 0.0011 11 0.00000 0.00000 -12.11 1.78 0.0032 0.0003 12 0.00000 0.00000 -6.40 1.84 0.0067 0.0017 13 0.00001 0.00000 -0.96 1.82 0.0091 0.0016 14 0.00017 0.00000 -6.42 0.03 0.2526 0.0019 15 0.00000 0.00000 -2.26 5.76 0.0055 0.0014 16 0.00000 0.00000 2.27 8.42 0.0062 0.0022 The magnetic center is at X = 51.2 +- 0.8 microns Y = 79.0 +- 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: 04-04-1995 Time: 10:18:38 Magnet Name: 146 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0607 +- 8.852153E-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 0.00028 0.00000 -153.09 0.36 0.2073 0.0016 2 0.13732 0.00001 45.01 0.00 100.0000 0.0000 3 0.00005 0.00000 32.48 0.65 0.0357 0.0020 4 0.00009 0.00000 -25.51 0.40 0.0656 0.0019 5 0.00002 0.00000 16.81 0.76 0.0155 0.0029 6 0.00031 0.00000 15.24 0.06 0.2228 0.0016 7 0.00001 0.00000 20.11 1.85 0.0062 0.0009 8 0.00001 0.00000 -11.33 0.95 0.0045 0.0013 9 0.00001 0.00000 -0.68 1.71 0.0045 0.0021 10 0.00041 0.00000 -8.99 0.02 0.3016 0.0015 11 0.00000 0.00000 -4.92 11.97 0.0024 0.0013 12 0.00001 0.00000 -8.72 0.94 0.0058 0.0011 13 0.00001 0.00000 0.09 1.87 0.0056 0.0028 14 0.00035 0.00000 -6.41 0.02 0.2545 0.0019 15 0.00001 0.00000 3.27 5.19 0.0044 0.0015 16 0.00001 0.00000 -1.72 6.25 0.0061 0.0026 The magnetic center is at X = 41.9 +- 0.6 microns Y = 82.6 +- 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: 04-04-1995 Time: 10:24:52 Magnet Name: 146 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0775 +- 8.743566E-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 0.00000 -154.22 0.57 0.2079 0.0015 2 0.20557 0.00002 44.98 0.00 100.0000 0.0000 3 0.00007 0.00000 33.16 1.37 0.0348 0.0010 4 0.00013 0.00000 -25.37 0.46 0.0631 0.0022 5 0.00003 0.00000 16.03 1.78 0.0152 0.0011 6 0.00044 0.00000 15.19 0.04 0.2136 0.0013 7 0.00001 0.00000 19.20 0.83 0.0061 0.0017 8 0.00001 0.00000 -12.92 2.35 0.0037 0.0011 9 0.00001 0.00000 0.38 1.69 0.0056 0.0014 10 0.00063 0.00000 -8.97 0.02 0.3051 0.0016 11 0.00001 0.00000 -3.76 7.86 0.0026 0.0009 12 0.00002 0.00000 -10.32 1.23 0.0075 0.0017 13 0.00001 0.00001 -1.31 2.05 0.0059 0.0037 14 0.00052 0.00000 -6.44 0.03 0.2548 0.0010 15 0.00001 0.00000 1.38 3.98 0.0045 0.0014 16 0.00002 0.00000 2.33 8.00 0.0074 0.0024 The magnetic center is at X = 40.4 +- 0.9 microns Y = 83.6 +- 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: 04-04-1995 Time: 10:31:07 Magnet Name: 146 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3223 +- 5.380752E-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 0.00057 0.00000 -153.97 0.44 0.2084 0.0007 2 0.27327 0.00003 44.98 0.00 100.0000 0.0000 3 0.00010 0.00000 34.80 0.61 0.0352 0.0011 4 0.00018 0.00000 -28.74 0.28 0.0662 0.0015 5 0.00004 0.00000 16.64 1.33 0.0133 0.0015 6 0.00056 0.00001 15.23 0.05 0.2047 0.0023 7 0.00001 0.00000 19.46 3.32 0.0049 0.0012 8 0.00003 0.00000 -3.64 0.99 0.0104 0.0014 9 0.00002 0.00000 0.52 0.64 0.0057 0.0009 10 0.00084 0.00000 -9.00 0.02 0.3071 0.0012 11 0.00001 0.00000 -12.08 2.22 0.0029 0.0007 12 0.00002 0.00001 -7.41 1.31 0.0076 0.0033 13 0.00002 0.00000 -1.57 0.64 0.0091 0.0013 14 0.00070 0.00001 -6.41 0.02 0.2564 0.0025 15 0.00001 0.00000 -0.95 7.84 0.0032 0.0005 16 0.00002 0.00001 -3.50 8.27 0.0069 0.0037 The magnetic center is at X = 40.9 +- 0.7 microns Y = 83.7 +- 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 Date: 04-04-1995 Time: 10:37:24 Magnet Name: 146 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.425 +- 2.554423E-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 0.00071 0.00001 -155.72 0.53 0.2091 0.0023 2 0.33818 0.00005 44.98 0.00 100.0000 0.0000 3 0.00013 0.00001 36.51 1.31 0.0373 0.0024 4 0.00020 0.00001 -27.62 0.51 0.0601 0.0023 5 0.00004 0.00001 17.72 1.96 0.0118 0.0031 6 0.00062 0.00000 15.28 0.06 0.1819 0.0014 7 0.00001 0.00000 19.67 1.77 0.0033 0.0013 8 0.00002 0.00000 -17.19 1.39 0.0066 0.0011 9 0.00002 0.00001 0.51 2.36 0.0048 0.0016 10 0.00105 0.00000 -9.00 0.01 0.3095 0.0010 11 0.00001 0.00000 -10.13 1.71 0.0041 0.0011 12 0.00004 0.00001 -2.26 1.54 0.0108 0.0018 13 0.00003 0.00001 -0.38 0.91 0.0077 0.0016 14 0.00087 0.00000 -6.44 0.03 0.2563 0.0007 15 0.00001 0.00001 3.23 6.01 0.0038 0.0018 16 0.00001 0.00000 -0.52 7.23 0.0044 0.0010 The magnetic center is at X = 38.4 +- 0.9 microns Y = 85.1 +- 1.0 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 Date: 04-04-1995 Time: 10:43:41 Magnet Name: 146 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4119 +- 8.294664E-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 0.00076 0.00001 -153.33 0.56 0.1950 0.0024 2 0.39005 0.00004 44.98 0.00 100.0000 0.0000 3 0.00017 0.00001 39.62 1.39 0.0440 0.0021 4 0.00022 0.00001 -26.51 0.52 0.0575 0.0023 5 0.00005 0.00001 17.93 1.39 0.0121 0.0020 6 0.00050 0.00001 15.31 0.15 0.1288 0.0015 7 0.00002 0.00000 20.79 2.05 0.0042 0.0011 8 0.00003 0.00000 -18.06 1.09 0.0065 0.0011 9 0.00002 0.00001 1.59 2.71 0.0051 0.0015 10 0.00125 0.00001 -9.03 0.02 0.3196 0.0018 11 0.00001 0.00001 -9.11 6.45 0.0015 0.0018 12 0.00001 0.00000 -4.92 4.95 0.0033 0.0012 13 0.00002 0.00001 -0.37 3.50 0.0063 0.0019 14 0.00100 0.00000 -6.42 0.02 0.2571 0.0013 15 0.00002 0.00001 -0.15 4.52 0.0060 0.0021 16 0.00002 0.00001 3.62 3.52 0.0045 0.0019 The magnetic center is at X = 39.1 +- 0.9 microns Y = 77.8 +- 1.0 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 Date: 04-04-1995 Time: 10:49:58 Magnet Name: 146 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4194 +- 1.49684E-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 0.00083 0.00000 -151.30 0.52 0.1950 0.0008 2 0.42636 0.00006 44.98 0.00 100.0000 0.0000 3 0.00018 0.00001 41.76 1.15 0.0411 0.0032 4 0.00023 0.00001 -26.92 0.58 0.0536 0.0019 5 0.00005 0.00001 16.51 3.00 0.0111 0.0016 6 0.00031 0.00000 15.54 0.19 0.0717 0.0009 7 0.00001 0.00000 17.42 3.78 0.0027 0.0005 8 0.00002 0.00001 -16.23 2.02 0.0055 0.0013 9 0.00002 0.00000 1.43 0.64 0.0057 0.0009 10 0.00141 0.00001 -9.03 0.03 0.3318 0.0017 11 0.00001 0.00000 4.68 8.59 0.0020 0.0011 12 0.00003 0.00001 -7.33 1.29 0.0062 0.0024 13 0.00004 0.00001 0.57 1.53 0.0082 0.0027 14 0.00107 0.00001 -6.44 0.03 0.2521 0.0012 15 0.00002 0.00001 0.78 4.88 0.0045 0.0023 16 0.00002 0.00002 -1.09 3.49 0.0047 0.0043 The magnetic center is at X = 41.8 +- 0.7 microns Y = 76.4 +- 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 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)