SLAC Magnetic Measurements Date: 04-04-1995 Time: 06:44:37 Magnet Name (Serial #): 184 Bar Code Number: 493 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: 04-04-1995 Time: 07:31:50 Magnet Name: 184 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.998005 +- 4.012213E-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 -136.73 0.43 0.5139 0.0040 2 0.01486 0.00000 44.99 0.00 100.0000 0.0000 3 0.00002 0.00000 6.96 0.50 0.1405 0.0026 4 0.00000 0.00000 -18.69 1.13 0.0148 0.0021 5 0.00000 0.00000 24.35 2.96 0.0179 0.0014 6 0.00003 0.00000 14.94 0.03 0.2170 0.0009 7 0.00000 0.00000 20.56 0.53 0.0118 0.0009 8 0.00000 0.00000 -18.42 4.18 0.0032 0.0014 9 0.00000 0.00000 3.38 1.43 0.0048 0.0020 10 0.00004 0.00000 -9.00 0.01 0.2954 0.0017 11 0.00000 0.00000 -0.14 10.07 0.0020 0.0014 12 0.00000 0.00000 -4.51 7.01 0.0029 0.0009 13 0.00000 0.00000 -0.76 2.92 0.0092 0.0012 14 0.00004 0.00000 -6.48 0.03 0.2564 0.0011 15 0.00000 0.00000 2.64 5.66 0.0041 0.0018 16 0.00000 0.00000 7.82 0.95 0.0046 0.0026 The magnetic center is at X = 157.4 +- 1.8 microns Y = 167.1 +- 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: 04-04-1995 Time: 07:37:57 Magnet Name: 184 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.09866 +- 2.334964E-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 0.00010 0.00000 -131.46 0.88 0.2805 0.0032 2 0.03493 0.00001 44.99 0.00 100.0000 0.0000 3 0.00002 0.00000 29.90 0.42 0.0691 0.0051 4 0.00001 0.00000 -24.38 1.59 0.0173 0.0017 5 0.00001 0.00000 17.40 0.85 0.0161 0.0035 6 0.00008 0.00000 14.91 0.02 0.2224 0.0015 7 0.00000 0.00000 15.56 1.66 0.0058 0.0009 8 0.00000 0.00000 -22.18 0.26 0.0110 0.0006 9 0.00000 0.00000 -0.44 1.79 0.0050 0.0013 10 0.00010 0.00000 -9.00 0.03 0.2964 0.0013 11 0.00000 0.00000 0.52 10.07 0.0024 0.0007 12 0.00000 0.00000 -2.76 1.18 0.0055 0.0024 13 0.00000 0.00000 2.56 1.03 0.0101 0.0042 14 0.00009 0.00000 -6.43 0.05 0.2549 0.0018 15 0.00000 0.00000 -3.43 4.71 0.0022 0.0011 16 0.00000 0.00000 -0.41 2.24 0.0056 0.0029 The magnetic center is at X = 93.9 +- 1.7 microns Y = 82.9 +- 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: 04-04-1995 Time: 07:44:08 Magnet Name: 184 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06283 +- 5.892071E-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 0.00016 0.00000 -136.61 1.22 0.2377 0.0047 2 0.06880 0.00001 44.99 0.00 100.0000 0.0000 3 0.00005 0.00000 34.20 1.61 0.0756 0.0032 4 0.00001 0.00000 -19.13 1.90 0.0190 0.0024 5 0.00001 0.00000 16.88 0.92 0.0165 0.0009 6 0.00015 0.00000 14.97 0.06 0.2219 0.0008 7 0.00000 0.00000 12.32 4.11 0.0040 0.0011 8 0.00000 0.00000 -1.53 20.09 0.0020 0.0006 9 0.00000 0.00000 2.18 0.45 0.0060 0.0006 10 0.00021 0.00000 -8.98 0.01 0.2991 0.0010 11 0.00000 0.00000 -1.48 6.49 0.0022 0.0009 12 0.00000 0.00000 -9.06 1.78 0.0049 0.0016 13 0.00001 0.00000 0.30 1.80 0.0101 0.0016 14 0.00017 0.00000 -6.44 0.04 0.2515 0.0016 15 0.00000 0.00000 5.17 2.53 0.0040 0.0013 16 0.00000 0.00000 -2.29 6.50 0.0057 0.0009 The magnetic center is at X = 72.9 +- 2.2 microns Y = 77.2 +- 2.2 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: 07:50:24 Magnet Name: 184 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0607 +- 7.37234E-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 0.00032 0.00001 -141.24 0.53 0.2324 0.0048 2 0.13725 0.00001 44.99 0.00 100.0000 0.0000 3 0.00010 0.00000 35.00 1.11 0.0743 0.0019 4 0.00003 0.00000 -19.95 1.84 0.0197 0.0020 5 0.00002 0.00000 16.38 0.90 0.0146 0.0019 6 0.00030 0.00000 15.02 0.06 0.2221 0.0018 7 0.00001 0.00000 3.49 13.61 0.0038 0.0020 8 0.00000 0.00000 5.65 16.98 0.0018 0.0009 9 0.00001 0.00000 0.45 1.15 0.0043 0.0015 10 0.00041 0.00000 -9.02 0.02 0.2984 0.0014 11 0.00000 0.00000 -2.68 7.17 0.0022 0.0006 12 0.00000 0.00000 -3.48 9.32 0.0023 0.0015 13 0.00002 0.00000 1.08 1.27 0.0114 0.0030 14 0.00035 0.00000 -6.45 0.03 0.2549 0.0029 15 0.00000 0.00000 -5.53 4.47 0.0033 0.0010 16 0.00001 0.00000 -2.85 6.15 0.0056 0.0014 The magnetic center is at X = 65.0 +- 1.5 microns Y = 80.9 +- 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: 04-04-1995 Time: 07:56:39 Magnet Name: 184 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0757 +- 5.596565E-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 0.00046 0.00001 -142.05 0.81 0.2237 0.0042 2 0.20549 0.00003 44.96 0.00 100.0000 0.0000 3 0.00015 0.00001 35.63 0.99 0.0737 0.0034 4 0.00004 0.00001 -19.50 1.50 0.0215 0.0026 5 0.00003 0.00000 16.50 2.49 0.0151 0.0024 6 0.00044 0.00000 14.99 0.08 0.2131 0.0007 7 0.00001 0.00000 11.89 2.52 0.0043 0.0008 8 0.00001 0.00000 10.99 18.32 0.0040 0.0011 9 0.00001 0.00000 3.05 3.10 0.0039 0.0013 10 0.00062 0.00000 -9.05 0.02 0.3030 0.0008 11 0.00000 0.00000 -0.95 10.11 0.0023 0.0014 12 0.00001 0.00000 -13.07 1.43 0.0064 0.0011 13 0.00002 0.00000 -0.82 0.59 0.0087 0.0022 14 0.00052 0.00000 -6.48 0.02 0.2539 0.0018 15 0.00001 0.00001 4.67 3.65 0.0047 0.0040 16 0.00001 0.00001 -3.87 6.62 0.0062 0.0025 The magnetic center is at X = 61.4 +- 1.6 microns Y = 78.8 +- 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: 04-04-1995 Time: 08:02:54 Magnet Name: 184 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3194 +- 7.090413E-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 0.00058 0.00001 -141.00 0.94 0.2127 0.0048 2 0.27320 0.00004 44.96 0.00 100.0000 0.0000 3 0.00021 0.00001 36.52 1.12 0.0762 0.0018 4 0.00007 0.00001 -29.43 1.24 0.0259 0.0019 5 0.00004 0.00000 17.19 0.63 0.0152 0.0018 6 0.00056 0.00000 15.01 0.05 0.2053 0.0016 7 0.00001 0.00000 14.83 3.90 0.0041 0.0018 8 0.00002 0.00000 -0.38 0.98 0.0055 0.0013 9 0.00001 0.00000 -0.66 1.32 0.0050 0.0013 10 0.00083 0.00000 -9.06 0.02 0.3041 0.0009 11 0.00000 0.00000 -7.82 6.95 0.0017 0.0014 12 0.00001 0.00000 -5.07 9.17 0.0039 0.0013 13 0.00003 0.00001 0.58 1.47 0.0095 0.0026 14 0.00070 0.00001 -6.47 0.01 0.2553 0.0023 15 0.00001 0.00000 2.43 4.06 0.0036 0.0016 16 0.00002 0.00001 3.72 8.35 0.0070 0.0025 The magnetic center is at X = 59.8 +- 1.8 microns Y = 73.8 +- 1.9 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: 04-04-1995 Time: 08:09:11 Magnet Name: 184 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4204 +- 3.185215E-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 0.00063 0.00002 -135.57 0.52 0.1874 0.0052 2 0.33821 0.00002 44.96 0.00 100.0000 0.0000 3 0.00028 0.00001 40.44 0.62 0.0813 0.0033 4 0.00009 0.00001 -25.92 1.23 0.0258 0.0021 5 0.00005 0.00001 15.99 2.55 0.0142 0.0016 6 0.00062 0.00000 15.05 0.09 0.1833 0.0009 7 0.00001 0.00000 8.42 5.59 0.0040 0.0012 8 0.00002 0.00000 0.69 20.76 0.0063 0.0009 9 0.00002 0.00001 0.46 1.29 0.0052 0.0015 10 0.00104 0.00000 -9.02 0.03 0.3067 0.0012 11 0.00000 0.00000 4.66 6.45 0.0014 0.0005 12 0.00002 0.00001 -2.76 1.84 0.0071 0.0035 13 0.00003 0.00001 0.81 0.86 0.0086 0.0026 14 0.00085 0.00000 -6.46 0.02 0.2507 0.0015 15 0.00002 0.00001 2.30 6.49 0.0045 0.0018 16 0.00002 0.00001 6.35 3.05 0.0057 0.0016 The magnetic center is at X = 58.6 +- 1.7 microns Y = 59.8 +- 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: 04-04-1995 Time: 08:15:28 Magnet Name: 184 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4084 +- 3.571991E-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 0.00062 0.00001 -134.91 1.69 0.1588 0.0015 2 0.39011 0.00013 44.96 0.00 100.0000 0.0000 3 0.00039 0.00001 40.94 0.49 0.0997 0.0021 4 0.00010 0.00001 -22.71 1.20 0.0253 0.0013 5 0.00006 0.00001 14.72 0.92 0.0146 0.0030 6 0.00052 0.00000 15.10 0.08 0.1329 0.0009 7 0.00001 0.00001 4.43 3.42 0.0036 0.0020 8 0.00003 0.00001 -11.18 18.74 0.0079 0.0015 9 0.00002 0.00000 0.79 2.18 0.0055 0.0010 10 0.00124 0.00001 -9.04 0.02 0.3166 0.0021 11 0.00001 0.00001 -1.94 12.55 0.0023 0.0016 12 0.00001 0.00001 -3.15 4.11 0.0037 0.0016 13 0.00003 0.00001 -0.15 1.49 0.0076 0.0025 14 0.00099 0.00001 -6.44 0.02 0.2549 0.0018 15 0.00002 0.00001 1.44 2.86 0.0043 0.0014 16 0.00003 0.00001 -1.90 3.45 0.0070 0.0032 The magnetic center is at X = 50.2 +- 1.5 microns Y = 50.1 +- 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: 04-04-1995 Time: 08:21:44 Magnet Name: 184 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4143 +- 1.188326E-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 0.00064 0.00002 -128.41 1.86 0.1494 0.0044 2 0.42644 0.00010 44.96 0.00 100.0000 0.0000 3 0.00043 0.00002 43.10 0.51 0.1009 0.0057 4 0.00011 0.00001 -22.96 1.62 0.0255 0.0017 5 0.00007 0.00001 14.43 1.27 0.0162 0.0017 6 0.00032 0.00001 15.13 0.09 0.0751 0.0022 7 0.00001 0.00000 4.85 3.74 0.0035 0.0006 8 0.00002 0.00000 10.85 18.26 0.0053 0.0009 9 0.00002 0.00000 1.74 2.00 0.0048 0.0011 10 0.00140 0.00000 -9.03 0.01 0.3284 0.0007 11 0.00001 0.00001 2.64 9.97 0.0030 0.0015 12 0.00002 0.00001 -10.10 2.19 0.0047 0.0015 13 0.00003 0.00000 0.78 1.34 0.0076 0.0009 14 0.00108 0.00001 -6.47 0.04 0.2526 0.0024 15 0.00001 0.00001 -1.10 7.44 0.0023 0.0018 16 0.00004 0.00001 0.19 0.41 0.0095 0.0022 The magnetic center is at X = 52.3 +- 2.0 microns Y = 41.5 +- 2.1 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 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)