SLAC Magnetic Measurements Date: 02-28-1995 Time: 10:24:50 Magnet Name (Serial #): 102 Bar Code Number: 433 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: 02-28-1995 Time: 11:12:16 Magnet Name: 102 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.998345 +- 5.360997E-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 0.00019 0.00000 109.64 0.21 1.2698 0.0037 2 0.01486 0.00000 45.08 0.00 100.0000 0.0000 3 0.00001 0.00000 35.95 0.96 0.0591 0.0011 4 0.00000 0.00000 -39.57 3.51 0.0058 0.0005 5 0.00000 0.00000 19.54 0.87 0.0296 0.0013 6 0.00003 0.00000 15.16 0.05 0.2202 0.0012 7 0.00000 0.00000 4.09 7.37 0.0037 0.0020 8 0.00000 0.00000 -8.42 3.47 0.0046 0.0007 9 0.00001 0.00000 -8.06 0.17 0.0370 0.0016 10 0.00004 0.00000 -8.94 0.03 0.3019 0.0014 11 0.00000 0.00000 1.30 11.83 0.0048 0.0013 12 0.00000 0.00000 -4.20 1.31 0.0077 0.0014 13 0.00001 0.00000 -5.05 0.22 0.0510 0.0016 14 0.00004 0.00000 -6.29 0.06 0.2595 0.0029 15 0.00000 0.00000 -3.54 4.67 0.0087 0.0027 16 0.00000 0.00000 -1.79 5.78 0.0054 0.0007 The magnetic center is at X = -534.2 +- 1.7 microns Y = 190.6 +- 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 Date: 02-28-1995 Time: 11:18:20 Magnet Name: 102 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.09663 +- 3.461562E-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 0.00048 0.00000 111.45 0.11 1.3612 0.0025 2 0.03496 0.00001 45.08 0.00 100.0000 0.0000 3 0.00002 0.00000 35.20 1.16 0.0432 0.0025 4 0.00000 0.00000 -41.23 2.01 0.0114 0.0020 5 0.00001 0.00000 19.53 0.51 0.0296 0.0010 6 0.00008 0.00000 15.12 0.08 0.2248 0.0013 7 0.00000 0.00000 11.36 4.87 0.0062 0.0020 8 0.00000 0.00000 -16.56 0.94 0.0069 0.0010 9 0.00001 0.00000 -8.06 0.07 0.0389 0.0006 10 0.00011 0.00000 -8.94 0.03 0.3030 0.0019 11 0.00000 0.00000 -9.47 1.33 0.0041 0.0006 12 0.00000 0.00000 -2.36 0.65 0.0109 0.0007 13 0.00002 0.00000 -5.08 0.12 0.0500 0.0012 14 0.00009 0.00000 -6.33 0.05 0.2580 0.0038 15 0.00000 0.00000 -5.81 3.23 0.0072 0.0026 16 0.00000 0.00000 -0.35 2.45 0.0094 0.0011 The magnetic center is at X = -565.9 +- 1.1 microns Y = 222.4 +- 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: 02-28-1995 Time: 11:24:30 Magnet Name: 102 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.05848 +- 4.246539E-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 0.00096 0.00000 111.61 0.03 1.4006 0.0018 2 0.06886 0.00000 45.08 0.00 100.0000 0.0000 3 0.00003 0.00000 37.20 1.12 0.0418 0.0034 4 0.00001 0.00000 -39.78 2.34 0.0075 0.0020 5 0.00002 0.00000 19.37 0.95 0.0314 0.0013 6 0.00016 0.00000 15.09 0.05 0.2257 0.0018 7 0.00000 0.00000 12.45 3.04 0.0039 0.0015 8 0.00000 0.00000 -7.53 0.91 0.0030 0.0014 9 0.00003 0.00000 -8.02 0.13 0.0392 0.0015 10 0.00021 0.00000 -8.91 0.03 0.3042 0.0017 11 0.00000 0.00000 -12.20 1.26 0.0045 0.0016 12 0.00001 0.00000 -4.25 0.54 0.0080 0.0021 13 0.00003 0.00000 -5.11 0.09 0.0501 0.0016 14 0.00018 0.00000 -6.25 0.05 0.2566 0.0023 15 0.00000 0.00000 -5.42 1.78 0.0048 0.0030 16 0.00000 0.00000 -0.16 9.59 0.0055 0.0035 The magnetic center is at X = -581.6 +- 0.8 microns Y = 230.4 +- 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: 02-28-1995 Time: 11:30:45 Magnet Name: 102 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0504 +- 1.556686E-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 0.00195 0.00000 111.82 0.18 1.4207 0.0019 2 0.13743 0.00002 45.08 0.00 100.0000 0.0000 3 0.00006 0.00000 37.67 1.31 0.0417 0.0029 4 0.00001 0.00000 -38.95 3.51 0.0061 0.0019 5 0.00004 0.00000 19.36 0.43 0.0306 0.0006 6 0.00031 0.00000 15.13 0.06 0.2265 0.0013 7 0.00001 0.00000 14.61 3.46 0.0048 0.0012 8 0.00001 0.00000 -5.19 1.85 0.0038 0.0010 9 0.00005 0.00000 -7.99 0.24 0.0391 0.0011 10 0.00042 0.00000 -8.92 0.03 0.3026 0.0007 11 0.00000 0.00000 0.30 11.05 0.0024 0.0015 12 0.00001 0.00000 -5.27 1.36 0.0077 0.0003 13 0.00007 0.00000 -5.15 0.09 0.0505 0.0008 14 0.00035 0.00001 -6.35 0.01 0.2572 0.0037 15 0.00001 0.00000 -1.68 1.60 0.0058 0.0010 16 0.00001 0.00000 0.61 4.98 0.0052 0.0024 The magnetic center is at X = -589.1 +- 1.1 microns Y = 235.9 +- 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: 02-28-1995 Time: 11:36:58 Magnet Name: 102 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0607 +- 4.611841E-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 0.00295 0.00001 111.57 0.09 1.4325 0.0035 2 0.20571 0.00002 45.06 0.00 100.0000 0.0000 3 0.00009 0.00000 37.29 1.83 0.0427 0.0018 4 0.00001 0.00000 -13.45 31.11 0.0053 0.0017 5 0.00007 0.00000 19.49 0.75 0.0317 0.0018 6 0.00045 0.00000 15.07 0.08 0.2176 0.0011 7 0.00001 0.00000 12.83 5.96 0.0045 0.0009 8 0.00001 0.00001 -6.05 2.40 0.0035 0.0031 9 0.00008 0.00000 -8.02 0.15 0.0379 0.0021 10 0.00064 0.00000 -8.90 0.03 0.3096 0.0010 11 0.00001 0.00000 0.50 12.70 0.0031 0.0020 12 0.00001 0.00000 -7.34 0.79 0.0067 0.0019 13 0.00010 0.00000 -5.33 0.18 0.0497 0.0014 14 0.00054 0.00001 -6.35 0.04 0.2603 0.0043 15 0.00001 0.00001 -5.70 3.81 0.0037 0.0043 16 0.00001 0.00000 4.11 5.65 0.0057 0.0020 The magnetic center is at X = -595.0 +- 1.5 microns Y = 235.2 +- 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: 02-28-1995 Time: 11:43:12 Magnet Name: 102 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.2994 +- 9.230937E-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 0.00393 0.00000 111.47 0.10 1.4384 0.0016 2 0.27338 0.00009 45.05 0.00 100.0000 0.0000 3 0.00011 0.00001 37.95 0.85 0.0406 0.0032 4 0.00005 0.00000 -42.68 0.99 0.0197 0.0018 5 0.00008 0.00000 19.30 0.85 0.0299 0.0014 6 0.00057 0.00000 15.12 0.12 0.2091 0.0016 7 0.00001 0.00000 8.43 14.34 0.0033 0.0014 8 0.00003 0.00000 -3.38 0.91 0.0120 0.0017 9 0.00011 0.00000 -7.92 0.09 0.0387 0.0016 10 0.00085 0.00000 -8.96 0.04 0.3094 0.0018 11 0.00001 0.00000 -9.46 3.55 0.0045 0.0017 12 0.00002 0.00000 -4.75 0.37 0.0069 0.0017 13 0.00014 0.00000 -5.19 0.05 0.0504 0.0006 14 0.00070 0.00000 -6.37 0.04 0.2575 0.0016 15 0.00002 0.00001 -0.86 1.71 0.0060 0.0020 16 0.00002 0.00000 -4.36 8.04 0.0059 0.0007 The magnetic center is at X = -597.9 +- 0.7 microns Y = 235.2 +- 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: 02-28-1995 Time: 11:49:27 Magnet Name: 102 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.3963 +- 9.062616E-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 0.00486 0.00001 111.38 0.10 1.4367 0.0021 2 0.33832 0.00005 45.05 0.00 100.0000 0.0000 3 0.00014 0.00000 37.85 1.37 0.0413 0.0013 4 0.00005 0.00000 -19.75 36.26 0.0134 0.0012 5 0.00009 0.00001 19.48 0.81 0.0278 0.0016 6 0.00062 0.00000 15.18 0.09 0.1844 0.0010 7 0.00001 0.00001 14.19 4.65 0.0030 0.0019 8 0.00003 0.00000 -18.95 1.21 0.0074 0.0004 9 0.00014 0.00000 -8.04 0.08 0.0411 0.0013 10 0.00106 0.00001 -8.95 0.03 0.3139 0.0020 11 0.00001 0.00001 -1.74 9.77 0.0037 0.0018 12 0.00004 0.00001 -1.72 0.42 0.0117 0.0022 13 0.00016 0.00000 -5.34 0.13 0.0464 0.0015 14 0.00087 0.00001 -6.38 0.03 0.2573 0.0019 15 0.00003 0.00001 -1.45 4.17 0.0087 0.0033 16 0.00001 0.00001 2.14 2.87 0.0029 0.0019 The magnetic center is at X = -597.6 +- 1.0 microns Y = 233.9 +- 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: 02-28-1995 Time: 11:55:42 Magnet Name: 102 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3793 +- 5.620954E-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 0.00567 0.00001 111.76 0.05 1.4528 0.0016 2 0.39049 0.00005 45.05 0.00 100.0000 0.0000 3 0.00017 0.00000 34.82 0.60 0.0443 0.0013 4 0.00002 0.00000 -17.91 35.78 0.0064 0.0010 5 0.00010 0.00000 18.62 1.12 0.0244 0.0008 6 0.00051 0.00000 15.12 0.06 0.1311 0.0010 7 0.00001 0.00000 18.94 3.91 0.0036 0.0005 8 0.00002 0.00001 -13.86 1.82 0.0054 0.0019 9 0.00016 0.00000 -7.63 0.30 0.0414 0.0012 10 0.00126 0.00000 -8.93 0.02 0.3226 0.0010 11 0.00002 0.00001 -12.19 2.33 0.0052 0.0016 12 0.00004 0.00001 -3.63 0.26 0.0105 0.0018 13 0.00019 0.00000 -5.11 0.16 0.0487 0.0009 14 0.00099 0.00001 -6.37 0.04 0.2525 0.0022 15 0.00003 0.00001 1.15 1.65 0.0089 0.0032 16 0.00002 0.00001 -3.79 2.57 0.0064 0.0019 The magnetic center is at X = -602.7 +- 0.7 microns Y = 240.6 +- 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: 02-28-1995 Time: 12:01:57 Magnet Name: 102 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3817 +- 9.800135E-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 0.00623 0.00001 111.89 0.10 1.4599 0.0021 2 0.42705 0.00005 45.05 0.00 100.0000 0.0000 3 0.00019 0.00001 33.58 0.71 0.0437 0.0024 4 0.00003 0.00001 -38.91 2.46 0.0066 0.0012 5 0.00008 0.00001 18.15 1.07 0.0182 0.0024 6 0.00031 0.00000 15.21 0.26 0.0734 0.0006 7 0.00002 0.00000 9.17 20.17 0.0043 0.0007 8 0.00002 0.00001 -12.56 1.74 0.0052 0.0014 9 0.00019 0.00001 -7.92 0.24 0.0439 0.0017 10 0.00143 0.00001 -8.94 0.01 0.3339 0.0012 11 0.00001 0.00000 -5.38 12.02 0.0032 0.0009 12 0.00003 0.00001 -5.58 1.49 0.0070 0.0017 13 0.00021 0.00001 -5.17 0.13 0.0490 0.0023 14 0.00107 0.00000 -6.35 0.03 0.2517 0.0009 15 0.00003 0.00001 1.08 6.49 0.0072 0.0035 16 0.00003 0.00001 -0.88 1.99 0.0063 0.0029 The magnetic center is at X = -605.1 +- 0.9 microns Y = 243.1 +- 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 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)