SLAC Magnetic Measurements Date: 02-24-1995 Time: 11:24:25 Magnet Name (Serial #): 156 Bar Code Number: 507 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: 02-24-1995 Time: 12:11:30 Magnet Name: 156 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00081 +- 7.821002E-05 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 0.00005 0.00000 137.25 0.09 0.3323 0.0013 2 0.01491 0.00000 45.10 0.00 100.0000 0.0000 3 0.00002 0.00000 35.34 0.22 0.1017 0.0013 4 0.00000 0.00000 17.97 1.32 0.0189 0.0007 5 0.00000 0.00000 21.75 1.67 0.0241 0.0031 6 0.00003 0.00000 15.31 0.17 0.2076 0.0020 7 0.00000 0.00000 9.07 20.25 0.0038 0.0017 8 0.00000 0.00000 -0.40 3.93 0.0029 0.0005 9 0.00000 0.00000 -3.76 1.97 0.0114 0.0028 10 0.00004 0.00000 -8.94 0.02 0.2978 0.0016 11 0.00000 0.00000 -8.13 7.12 0.0034 0.0010 12 0.00000 0.00000 2.55 5.45 0.0031 0.0006 13 0.00000 0.00000 -2.86 0.93 0.0155 0.0016 14 0.00004 0.00000 -6.31 0.04 0.2602 0.0003 15 0.00000 0.00000 0.89 4.20 0.0031 0.0007 16 0.00000 0.00000 -1.19 6.44 0.0041 0.0029 The magnetic center is at X = -100.8 +- 0.4 microns Y = 109.0 +- 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: 02-24-1995 Time: 12:17:34 Magnet Name: 156 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10085 +- 2.396419E-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 0.00013 0.00000 152.98 0.09 0.3576 0.0007 2 0.03499 0.00001 45.10 0.00 100.0000 0.0000 3 0.00002 0.00000 41.72 0.55 0.0513 0.0021 4 0.00000 0.00000 23.04 1.77 0.0111 0.0031 5 0.00001 0.00000 22.50 1.02 0.0200 0.0020 6 0.00007 0.00000 15.32 0.05 0.2081 0.0029 7 0.00000 0.00000 20.51 3.09 0.0043 0.0015 8 0.00000 0.00000 19.55 2.16 0.0061 0.0007 9 0.00000 0.00000 -2.64 1.64 0.0092 0.0023 10 0.00010 0.00000 -8.90 0.02 0.2996 0.0019 11 0.00000 0.00000 -10.55 5.07 0.0039 0.0024 12 0.00000 0.00000 1.10 1.88 0.0068 0.0028 13 0.00001 0.00000 -2.47 0.57 0.0152 0.0010 14 0.00009 0.00000 -6.34 0.02 0.2574 0.0029 15 0.00000 0.00000 -0.09 7.16 0.0034 0.0015 16 0.00000 0.00000 -0.35 1.48 0.0099 0.0008 The magnetic center is at X = -72.6 +- 0.3 microns Y = 142.3 +- 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: 02-24-1995 Time: 12:23:44 Magnet Name: 156 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06147 +- 8.406865E-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 0.00026 0.00000 155.59 0.18 0.3738 0.0018 2 0.06890 0.00001 45.10 0.00 100.0000 0.0000 3 0.00003 0.00000 44.73 0.60 0.0439 0.0016 4 0.00001 0.00000 15.85 2.04 0.0084 0.0023 5 0.00001 0.00000 22.29 1.72 0.0173 0.0014 6 0.00015 0.00000 15.20 0.06 0.2110 0.0012 7 0.00000 0.00000 18.46 2.32 0.0044 0.0018 8 0.00000 0.00000 4.93 2.40 0.0040 0.0013 9 0.00001 0.00000 -1.33 0.71 0.0084 0.0007 10 0.00021 0.00000 -8.90 0.03 0.3004 0.0014 11 0.00000 0.00000 -3.56 11.42 0.0033 0.0003 12 0.00000 0.00000 -0.87 8.96 0.0022 0.0007 13 0.00001 0.00000 -3.13 0.58 0.0148 0.0007 14 0.00018 0.00000 -6.35 0.03 0.2570 0.0034 15 0.00000 0.00000 -1.92 0.74 0.0049 0.0010 16 0.00000 0.00000 1.12 8.54 0.0044 0.0022 The magnetic center is at X = -69.0 +- 0.6 microns Y = 152.0 +- 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: 02-24-1995 Time: 12:57:37 Magnet Name: 156 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0517 +- 5.176053E-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 0.00149 0.00166 133.07 40.36 0.9811 1.0349 2 0.14290 0.00848 25.07 34.69 100.0000 0.0000 3 0.00098 0.00160 49.74 6.06 0.6250 1.0135 4 0.00059 0.00101 4.28 21.19 0.3777 0.6412 5 0.00023 0.00036 12.05 17.76 0.1492 0.2284 6 0.00030 0.00001 6.03 16.23 0.2069 0.0047 7 0.00022 0.00038 8.15 16.70 0.1431 0.2398 8 0.00017 0.00029 0.64 8.23 0.1102 0.1809 9 0.00006 0.00008 -5.55 4.23 0.0371 0.0504 10 0.00049 0.00013 -10.83 3.39 0.3382 0.0638 11 0.00014 0.00023 -11.48 1.18 0.0879 0.1436 12 0.00008 0.00013 0.12 6.21 0.0497 0.0808 13 0.00006 0.00008 -5.51 4.21 0.0425 0.0473 14 0.00039 0.00007 -7.57 2.06 0.2718 0.0286 15 0.00010 0.00015 1.61 6.57 0.0609 0.0969 16 0.00004 0.00007 2.05 6.57 0.0288 0.0412 The magnetic center is at X = -340.1 +- 441.3 microns Y = 317.9 +- 428.6 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: 02-24-1995 Time: 13:03:51 Magnet Name: 156 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0619 +- 2.998847E-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 0.00079 0.00000 157.03 0.23 0.3839 0.0010 2 0.20578 0.00003 45.08 0.00 100.0000 0.0000 3 0.00007 0.00000 45.68 1.42 0.0356 0.0023 4 0.00001 0.00000 14.60 5.93 0.0065 0.0020 5 0.00004 0.00000 21.36 0.31 0.0172 0.0013 6 0.00041 0.00000 15.30 0.05 0.1996 0.0008 7 0.00001 0.00000 16.55 1.84 0.0045 0.0006 8 0.00001 0.00000 3.09 2.21 0.0036 0.0006 9 0.00002 0.00000 -2.25 0.34 0.0093 0.0008 10 0.00063 0.00000 -8.94 0.02 0.3040 0.0013 11 0.00000 0.00000 0.20 15.02 0.0024 0.0014 12 0.00001 0.00000 4.30 10.33 0.0037 0.0014 13 0.00003 0.00000 -2.36 0.47 0.0159 0.0022 14 0.00053 0.00000 -6.40 0.02 0.2567 0.0016 15 0.00001 0.00000 3.29 6.39 0.0056 0.0011 16 0.00001 0.00000 -10.44 0.66 0.0057 0.0016 The magnetic center is at X = -66.9 +- 0.7 microns Y = 157.9 +- 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: 02-24-1995 Time: 13:10:04 Magnet Name: 156 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.302 +- 1.355029E-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 0.00104 0.00001 156.65 0.31 0.3791 0.0023 2 0.27346 0.00004 45.07 0.00 100.0000 0.0000 3 0.00010 0.00001 48.31 0.45 0.0358 0.0023 4 0.00003 0.00001 39.32 3.38 0.0122 0.0018 5 0.00004 0.00001 21.08 1.08 0.0147 0.0029 6 0.00052 0.00000 15.32 0.08 0.1915 0.0008 7 0.00001 0.00000 19.26 1.95 0.0046 0.0005 8 0.00003 0.00000 0.72 1.13 0.0127 0.0013 9 0.00002 0.00000 -3.16 1.33 0.0071 0.0011 10 0.00083 0.00001 -8.90 0.02 0.3053 0.0022 11 0.00001 0.00000 -11.04 3.53 0.0034 0.0009 12 0.00001 0.00001 2.26 6.24 0.0042 0.0020 13 0.00004 0.00000 -2.52 0.43 0.0159 0.0011 14 0.00070 0.00001 -6.36 0.04 0.2568 0.0031 15 0.00001 0.00001 0.19 5.92 0.0049 0.0033 16 0.00002 0.00001 -4.11 8.35 0.0078 0.0047 The magnetic center is at X = -67.1 +- 0.9 microns Y = 155.5 +- 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: 02-24-1995 Time: 13:16:19 Magnet Name: 156 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.3987 +- 6.55329E-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 156.54 0.10 0.3595 0.0021 2 0.33834 0.00001 45.07 0.00 100.0000 0.0000 3 0.00014 0.00001 51.32 1.46 0.0408 0.0021 4 0.00003 0.00001 34.10 4.14 0.0075 0.0017 5 0.00005 0.00000 19.24 1.55 0.0138 0.0011 6 0.00056 0.00001 15.36 0.05 0.1647 0.0020 7 0.00002 0.00000 14.05 2.47 0.0047 0.0007 8 0.00002 0.00001 18.10 1.48 0.0053 0.0020 9 0.00002 0.00000 -2.96 0.69 0.0068 0.0008 10 0.00104 0.00001 -8.91 0.01 0.3075 0.0026 11 0.00001 0.00000 -10.56 1.26 0.0033 0.0008 12 0.00003 0.00000 0.10 0.59 0.0098 0.0010 13 0.00005 0.00001 -2.99 0.43 0.0150 0.0024 14 0.00087 0.00001 -6.41 0.01 0.2568 0.0025 15 0.00001 0.00001 1.10 7.11 0.0027 0.0015 16 0.00001 0.00001 0.83 7.63 0.0044 0.0016 The magnetic center is at X = -63.9 +- 0.5 microns Y = 147.3 +- 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: 02-24-1995 Time: 13:22:32 Magnet Name: 156 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3792 +- 6.534611E-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 0.00140 0.00001 155.52 0.15 0.3591 0.0031 2 0.39036 0.00010 45.07 0.00 100.0000 0.0000 3 0.00017 0.00001 49.22 0.20 0.0427 0.0030 4 0.00002 0.00001 20.20 11.35 0.0043 0.0021 5 0.00005 0.00001 18.60 2.54 0.0139 0.0015 6 0.00044 0.00001 15.51 0.12 0.1120 0.0023 7 0.00002 0.00000 17.58 2.25 0.0052 0.0007 8 0.00001 0.00000 8.75 4.97 0.0017 0.0004 9 0.00003 0.00000 -2.09 0.49 0.0066 0.0005 10 0.00125 0.00000 -8.90 0.03 0.3190 0.0007 11 0.00001 0.00000 -12.93 1.25 0.0037 0.0009 12 0.00001 0.00000 0.70 2.92 0.0033 0.0008 13 0.00006 0.00000 -2.97 0.80 0.0157 0.0012 14 0.00100 0.00001 -6.38 0.01 0.2570 0.0026 15 0.00001 0.00001 -2.53 5.52 0.0035 0.0015 16 0.00003 0.00001 1.31 1.49 0.0085 0.0023 The magnetic center is at X = -66.5 +- 0.7 microns Y = 146.0 +- 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: 02-24-1995 Time: 13:28:47 Magnet Name: 156 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3804 +- 1.039503E-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 0.00150 0.00001 155.12 0.18 0.3520 0.0029 2 0.42698 0.00009 45.07 0.00 100.0000 0.0000 3 0.00019 0.00001 49.77 0.52 0.0447 0.0016 4 0.00001 0.00000 -12.90 18.23 0.0022 0.0012 5 0.00005 0.00000 15.82 1.42 0.0114 0.0006 6 0.00024 0.00000 15.98 0.13 0.0563 0.0011 7 0.00001 0.00000 7.26 18.62 0.0031 0.0011 8 0.00001 0.00000 -1.49 10.17 0.0024 0.0008 9 0.00003 0.00000 -3.42 0.85 0.0077 0.0007 10 0.00140 0.00000 -8.87 0.04 0.3279 0.0008 11 0.00002 0.00001 -12.89 2.66 0.0040 0.0017 12 0.00001 0.00001 10.34 5.16 0.0034 0.0015 13 0.00006 0.00000 -2.56 0.56 0.0146 0.0005 14 0.00109 0.00001 -6.36 0.03 0.2556 0.0017 15 0.00001 0.00001 -1.34 4.16 0.0027 0.0013 16 0.00004 0.00001 1.04 2.76 0.0097 0.0018 The magnetic center is at X = -66.1 +- 0.7 microns Y = 142.6 +- 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 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)