SLAC Magnetic Measurements Date: 03-21-1995 Time: 14:10:00 Magnet Name (Serial #): 182 Bar Code Number: 545 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: 03-21-1995 Time: 14:57:07 Magnet Name: 182 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00089 +- 6.981537E-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 0.00003 0.00000 134.44 1.31 0.2314 0.0059 2 0.01489 0.00000 44.97 0.00 100.0000 0.0000 3 0.00001 0.00000 19.13 0.84 0.0991 0.0033 4 0.00000 0.00000 -37.18 1.45 0.0066 0.0016 5 0.00000 0.00000 12.37 1.66 0.0171 0.0014 6 0.00003 0.00000 15.20 0.08 0.2194 0.0019 7 0.00000 0.00000 17.48 0.66 0.0036 0.0012 8 0.00000 0.00000 1.12 14.19 0.0013 0.0003 9 0.00000 0.00000 -5.49 0.25 0.0067 0.0005 10 0.00004 0.00000 -9.07 0.03 0.2987 0.0010 11 0.00000 0.00000 9.75 4.17 0.0023 0.0016 12 0.00000 0.00000 1.26 10.80 0.0019 0.0008 13 0.00000 0.00000 -3.93 1.45 0.0114 0.0022 14 0.00004 0.00000 -6.45 0.03 0.2611 0.0022 15 0.00000 0.00000 -3.76 1.98 0.0068 0.0028 16 0.00000 0.00000 7.27 2.36 0.0069 0.0017 The magnetic center is at X = -73.8 +- 2.5 microns Y = 72.4 +- 2.5 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: 03-21-1995 Time: 15:03:14 Magnet Name: 182 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10148 +- 3.308466E-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 0.00011 0.00000 119.18 0.80 0.3251 0.0051 2 0.03495 0.00001 44.97 0.00 100.0000 0.0000 3 0.00003 0.00000 25.05 0.40 0.0859 0.0045 4 0.00000 0.00000 -35.87 2.66 0.0108 0.0028 5 0.00001 0.00000 11.42 0.54 0.0180 0.0015 6 0.00008 0.00000 15.15 0.09 0.2242 0.0016 7 0.00000 0.00000 12.08 5.22 0.0027 0.0010 8 0.00000 0.00000 10.79 18.54 0.0086 0.0014 9 0.00000 0.00000 -6.53 1.14 0.0080 0.0018 10 0.00010 0.00000 -9.06 0.05 0.2991 0.0025 11 0.00000 0.00000 -0.19 5.35 0.0023 0.0017 12 0.00000 0.00000 -1.75 2.84 0.0074 0.0006 13 0.00000 0.00000 -4.12 1.48 0.0125 0.0018 14 0.00009 0.00000 -6.46 0.03 0.2583 0.0025 15 0.00000 0.00000 -6.00 2.26 0.0081 0.0029 16 0.00000 0.00000 2.22 4.22 0.0090 0.0047 The magnetic center is at X = -126.8 +- 2.2 microns Y = 70.8 +- 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 Date: 03-21-1995 Time: 15:09:25 Magnet Name: 182 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06455 +- 3.577944E-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 0.00025 0.00000 116.77 0.97 0.3624 0.0019 2 0.06883 0.00001 44.97 0.00 100.0000 0.0000 3 0.00006 0.00000 27.06 1.23 0.0812 0.0034 4 0.00000 0.00000 -26.47 5.77 0.0064 0.0016 5 0.00001 0.00000 11.16 1.23 0.0180 0.0020 6 0.00015 0.00000 15.14 0.08 0.2238 0.0012 7 0.00000 0.00000 16.46 3.42 0.0031 0.0014 8 0.00000 0.00000 6.20 8.54 0.0024 0.0005 9 0.00001 0.00000 -7.32 0.87 0.0079 0.0018 10 0.00021 0.00000 -9.05 0.02 0.3005 0.0008 11 0.00000 0.00000 -9.28 7.31 0.0016 0.0004 12 0.00000 0.00000 -1.83 9.70 0.0044 0.0016 13 0.00001 0.00000 -4.46 0.95 0.0107 0.0024 14 0.00018 0.00000 -6.45 0.04 0.2559 0.0019 15 0.00000 0.00000 -5.03 1.54 0.0062 0.0023 16 0.00000 0.00000 4.81 3.29 0.0060 0.0038 The magnetic center is at X = -144.5 +- 1.4 microns Y = 72.9 +- 2.5 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: 03-21-1995 Time: 15:15:40 Magnet Name: 182 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0579 +- 1.002293E-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 0.00053 0.00000 116.33 0.86 0.3839 0.0032 2 0.13729 0.00003 44.97 0.00 100.0000 0.0000 3 0.00011 0.00000 27.46 1.43 0.0799 0.0035 4 0.00001 0.00000 -25.07 4.02 0.0073 0.0011 5 0.00002 0.00000 10.95 1.81 0.0176 0.0023 6 0.00031 0.00000 15.12 0.07 0.2237 0.0011 7 0.00000 0.00000 15.44 3.40 0.0028 0.0012 8 0.00000 0.00000 -3.07 3.67 0.0019 0.0009 9 0.00001 0.00000 -7.14 0.88 0.0071 0.0022 10 0.00042 0.00000 -9.05 0.01 0.3034 0.0015 11 0.00000 0.00000 -0.30 13.36 0.0025 0.0013 12 0.00000 0.00000 2.33 9.91 0.0031 0.0016 13 0.00002 0.00000 -4.24 0.57 0.0117 0.0013 14 0.00035 0.00000 -6.44 0.06 0.2584 0.0018 15 0.00001 0.00000 -6.28 0.78 0.0085 0.0018 16 0.00001 0.00000 1.92 7.72 0.0076 0.0012 The magnetic center is at X = -153.7 +- 1.7 microns Y = 76.1 +- 2.4 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: 03-21-1995 Time: 15:21:55 Magnet Name: 182 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0715 +- 5.906748E-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 114.27 0.85 0.3827 0.0023 2 0.20544 0.00004 44.94 0.00 100.0000 0.0000 3 0.00016 0.00001 27.42 1.19 0.0779 0.0043 4 0.00001 0.00000 -21.62 7.97 0.0062 0.0012 5 0.00004 0.00001 11.66 1.28 0.0185 0.0025 6 0.00044 0.00000 15.11 0.13 0.2159 0.0018 7 0.00001 0.00000 5.60 17.83 0.0035 0.0012 8 0.00000 0.00000 -1.38 8.63 0.0023 0.0006 9 0.00001 0.00000 -7.34 0.67 0.0073 0.0010 10 0.00063 0.00000 -9.06 0.02 0.3048 0.0007 11 0.00001 0.00000 -1.26 12.68 0.0030 0.0011 12 0.00001 0.00000 -3.38 8.59 0.0032 0.0015 13 0.00002 0.00001 -4.34 1.05 0.0101 0.0034 14 0.00053 0.00000 -6.50 0.02 0.2557 0.0017 15 0.00001 0.00001 -5.52 2.11 0.0070 0.0033 16 0.00001 0.00000 1.58 5.18 0.0056 0.0019 The magnetic center is at X = -155.8 +- 1.4 microns Y = 70.3 +- 2.4 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: 03-21-1995 Time: 15:28:10 Magnet Name: 182 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3138 +- 3.864723E-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 0.00105 0.00001 113.20 0.98 0.3859 0.0037 2 0.27308 0.00002 44.94 0.00 100.0000 0.0000 3 0.00021 0.00001 28.26 1.17 0.0767 0.0034 4 0.00005 0.00001 -38.80 1.25 0.0166 0.0024 5 0.00005 0.00001 10.41 1.96 0.0185 0.0020 6 0.00057 0.00000 15.17 0.07 0.2073 0.0018 7 0.00001 0.00001 15.09 4.06 0.0031 0.0019 8 0.00003 0.00000 -0.11 0.74 0.0096 0.0007 9 0.00002 0.00001 -6.32 1.86 0.0065 0.0025 10 0.00084 0.00000 -9.05 0.03 0.3078 0.0013 11 0.00001 0.00000 -7.87 8.24 0.0019 0.0005 12 0.00001 0.00001 0.01 8.38 0.0036 0.0027 13 0.00003 0.00001 -5.05 1.08 0.0117 0.0019 14 0.00070 0.00001 -6.51 0.03 0.2579 0.0021 15 0.00002 0.00001 -3.70 0.69 0.0088 0.0022 16 0.00003 0.00001 8.47 1.27 0.0120 0.0033 The magnetic center is at X = -158.4 +- 1.9 microns Y = 67.9 +- 2.8 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: 03-21-1995 Time: 15:34:26 Magnet Name: 182 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4124 +- 7.46317E-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 0.00134 0.00000 113.18 0.48 0.3964 0.0014 2 0.33785 0.00006 44.94 0.00 100.0000 0.0000 3 0.00027 0.00000 27.59 0.74 0.0807 0.0014 4 0.00003 0.00001 -34.70 1.87 0.0098 0.0017 5 0.00006 0.00000 10.54 1.65 0.0179 0.0014 6 0.00062 0.00001 15.14 0.05 0.1848 0.0019 7 0.00001 0.00000 11.62 4.14 0.0019 0.0010 8 0.00001 0.00000 -10.12 18.77 0.0019 0.0005 9 0.00002 0.00001 -6.96 1.39 0.0068 0.0015 10 0.00105 0.00000 -9.08 0.02 0.3101 0.0009 11 0.00001 0.00000 0.33 12.02 0.0020 0.0011 12 0.00002 0.00000 -0.38 0.33 0.0071 0.0012 13 0.00004 0.00000 -5.77 0.71 0.0127 0.0013 14 0.00087 0.00001 -6.52 0.02 0.2572 0.0019 15 0.00002 0.00001 -5.97 1.19 0.0064 0.0023 16 0.00003 0.00001 8.47 1.87 0.0090 0.0019 The magnetic center is at X = -162.8 +- 0.8 microns Y = 69.7 +- 1.4 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: 03-21-1995 Time: 15:40:41 Magnet Name: 182 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3979 +- 1.055948E-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 0.00171 0.00001 117.78 0.74 0.4386 0.0032 2 0.38988 0.00008 44.94 0.00 100.0000 0.0000 3 0.00039 0.00002 23.10 1.11 0.1000 0.0040 4 0.00003 0.00001 -28.23 4.33 0.0085 0.0025 5 0.00006 0.00001 11.38 1.17 0.0154 0.0030 6 0.00052 0.00001 15.30 0.08 0.1323 0.0016 7 0.00002 0.00000 10.04 19.72 0.0041 0.0008 8 0.00002 0.00000 0.38 21.51 0.0051 0.0005 9 0.00003 0.00000 -5.47 1.71 0.0087 0.0009 10 0.00126 0.00001 -9.07 0.03 0.3221 0.0014 11 0.00001 0.00000 -9.68 4.01 0.0020 0.0008 12 0.00002 0.00000 -6.24 1.87 0.0057 0.0011 13 0.00004 0.00001 -3.87 0.53 0.0105 0.0020 14 0.00100 0.00001 -6.44 0.05 0.2576 0.0016 15 0.00003 0.00001 -6.95 0.97 0.0078 0.0023 16 0.00004 0.00001 3.70 0.83 0.0099 0.0037 The magnetic center is at X = -173.3 +- 1.7 microns Y = 91.3 +- 2.3 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: 03-21-1995 Time: 15:46:57 Magnet Name: 182 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4018 +- 3.13827E-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 0.00197 0.00002 121.15 0.98 0.4625 0.0050 2 0.42623 0.00010 44.94 0.00 100.0000 0.0000 3 0.00047 0.00002 20.03 1.09 0.1110 0.0051 4 0.00004 0.00001 -29.56 3.91 0.0092 0.0020 5 0.00006 0.00001 12.56 1.23 0.0152 0.0023 6 0.00032 0.00001 15.56 0.27 0.0751 0.0022 7 0.00002 0.00000 -0.90 22.62 0.0044 0.0007 8 0.00001 0.00000 -8.99 18.07 0.0024 0.0011 9 0.00004 0.00000 -6.49 1.94 0.0086 0.0004 10 0.00142 0.00001 -9.07 0.04 0.3323 0.0016 11 0.00001 0.00000 -4.59 7.32 0.0024 0.0008 12 0.00002 0.00000 -8.86 2.62 0.0049 0.0008 13 0.00004 0.00001 -4.88 0.72 0.0100 0.0030 14 0.00108 0.00001 -6.48 0.06 0.2538 0.0023 15 0.00003 0.00001 -5.09 0.65 0.0080 0.0028 16 0.00005 0.00001 5.18 0.75 0.0127 0.0022 The magnetic center is at X = -176.8 +- 2.7 microns Y = 106.9 +- 3.2 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)