SLAC Magnetic Measurements Date: 04-05-1995 Time: 11:25:48 Magnet Name (Serial #): 108 Bar Code Number: 413 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl Run Number: 2 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: 04-05-1995 Time: 12:12:57 Magnet Name: 108 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00353 +- 3.099442E-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 -110.60 0.33 0.5181 0.0022 2 0.01492 0.00001 45.01 0.00 100.0000 0.0000 3 0.00000 0.00000 26.99 8.33 0.0119 0.0024 4 0.00000 0.00000 -15.25 31.74 0.0051 0.0026 5 0.00000 0.00000 14.47 5.00 0.0107 0.0021 6 0.00003 0.00000 15.11 0.12 0.2133 0.0011 7 0.00000 0.00000 13.61 1.96 0.0092 0.0014 8 0.00000 0.00000 9.36 15.49 0.0024 0.0003 9 0.00000 0.00000 4.69 0.66 0.0091 0.0013 10 0.00004 0.00000 -9.02 0.04 0.2974 0.0013 11 0.00000 0.00000 -5.94 12.08 0.0019 0.0008 12 0.00000 0.00000 2.51 12.05 0.0050 0.0018 13 0.00000 0.00000 1.31 1.42 0.0125 0.0014 14 0.00004 0.00000 -6.42 0.05 0.2542 0.0028 15 0.00000 0.00000 -1.14 5.54 0.0048 0.0016 16 0.00000 0.00000 2.98 6.61 0.0032 0.0011 The magnetic center is at X = 216.6 +- 1.0 microns Y = 81.4 +- 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: 04-05-1995 Time: 12:19:02 Magnet Name: 108 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10585 +- 6.380979E-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 0.00014 0.00000 -131.78 0.32 0.3972 0.0030 2 0.03502 0.00000 45.01 0.00 100.0000 0.0000 3 0.00002 0.00000 25.87 0.54 0.0521 0.0021 4 0.00000 0.00000 -40.61 2.63 0.0108 0.0026 5 0.00000 0.00000 14.63 0.76 0.0132 0.0020 6 0.00008 0.00000 15.15 0.10 0.2208 0.0022 7 0.00000 0.00000 13.59 2.60 0.0064 0.0021 8 0.00000 0.00000 10.31 18.75 0.0102 0.0009 9 0.00000 0.00000 4.09 1.26 0.0086 0.0005 10 0.00010 0.00000 -9.00 0.02 0.2994 0.0019 11 0.00000 0.00000 7.44 3.98 0.0030 0.0018 12 0.00000 0.00000 -3.45 3.24 0.0062 0.0028 13 0.00000 0.00000 0.84 1.25 0.0131 0.0037 14 0.00009 0.00000 -6.45 0.01 0.2533 0.0022 15 0.00000 0.00000 4.41 3.86 0.0044 0.0035 16 0.00000 0.00000 -0.02 4.99 0.0046 0.0012 The magnetic center is at X = 132.3 +- 1.2 microns Y = 118.2 +- 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: 04-05-1995 Time: 12:25:13 Magnet Name: 108 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.06839 +- 7.566527E-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 -140.83 0.33 0.3690 0.0026 2 0.06899 0.00001 45.01 0.00 100.0000 0.0000 3 0.00004 0.00000 26.60 1.01 0.0635 0.0018 4 0.00000 0.00000 -36.07 6.11 0.0069 0.0020 5 0.00001 0.00000 17.12 2.21 0.0128 0.0022 6 0.00015 0.00000 15.09 0.09 0.2215 0.0014 7 0.00000 0.00000 14.30 3.55 0.0044 0.0019 8 0.00000 0.00000 6.00 14.36 0.0023 0.0004 9 0.00001 0.00000 5.17 0.94 0.0085 0.0015 10 0.00021 0.00000 -8.98 0.03 0.3013 0.0007 11 0.00000 0.00000 8.92 4.23 0.0023 0.0006 12 0.00000 0.00000 -4.95 7.85 0.0057 0.0012 13 0.00001 0.00000 2.44 0.66 0.0102 0.0046 14 0.00017 0.00000 -6.45 0.03 0.2509 0.0035 15 0.00001 0.00000 -3.09 2.03 0.0074 0.0020 16 0.00001 0.00000 6.51 2.66 0.0081 0.0052 The magnetic center is at X = 104.1 +- 1.1 microns Y = 127.8 +- 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: 04-05-1995 Time: 12:31:30 Magnet Name: 108 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0645 +- 8.570343E-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 0.00050 0.00000 -144.86 0.23 0.3634 0.0012 2 0.13766 0.00003 45.01 0.00 100.0000 0.0000 3 0.00009 0.00000 26.62 0.35 0.0651 0.0020 4 0.00001 0.00000 -31.66 2.41 0.0062 0.0027 5 0.00002 0.00000 16.52 1.10 0.0146 0.0012 6 0.00030 0.00000 15.11 0.08 0.2214 0.0020 7 0.00001 0.00000 14.00 1.55 0.0054 0.0012 8 0.00000 0.00000 2.57 14.71 0.0018 0.0011 9 0.00001 0.00000 4.14 1.56 0.0091 0.0015 10 0.00042 0.00000 -9.02 0.04 0.3029 0.0013 11 0.00000 0.00000 5.67 2.62 0.0020 0.0007 12 0.00001 0.00000 -8.43 2.36 0.0064 0.0008 13 0.00002 0.00000 2.16 1.70 0.0135 0.0027 14 0.00035 0.00000 -6.47 0.04 0.2521 0.0016 15 0.00001 0.00000 2.53 2.44 0.0053 0.0014 16 0.00001 0.00000 1.65 7.50 0.0047 0.0022 The magnetic center is at X = 93.4 +- 0.6 microns Y = 132.7 +- 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: 04-05-1995 Time: 12:37:45 Magnet Name: 108 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0795 +- 8.325833E-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 0.00074 0.00000 -147.59 0.24 0.3587 0.0007 2 0.20600 0.00003 44.99 0.00 100.0000 0.0000 3 0.00014 0.00000 26.34 0.16 0.0701 0.0007 4 0.00001 0.00001 -28.65 7.28 0.0063 0.0027 5 0.00003 0.00000 16.15 1.75 0.0126 0.0011 6 0.00044 0.00001 15.11 0.12 0.2149 0.0032 7 0.00001 0.00000 11.65 2.20 0.0040 0.0007 8 0.00000 0.00000 2.28 15.43 0.0022 0.0011 9 0.00002 0.00000 3.51 0.20 0.0083 0.0013 10 0.00063 0.00000 -9.01 0.04 0.3055 0.0016 11 0.00000 0.00000 9.56 4.00 0.0015 0.0002 12 0.00001 0.00000 3.24 11.32 0.0065 0.0022 13 0.00002 0.00001 1.17 2.30 0.0116 0.0025 14 0.00053 0.00001 -6.47 0.03 0.2550 0.0029 15 0.00001 0.00000 -0.26 2.80 0.0043 0.0013 16 0.00001 0.00001 -0.11 9.43 0.0065 0.0037 The magnetic center is at X = 85.9 +- 0.6 microns Y = 135.3 +- 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: 04-05-1995 Time: 12:44:00 Magnet Name: 108 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3269 +- 9.691133E-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 0.00098 0.00000 -149.93 0.27 0.3583 0.0008 2 0.27379 0.00004 44.99 0.00 100.0000 0.0000 3 0.00020 0.00000 25.58 0.21 0.0735 0.0006 4 0.00005 0.00000 -41.73 1.99 0.0193 0.0017 5 0.00004 0.00001 15.53 0.63 0.0146 0.0021 6 0.00056 0.00000 15.09 0.08 0.2044 0.0013 7 0.00001 0.00000 14.52 3.15 0.0050 0.0006 8 0.00002 0.00000 0.61 1.27 0.0068 0.0009 9 0.00002 0.00000 4.55 0.64 0.0091 0.0007 10 0.00084 0.00000 -9.03 0.02 0.3081 0.0014 11 0.00001 0.00000 3.84 11.23 0.0029 0.0017 12 0.00001 0.00000 2.52 10.62 0.0052 0.0006 13 0.00003 0.00001 1.84 1.11 0.0097 0.0051 14 0.00070 0.00001 -6.48 0.07 0.2548 0.0021 15 0.00002 0.00000 2.44 4.34 0.0057 0.0015 16 0.00001 0.00001 3.86 7.58 0.0048 0.0024 The magnetic center is at X = 80.2 +- 0.7 microns Y = 138.5 +- 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: 04-05-1995 Time: 12:50:17 Magnet Name: 108 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4301 +- 1.367812E-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 0.00119 0.00000 -149.65 0.13 0.3512 0.0012 2 0.33881 0.00006 44.99 0.00 100.0000 0.0000 3 0.00025 0.00001 26.23 0.63 0.0751 0.0025 4 0.00004 0.00001 -40.87 1.68 0.0114 0.0024 5 0.00005 0.00001 15.45 1.19 0.0144 0.0027 6 0.00062 0.00001 15.15 0.06 0.1819 0.0016 7 0.00001 0.00000 10.46 3.45 0.0037 0.0005 8 0.00002 0.00000 21.03 0.29 0.0069 0.0012 9 0.00004 0.00000 4.79 0.58 0.0105 0.0014 10 0.00105 0.00000 -9.05 0.02 0.3107 0.0011 11 0.00001 0.00001 4.79 9.25 0.0024 0.0017 12 0.00002 0.00001 1.11 5.14 0.0054 0.0034 13 0.00004 0.00000 1.55 0.49 0.0127 0.0013 14 0.00086 0.00001 -6.43 0.07 0.2526 0.0035 15 0.00002 0.00000 1.75 4.72 0.0051 0.0005 16 0.00002 0.00001 -0.70 8.62 0.0064 0.0027 The magnetic center is at X = 79.2 +- 0.4 microns Y = 135.4 +- 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 Date: 04-05-1995 Time: 12:56:33 Magnet Name: 108 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4152 +- 6.593139E-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 0.00143 0.00000 -147.38 0.18 0.3662 0.0012 2 0.39084 0.00010 44.99 0.00 100.0000 0.0000 3 0.00025 0.00001 25.12 0.90 0.0650 0.0027 4 0.00002 0.00001 -34.33 5.81 0.0053 0.0027 5 0.00006 0.00001 15.89 2.20 0.0143 0.0019 6 0.00049 0.00001 15.08 0.13 0.1262 0.0020 7 0.00002 0.00000 15.84 1.90 0.0045 0.0005 8 0.00002 0.00000 21.25 0.85 0.0057 0.0007 9 0.00003 0.00000 4.52 0.78 0.0077 0.0005 10 0.00126 0.00001 -9.01 0.04 0.3230 0.0014 11 0.00001 0.00000 4.91 11.66 0.0027 0.0009 12 0.00002 0.00000 -3.02 7.13 0.0040 0.0010 13 0.00004 0.00002 1.99 1.10 0.0091 0.0040 14 0.00101 0.00001 -6.42 0.06 0.2572 0.0029 15 0.00003 0.00001 1.46 3.71 0.0068 0.0020 16 0.00003 0.00001 -3.63 1.89 0.0065 0.0029 The magnetic center is at X = 88.2 +- 0.5 microns Y = 137.8 +- 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: 04-05-1995 Time: 13:02:49 Magnet Name: 108 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4227 +- 1.003606E-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 0.00158 0.00001 -145.78 0.37 0.3694 0.0022 2 0.42725 0.00010 44.98 0.00 100.0000 0.0000 3 0.00026 0.00000 25.18 0.67 0.0602 0.0011 4 0.00003 0.00001 -19.60 35.96 0.0070 0.0021 5 0.00006 0.00001 14.90 2.04 0.0148 0.0035 6 0.00029 0.00001 15.34 0.24 0.0677 0.0013 7 0.00002 0.00001 15.03 1.81 0.0043 0.0014 8 0.00002 0.00000 9.27 18.22 0.0040 0.0004 9 0.00005 0.00000 4.42 0.64 0.0107 0.0010 10 0.00141 0.00001 -9.05 0.01 0.3308 0.0027 11 0.00001 0.00000 -1.58 10.99 0.0020 0.0008 12 0.00003 0.00001 1.21 12.02 0.0070 0.0021 13 0.00004 0.00001 2.10 1.43 0.0092 0.0014 14 0.00106 0.00001 -6.43 0.04 0.2480 0.0021 15 0.00002 0.00001 -4.04 1.37 0.0057 0.0015 16 0.00003 0.00001 0.78 2.86 0.0078 0.0030 The magnetic center is at X = 92.8 +- 1.0 microns Y = 136.4 +- 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 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)