SLAC Magnetic Measurements Date: 03-15-1995 Time: 07:31:02 Magnet Name (Serial #): 149 Bar Code Number: 235 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: 03-15-1995 Time: 08:18:21 Magnet Name: 149 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.997895 +- 2.005433E-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 -39.84 0.19 0.5221 0.0020 2 0.01485 0.00001 -45.02 0.00 100.0000 0.0000 3 0.00002 0.00000 -25.77 0.75 0.1115 0.0012 4 0.00001 0.00000 -24.82 1.13 0.0428 0.0021 5 0.00000 0.00000 -20.68 0.94 0.0226 0.0036 6 0.00003 0.00000 -15.07 0.04 0.2155 0.0013 7 0.00000 0.00000 -16.82 3.04 0.0044 0.0020 8 0.00000 0.00000 -7.73 9.62 0.0014 0.0005 9 0.00000 0.00000 17.26 0.45 0.0091 0.0024 10 0.00004 0.00000 8.97 0.02 0.3025 0.0013 11 0.00000 0.00000 10.45 4.62 0.0012 0.0005 12 0.00000 0.00000 -8.52 2.25 0.0039 0.0015 13 0.00000 0.00000 11.98 0.91 0.0100 0.0032 14 0.00004 0.00000 6.44 0.05 0.2584 0.0018 15 0.00000 0.00000 1.80 5.39 0.0051 0.0021 16 0.00000 0.00000 -0.95 6.31 0.0055 0.0019 The magnetic center is at X = -149.4 +- 0.8 microns Y = 179.1 +- 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 ^ | S N --> x N S Date: 03-15-1995 Time: 08:24:31 Magnet Name: 149 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.09737 +- 3.062973E-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 0.00015 0.00000 -26.71 0.14 0.4284 0.0023 2 0.03491 0.00002 -45.02 0.00 100.0000 0.0000 3 0.00003 0.00000 -30.88 0.27 0.0910 0.0017 4 0.00001 0.00000 -30.32 1.40 0.0412 0.0025 5 0.00001 0.00000 -18.44 1.62 0.0196 0.0040 6 0.00008 0.00000 -15.02 0.06 0.2183 0.0012 7 0.00000 0.00000 -14.40 3.84 0.0058 0.0009 8 0.00000 0.00000 -4.39 1.57 0.0056 0.0011 9 0.00000 0.00000 17.81 0.53 0.0093 0.0008 10 0.00011 0.00000 8.96 0.01 0.3031 0.0013 11 0.00000 0.00000 3.35 0.98 0.0012 0.0004 12 0.00000 0.00000 -5.90 3.08 0.0056 0.0019 13 0.00000 0.00000 12.75 0.67 0.0127 0.0022 14 0.00009 0.00000 6.41 0.02 0.2542 0.0022 15 0.00000 0.00000 0.04 7.48 0.0042 0.0005 16 0.00000 0.00000 -3.69 8.20 0.0078 0.0023 The magnetic center is at X = -86.0 +- 0.6 microns Y = 170.9 +- 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 ^ | S N --> x N S Date: 03-15-1995 Time: 08:30:47 Magnet Name: 149 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06037 +- 1.174221E-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 0.00027 0.00000 -22.41 0.12 0.3971 0.0018 2 0.06876 0.00004 -45.02 0.00 100.0000 0.0000 3 0.00006 0.00000 -31.46 0.24 0.0888 0.0032 4 0.00002 0.00000 -26.95 0.99 0.0333 0.0021 5 0.00001 0.00000 -16.46 1.28 0.0181 0.0024 6 0.00015 0.00000 -14.99 0.11 0.2206 0.0009 7 0.00000 0.00000 -16.98 1.24 0.0052 0.0008 8 0.00000 0.00000 5.52 14.95 0.0043 0.0019 9 0.00001 0.00000 18.30 0.46 0.0114 0.0011 10 0.00021 0.00000 8.97 0.02 0.3038 0.0008 11 0.00000 0.00000 4.55 2.32 0.0019 0.0004 12 0.00001 0.00000 -4.60 11.42 0.0076 0.0029 13 0.00001 0.00000 6.12 11.50 0.0124 0.0023 14 0.00018 0.00000 6.39 0.03 0.2553 0.0021 15 0.00000 0.00000 -1.22 7.34 0.0045 0.0027 16 0.00000 0.00000 -0.10 7.67 0.0033 0.0010 The magnetic center is at X = -67.6 +- 0.5 microns Y = 164.0 +- 0.7 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 ^ | S N --> x N S Date: 03-15-1995 Time: 08:37:08 Magnet Name: 149 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.054 +- 3.866794E-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 0.00052 0.00000 -19.62 0.25 0.3771 0.0012 2 0.13723 0.00005 -45.02 0.00 100.0000 0.0000 3 0.00012 0.00000 -31.49 0.51 0.0840 0.0031 4 0.00004 0.00000 -26.99 1.16 0.0318 0.0023 5 0.00002 0.00000 -17.01 1.64 0.0174 0.0010 6 0.00031 0.00000 -14.95 0.07 0.2239 0.0009 7 0.00001 0.00000 -14.77 3.11 0.0040 0.0007 8 0.00000 0.00000 -7.84 7.48 0.0018 0.0010 9 0.00001 0.00000 18.72 0.54 0.0094 0.0003 10 0.00042 0.00000 8.98 0.02 0.3048 0.0007 11 0.00000 0.00000 5.50 1.48 0.0021 0.0004 12 0.00001 0.00000 -9.79 4.29 0.0038 0.0017 13 0.00001 0.00000 5.36 10.48 0.0103 0.0008 14 0.00035 0.00000 6.44 0.04 0.2531 0.0031 15 0.00001 0.00000 0.66 3.46 0.0057 0.0009 16 0.00001 0.00000 3.80 4.72 0.0047 0.0028 The magnetic center is at X = -56.6 +- 0.7 microns Y = 158.7 +- 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 ^ | S N --> x N S Date: 03-15-1995 Time: 08:43:28 Magnet Name: 149 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0677 +- 4.055797E-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 0.00073 0.00000 -17.75 0.31 0.3568 0.0010 2 0.20541 0.00007 -45.04 0.00 100.0000 0.0000 3 0.00018 0.00001 -31.98 0.29 0.0856 0.0027 4 0.00006 0.00000 -24.89 0.61 0.0297 0.0018 5 0.00003 0.00000 -17.18 0.66 0.0156 0.0024 6 0.00044 0.00000 -14.98 0.06 0.2163 0.0013 7 0.00001 0.00000 0.63 15.37 0.0025 0.0014 8 0.00001 0.00000 -0.61 18.05 0.0031 0.0014 9 0.00002 0.00000 9.20 16.62 0.0102 0.0015 10 0.00062 0.00000 8.97 0.03 0.3029 0.0014 11 0.00000 0.00000 0.70 1.15 0.0023 0.0007 12 0.00002 0.00000 -12.81 1.45 0.0076 0.0014 13 0.00002 0.00001 12.25 0.44 0.0112 0.0031 14 0.00052 0.00001 6.36 0.05 0.2529 0.0038 15 0.00001 0.00000 5.79 2.28 0.0050 0.0005 16 0.00002 0.00000 -0.20 1.26 0.0086 0.0011 The magnetic center is at X = -48.6 +- 0.8 microns Y = 151.8 +- 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 ^ | S N --> x N S Date: 03-15-1995 Time: 08:49:48 Magnet Name: 149 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3086 +- 9.255811E-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 0.00095 0.00001 -17.20 0.27 0.3465 0.0019 2 0.27296 0.00010 -45.04 0.00 100.0000 0.0000 3 0.00023 0.00000 -31.74 0.51 0.0837 0.0012 4 0.00008 0.00001 -27.95 1.23 0.0306 0.0019 5 0.00004 0.00000 -17.53 1.54 0.0158 0.0016 6 0.00057 0.00000 -14.93 0.05 0.2072 0.0009 7 0.00001 0.00001 -17.60 1.92 0.0047 0.0020 8 0.00001 0.00000 -0.29 2.85 0.0045 0.0010 9 0.00003 0.00000 9.45 16.31 0.0092 0.0006 10 0.00084 0.00000 8.97 0.01 0.3092 0.0010 11 0.00001 0.00000 5.09 4.72 0.0019 0.0008 12 0.00001 0.00000 -3.39 10.03 0.0031 0.0008 13 0.00003 0.00000 11.75 0.91 0.0110 0.0014 14 0.00070 0.00001 6.34 0.03 0.2561 0.0031 15 0.00002 0.00000 -0.88 5.83 0.0055 0.0015 16 0.00002 0.00001 -7.18 1.10 0.0058 0.0020 The magnetic center is at X = -45.8 +- 0.7 microns Y = 147.8 +- 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 ^ | S N --> x N S Date: 03-15-1995 Time: 08:56:08 Magnet Name: 149 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4069 +- 3.039335E-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 0.00111 0.00001 -16.95 0.27 0.3286 0.0023 2 0.33780 0.00023 -45.04 0.00 100.0000 0.0000 3 0.00027 0.00000 -30.03 0.44 0.0812 0.0007 4 0.00012 0.00001 -32.68 0.75 0.0362 0.0021 5 0.00005 0.00000 -17.32 1.01 0.0145 0.0007 6 0.00060 0.00000 -14.95 0.07 0.1788 0.0006 7 0.00002 0.00000 -18.49 3.11 0.0048 0.0008 8 0.00003 0.00000 0.28 0.70 0.0097 0.0009 9 0.00004 0.00000 -0.16 19.43 0.0106 0.0010 10 0.00106 0.00000 8.97 0.00 0.3151 0.0010 11 0.00001 0.00000 3.07 3.23 0.0018 0.0012 12 0.00001 0.00001 -5.65 10.30 0.0021 0.0017 13 0.00003 0.00000 12.30 1.44 0.0103 0.0011 14 0.00085 0.00001 6.38 0.02 0.2521 0.0040 15 0.00002 0.00001 4.43 2.91 0.0054 0.0028 16 0.00002 0.00001 -4.48 8.70 0.0064 0.0018 The magnetic center is at X = -42.8 +- 0.7 microns Y = 140.4 +- 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 ^ | S N --> x N S Date: 03-15-1995 Time: 09:02:28 Magnet Name: 149 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3923 +- 1.473402E-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 -17.91 0.41 0.3064 0.0007 2 0.38991 0.00014 -45.04 0.00 100.0000 0.0000 3 0.00031 0.00001 -27.62 0.18 0.0796 0.0015 4 0.00013 0.00001 -31.31 0.81 0.0330 0.0018 5 0.00005 0.00000 -18.82 1.29 0.0125 0.0011 6 0.00052 0.00001 -14.85 0.04 0.1336 0.0014 7 0.00002 0.00001 2.86 21.82 0.0043 0.0014 8 0.00001 0.00000 -3.93 12.61 0.0019 0.0007 9 0.00004 0.00000 18.55 0.28 0.0106 0.0007 10 0.00127 0.00001 8.96 0.01 0.3263 0.0012 11 0.00002 0.00000 7.17 0.92 0.0041 0.0004 12 0.00002 0.00001 -3.17 2.09 0.0040 0.0021 13 0.00005 0.00001 12.70 0.11 0.0118 0.0026 14 0.00098 0.00001 6.40 0.06 0.2510 0.0028 15 0.00002 0.00001 -1.68 7.73 0.0051 0.0027 16 0.00002 0.00001 -5.12 8.78 0.0055 0.0025 The magnetic center is at X = -42.1 +- 0.9 microns Y = 130.2 +- 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 ^ | S N --> x N S Date: 03-15-1995 Time: 09:08:48 Magnet Name: 149 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3983 +- 4.564903E-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 -18.76 0.19 0.2865 0.0021 2 0.42618 0.00024 -45.05 0.00 100.0000 0.0000 3 0.00034 0.00001 -25.66 0.36 0.0802 0.0016 4 0.00013 0.00000 -31.06 0.79 0.0293 0.0005 5 0.00005 0.00001 -21.18 1.51 0.0125 0.0019 6 0.00032 0.00000 -14.55 0.11 0.0754 0.0010 7 0.00002 0.00001 -21.44 0.55 0.0056 0.0015 8 0.00002 0.00000 21.10 0.64 0.0051 0.0011 9 0.00005 0.00001 -9.94 16.77 0.0106 0.0021 10 0.00143 0.00000 8.99 0.01 0.3349 0.0013 11 0.00001 0.00000 3.50 2.37 0.0029 0.0006 12 0.00002 0.00000 -4.07 1.12 0.0038 0.0007 13 0.00005 0.00001 12.46 0.97 0.0108 0.0013 14 0.00105 0.00001 6.37 0.06 0.2465 0.0029 15 0.00002 0.00001 -0.19 6.23 0.0050 0.0028 16 0.00001 0.00001 -3.79 2.62 0.0031 0.0020 The magnetic center is at X = -41.2 +- 0.5 microns Y = 121.2 +- 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 ^ | S N --> x N S 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)