SLAC Magnetic Measurements Date: 04-18-1995 Time: 08:57:36 Magnet Name (Serial #): 186 Bar Code Number: 571 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl Run Number: 3 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: 04-18-1995 Time: 09:44:45 Magnet Name: 186 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 9.999995 +- 4.369978E-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 0.00007 0.00000 -128.40 0.36 0.4535 0.0025 2 0.01491 0.00000 45.02 0.00 100.0000 0.0000 3 0.00001 0.00000 17.45 0.97 0.0857 0.0033 4 0.00000 0.00000 20.47 7.52 0.0052 0.0017 5 0.00000 0.00000 14.64 2.14 0.0148 0.0025 6 0.00003 0.00000 15.20 0.05 0.2211 0.0012 7 0.00000 0.00000 9.66 0.39 0.0089 0.0016 8 0.00000 0.00000 -1.41 7.67 0.0018 0.0008 9 0.00000 0.00000 6.11 0.37 0.0150 0.0014 10 0.00004 0.00000 -9.04 0.03 0.2989 0.0004 11 0.00000 0.00000 -1.63 13.87 0.0033 0.0013 12 0.00000 0.00000 -1.20 7.08 0.0038 0.0007 13 0.00000 0.00000 2.94 0.81 0.0115 0.0021 14 0.00004 0.00000 -6.45 0.03 0.2593 0.0031 15 0.00000 0.00000 -5.97 1.19 0.0077 0.0030 16 0.00000 0.00000 -3.81 6.77 0.0040 0.0027 The magnetic center is at X = 158.7 +- 1.2 microns Y = 125.8 +- 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: 04-18-1995 Time: 09:50:50 Magnet Name: 186 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 25.10212 +- 4.796991E-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 -136.43 0.48 0.4160 0.0039 2 0.03497 0.00000 45.01 0.00 100.0000 0.0000 3 0.00002 0.00000 19.85 1.37 0.0635 0.0041 4 0.00000 0.00000 -20.02 35.78 0.0071 0.0024 5 0.00001 0.00000 15.36 1.61 0.0162 0.0021 6 0.00008 0.00000 15.15 0.04 0.2217 0.0013 7 0.00000 0.00000 8.06 0.62 0.0084 0.0003 8 0.00000 0.00000 -10.91 18.12 0.0076 0.0008 9 0.00000 0.00000 5.98 0.62 0.0130 0.0014 10 0.00010 0.00000 -9.01 0.02 0.2967 0.0013 11 0.00000 0.00000 6.77 12.44 0.0025 0.0016 12 0.00000 0.00000 -0.39 1.43 0.0096 0.0025 13 0.00000 0.00000 2.95 0.86 0.0125 0.0008 14 0.00009 0.00000 -6.43 0.06 0.2554 0.0019 15 0.00000 0.00000 -8.50 0.77 0.0086 0.0018 16 0.00000 0.00000 8.09 1.92 0.0057 0.0017 The magnetic center is at X = 128.1 +- 1.6 microns Y = 134.6 +- 1.6 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: 04-18-1995 Time: 09:57:02 Magnet Name: 186 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 50.06658 +- 5.416635E-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 0.00028 0.00000 -141.89 0.60 0.4032 0.0010 2 0.06885 0.00001 45.01 0.00 100.0000 0.0000 3 0.00004 0.00000 20.77 0.06 0.0625 0.0053 4 0.00000 0.00000 -28.82 8.66 0.0044 0.0020 5 0.00001 0.00000 16.01 0.64 0.0169 0.0032 6 0.00015 0.00000 15.16 0.02 0.2191 0.0013 7 0.00001 0.00000 8.73 0.44 0.0097 0.0009 8 0.00000 0.00000 -8.18 5.11 0.0022 0.0010 9 0.00001 0.00000 5.30 0.76 0.0132 0.0013 10 0.00021 0.00000 -9.01 0.03 0.2979 0.0012 11 0.00000 0.00000 7.16 13.33 0.0028 0.0011 12 0.00000 0.00000 2.91 8.55 0.0017 0.0009 13 0.00001 0.00000 2.40 0.93 0.0119 0.0025 14 0.00017 0.00000 -6.42 0.03 0.2534 0.0013 15 0.00001 0.00000 -6.77 1.31 0.0083 0.0028 16 0.00000 0.00000 4.06 8.33 0.0047 0.0031 The magnetic center is at X = 111.1 +- 1.5 microns Y = 141.7 +- 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: 04-18-1995 Time: 10:03:18 Magnet Name: 186 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 100.0645 +- 8.088687E-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 0.00055 0.00001 -145.80 0.52 0.3983 0.0045 2 0.13734 0.00001 45.01 0.00 100.0000 0.0000 3 0.00009 0.00000 20.91 1.42 0.0663 0.0029 4 0.00001 0.00000 -23.87 4.31 0.0053 0.0013 5 0.00002 0.00000 17.51 1.69 0.0181 0.0027 6 0.00030 0.00000 15.16 0.08 0.2182 0.0010 7 0.00001 0.00000 8.27 0.53 0.0105 0.0008 8 0.00000 0.00000 -11.83 2.63 0.0019 0.0007 9 0.00002 0.00000 5.79 0.46 0.0140 0.0023 10 0.00041 0.00000 -9.04 0.01 0.3011 0.0015 11 0.00000 0.00000 -15.11 0.69 0.0025 0.0012 12 0.00000 0.00000 -3.25 7.30 0.0029 0.0018 13 0.00001 0.00000 3.24 0.37 0.0106 0.0010 14 0.00035 0.00000 -6.41 0.01 0.2559 0.0032 15 0.00001 0.00000 -6.77 1.58 0.0107 0.0018 16 0.00000 0.00000 4.07 4.28 0.0031 0.0013 The magnetic center is at X = 100.0 +- 1.7 microns Y = 147.1 +- 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: 04-18-1995 Time: 10:09:34 Magnet Name: 186 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 150.0815 +- 4.518122E-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 0.00080 0.00001 -146.15 0.62 0.3894 0.0040 2 0.20553 0.00004 44.99 0.00 100.0000 0.0000 3 0.00014 0.00001 21.47 1.11 0.0679 0.0036 4 0.00001 0.00000 -20.54 3.70 0.0061 0.0022 5 0.00004 0.00001 17.51 1.67 0.0189 0.0026 6 0.00043 0.00000 15.19 0.05 0.2089 0.0017 7 0.00002 0.00000 7.00 0.71 0.0094 0.0015 8 0.00000 0.00000 -2.01 2.41 0.0023 0.0005 9 0.00003 0.00001 5.70 0.48 0.0135 0.0029 10 0.00062 0.00000 -9.08 0.03 0.3026 0.0023 11 0.00001 0.00000 6.62 13.03 0.0050 0.0018 12 0.00001 0.00000 -1.23 13.44 0.0061 0.0008 13 0.00002 0.00000 2.98 0.79 0.0092 0.0013 14 0.00052 0.00001 -6.42 0.03 0.2547 0.0028 15 0.00002 0.00001 -7.06 1.83 0.0098 0.0030 16 0.00001 0.00000 5.02 7.97 0.0061 0.0022 The magnetic center is at X = 96.9 +- 1.9 microns Y = 144.4 +- 1.8 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: 04-18-1995 Time: 10:15:49 Magnet Name: 186 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 200.3299 +- 1.126854E-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 -146.77 0.60 0.3814 0.0043 2 0.27312 0.00002 44.99 0.00 100.0000 0.0000 3 0.00019 0.00001 22.84 1.14 0.0693 0.0040 4 0.00005 0.00001 -38.55 1.39 0.0171 0.0020 5 0.00005 0.00001 17.39 2.07 0.0183 0.0026 6 0.00055 0.00000 15.14 0.02 0.2001 0.0013 7 0.00003 0.00000 7.50 0.99 0.0097 0.0006 8 0.00002 0.00000 -1.61 0.73 0.0089 0.0005 9 0.00004 0.00000 5.59 0.17 0.0140 0.0014 10 0.00083 0.00000 -9.03 0.02 0.3043 0.0011 11 0.00001 0.00000 -8.03 12.88 0.0048 0.0008 12 0.00001 0.00000 2.15 4.42 0.0043 0.0014 13 0.00003 0.00000 2.62 0.66 0.0110 0.0015 14 0.00070 0.00000 -6.46 0.02 0.2557 0.0010 15 0.00001 0.00001 -6.08 2.11 0.0050 0.0027 16 0.00002 0.00000 2.92 8.06 0.0066 0.0014 The magnetic center is at X = 93.4 +- 1.8 microns Y = 142.5 +- 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: 04-18-1995 Time: 10:22:05 Magnet Name: 186 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 250.4336 +- 3.541716E-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 0.00129 0.00001 -148.12 0.54 0.3814 0.0041 2 0.33778 0.00011 44.99 0.00 100.0000 0.0000 3 0.00025 0.00002 23.26 0.80 0.0731 0.0049 4 0.00004 0.00001 -32.23 2.20 0.0118 0.0030 5 0.00006 0.00001 18.44 1.41 0.0192 0.0029 6 0.00059 0.00000 15.13 0.09 0.1749 0.0011 7 0.00003 0.00000 7.78 0.85 0.0096 0.0001 8 0.00001 0.00000 -8.14 17.61 0.0040 0.0006 9 0.00005 0.00001 5.92 0.43 0.0143 0.0024 10 0.00104 0.00000 -9.07 0.03 0.3090 0.0011 11 0.00001 0.00000 6.08 12.79 0.0024 0.0015 12 0.00003 0.00001 0.81 1.22 0.0076 0.0031 13 0.00004 0.00000 3.43 1.09 0.0127 0.0013 14 0.00086 0.00001 -6.45 0.02 0.2547 0.0015 15 0.00003 0.00001 -7.03 1.51 0.0079 0.0016 16 0.00002 0.00001 2.58 8.46 0.0048 0.0037 The magnetic center is at X = 90.0 +- 1.7 microns Y = 144.7 +- 1.8 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: 04-18-1995 Time: 10:28:21 Magnet Name: 186 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 300.4228 +- 4.868486E-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 0.00152 0.00002 -148.30 0.54 0.3893 0.0044 2 0.38950 0.00006 44.99 0.00 100.0000 0.0000 3 0.00028 0.00002 22.43 0.73 0.0722 0.0053 4 0.00004 0.00001 -26.13 4.20 0.0110 0.0019 5 0.00008 0.00001 18.59 1.13 0.0195 0.0030 6 0.00049 0.00001 15.23 0.08 0.1247 0.0016 7 0.00004 0.00001 7.61 0.52 0.0108 0.0014 8 0.00002 0.00000 -9.59 18.40 0.0063 0.0008 9 0.00006 0.00001 5.54 0.88 0.0146 0.0016 10 0.00124 0.00000 -9.03 0.01 0.3186 0.0009 11 0.00001 0.00000 5.92 12.87 0.0024 0.0008 12 0.00002 0.00001 0.92 3.30 0.0064 0.0029 13 0.00005 0.00001 3.00 0.15 0.0116 0.0015 14 0.00100 0.00001 -6.46 0.04 0.2572 0.0032 15 0.00004 0.00001 -6.91 0.51 0.0100 0.0016 16 0.00002 0.00001 3.79 3.00 0.0046 0.0027 The magnetic center is at X = 91.4 +- 1.7 microns Y = 147.9 +- 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: 04-18-1995 Time: 10:34:37 Magnet Name: 186 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 350.4311 +- 7.709842E-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 0.00168 0.00002 -148.84 0.50 0.3942 0.0044 2 0.42582 0.00001 44.99 0.00 100.0000 0.0000 3 0.00031 0.00002 22.03 0.90 0.0727 0.0043 4 0.00005 0.00001 -25.84 3.10 0.0115 0.0022 5 0.00009 0.00001 17.06 1.38 0.0208 0.0020 6 0.00028 0.00001 15.47 0.19 0.0650 0.0014 7 0.00004 0.00000 8.01 0.95 0.0096 0.0006 8 0.00002 0.00000 -9.22 17.80 0.0037 0.0009 9 0.00006 0.00001 5.37 0.30 0.0153 0.0015 10 0.00140 0.00000 -9.05 0.03 0.3287 0.0009 11 0.00001 0.00000 -0.31 14.19 0.0026 0.0004 12 0.00002 0.00001 -2.71 4.87 0.0035 0.0019 13 0.00005 0.00000 2.72 0.25 0.0118 0.0010 14 0.00108 0.00001 -6.47 0.04 0.2543 0.0023 15 0.00003 0.00001 -6.66 1.29 0.0073 0.0032 16 0.00004 0.00001 0.44 1.05 0.0096 0.0027 The magnetic center is at X = 91.1 +- 1.7 microns Y = 150.7 +- 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 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)