SLAC Magnetic Measurements Date: 04-20-1995 Time: 10:10:51 Magnet Name (Serial #): 194 Bar Code Number: 553 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: 04-20-1995 Time: 10:58:00 Magnet Name: 194 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00001 +- 2.468645E-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 0.00005 0.00000 -160.91 0.85 0.3030 0.0038 2 0.01489 0.00000 45.10 0.00 100.0000 0.0000 3 0.00002 0.00000 18.21 0.16 0.1478 0.0022 4 0.00000 0.00000 -14.46 23.87 0.0037 0.0008 5 0.00000 0.00000 14.81 0.25 0.0229 0.0018 6 0.00003 0.00000 15.34 0.05 0.2203 0.0014 7 0.00000 0.00000 12.73 1.11 0.0044 0.0009 8 0.00000 0.00000 13.03 12.34 0.0010 0.0006 9 0.00000 0.00000 1.72 1.30 0.0106 0.0011 10 0.00004 0.00000 -8.97 0.02 0.2978 0.0017 11 0.00000 0.00000 -5.99 3.79 0.0024 0.0011 12 0.00000 0.00000 0.28 12.44 0.0048 0.0004 13 0.00000 0.00000 -0.95 0.38 0.0124 0.0039 14 0.00004 0.00000 -6.31 0.03 0.2624 0.0013 15 0.00000 0.00000 -10.75 0.58 0.0091 0.0017 16 0.00000 0.00000 4.66 3.51 0.0075 0.0034 The magnetic center is at X = 44.3 +- 2.0 microns Y = 127.9 +- 1.7 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 ^ | N S --> x S N Date: 04-20-1995 Time: 11:04:06 Magnet Name: 194 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10187 +- 4.358719E-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 -160.05 0.68 0.3118 0.0040 2 0.03495 0.00000 45.09 0.00 100.0000 0.0000 3 0.00003 0.00000 15.58 1.13 0.0782 0.0065 4 0.00000 0.00000 -38.71 2.65 0.0074 0.0026 5 0.00001 0.00000 10.92 1.09 0.0180 0.0013 6 0.00008 0.00000 15.26 0.08 0.2206 0.0007 7 0.00000 0.00000 11.23 1.17 0.0093 0.0008 8 0.00000 0.00000 11.06 19.11 0.0103 0.0011 9 0.00000 0.00000 3.28 1.03 0.0093 0.0006 10 0.00010 0.00000 -8.93 0.02 0.2981 0.0010 11 0.00000 0.00000 1.81 10.80 0.0019 0.0011 12 0.00000 0.00000 1.02 1.05 0.0047 0.0014 13 0.00000 0.00000 -0.19 1.17 0.0124 0.0041 14 0.00009 0.00000 -6.32 0.01 0.2585 0.0015 15 0.00000 0.00000 -8.02 1.92 0.0092 0.0032 16 0.00000 0.00000 2.17 1.65 0.0101 0.0033 The magnetic center is at X = 47.5 +- 1.7 microns Y = 130.9 +- 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: 04-20-1995 Time: 11:10:17 Magnet Name: 194 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.06625 +- 6.292603E-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 0.00022 0.00001 -164.04 0.92 0.3139 0.0082 2 0.06886 0.00001 45.09 0.00 100.0000 0.0000 3 0.00005 0.00000 14.94 1.11 0.0690 0.0029 4 0.00001 0.00000 -28.68 1.02 0.0074 0.0018 5 0.00001 0.00000 11.15 1.98 0.0190 0.0018 6 0.00015 0.00000 15.30 0.04 0.2197 0.0010 7 0.00001 0.00000 10.32 1.23 0.0076 0.0004 8 0.00000 0.00000 10.45 15.98 0.0020 0.0009 9 0.00001 0.00000 3.61 0.12 0.0091 0.0004 10 0.00021 0.00000 -8.95 0.03 0.3004 0.0023 11 0.00000 0.00000 -5.74 8.31 0.0031 0.0010 12 0.00000 0.00000 -2.60 10.75 0.0047 0.0028 13 0.00001 0.00000 -0.19 0.89 0.0169 0.0012 14 0.00018 0.00000 -6.29 0.03 0.2573 0.0015 15 0.00001 0.00000 -5.43 9.45 0.0132 0.0006 16 0.00000 0.00000 4.02 4.67 0.0057 0.0034 The magnetic center is at X = 38.6 +- 2.4 microns Y = 134.8 +- 3.6 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: 04-20-1995 Time: 11:16:34 Magnet Name: 194 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0651 +- 1.146125E-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 0.00044 0.00001 -167.98 0.88 0.3220 0.0058 2 0.13736 0.00003 45.09 0.00 100.0000 0.0000 3 0.00008 0.00001 14.11 1.70 0.0617 0.0057 4 0.00001 0.00000 -29.66 1.24 0.0086 0.0021 5 0.00003 0.00000 11.73 1.29 0.0187 0.0015 6 0.00030 0.00000 15.33 0.06 0.2191 0.0021 7 0.00001 0.00000 10.20 1.31 0.0077 0.0008 8 0.00000 0.00000 1.68 19.01 0.0012 0.0007 9 0.00001 0.00000 3.53 0.91 0.0104 0.0002 10 0.00041 0.00000 -8.97 0.02 0.3007 0.0009 11 0.00001 0.00000 -0.14 9.54 0.0040 0.0014 12 0.00000 0.00000 9.00 4.97 0.0032 0.0019 13 0.00002 0.00000 -0.13 0.64 0.0148 0.0015 14 0.00035 0.00000 -6.32 0.02 0.2573 0.0011 15 0.00002 0.00000 -10.56 1.16 0.0123 0.0014 16 0.00001 0.00000 1.96 2.80 0.0065 0.0007 The magnetic center is at X = 30.0 +- 2.2 microns Y = 140.7 +- 2.6 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: 04-20-1995 Time: 11:22:49 Magnet Name: 194 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0826 +- 5.117953E-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 0.00067 0.00001 -168.45 0.83 0.3242 0.0055 2 0.20554 0.00002 45.07 0.00 100.0000 0.0000 3 0.00013 0.00001 14.04 1.56 0.0632 0.0030 4 0.00002 0.00001 -24.83 4.25 0.0094 0.0027 5 0.00004 0.00000 11.33 1.68 0.0178 0.0021 6 0.00043 0.00000 15.27 0.02 0.2103 0.0022 7 0.00002 0.00000 9.65 1.56 0.0083 0.0007 8 0.00000 0.00000 6.42 5.57 0.0020 0.0013 9 0.00002 0.00000 3.87 0.89 0.0110 0.0010 10 0.00062 0.00000 -9.00 0.04 0.3040 0.0011 11 0.00000 0.00000 -2.42 9.78 0.0018 0.0007 12 0.00002 0.00000 -0.47 14.16 0.0081 0.0013 13 0.00003 0.00000 -0.01 1.18 0.0160 0.0018 14 0.00053 0.00000 -6.35 0.03 0.2564 0.0017 15 0.00002 0.00000 -10.16 0.97 0.0080 0.0016 16 0.00001 0.00000 0.78 7.09 0.0043 0.0015 The magnetic center is at X = 29.0 +- 2.1 microns Y = 141.9 +- 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: 04-20-1995 Time: 11:29:05 Magnet Name: 194 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3307 +- 7.311492E-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 0.00087 0.00001 -167.11 0.63 0.3187 0.0046 2 0.27325 0.00009 45.07 0.00 100.0000 0.0000 3 0.00016 0.00001 14.42 0.74 0.0578 0.0054 4 0.00006 0.00000 -39.37 1.68 0.0205 0.0011 5 0.00005 0.00000 11.59 1.37 0.0166 0.0014 6 0.00055 0.00000 15.36 0.05 0.2020 0.0008 7 0.00002 0.00000 9.97 1.23 0.0079 0.0009 8 0.00002 0.00000 -0.20 0.36 0.0071 0.0007 9 0.00003 0.00000 3.14 0.91 0.0103 0.0017 10 0.00084 0.00000 -8.98 0.05 0.3076 0.0011 11 0.00001 0.00000 -8.23 3.85 0.0042 0.0009 12 0.00001 0.00000 5.06 11.56 0.0024 0.0012 13 0.00004 0.00001 -1.04 0.64 0.0137 0.0023 14 0.00071 0.00001 -6.37 0.03 0.2592 0.0020 15 0.00003 0.00001 -10.42 0.82 0.0104 0.0037 16 0.00002 0.00001 5.69 4.41 0.0057 0.0022 The magnetic center is at X = 31.7 +- 1.6 microns Y = 138.8 +- 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: 04-20-1995 Time: 11:35:21 Magnet Name: 194 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4351 +- 3.358667E-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 0.00104 0.00002 -164.85 0.80 0.3071 0.0054 2 0.33815 0.00008 45.07 0.00 100.0000 0.0000 3 0.00016 0.00000 14.31 1.03 0.0471 0.0014 4 0.00005 0.00001 -35.86 1.72 0.0145 0.0015 5 0.00005 0.00001 9.68 0.48 0.0139 0.0018 6 0.00060 0.00000 15.32 0.09 0.1784 0.0006 7 0.00002 0.00000 9.20 0.92 0.0068 0.0009 8 0.00002 0.00000 11.01 18.73 0.0047 0.0010 9 0.00003 0.00000 3.96 0.76 0.0102 0.0009 10 0.00104 0.00001 -9.00 0.03 0.3088 0.0016 11 0.00002 0.00001 -6.02 7.03 0.0045 0.0020 12 0.00001 0.00001 -0.24 4.03 0.0038 0.0023 13 0.00005 0.00001 1.50 0.53 0.0156 0.0026 14 0.00086 0.00001 -6.32 0.01 0.2551 0.0017 15 0.00005 0.00002 -8.38 0.71 0.0137 0.0045 16 0.00003 0.00001 5.81 1.53 0.0082 0.0044 The magnetic center is at X = 35.8 +- 1.9 microns Y = 132.4 +- 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: 04-20-1995 Time: 11:41:38 Magnet Name: 194 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4244 +- 3.571991E-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 0.00117 0.00003 -168.90 0.57 0.3002 0.0066 2 0.38986 0.00006 45.07 0.00 100.0000 0.0000 3 0.00022 0.00002 17.19 2.11 0.0568 0.0043 4 0.00004 0.00001 -31.23 2.63 0.0096 0.0016 5 0.00006 0.00001 9.61 2.56 0.0159 0.0017 6 0.00049 0.00000 15.46 0.06 0.1268 0.0011 7 0.00003 0.00000 8.37 1.04 0.0067 0.0009 8 0.00003 0.00000 21.62 0.53 0.0072 0.0004 9 0.00004 0.00000 2.45 0.48 0.0107 0.0010 10 0.00124 0.00001 -9.00 0.01 0.3192 0.0017 11 0.00001 0.00001 -7.56 2.03 0.0027 0.0017 12 0.00001 0.00000 -5.24 7.63 0.0019 0.0010 13 0.00006 0.00001 0.12 0.78 0.0144 0.0023 14 0.00101 0.00001 -6.33 0.02 0.2590 0.0017 15 0.00004 0.00002 -9.67 0.98 0.0110 0.0041 16 0.00006 0.00001 1.17 1.45 0.0143 0.0014 The magnetic center is at X = 25.8 +- 1.4 microns Y = 131.6 +- 2.9 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: 04-20-1995 Time: 11:47:54 Magnet Name: 194 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.433 +- 3.601203E-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 0.00002 -170.81 0.72 0.2863 0.0046 2 0.42634 0.00005 45.07 0.00 100.0000 0.0000 3 0.00024 0.00003 21.49 2.24 0.0574 0.0068 4 0.00003 0.00001 -34.99 2.79 0.0079 0.0025 5 0.00007 0.00001 8.90 0.94 0.0169 0.0018 6 0.00029 0.00000 15.81 0.26 0.0683 0.0007 7 0.00003 0.00000 7.86 1.24 0.0067 0.0008 8 0.00002 0.00000 19.89 1.60 0.0050 0.0012 9 0.00005 0.00000 2.95 0.44 0.0109 0.0002 10 0.00140 0.00000 -8.99 0.02 0.3280 0.0007 11 0.00002 0.00000 -0.68 7.94 0.0037 0.0009 12 0.00001 0.00001 -2.94 10.56 0.0023 0.0013 13 0.00005 0.00002 0.44 0.58 0.0123 0.0037 14 0.00108 0.00000 -6.34 0.01 0.2541 0.0009 15 0.00004 0.00002 -9.46 0.88 0.0102 0.0036 16 0.00007 0.00001 1.66 0.80 0.0153 0.0022 The magnetic center is at X = 20.4 +- 1.6 microns Y = 126.3 +- 2.0 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)