SLAC Magnetic Measurements Date: 03-13-1995 Time: 14:33:53 Magnet Name (Serial #): 121 Bar Code Number: 372 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: 03-13-1995 Time: 15:21:07 Magnet Name: 121 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00066 +- 9.442356E-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 0.00009 0.00000 -41.68 0.20 0.6182 0.0028 2 0.01480 0.00001 -45.07 0.00 100.0000 0.0000 3 0.00001 0.00000 -25.68 1.11 0.0446 0.0030 4 0.00000 0.00000 29.00 0.68 0.0297 0.0047 5 0.00000 0.00000 -16.36 1.12 0.0245 0.0021 6 0.00003 0.00000 -15.08 0.06 0.2268 0.0012 7 0.00000 0.00000 -9.04 3.90 0.0022 0.0009 8 0.00000 0.00000 13.04 5.65 0.0015 0.0006 9 0.00000 0.00000 16.73 0.72 0.0096 0.0007 10 0.00004 0.00000 8.92 0.02 0.2990 0.0016 11 0.00000 0.00000 0.46 1.51 0.0021 0.0001 12 0.00000 0.00000 3.46 9.86 0.0040 0.0015 13 0.00000 0.00000 10.86 0.46 0.0123 0.0021 14 0.00004 0.00000 6.37 0.06 0.2595 0.0007 15 0.00000 0.00000 7.78 4.18 0.0037 0.0028 16 0.00000 0.00000 -2.22 7.25 0.0041 0.0025 The magnetic center is at X = -183.6 +- 1.1 microns Y = 206.2 +- 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 ^ | S N --> x N S Date: 03-13-1995 Time: 15:27:15 Magnet Name: 121 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.1004 +- 4.322891E-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 0.00017 0.00000 -38.99 0.05 0.4840 0.0018 2 0.03486 0.00003 -45.07 0.00 100.0000 0.0000 3 0.00002 0.00000 -20.33 0.94 0.0465 0.0024 4 0.00001 0.00000 33.95 0.66 0.0423 0.0016 5 0.00001 0.00000 -15.85 0.99 0.0216 0.0025 6 0.00008 0.00000 -15.07 0.06 0.2278 0.0018 7 0.00000 0.00000 -11.72 4.67 0.0031 0.0013 8 0.00000 0.00000 2.66 2.10 0.0027 0.0016 9 0.00000 0.00000 16.59 0.70 0.0100 0.0005 10 0.00010 0.00000 8.92 0.02 0.2992 0.0009 11 0.00000 0.00000 2.27 2.70 0.0021 0.0009 12 0.00000 0.00000 6.60 4.10 0.0034 0.0019 13 0.00001 0.00000 10.46 0.49 0.0153 0.0013 14 0.00009 0.00000 6.37 0.04 0.2545 0.0016 15 0.00000 0.00000 2.74 6.64 0.0044 0.0023 16 0.00000 0.00000 3.74 8.48 0.0061 0.0013 The magnetic center is at X = -136.0 +- 0.5 microns Y = 168.0 +- 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: 03-13-1995 Time: 15:33:30 Magnet Name: 121 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06328 +- 5.971403E-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 0.00030 0.00000 -37.70 0.15 0.4378 0.0015 2 0.06870 0.00002 -45.07 0.00 100.0000 0.0000 3 0.00003 0.00000 -18.90 1.23 0.0478 0.0021 4 0.00002 0.00000 29.94 0.97 0.0354 0.0015 5 0.00001 0.00000 -15.95 0.71 0.0217 0.0020 6 0.00016 0.00000 -15.06 0.05 0.2302 0.0019 7 0.00000 0.00000 -12.22 3.91 0.0034 0.0015 8 0.00000 0.00000 12.16 6.89 0.0021 0.0008 9 0.00001 0.00000 16.92 0.41 0.0098 0.0004 10 0.00021 0.00000 8.90 0.02 0.3005 0.0017 11 0.00000 0.00000 2.03 1.09 0.0037 0.0013 12 0.00000 0.00000 10.38 2.50 0.0034 0.0016 13 0.00001 0.00000 10.57 0.30 0.0144 0.0004 14 0.00018 0.00000 6.38 0.01 0.2572 0.0003 15 0.00000 0.00000 2.82 7.56 0.0033 0.0011 16 0.00000 0.00000 -7.85 1.81 0.0028 0.0012 The magnetic center is at X = -119.6 +- 0.6 microns Y = 154.7 +- 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: 03-13-1995 Time: 15:39:50 Magnet Name: 121 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0574 +- 8.607449E-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 0.00057 0.00000 -36.56 0.21 0.4136 0.0029 2 0.13708 0.00004 -45.07 0.00 100.0000 0.0000 3 0.00006 0.00001 -18.80 1.15 0.0462 0.0037 4 0.00005 0.00000 29.75 1.45 0.0360 0.0030 5 0.00003 0.00000 -16.51 0.84 0.0215 0.0009 6 0.00032 0.00000 -15.02 0.05 0.2316 0.0011 7 0.00000 0.00000 -14.68 5.27 0.0034 0.0012 8 0.00000 0.00000 16.03 0.79 0.0026 0.0012 9 0.00001 0.00000 16.78 0.51 0.0106 0.0016 10 0.00041 0.00000 8.92 0.02 0.3025 0.0012 11 0.00000 0.00000 4.32 2.61 0.0025 0.0010 12 0.00001 0.00000 12.37 2.61 0.0039 0.0011 13 0.00002 0.00000 10.89 0.28 0.0148 0.0010 14 0.00035 0.00000 6.36 0.03 0.2534 0.0012 15 0.00000 0.00000 1.03 4.46 0.0031 0.0019 16 0.00000 0.00000 -1.96 5.60 0.0023 0.0012 The magnetic center is at X = -110.0 +- 0.9 microns Y = 148.4 +- 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 ^ | S N --> x N S Date: 03-13-1995 Time: 15:46:09 Magnet Name: 121 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0689 +- 2.219092E-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 0.00000 -35.79 0.38 0.3910 0.0009 2 0.20523 0.00012 -45.09 0.00 100.0000 0.0000 3 0.00010 0.00001 -19.34 1.47 0.0477 0.0031 4 0.00007 0.00000 29.27 0.80 0.0332 0.0017 5 0.00004 0.00000 -16.78 1.08 0.0201 0.0019 6 0.00046 0.00000 -15.02 0.05 0.2230 0.0011 7 0.00001 0.00000 -14.22 3.38 0.0033 0.0009 8 0.00001 0.00000 14.43 4.10 0.0027 0.0009 9 0.00002 0.00000 16.26 0.33 0.0106 0.0007 10 0.00062 0.00000 8.90 0.02 0.2998 0.0010 11 0.00000 0.00000 2.13 3.93 0.0024 0.0008 12 0.00001 0.00000 12.00 0.76 0.0072 0.0013 13 0.00003 0.00000 10.67 0.47 0.0141 0.0008 14 0.00053 0.00000 6.37 0.05 0.2579 0.0018 15 0.00001 0.00001 8.60 3.34 0.0051 0.0033 16 0.00001 0.00000 -0.60 0.82 0.0066 0.0011 The magnetic center is at X = -102.1 +- 1.0 microns Y = 141.7 +- 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: 03-13-1995 Time: 15:52:28 Magnet Name: 121 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3125 +- 7.261565E-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 0.00001 -35.58 0.22 0.3809 0.0020 2 0.27276 0.00013 -45.09 0.00 100.0000 0.0000 3 0.00013 0.00000 -17.35 1.58 0.0474 0.0007 4 0.00009 0.00000 29.36 0.88 0.0338 0.0011 5 0.00005 0.00001 -16.56 1.43 0.0197 0.0019 6 0.00058 0.00001 -15.05 0.08 0.2140 0.0023 7 0.00001 0.00000 -16.05 6.53 0.0038 0.0007 8 0.00001 0.00000 5.98 3.58 0.0036 0.0002 9 0.00003 0.00000 16.07 0.75 0.0105 0.0016 10 0.00084 0.00000 8.90 0.02 0.3070 0.0009 11 0.00001 0.00000 1.93 2.62 0.0028 0.0006 12 0.00001 0.00001 1.42 11.35 0.0048 0.0026 13 0.00004 0.00001 11.00 0.39 0.0159 0.0030 14 0.00070 0.00001 6.37 0.07 0.2574 0.0028 15 0.00001 0.00000 -0.75 7.81 0.0035 0.0011 16 0.00001 0.00000 -10.79 0.55 0.0044 0.0018 The magnetic center is at X = -99.0 +- 0.7 microns Y = 138.4 +- 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: 03-13-1995 Time: 15:58:49 Magnet Name: 121 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4116 +- 1.267238E-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 0.00126 0.00000 -36.14 0.23 0.3737 0.0005 2 0.33766 0.00008 -45.09 0.00 100.0000 0.0000 3 0.00017 0.00000 -17.55 0.89 0.0508 0.0014 4 0.00014 0.00001 33.48 0.35 0.0427 0.0015 5 0.00007 0.00001 -16.73 0.68 0.0196 0.0015 6 0.00063 0.00000 -15.07 0.13 0.1870 0.0010 7 0.00001 0.00000 -16.62 4.54 0.0031 0.0011 8 0.00002 0.00000 1.95 1.98 0.0054 0.0011 9 0.00004 0.00001 16.04 0.63 0.0124 0.0015 10 0.00106 0.00000 8.90 0.03 0.3129 0.0013 11 0.00001 0.00000 4.20 3.01 0.0025 0.0010 12 0.00001 0.00000 1.95 9.20 0.0018 0.0006 13 0.00005 0.00000 10.83 0.13 0.0149 0.0008 14 0.00085 0.00000 6.36 0.03 0.2520 0.0007 15 0.00001 0.00000 9.07 2.93 0.0040 0.0012 16 0.00002 0.00001 0.09 10.44 0.0064 0.0017 The magnetic center is at X = -98.4 +- 0.6 microns Y = 134.8 +- 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: 03-13-1995 Time: 16:05:10 Magnet Name: 121 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.395 +- 1.509309E-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 0.00152 0.00001 -37.70 0.11 0.3902 0.0016 2 0.38911 0.00016 -45.09 0.00 100.0000 0.0000 3 0.00022 0.00001 -19.22 0.12 0.0569 0.0030 4 0.00014 0.00001 32.85 1.15 0.0362 0.0020 5 0.00008 0.00000 -17.15 1.08 0.0197 0.0007 6 0.00055 0.00000 -14.99 0.07 0.1422 0.0002 7 0.00001 0.00001 -2.54 16.40 0.0030 0.0013 8 0.00002 0.00000 18.04 0.78 0.0048 0.0010 9 0.00005 0.00000 16.20 0.35 0.0116 0.0011 10 0.00125 0.00000 8.90 0.03 0.3202 0.0006 11 0.00001 0.00000 0.93 1.10 0.0026 0.0009 12 0.00003 0.00000 1.16 0.67 0.0067 0.0008 13 0.00006 0.00001 10.79 0.57 0.0146 0.0016 14 0.00098 0.00001 6.38 0.03 0.2531 0.0022 15 0.00001 0.00000 -3.73 8.24 0.0036 0.0011 16 0.00002 0.00000 -10.16 0.76 0.0042 0.0010 The magnetic center is at X = -106.6 +- 0.5 microns Y = 137.9 +- 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: 03-13-1995 Time: 16:11:31 Magnet Name: 121 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.399 +- 8.282023E-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 0.00170 0.00001 -38.30 0.19 0.3998 0.0014 2 0.42542 0.00028 -45.09 0.00 100.0000 0.0000 3 0.00027 0.00001 -22.02 0.23 0.0624 0.0026 4 0.00015 0.00001 31.91 0.82 0.0347 0.0017 5 0.00008 0.00001 -17.60 1.90 0.0196 0.0014 6 0.00037 0.00000 -15.01 0.13 0.0862 0.0007 7 0.00001 0.00000 -12.76 6.00 0.0023 0.0005 8 0.00003 0.00001 20.14 0.64 0.0077 0.0013 9 0.00005 0.00000 16.36 0.44 0.0119 0.0006 10 0.00141 0.00001 8.89 0.01 0.3310 0.0012 11 0.00001 0.00000 1.11 2.68 0.0027 0.0011 12 0.00001 0.00000 4.03 1.58 0.0032 0.0007 13 0.00006 0.00001 10.70 0.27 0.0145 0.0015 14 0.00107 0.00001 6.37 0.01 0.2510 0.0015 15 0.00003 0.00001 2.43 7.56 0.0059 0.0024 16 0.00002 0.00001 1.09 0.62 0.0050 0.0031 The magnetic center is at X = -110.7 +- 0.7 microns Y = 140.1 +- 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 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)