SLAC Magnetic Measurements Date: 03-09-1995 Time: 08:32:22 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: 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: 03-09-1995 Time: 09:19:47 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00183 +- 5.278301E-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 -133.62 0.37 0.3125 0.0022 2 0.01492 0.00000 44.96 0.00 100.0000 0.0000 3 0.00001 0.00000 25.25 0.89 0.0691 0.0049 4 0.00000 0.00000 23.20 5.49 0.0102 0.0012 5 0.00000 0.00000 19.26 1.61 0.0129 0.0017 6 0.00003 0.00000 15.12 0.08 0.2225 0.0007 7 0.00000 0.00000 8.92 11.50 0.0035 0.0010 8 0.00000 0.00000 -11.78 5.41 0.0035 0.0020 9 0.00000 0.00000 3.25 1.27 0.0091 0.0022 10 0.00004 0.00000 -9.07 0.06 0.3011 0.0013 11 0.00000 0.00000 1.44 13.73 0.0058 0.0059 12 0.00000 0.00000 3.27 2.56 0.0077 0.0031 13 0.00000 0.00000 2.33 0.73 0.0126 0.0019 14 0.00004 0.00000 -6.48 0.03 0.2482 0.0052 15 0.00000 0.00000 5.11 4.14 0.0084 0.0046 16 0.00000 0.00000 1.65 2.17 0.0059 0.0008 The magnetic center is at X = 101.1 +- 1.0 microns Y = 96.3 +- 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 ^ | N S --> x S N Date: 03-09-1995 Time: 09:25:55 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10335 +- 6.673015E-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 0.00012 0.00000 -136.71 0.47 0.3571 0.0034 2 0.03500 0.00001 44.96 0.00 100.0000 0.0000 3 0.00002 0.00000 29.77 0.38 0.0511 0.0060 4 0.00000 0.00000 39.79 3.18 0.0136 0.0020 5 0.00001 0.00000 18.34 0.97 0.0153 0.0007 6 0.00008 0.00000 15.08 0.07 0.2213 0.0019 7 0.00000 0.00000 8.67 2.90 0.0090 0.0044 8 0.00000 0.00000 -2.45 3.34 0.0051 0.0026 9 0.00000 0.00000 4.02 0.54 0.0098 0.0013 10 0.00011 0.00000 -9.06 0.04 0.3020 0.0011 11 0.00000 0.00000 -6.51 11.82 0.0032 0.0015 12 0.00000 0.00000 2.10 2.23 0.0059 0.0025 13 0.00000 0.00000 2.34 0.91 0.0120 0.0020 14 0.00009 0.00000 -6.46 0.03 0.2520 0.0056 15 0.00000 0.00000 -1.41 5.41 0.0045 0.0026 16 0.00000 0.00000 -1.66 8.01 0.0077 0.0021 The magnetic center is at X = 109.4 +- 1.4 microns Y = 116.1 +- 1.4 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: 03-09-1995 Time: 09:32:09 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.06512 +- 7.115331E-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 -141.03 0.29 0.3629 0.0020 2 0.06892 0.00002 44.96 0.00 100.0000 0.0000 3 0.00003 0.00000 31.25 0.58 0.0474 0.0021 4 0.00000 0.00000 39.05 3.46 0.0040 0.0022 5 0.00001 0.00000 19.19 0.56 0.0170 0.0008 6 0.00015 0.00000 15.13 0.06 0.2203 0.0018 7 0.00000 0.00000 8.79 2.01 0.0069 0.0035 8 0.00000 0.00000 -5.90 4.77 0.0030 0.0013 9 0.00001 0.00000 4.58 0.74 0.0095 0.0008 10 0.00021 0.00000 -9.06 0.01 0.3023 0.0006 11 0.00000 0.00000 -11.73 2.60 0.0031 0.0013 12 0.00000 0.00000 4.19 2.39 0.0052 0.0036 13 0.00001 0.00000 2.51 0.47 0.0142 0.0019 14 0.00017 0.00000 -6.43 0.06 0.2517 0.0048 15 0.00000 0.00000 1.25 3.39 0.0050 0.0021 16 0.00000 0.00000 7.29 2.67 0.0055 0.0031 The magnetic center is at X = 101.9 +- 0.9 microns Y = 126.0 +- 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 ^ | N S --> x S N Date: 03-09-1995 Time: 09:38:28 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0569 +- 4.3521E-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 -144.66 0.33 0.3629 0.0013 2 0.13747 0.00003 44.96 0.00 100.0000 0.0000 3 0.00007 0.00001 32.14 1.74 0.0501 0.0042 4 0.00000 0.00000 17.43 34.00 0.0034 0.0012 5 0.00002 0.00000 20.22 0.97 0.0178 0.0016 6 0.00030 0.00000 15.13 0.06 0.2200 0.0024 7 0.00001 0.00000 8.23 4.03 0.0064 0.0026 8 0.00000 0.00000 -4.27 15.29 0.0022 0.0012 9 0.00001 0.00000 4.38 0.71 0.0103 0.0010 10 0.00042 0.00000 -9.08 0.02 0.3026 0.0009 11 0.00000 0.00000 8.10 13.71 0.0032 0.0014 12 0.00001 0.00000 1.24 4.01 0.0040 0.0023 13 0.00002 0.00000 2.81 0.95 0.0150 0.0008 14 0.00034 0.00000 -6.48 0.05 0.2510 0.0021 15 0.00001 0.00000 3.37 2.33 0.0054 0.0024 16 0.00001 0.00000 -1.10 4.36 0.0052 0.0022 The magnetic center is at X = 93.8 +- 0.8 microns Y = 132.2 +- 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 ^ | N S --> x S N Date: 03-09-1995 Time: 09:44:45 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0685 +- 7.682993E-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 -145.11 0.21 0.3590 0.0021 2 0.20568 0.00007 44.94 0.00 100.0000 0.0000 3 0.00012 0.00000 32.54 0.35 0.0565 0.0005 4 0.00001 0.00000 1.16 25.38 0.0027 0.0017 5 0.00004 0.00000 20.62 0.55 0.0189 0.0009 6 0.00043 0.00000 15.07 0.09 0.2112 0.0011 7 0.00001 0.00000 7.80 2.45 0.0059 0.0020 8 0.00001 0.00000 -8.46 5.04 0.0029 0.0012 9 0.00002 0.00000 4.38 1.27 0.0096 0.0008 10 0.00062 0.00000 -9.10 0.02 0.3018 0.0014 11 0.00000 0.00000 -3.31 12.02 0.0024 0.0010 12 0.00001 0.00001 8.50 3.41 0.0060 0.0028 13 0.00002 0.00001 1.48 0.84 0.0113 0.0033 14 0.00053 0.00001 -6.42 0.13 0.2558 0.0046 15 0.00001 0.00000 -6.05 3.57 0.0043 0.0005 16 0.00001 0.00000 1.47 1.65 0.0044 0.0013 The magnetic center is at X = 91.7 +- 0.7 microns Y = 131.5 +- 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 ^ | N S --> x S N Date: 03-09-1995 Time: 09:51:03 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3127 +- 4.405273E-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 0.00097 0.00001 -146.60 0.18 0.3536 0.0023 2 0.27328 0.00008 44.94 0.00 100.0000 0.0000 3 0.00017 0.00001 32.00 0.51 0.0625 0.0031 4 0.00001 0.00001 -13.16 26.58 0.0046 0.0022 5 0.00006 0.00000 19.86 0.30 0.0205 0.0011 6 0.00055 0.00000 15.16 0.04 0.2021 0.0008 7 0.00002 0.00000 9.37 1.15 0.0070 0.0010 8 0.00001 0.00000 -6.87 4.28 0.0023 0.0007 9 0.00003 0.00000 5.00 0.69 0.0098 0.0013 10 0.00085 0.00000 -9.10 0.03 0.3092 0.0007 11 0.00001 0.00001 -7.66 12.15 0.0045 0.0018 12 0.00001 0.00001 -1.34 4.28 0.0041 0.0034 13 0.00004 0.00001 2.07 1.23 0.0138 0.0027 14 0.00070 0.00001 -6.50 0.05 0.2570 0.0030 15 0.00002 0.00001 3.81 5.05 0.0060 0.0032 16 0.00002 0.00000 2.50 2.66 0.0066 0.0006 The magnetic center is at X = 87.0 +- 0.7 microns Y = 131.9 +- 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 ^ | N S --> x S N Date: 03-09-1995 Time: 09:57:21 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4114 +- 3.967285E-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 0.00118 0.00001 -148.17 0.20 0.3490 0.0021 2 0.33806 0.00011 44.94 0.00 100.0000 0.0000 3 0.00022 0.00000 32.07 0.16 0.0662 0.0009 4 0.00005 0.00000 -18.72 36.76 0.0150 0.0010 5 0.00007 0.00000 19.93 0.66 0.0202 0.0004 6 0.00059 0.00000 15.19 0.09 0.1741 0.0006 7 0.00002 0.00001 8.15 0.72 0.0066 0.0017 8 0.00001 0.00000 -3.36 4.01 0.0036 0.0009 9 0.00003 0.00000 3.60 1.00 0.0094 0.0007 10 0.00105 0.00001 -9.09 0.02 0.3116 0.0016 11 0.00001 0.00000 -7.08 10.98 0.0023 0.0009 12 0.00002 0.00001 4.61 3.37 0.0073 0.0037 13 0.00005 0.00001 1.99 0.48 0.0160 0.0016 14 0.00084 0.00002 -6.52 0.09 0.2481 0.0056 15 0.00002 0.00001 1.70 2.17 0.0060 0.0022 16 0.00002 0.00001 -9.36 1.69 0.0046 0.0042 The magnetic center is at X = 82.2 +- 0.7 microns Y = 132.4 +- 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 ^ | N S --> x S N Date: 03-09-1995 Time: 10:03:40 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.3948 +- 5.602282E-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 0.00139 0.00000 -147.87 0.22 0.3572 0.0012 2 0.38977 0.00006 44.93 0.00 100.0000 0.0000 3 0.00023 0.00001 31.50 0.44 0.0601 0.0025 4 0.00004 0.00001 -39.53 3.67 0.0103 0.0018 5 0.00007 0.00001 20.44 1.36 0.0188 0.0019 6 0.00051 0.00000 15.22 0.14 0.1303 0.0011 7 0.00002 0.00001 7.17 4.50 0.0051 0.0022 8 0.00004 0.00000 -20.56 0.95 0.0090 0.0007 9 0.00005 0.00000 3.86 0.98 0.0121 0.0012 10 0.00125 0.00000 -9.09 0.02 0.3209 0.0011 11 0.00001 0.00001 -6.34 8.81 0.0024 0.0013 12 0.00006 0.00002 -0.65 0.32 0.0142 0.0039 13 0.00006 0.00001 1.15 0.71 0.0142 0.0015 14 0.00099 0.00002 -6.38 0.05 0.2543 0.0050 15 0.00003 0.00001 0.41 5.40 0.0069 0.0034 16 0.00002 0.00000 2.72 7.29 0.0055 0.0009 The magnetic center is at X = 84.9 +- 0.6 microns Y = 135.1 +- 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: 03-09-1995 Time: 10:09:58 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.3981 +- 9.969724E-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 0.00155 0.00001 -147.53 0.32 0.3637 0.0016 2 0.42608 0.00013 44.93 0.00 100.0000 0.0000 3 0.00025 0.00001 31.44 0.72 0.0589 0.0017 4 0.00003 0.00001 -34.41 3.26 0.0080 0.0024 5 0.00009 0.00001 20.47 0.97 0.0204 0.0016 6 0.00031 0.00001 15.53 0.28 0.0720 0.0016 7 0.00003 0.00001 8.47 2.36 0.0062 0.0016 8 0.00004 0.00001 -20.45 0.89 0.0091 0.0016 9 0.00005 0.00001 3.81 0.58 0.0116 0.0016 10 0.00141 0.00000 -9.11 0.02 0.3320 0.0003 11 0.00001 0.00001 -4.68 11.30 0.0026 0.0013 12 0.00006 0.00000 1.51 1.23 0.0129 0.0008 13 0.00006 0.00000 2.22 1.24 0.0135 0.0003 14 0.00105 0.00002 -6.41 0.05 0.2454 0.0057 15 0.00002 0.00001 1.45 5.36 0.0050 0.0021 16 0.00004 0.00001 -1.11 3.01 0.0084 0.0019 The magnetic center is at X = 87.2 +- 0.9 microns Y = 137.1 +- 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 ^ | 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)