SLAC Magnetic Measurements Date: 04-07-1995 Time: 13:05:25 Magnet Name (Serial #): 175 Bar Code Number: 501 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: 04-07-1995 Time: 13:52:33 Magnet Name: 175 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00476 +- 2.311642E-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 -115.15 0.37 0.5283 0.0023 2 0.01507 0.00000 44.99 0.00 100.0000 0.0000 3 0.00001 0.00000 -0.88 0.79 0.0614 0.0042 4 0.00000 0.00000 21.31 0.60 0.0183 0.0013 5 0.00000 0.00000 19.81 1.10 0.0124 0.0019 6 0.00003 0.00000 15.04 0.12 0.1980 0.0016 7 0.00000 0.00000 18.85 3.12 0.0074 0.0021 8 0.00000 0.00000 -19.80 1.45 0.0027 0.0010 9 0.00000 0.00000 4.49 2.28 0.0061 0.0011 10 0.00005 0.00000 -9.01 0.05 0.2994 0.0012 11 0.00000 0.00000 -7.29 6.15 0.0027 0.0013 12 0.00000 0.00000 0.06 9.32 0.0040 0.0015 13 0.00000 0.00000 -0.37 2.01 0.0089 0.0029 14 0.00004 0.00000 -6.45 0.02 0.2617 0.0011 15 0.00000 0.00000 -0.78 4.08 0.0057 0.0015 16 0.00000 0.00000 -3.96 4.62 0.0051 0.0048 The magnetic center is at X = 213.6 +- 1.1 microns Y = 100.3 +- 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: 04-07-1995 Time: 13:58:39 Magnet Name: 175 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10812 +- 6.62525E-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 0.00013 0.00000 -135.02 0.22 0.3575 0.0022 2 0.03527 0.00001 44.98 0.00 100.0000 0.0000 3 0.00002 0.00000 14.34 0.58 0.0678 0.0012 4 0.00000 0.00000 30.07 2.19 0.0113 0.0012 5 0.00001 0.00000 16.65 0.46 0.0147 0.0005 6 0.00007 0.00000 15.09 0.07 0.2004 0.0014 7 0.00000 0.00000 18.52 4.06 0.0052 0.0010 8 0.00000 0.00000 10.16 18.60 0.0096 0.0013 9 0.00000 0.00000 4.26 1.29 0.0052 0.0012 10 0.00011 0.00000 -8.99 0.03 0.3000 0.0010 11 0.00000 0.00000 5.75 5.16 0.0015 0.0009 12 0.00000 0.00000 -1.91 3.07 0.0051 0.0015 13 0.00000 0.00000 0.84 1.04 0.0084 0.0018 14 0.00009 0.00000 -6.45 0.01 0.2587 0.0015 15 0.00000 0.00000 1.54 6.81 0.0031 0.0016 16 0.00000 0.00000 -0.98 0.99 0.0083 0.0038 The magnetic center is at X = 112.9 +- 0.8 microns Y = 113.0 +- 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: 04-07-1995 Time: 14:04:51 Magnet Name: 175 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.07157 +- 4.089651E-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 0.00023 0.00000 -145.02 0.17 0.3244 0.0021 2 0.06940 0.00002 44.98 0.00 100.0000 0.0000 3 0.00005 0.00000 17.49 0.63 0.0724 0.0018 4 0.00001 0.00000 26.06 1.72 0.0080 0.0028 5 0.00001 0.00000 18.18 1.71 0.0150 0.0013 6 0.00014 0.00000 15.12 0.07 0.2021 0.0008 7 0.00000 0.00000 21.89 1.31 0.0051 0.0018 8 0.00000 0.00000 -0.99 16.94 0.0023 0.0013 9 0.00000 0.00000 3.13 3.13 0.0035 0.0015 10 0.00021 0.00000 -9.00 0.03 0.3010 0.0010 11 0.00000 0.00000 3.45 3.24 0.0026 0.0014 12 0.00000 0.00000 -2.61 10.98 0.0040 0.0016 13 0.00001 0.00000 1.05 1.35 0.0129 0.0031 14 0.00018 0.00000 -6.46 0.02 0.2570 0.0011 15 0.00000 0.00000 -4.28 7.52 0.0023 0.0016 16 0.00001 0.00000 -9.28 2.03 0.0076 0.0015 The magnetic center is at X = 83.1 +- 0.7 microns Y = 118.7 +- 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: 04-07-1995 Time: 14:11:06 Magnet Name: 175 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0664 +- 3.284408E-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 0.00044 0.00000 -150.43 0.50 0.3168 0.0028 2 0.13844 0.00001 44.98 0.00 100.0000 0.0000 3 0.00010 0.00000 17.79 0.77 0.0725 0.0020 4 0.00001 0.00000 28.68 4.63 0.0083 0.0020 5 0.00002 0.00000 17.89 0.56 0.0146 0.0017 6 0.00028 0.00000 15.07 0.03 0.2024 0.0019 7 0.00001 0.00000 9.49 18.21 0.0050 0.0010 8 0.00000 0.00000 -0.29 16.12 0.0017 0.0004 9 0.00001 0.00000 3.57 1.91 0.0045 0.0010 10 0.00042 0.00000 -9.01 0.03 0.3036 0.0020 11 0.00000 0.00000 -5.92 7.15 0.0022 0.0010 12 0.00001 0.00000 -2.49 10.11 0.0041 0.0007 13 0.00001 0.00000 0.49 2.41 0.0092 0.0015 14 0.00036 0.00000 -6.45 0.03 0.2597 0.0028 15 0.00001 0.00000 1.69 5.21 0.0058 0.0013 16 0.00001 0.00000 -0.59 6.48 0.0071 0.0012 The magnetic center is at X = 69.8 +- 1.2 microns Y = 123.1 +- 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: 04-07-1995 Time: 14:17:21 Magnet Name: 175 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0817 +- 5.341666E-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 0.00065 0.00000 -153.67 0.15 0.3140 0.0021 2 0.20711 0.00003 44.96 0.00 100.0000 0.0000 3 0.00016 0.00000 18.37 0.61 0.0762 0.0009 4 0.00002 0.00000 29.38 3.25 0.0079 0.0024 5 0.00003 0.00000 18.59 1.13 0.0155 0.0015 6 0.00040 0.00000 15.07 0.08 0.1917 0.0020 7 0.00001 0.00000 22.43 2.57 0.0060 0.0017 8 0.00001 0.00000 0.29 21.40 0.0028 0.0007 9 0.00001 0.00000 0.04 2.60 0.0031 0.0018 10 0.00064 0.00000 -9.03 0.02 0.3068 0.0021 11 0.00001 0.00000 3.50 7.11 0.0025 0.0008 12 0.00001 0.00000 7.36 10.70 0.0045 0.0016 13 0.00002 0.00000 2.07 0.73 0.0086 0.0010 14 0.00053 0.00000 -6.47 0.04 0.2577 0.0008 15 0.00001 0.00001 -2.98 3.29 0.0033 0.0035 16 0.00002 0.00001 -9.54 0.72 0.0083 0.0043 The magnetic center is at X = 62.2 +- 0.5 microns Y = 125.7 +- 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: 04-07-1995 Time: 14:23:36 Magnet Name: 175 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3308 +- 1.989503E-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 0.00084 0.00001 -157.46 0.23 0.3066 0.0028 2 0.27529 0.00007 44.96 0.00 100.0000 0.0000 3 0.00023 0.00001 18.51 0.52 0.0848 0.0022 4 0.00006 0.00000 39.78 1.33 0.0205 0.0016 5 0.00004 0.00000 17.95 2.04 0.0144 0.0014 6 0.00050 0.00000 15.09 0.03 0.1813 0.0012 7 0.00001 0.00000 9.98 19.65 0.0045 0.0009 8 0.00002 0.00000 1.42 1.80 0.0064 0.0017 9 0.00001 0.00000 5.93 1.79 0.0034 0.0005 10 0.00085 0.00001 -9.02 0.03 0.3096 0.0019 11 0.00001 0.00000 4.70 4.71 0.0026 0.0011 12 0.00001 0.00001 -5.59 5.70 0.0040 0.0025 13 0.00002 0.00001 2.89 3.31 0.0076 0.0032 14 0.00071 0.00000 -6.50 0.01 0.2578 0.0008 15 0.00002 0.00001 2.06 3.38 0.0056 0.0026 16 0.00003 0.00001 -4.00 7.63 0.0092 0.0032 The magnetic center is at X = 52.5 +- 0.7 microns Y = 126.5 +- 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: 04-07-1995 Time: 14:29:53 Magnet Name: 175 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4331 +- 8.581628E-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 0.00102 0.00001 -162.37 0.41 0.2994 0.0018 2 0.34041 0.00007 44.96 0.00 100.0000 0.0000 3 0.00033 0.00001 19.19 0.34 0.0982 0.0019 4 0.00006 0.00001 38.71 2.81 0.0162 0.0020 5 0.00004 0.00001 16.50 0.90 0.0132 0.0027 6 0.00052 0.00000 15.10 0.14 0.1542 0.0011 7 0.00002 0.00000 -11.54 20.69 0.0053 0.0011 8 0.00003 0.00000 -10.88 18.83 0.0092 0.0005 9 0.00002 0.00000 5.15 2.01 0.0050 0.0012 10 0.00106 0.00001 -9.04 0.03 0.3122 0.0020 11 0.00000 0.00000 0.08 7.69 0.0013 0.0006 12 0.00001 0.00000 -0.71 1.65 0.0043 0.0014 13 0.00003 0.00001 0.99 2.72 0.0092 0.0027 14 0.00088 0.00000 -6.45 0.02 0.2571 0.0011 15 0.00002 0.00001 -0.21 4.20 0.0064 0.0033 16 0.00002 0.00001 1.26 8.04 0.0069 0.0015 The magnetic center is at X = 40.5 +- 1.0 microns Y = 127.5 +- 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: 04-07-1995 Time: 14:36:09 Magnet Name: 175 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4178 +- 1.086914E-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 0.00115 0.00001 -161.93 0.12 0.2927 0.0031 2 0.39241 0.00007 44.96 0.00 100.0000 0.0000 3 0.00038 0.00001 20.18 0.52 0.0970 0.0031 4 0.00004 0.00001 35.79 1.23 0.0107 0.0016 5 0.00005 0.00001 15.38 2.77 0.0133 0.0019 6 0.00038 0.00001 15.16 0.15 0.0970 0.0015 7 0.00002 0.00000 -11.26 20.15 0.0050 0.0004 8 0.00003 0.00000 -10.67 19.02 0.0072 0.0005 9 0.00002 0.00000 3.22 1.32 0.0047 0.0006 10 0.00127 0.00001 -9.03 0.01 0.3232 0.0020 11 0.00001 0.00000 -0.16 3.03 0.0022 0.0011 12 0.00001 0.00001 1.80 3.29 0.0021 0.0015 13 0.00003 0.00002 1.24 1.19 0.0084 0.0039 14 0.00101 0.00001 -6.49 0.03 0.2577 0.0034 15 0.00001 0.00001 1.02 4.98 0.0032 0.0014 16 0.00004 0.00003 -3.00 4.21 0.0096 0.0084 The magnetic center is at X = 40.6 +- 0.5 microns Y = 124.3 +- 1.3 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: 04-07-1995 Time: 14:42:26 Magnet Name: 175 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4244 +- 2.063381E-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 0.00127 0.00001 -161.90 0.66 0.2964 0.0016 2 0.42894 0.00008 44.95 0.00 100.0000 0.0000 3 0.00042 0.00000 18.50 0.15 0.0986 0.0005 4 0.00006 0.00000 38.47 1.74 0.0131 0.0011 5 0.00006 0.00001 14.14 1.32 0.0135 0.0033 6 0.00015 0.00001 15.32 0.40 0.0356 0.0018 7 0.00002 0.00000 -11.04 20.99 0.0045 0.0008 8 0.00002 0.00000 10.68 19.04 0.0042 0.0006 9 0.00002 0.00000 2.25 1.27 0.0051 0.0008 10 0.00142 0.00000 -9.02 0.01 0.3322 0.0007 11 0.00001 0.00001 1.16 4.72 0.0025 0.0017 12 0.00001 0.00000 4.98 6.43 0.0026 0.0009 13 0.00004 0.00001 3.49 1.34 0.0087 0.0027 14 0.00108 0.00001 -6.48 0.03 0.2523 0.0012 15 0.00003 0.00001 -7.87 2.57 0.0060 0.0027 16 0.00003 0.00001 0.45 1.76 0.0067 0.0026 The magnetic center is at X = 41.1 +- 1.5 microns Y = 125.8 +- 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 ^ | 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)