SLAC Magnetic Measurements Date: 04-19-1995 Time: 11:33:54 Magnet Name (Serial #): 113 Bar Code Number: 409 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: 04-19-1995 Time: 12:21:03 Magnet Name: 113 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00381 +- 5.475145E-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 0.00004 0.00000 -121.78 0.81 0.3016 0.0035 2 0.01491 0.00000 45.01 0.00 100.0000 0.0000 3 0.00001 0.00000 15.45 1.83 0.0555 0.0047 4 0.00000 0.00000 -22.57 1.43 0.0146 0.0016 5 0.00000 0.00000 10.24 1.36 0.0167 0.0014 6 0.00003 0.00000 15.11 0.08 0.2117 0.0010 7 0.00000 0.00000 5.73 1.34 0.0068 0.0010 8 0.00000 0.00000 3.33 18.96 0.0032 0.0012 9 0.00000 0.00000 4.42 1.35 0.0129 0.0005 10 0.00004 0.00000 -9.07 0.02 0.2971 0.0018 11 0.00000 0.00000 -0.83 10.26 0.0022 0.0012 12 0.00000 0.00000 -4.33 10.31 0.0045 0.0015 13 0.00000 0.00000 1.72 1.41 0.0122 0.0008 14 0.00004 0.00000 -6.44 0.03 0.2579 0.0021 15 0.00000 0.00000 -9.64 1.66 0.0093 0.0033 16 0.00000 0.00000 2.86 2.56 0.0068 0.0021 The magnetic center is at X = 114.5 +- 1.7 microns Y = 71.0 +- 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: 04-19-1995 Time: 12:27:08 Magnet Name: 113 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10785 +- 3.705243E-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 -152.55 0.64 0.2661 0.0059 2 0.03497 0.00001 45.01 0.00 100.0000 0.0000 3 0.00002 0.00000 15.03 1.07 0.0704 0.0025 4 0.00001 0.00000 -27.67 2.44 0.0196 0.0013 5 0.00001 0.00000 9.22 1.28 0.0162 0.0023 6 0.00008 0.00000 15.09 0.01 0.2185 0.0009 7 0.00000 0.00000 5.15 1.06 0.0064 0.0011 8 0.00000 0.00000 -10.87 19.11 0.0102 0.0019 9 0.00000 0.00000 3.72 1.15 0.0108 0.0021 10 0.00010 0.00000 -9.05 0.03 0.2973 0.0022 11 0.00000 0.00000 1.89 9.86 0.0018 0.0006 12 0.00000 0.00000 0.09 2.62 0.0051 0.0011 13 0.00000 0.00000 1.23 0.68 0.0095 0.0024 14 0.00009 0.00000 -6.42 0.02 0.2562 0.0013 15 0.00000 0.00000 -8.16 1.03 0.0062 0.0011 16 0.00000 0.00000 1.42 1.86 0.0069 0.0006 The magnetic center is at X = 54.8 +- 1.7 microns Y = 105.5 +- 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: 04-19-1995 Time: 12:33:21 Magnet Name: 113 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.07126 +- 1.869299E-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 0.00019 0.00000 -161.56 0.78 0.2702 0.0038 2 0.06887 0.00002 45.01 0.00 100.0000 0.0000 3 0.00005 0.00000 14.68 1.48 0.0690 0.0044 4 0.00001 0.00000 -23.78 1.38 0.0203 0.0026 5 0.00001 0.00000 10.37 1.88 0.0151 0.0022 6 0.00015 0.00000 15.10 0.08 0.2192 0.0005 7 0.00000 0.00000 5.63 3.26 0.0067 0.0007 8 0.00000 0.00000 20.31 1.63 0.0020 0.0008 9 0.00001 0.00000 4.28 0.87 0.0111 0.0010 10 0.00021 0.00000 -9.02 0.05 0.3009 0.0006 11 0.00000 0.00000 -7.67 3.32 0.0018 0.0009 12 0.00000 0.00000 -11.94 2.16 0.0044 0.0024 13 0.00001 0.00000 0.89 1.22 0.0116 0.0019 14 0.00018 0.00000 -6.42 0.02 0.2548 0.0007 15 0.00001 0.00000 -9.47 0.45 0.0125 0.0048 16 0.00001 0.00000 3.85 3.95 0.0079 0.0016 The magnetic center is at X = 38.2 +- 1.6 microns Y = 114.5 +- 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: 04-19-1995 Time: 12:39:37 Magnet Name: 113 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0678 +- 5.500047E-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 0.00037 0.00001 -165.28 0.72 0.2729 0.0050 2 0.13743 0.00002 45.01 0.00 100.0000 0.0000 3 0.00009 0.00001 14.08 0.99 0.0647 0.0040 4 0.00003 0.00000 -24.43 0.76 0.0203 0.0021 5 0.00002 0.00000 9.46 1.30 0.0145 0.0015 6 0.00030 0.00000 15.05 0.04 0.2193 0.0013 7 0.00001 0.00000 7.35 1.42 0.0061 0.0016 8 0.00000 0.00000 9.81 17.84 0.0025 0.0002 9 0.00001 0.00000 4.91 0.94 0.0104 0.0003 10 0.00041 0.00000 -9.06 0.03 0.3018 0.0016 11 0.00000 0.00000 -8.85 1.60 0.0025 0.0008 12 0.00000 0.00000 7.52 5.40 0.0036 0.0019 13 0.00002 0.00000 0.44 0.48 0.0115 0.0035 14 0.00035 0.00000 -6.45 0.03 0.2574 0.0029 15 0.00001 0.00001 -10.36 0.83 0.0103 0.0045 16 0.00001 0.00000 3.12 2.43 0.0070 0.0017 The magnetic center is at X = 31.0 +- 1.6 microns Y = 117.9 +- 2.2 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: 04-19-1995 Time: 12:45:52 Magnet Name: 113 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.084 +- 9.687228E-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 0.00052 0.00001 -165.95 0.60 0.2546 0.0066 2 0.20562 0.00005 44.99 0.00 100.0000 0.0000 3 0.00013 0.00001 14.22 1.55 0.0612 0.0046 4 0.00004 0.00000 -23.70 1.61 0.0175 0.0016 5 0.00003 0.00000 9.22 1.56 0.0153 0.0019 6 0.00043 0.00000 15.07 0.04 0.2106 0.0012 7 0.00001 0.00000 5.75 0.43 0.0068 0.0012 8 0.00001 0.00000 -10.99 16.33 0.0029 0.0006 9 0.00002 0.00000 4.65 0.37 0.0107 0.0015 10 0.00063 0.00000 -9.07 0.02 0.3045 0.0019 11 0.00000 0.00000 -1.98 4.71 0.0022 0.0002 12 0.00001 0.00001 7.48 11.85 0.0066 0.0025 13 0.00002 0.00000 0.78 0.89 0.0114 0.0020 14 0.00053 0.00000 -6.44 0.03 0.2567 0.0022 15 0.00002 0.00000 -4.92 9.27 0.0083 0.0012 16 0.00001 0.00000 7.36 3.43 0.0055 0.0016 The magnetic center is at X = 27.6 +- 1.4 microns Y = 110.3 +- 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: 04-19-1995 Time: 12:52:08 Magnet Name: 113 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3354 +- 1.933386E-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 0.00068 0.00002 -166.86 0.59 0.2497 0.0056 2 0.27333 0.00003 44.99 0.00 100.0000 0.0000 3 0.00016 0.00001 14.77 1.09 0.0588 0.0041 4 0.00006 0.00001 -33.71 0.83 0.0231 0.0028 5 0.00004 0.00001 8.43 1.38 0.0153 0.0026 6 0.00055 0.00000 15.09 0.07 0.2020 0.0012 7 0.00002 0.00000 5.10 2.39 0.0065 0.0016 8 0.00001 0.00000 0.30 1.75 0.0052 0.0010 9 0.00002 0.00000 5.59 1.07 0.0091 0.0007 10 0.00084 0.00000 -9.08 0.01 0.3079 0.0011 11 0.00000 0.00000 -0.38 10.37 0.0015 0.0004 12 0.00001 0.00000 -1.80 10.33 0.0030 0.0007 13 0.00003 0.00001 0.67 0.59 0.0114 0.0031 14 0.00070 0.00001 -6.47 0.02 0.2570 0.0026 15 0.00002 0.00001 -9.94 1.08 0.0079 0.0020 16 0.00001 0.00001 -2.18 6.15 0.0041 0.0021 The magnetic center is at X = 25.3 +- 1.3 microns Y = 108.6 +- 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: 04-19-1995 Time: 12:58:24 Magnet Name: 113 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4392 +- 5.783262E-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 0.00082 0.00002 -165.92 0.68 0.2429 0.0056 2 0.33807 0.00005 44.99 0.00 100.0000 0.0000 3 0.00019 0.00001 15.58 1.09 0.0547 0.0042 4 0.00006 0.00001 -30.34 1.71 0.0168 0.0021 5 0.00005 0.00001 8.41 2.05 0.0139 0.0024 6 0.00061 0.00000 15.07 0.10 0.1798 0.0008 7 0.00003 0.00000 5.39 0.48 0.0081 0.0011 8 0.00002 0.00000 -10.94 18.69 0.0064 0.0008 9 0.00003 0.00000 4.97 0.99 0.0100 0.0006 10 0.00105 0.00001 -9.06 0.03 0.3115 0.0015 11 0.00001 0.00000 -3.26 11.31 0.0032 0.0014 12 0.00002 0.00000 -2.06 2.13 0.0072 0.0013 13 0.00003 0.00001 0.09 0.60 0.0099 0.0038 14 0.00086 0.00000 -6.47 0.02 0.2542 0.0012 15 0.00002 0.00001 -8.96 1.62 0.0061 0.0038 16 0.00001 0.00001 0.91 4.85 0.0037 0.0022 The magnetic center is at X = 26.4 +- 1.4 microns Y = 105.2 +- 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: 04-19-1995 Time: 13:04:40 Magnet Name: 113 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4265 +- 6.791447E-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 0.00093 0.00002 -162.04 0.95 0.2389 0.0045 2 0.38974 0.00004 44.98 0.00 100.0000 0.0000 3 0.00019 0.00002 14.62 1.79 0.0480 0.0041 4 0.00006 0.00001 -28.12 2.36 0.0145 0.0018 5 0.00006 0.00001 9.08 2.03 0.0146 0.0017 6 0.00049 0.00000 15.05 0.13 0.1262 0.0008 7 0.00004 0.00000 5.70 0.47 0.0092 0.0010 8 0.00003 0.00000 10.10 18.75 0.0081 0.0008 9 0.00004 0.00001 4.78 0.41 0.0113 0.0023 10 0.00125 0.00001 -9.09 0.03 0.3202 0.0016 11 0.00001 0.00000 -7.29 4.39 0.0015 0.0007 12 0.00001 0.00000 7.25 8.43 0.0017 0.0008 13 0.00004 0.00001 0.54 0.99 0.0106 0.0026 14 0.00100 0.00001 -6.44 0.02 0.2564 0.0023 15 0.00003 0.00001 -0.26 10.03 0.0073 0.0017 16 0.00004 0.00001 0.91 1.56 0.0114 0.0026 The magnetic center is at X = 32.9 +- 1.8 microns Y = 101.5 +- 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 Date: 04-19-1995 Time: 13:10:56 Magnet Name: 113 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4355 +- 1.062652E-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 0.00102 0.00002 -159.07 1.09 0.2388 0.0036 2 0.42599 0.00005 44.98 0.00 100.0000 0.0000 3 0.00018 0.00001 13.45 1.83 0.0428 0.0031 4 0.00005 0.00001 -29.10 2.43 0.0119 0.0016 5 0.00008 0.00001 7.96 1.92 0.0177 0.0017 6 0.00029 0.00001 15.29 0.14 0.0686 0.0013 7 0.00004 0.00000 4.71 0.79 0.0088 0.0003 8 0.00002 0.00000 9.93 18.60 0.0058 0.0002 9 0.00005 0.00000 4.12 0.34 0.0119 0.0005 10 0.00141 0.00000 -9.09 0.01 0.3298 0.0011 11 0.00001 0.00000 -2.29 13.60 0.0017 0.0003 12 0.00002 0.00001 6.03 11.20 0.0054 0.0019 13 0.00003 0.00001 0.95 2.66 0.0080 0.0028 14 0.00108 0.00001 -6.49 0.04 0.2534 0.0018 15 0.00002 0.00002 2.01 9.09 0.0047 0.0037 16 0.00007 0.00001 2.18 0.99 0.0157 0.0025 The magnetic center is at X = 38.1 +- 2.0 microns Y = 99.6 +- 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 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)