SLAC Magnetic Measurements Date: 03-30-1995 Time: 07:13:30 Magnet Name (Serial #): 114 Bar Code Number: 429 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: 03-30-1995 Time: 08:01:27 Magnet Name: 114 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 9.997335 +- 2.039665E-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 -176.00 0.77 0.3092 0.0044 2 0.01490 0.00000 45.01 0.00 100.0000 0.0000 3 0.00001 0.00000 28.31 0.92 0.0873 0.0055 4 0.00000 0.00000 31.20 1.87 0.0199 0.0021 5 0.00000 0.00000 13.04 2.10 0.0137 0.0022 6 0.00003 0.00000 15.07 0.06 0.2099 0.0007 7 0.00000 0.00000 3.12 1.01 0.0032 0.0012 8 0.00000 0.00000 14.44 3.13 0.0021 0.0015 9 0.00000 0.00000 -0.14 0.46 0.0126 0.0009 10 0.00004 0.00000 -9.01 0.04 0.2955 0.0011 11 0.00000 0.00000 -4.19 1.92 0.0052 0.0013 12 0.00000 0.00000 10.45 2.41 0.0048 0.0008 13 0.00000 0.00000 -0.91 1.08 0.0244 0.0042 14 0.00004 0.00000 -6.35 0.01 0.2606 0.0046 15 0.00000 0.00000 -2.93 4.68 0.0096 0.0063 16 0.00000 0.00000 3.09 5.51 0.0073 0.0035 The magnetic center is at X = 9.6 +- 1.8 microns Y = 137.8 +- 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: 03-30-1995 Time: 08:07:32 Magnet Name: 114 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.0973 +- 3.101216E-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 173.36 0.50 0.3761 0.0075 2 0.03494 0.00001 45.01 0.00 100.0000 0.0000 3 0.00002 0.00000 27.07 1.52 0.0673 0.0034 4 0.00001 0.00000 32.50 1.06 0.0206 0.0008 5 0.00000 0.00000 12.69 2.79 0.0118 0.0010 6 0.00008 0.00000 15.04 0.04 0.2162 0.0015 7 0.00000 0.00000 6.08 3.37 0.0034 0.0009 8 0.00000 0.00000 20.47 0.91 0.0101 0.0012 9 0.00000 0.00000 -0.58 0.56 0.0122 0.0011 10 0.00010 0.00000 -9.01 0.02 0.2984 0.0014 11 0.00000 0.00000 -5.11 0.72 0.0065 0.0035 12 0.00000 0.00000 1.70 1.31 0.0063 0.0037 13 0.00001 0.00000 -0.28 0.83 0.0211 0.0046 14 0.00009 0.00000 -6.39 0.06 0.2565 0.0034 15 0.00000 0.00000 -2.88 6.77 0.0081 0.0040 16 0.00000 0.00000 1.11 5.47 0.0058 0.0023 The magnetic center is at X = -19.4 +- 1.5 microns Y = 166.9 +- 3.3 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: 03-30-1995 Time: 08:13:44 Magnet Name: 114 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.06137 +- 6.821912E-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 0.00028 0.00000 169.84 0.53 0.4111 0.0056 2 0.06885 0.00001 45.01 0.00 100.0000 0.0000 3 0.00004 0.00000 25.79 1.26 0.0653 0.0025 4 0.00001 0.00000 28.61 1.92 0.0155 0.0026 5 0.00001 0.00000 14.47 1.87 0.0120 0.0026 6 0.00015 0.00000 15.06 0.05 0.2175 0.0006 7 0.00000 0.00000 7.01 1.86 0.0039 0.0005 8 0.00000 0.00000 14.38 2.51 0.0027 0.0010 9 0.00001 0.00000 -0.37 0.12 0.0124 0.0014 10 0.00021 0.00000 -9.00 0.03 0.2984 0.0010 11 0.00000 0.00000 -4.81 3.33 0.0047 0.0012 12 0.00000 0.00000 2.54 4.67 0.0063 0.0023 13 0.00001 0.00000 -1.62 2.74 0.0191 0.0031 14 0.00018 0.00000 -6.46 0.08 0.2556 0.0032 15 0.00001 0.00000 -3.09 2.07 0.0106 0.0059 16 0.00000 0.00000 -6.97 3.21 0.0027 0.0014 The magnetic center is at X = -32.4 +- 1.7 microns Y = 180.7 +- 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: 03-30-1995 Time: 08:20:01 Magnet Name: 114 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0573 +- 5.365993E-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 0.00059 0.00001 167.04 0.54 0.4297 0.0061 2 0.13740 0.00002 45.01 0.00 100.0000 0.0000 3 0.00009 0.00001 25.37 1.58 0.0679 0.0037 4 0.00002 0.00000 28.20 1.36 0.0163 0.0016 5 0.00001 0.00000 15.82 1.11 0.0102 0.0017 6 0.00030 0.00000 15.07 0.06 0.2183 0.0014 7 0.00000 0.00000 9.13 5.29 0.0024 0.0012 8 0.00000 0.00000 9.94 4.38 0.0026 0.0004 9 0.00002 0.00000 -1.21 0.61 0.0114 0.0025 10 0.00041 0.00000 -9.02 0.02 0.3005 0.0015 11 0.00001 0.00000 -5.30 3.80 0.0052 0.0016 12 0.00001 0.00000 8.84 6.91 0.0046 0.0018 13 0.00003 0.00001 -1.18 2.01 0.0212 0.0081 14 0.00035 0.00000 -6.37 0.05 0.2559 0.0023 15 0.00002 0.00001 -5.12 5.24 0.0147 0.0067 16 0.00001 0.00000 -3.09 0.88 0.0069 0.0030 The magnetic center is at X = -43.1 +- 1.9 microns Y = 187.0 +- 2.7 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: 03-30-1995 Time: 08:26:17 Magnet Name: 114 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0737 +- 1.060705E-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 0.00085 0.00002 165.37 0.65 0.4128 0.0078 2 0.20556 0.00003 44.99 0.00 100.0000 0.0000 3 0.00014 0.00001 25.60 1.31 0.0660 0.0033 4 0.00003 0.00000 26.96 3.04 0.0150 0.0013 5 0.00002 0.00000 16.01 3.73 0.0111 0.0014 6 0.00043 0.00000 15.07 0.04 0.2102 0.0005 7 0.00000 0.00000 4.24 5.67 0.0022 0.0004 8 0.00000 0.00000 7.36 11.55 0.0017 0.0007 9 0.00003 0.00000 -0.15 1.24 0.0134 0.0015 10 0.00063 0.00000 -9.03 0.02 0.3052 0.0012 11 0.00001 0.00000 -5.79 2.78 0.0055 0.0014 12 0.00001 0.00001 4.04 9.40 0.0070 0.0037 13 0.00004 0.00001 -2.26 1.76 0.0197 0.0030 14 0.00053 0.00001 -6.44 0.03 0.2576 0.0045 15 0.00002 0.00001 -3.81 2.82 0.0096 0.0042 16 0.00002 0.00000 -2.68 6.81 0.0079 0.0018 The magnetic center is at X = -46.6 +- 2.2 microns Y = 178.4 +- 3.4 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: 03-30-1995 Time: 08:32:33 Magnet Name: 114 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3165 +- 9.915865E-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 0.00113 0.00002 164.48 0.63 0.4154 0.0071 2 0.27321 0.00007 44.99 0.00 100.0000 0.0000 3 0.00018 0.00001 25.84 1.54 0.0669 0.0031 4 0.00007 0.00001 36.08 0.79 0.0241 0.0021 5 0.00003 0.00001 16.47 1.41 0.0106 0.0022 6 0.00055 0.00000 15.09 0.05 0.2012 0.0009 7 0.00001 0.00000 7.18 1.82 0.0031 0.0015 8 0.00002 0.00000 1.93 1.02 0.0081 0.0008 9 0.00003 0.00000 -0.59 0.55 0.0113 0.0012 10 0.00083 0.00000 -9.06 0.02 0.3045 0.0010 11 0.00001 0.00001 -6.41 3.82 0.0046 0.0026 12 0.00001 0.00000 0.05 9.52 0.0047 0.0011 13 0.00005 0.00002 0.25 1.65 0.0187 0.0082 14 0.00070 0.00001 -6.47 0.08 0.2544 0.0041 15 0.00003 0.00001 -3.97 6.74 0.0115 0.0051 16 0.00002 0.00000 6.83 6.60 0.0056 0.0017 The magnetic center is at X = -49.7 +- 2.1 microns Y = 178.8 +- 3.1 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: 03-30-1995 Time: 08:38:49 Magnet Name: 114 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4171 +- 6.33791E-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 0.00001 163.05 0.54 0.4126 0.0040 2 0.33801 0.00009 44.99 0.00 100.0000 0.0000 3 0.00024 0.00001 26.66 0.89 0.0716 0.0038 4 0.00007 0.00001 33.75 1.92 0.0195 0.0020 5 0.00003 0.00000 17.03 2.09 0.0103 0.0013 6 0.00060 0.00000 15.07 0.09 0.1772 0.0013 7 0.00001 0.00000 -3.46 12.96 0.0022 0.0009 8 0.00002 0.00000 19.98 1.11 0.0049 0.0009 9 0.00004 0.00000 -1.21 0.90 0.0106 0.0008 10 0.00104 0.00001 -9.04 0.03 0.3089 0.0023 11 0.00002 0.00001 -3.25 5.29 0.0052 0.0020 12 0.00002 0.00000 0.49 1.63 0.0068 0.0005 13 0.00009 0.00002 -0.71 2.66 0.0258 0.0046 14 0.00086 0.00001 -6.44 0.05 0.2542 0.0026 15 0.00005 0.00002 -1.91 7.66 0.0152 0.0054 16 0.00002 0.00000 3.17 5.72 0.0056 0.0012 The magnetic center is at X = -53.7 +- 1.7 microns Y = 176.3 +- 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: 03-30-1995 Time: 08:45:05 Magnet Name: 114 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4041 +- 7.306714E-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 0.00172 0.00002 162.20 0.48 0.4410 0.0063 2 0.38968 0.00012 44.99 0.00 100.0000 0.0000 3 0.00032 0.00002 23.02 0.84 0.0820 0.0049 4 0.00005 0.00001 29.65 1.42 0.0136 0.0019 5 0.00003 0.00001 17.43 2.05 0.0087 0.0018 6 0.00049 0.00001 15.18 0.12 0.1252 0.0020 7 0.00001 0.00000 -2.07 16.29 0.0013 0.0009 8 0.00002 0.00000 0.04 22.29 0.0062 0.0010 9 0.00005 0.00001 -0.40 0.29 0.0133 0.0017 10 0.00124 0.00000 -9.02 0.02 0.3189 0.0014 11 0.00001 0.00001 -5.76 2.40 0.0036 0.0027 12 0.00004 0.00001 1.09 2.54 0.0095 0.0025 13 0.00009 0.00004 -1.16 1.64 0.0234 0.0102 14 0.00101 0.00002 -6.47 0.02 0.2594 0.0054 15 0.00004 0.00003 4.33 4.93 0.0101 0.0076 16 0.00003 0.00002 -2.24 4.77 0.0087 0.0051 The magnetic center is at X = -60.2 +- 1.8 microns Y = 187.5 +- 2.7 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: 03-30-1995 Time: 08:51:21 Magnet Name: 114 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4103 +- 7.014066E-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 0.00191 0.00003 162.27 0.57 0.4476 0.0072 2 0.42604 0.00010 44.99 0.00 100.0000 0.0000 3 0.00036 0.00001 22.66 1.23 0.0850 0.0033 4 0.00006 0.00000 31.66 3.27 0.0130 0.0011 5 0.00004 0.00000 14.50 1.64 0.0098 0.0010 6 0.00029 0.00000 15.29 0.25 0.0675 0.0006 7 0.00001 0.00000 -7.39 13.84 0.0019 0.0010 8 0.00002 0.00000 9.38 17.67 0.0045 0.0011 9 0.00006 0.00001 -0.77 0.82 0.0134 0.0017 10 0.00140 0.00001 -9.00 0.02 0.3289 0.0017 11 0.00002 0.00001 -0.46 6.37 0.0044 0.0015 12 0.00001 0.00000 1.28 2.57 0.0034 0.0009 13 0.00009 0.00003 -1.34 0.89 0.0214 0.0067 14 0.00108 0.00002 -6.45 0.03 0.2536 0.0040 15 0.00004 0.00000 -1.77 7.64 0.0088 0.0010 16 0.00003 0.00001 0.54 1.82 0.0061 0.0016 The magnetic center is at X = -60.9 +- 2.1 microns Y = 190.4 +- 3.1 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 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)