SLAC Magnetic Measurements Date: 04-14-1995 Time: 06:16:57 Magnet Name (Serial #): 144 Bar Code Number: 549 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: 04-14-1995 Time: 07:04:15 Magnet Name: 144 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00027 +- 5.255812E-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 -107.59 0.24 0.3542 0.0026 2 0.01487 0.00000 45.03 0.00 100.0000 0.0000 3 0.00001 0.00000 15.32 0.33 0.0968 0.0021 4 0.00000 0.00000 24.13 1.56 0.0173 0.0018 5 0.00000 0.00000 8.98 3.97 0.0080 0.0006 6 0.00003 0.00000 15.07 0.08 0.2154 0.0007 7 0.00000 0.00000 12.65 2.04 0.0068 0.0003 8 0.00000 0.00000 16.03 4.53 0.0024 0.0011 9 0.00000 0.00000 6.92 1.05 0.0122 0.0017 10 0.00004 0.00000 -9.02 0.01 0.2980 0.0010 11 0.00000 0.00000 -7.03 0.93 0.0031 0.0004 12 0.00000 0.00000 13.72 0.75 0.0046 0.0003 13 0.00000 0.00000 2.30 1.59 0.0158 0.0044 14 0.00004 0.00000 -6.35 0.02 0.2575 0.0011 15 0.00000 0.00000 0.13 10.49 0.0113 0.0018 16 0.00000 0.00000 -0.10 5.43 0.0056 0.0044 The magnetic center is at X = 150.8 +- 1.2 microns Y = 47.8 +- 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: 04-14-1995 Time: 07:10:21 Magnet Name: 144 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10199 +- 7.406815E-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 0.00007 0.00000 -106.35 0.58 0.1950 0.0017 2 0.03490 0.00001 45.03 0.00 100.0000 0.0000 3 0.00004 0.00000 28.25 0.36 0.1014 0.0020 4 0.00001 0.00000 29.79 3.04 0.0162 0.0020 5 0.00001 0.00000 7.59 1.93 0.0147 0.0009 6 0.00008 0.00000 15.05 0.05 0.2182 0.0019 7 0.00000 0.00000 5.78 1.40 0.0050 0.0014 8 0.00000 0.00000 21.78 0.25 0.0091 0.0016 9 0.00000 0.00000 7.42 0.96 0.0113 0.0005 10 0.00010 0.00000 -8.98 0.01 0.2983 0.0009 11 0.00000 0.00000 -7.23 1.05 0.0040 0.0005 12 0.00000 0.00000 2.99 1.35 0.0062 0.0007 13 0.00001 0.00000 3.93 0.79 0.0147 0.0027 14 0.00009 0.00000 -6.35 0.05 0.2573 0.0017 15 0.00000 0.00000 -8.59 0.34 0.0118 0.0036 16 0.00000 0.00000 1.09 1.53 0.0048 0.0022 The magnetic center is at X = 83.6 +- 0.8 microns Y = 24.5 +- 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: 04-14-1995 Time: 07:16:33 Magnet Name: 144 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06515 +- 4.543095E-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 0.00011 0.00000 -114.26 0.69 0.1612 0.0010 2 0.06874 0.00002 45.03 0.00 100.0000 0.0000 3 0.00007 0.00000 29.48 0.27 0.1033 0.0019 4 0.00001 0.00000 26.91 2.37 0.0125 0.0019 5 0.00001 0.00000 7.70 1.98 0.0142 0.0015 6 0.00015 0.00000 15.00 0.09 0.2172 0.0011 7 0.00000 0.00000 6.31 0.66 0.0052 0.0004 8 0.00000 0.00000 13.50 6.33 0.0020 0.0007 9 0.00001 0.00000 8.28 0.89 0.0115 0.0010 10 0.00021 0.00000 -8.97 0.03 0.2995 0.0005 11 0.00000 0.00000 -7.59 2.06 0.0038 0.0005 12 0.00000 0.00000 6.72 3.63 0.0032 0.0013 13 0.00001 0.00000 2.85 0.68 0.0138 0.0030 14 0.00018 0.00000 -6.37 0.03 0.2570 0.0025 15 0.00001 0.00000 -10.05 1.26 0.0115 0.0045 16 0.00000 0.00000 1.77 3.65 0.0049 0.0019 The magnetic center is at X = 65.6 +- 0.5 microns Y = 29.6 +- 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: 04-14-1995 Time: 07:22:50 Magnet Name: 144 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0625 +- 6.702044E-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 0.00021 0.00000 -120.37 0.85 0.1564 0.0015 2 0.13717 0.00001 45.03 0.00 100.0000 0.0000 3 0.00014 0.00000 29.66 0.46 0.0990 0.0014 4 0.00002 0.00000 27.39 3.59 0.0110 0.0015 5 0.00002 0.00000 9.08 0.80 0.0115 0.0024 6 0.00030 0.00000 15.05 0.06 0.2166 0.0013 7 0.00001 0.00000 5.56 0.68 0.0047 0.0012 8 0.00000 0.00000 13.82 3.52 0.0026 0.0002 9 0.00002 0.00000 8.21 0.69 0.0111 0.0010 10 0.00041 0.00000 -8.99 0.01 0.3004 0.0011 11 0.00001 0.00000 -6.00 1.05 0.0039 0.0014 12 0.00000 0.00000 3.51 10.44 0.0033 0.0011 13 0.00002 0.00001 1.94 0.65 0.0153 0.0046 14 0.00035 0.00000 -6.38 0.02 0.2561 0.0019 15 0.00002 0.00000 -4.88 9.65 0.0126 0.0021 16 0.00001 0.00000 -0.27 0.64 0.0078 0.0030 The magnetic center is at X = 60.3 +- 0.8 microns Y = 35.3 +- 1.0 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: 04-14-1995 Time: 07:29:06 Magnet Name: 144 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0787 +- 5.75754E-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 0.00032 0.00000 -120.73 0.59 0.1557 0.0011 2 0.20526 0.00002 45.00 0.00 100.0000 0.0000 3 0.00019 0.00000 30.10 0.53 0.0944 0.0008 4 0.00002 0.00000 28.34 1.35 0.0099 0.0024 5 0.00002 0.00000 7.54 1.69 0.0121 0.0021 6 0.00043 0.00000 15.03 0.05 0.2095 0.0011 7 0.00001 0.00000 4.92 2.21 0.0048 0.0014 8 0.00000 0.00000 16.55 3.45 0.0019 0.0004 9 0.00002 0.00000 7.77 2.45 0.0105 0.0014 10 0.00062 0.00000 -9.01 0.02 0.3037 0.0008 11 0.00001 0.00000 -6.53 2.03 0.0051 0.0016 12 0.00002 0.00000 0.38 12.21 0.0075 0.0020 13 0.00004 0.00001 1.92 0.24 0.0217 0.0052 14 0.00052 0.00000 -6.39 0.04 0.2555 0.0023 15 0.00003 0.00001 -5.52 10.06 0.0158 0.0051 16 0.00001 0.00000 5.14 4.44 0.0037 0.0018 The magnetic center is at X = 59.8 +- 0.6 microns Y = 35.5 +- 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: 04-14-1995 Time: 07:35:22 Magnet Name: 144 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3241 +- 4.545736E-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 0.00041 0.00000 -119.18 0.41 0.1516 0.0011 2 0.27290 0.00004 45.00 0.00 100.0000 0.0000 3 0.00026 0.00000 31.16 0.34 0.0943 0.0010 4 0.00006 0.00001 40.64 1.34 0.0208 0.0027 5 0.00003 0.00000 6.70 1.35 0.0112 0.0009 6 0.00054 0.00000 15.07 0.08 0.1991 0.0015 7 0.00001 0.00000 3.85 1.82 0.0047 0.0015 8 0.00002 0.00000 1.64 0.57 0.0066 0.0010 9 0.00003 0.00001 8.03 2.06 0.0125 0.0024 10 0.00084 0.00001 -9.01 0.01 0.3069 0.0020 11 0.00001 0.00000 -7.88 3.07 0.0039 0.0016 12 0.00001 0.00000 0.15 11.34 0.0041 0.0014 13 0.00004 0.00001 2.77 1.36 0.0146 0.0028 14 0.00070 0.00000 -6.41 0.03 0.2563 0.0018 15 0.00003 0.00001 -5.08 8.61 0.0096 0.0029 16 0.00001 0.00001 0.45 8.10 0.0050 0.0032 The magnetic center is at X = 59.1 +- 0.5 microns Y = 33.0 +- 0.5 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: 04-14-1995 Time: 07:41:37 Magnet Name: 144 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4272 +- 2.973507E-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 0.00001 -115.02 0.39 0.1484 0.0021 2 0.33771 0.00002 45.00 0.00 100.0000 0.0000 3 0.00031 0.00001 32.50 0.27 0.0923 0.0020 4 0.00005 0.00000 40.50 1.38 0.0136 0.0012 5 0.00004 0.00001 6.36 1.28 0.0118 0.0019 6 0.00060 0.00000 15.01 0.07 0.1771 0.0011 7 0.00002 0.00000 1.84 1.32 0.0047 0.0010 8 0.00002 0.00000 10.25 18.65 0.0061 0.0009 9 0.00004 0.00001 8.49 1.04 0.0105 0.0019 10 0.00104 0.00000 -9.03 0.04 0.3091 0.0007 11 0.00001 0.00000 -7.45 4.70 0.0040 0.0011 12 0.00001 0.00001 -5.75 4.39 0.0025 0.0019 13 0.00005 0.00002 -0.06 3.80 0.0137 0.0049 14 0.00086 0.00000 -6.39 0.02 0.2546 0.0014 15 0.00004 0.00002 -2.27 7.45 0.0104 0.0052 16 0.00002 0.00001 4.29 7.36 0.0053 0.0037 The magnetic center is at X = 60.1 +- 0.9 microns Y = 28.0 +- 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 ^ | N S --> x S N Date: 04-14-1995 Time: 07:47:53 Magnet Name: 144 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4164 +- 9.719022E-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 0.00056 0.00001 -115.17 0.85 0.1426 0.0016 2 0.38947 0.00004 45.00 0.00 100.0000 0.0000 3 0.00037 0.00001 32.21 0.30 0.0957 0.0025 4 0.00004 0.00000 40.57 2.23 0.0098 0.0012 5 0.00005 0.00000 7.25 2.21 0.0125 0.0010 6 0.00049 0.00000 15.14 0.10 0.1247 0.0011 7 0.00002 0.00000 1.32 1.99 0.0052 0.0007 8 0.00003 0.00000 21.77 0.49 0.0076 0.0006 9 0.00004 0.00001 7.45 0.81 0.0115 0.0023 10 0.00124 0.00001 -9.04 0.02 0.3195 0.0022 11 0.00002 0.00000 -7.01 2.26 0.0048 0.0011 12 0.00001 0.00000 1.26 7.73 0.0024 0.0013 13 0.00008 0.00001 1.68 1.39 0.0204 0.0034 14 0.00100 0.00001 -6.38 0.03 0.2562 0.0029 15 0.00006 0.00001 -0.01 10.31 0.0163 0.0032 16 0.00005 0.00001 1.41 1.62 0.0118 0.0016 The magnetic center is at X = 57.7 +- 0.8 microns Y = 27.1 +- 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: 04-14-1995 Time: 07:54:09 Magnet Name: 144 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4241 +- 1.603698E-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 0.00063 0.00001 -114.19 0.53 0.1474 0.0017 2 0.42572 0.00007 45.00 0.00 100.0000 0.0000 3 0.00040 0.00001 32.33 0.53 0.0948 0.0013 4 0.00004 0.00001 42.09 1.84 0.0093 0.0021 5 0.00006 0.00000 7.40 1.90 0.0134 0.0009 6 0.00028 0.00001 15.25 0.14 0.0663 0.0022 7 0.00002 0.00000 2.27 1.08 0.0056 0.0004 8 0.00003 0.00001 10.25 18.80 0.0061 0.0016 9 0.00005 0.00001 7.07 0.57 0.0118 0.0014 10 0.00140 0.00000 -9.02 0.01 0.3292 0.0008 11 0.00001 0.00000 -9.83 1.97 0.0028 0.0010 12 0.00003 0.00001 -0.56 12.84 0.0066 0.0030 13 0.00005 0.00003 2.64 1.83 0.0112 0.0061 14 0.00107 0.00001 -6.36 0.04 0.2522 0.0029 15 0.00004 0.00002 -9.79 1.04 0.0100 0.0052 16 0.00007 0.00002 1.05 0.70 0.0154 0.0042 The magnetic center is at X = 60.1 +- 0.7 microns Y = 27.0 +- 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 ^ | 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)