SLAC Magnetic Measurements Date: 03-15-1995 Time: 10:09:18 Magnet Name (Serial #): 128 Bar Code Number: 365 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: 03-15-1995 Time: 10:56:32 Magnet Name: 128 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00063 +- 4.584161E-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 0.00003 0.00000 131.73 0.13 0.2145 0.0017 2 0.01489 0.00001 44.99 0.00 100.0000 0.0000 3 0.00001 0.00000 29.16 0.19 0.0967 0.0022 4 0.00000 0.00000 17.78 1.27 0.0215 0.0035 5 0.00000 0.00000 15.65 1.40 0.0174 0.0013 6 0.00003 0.00000 15.18 0.06 0.2061 0.0023 7 0.00000 0.00000 -11.53 20.88 0.0065 0.0016 8 0.00000 0.00000 3.62 7.93 0.0029 0.0017 9 0.00000 0.00000 -6.57 0.31 0.0096 0.0015 10 0.00004 0.00000 -9.03 0.02 0.3022 0.0026 11 0.00000 0.00000 -10.83 1.91 0.0029 0.0003 12 0.00000 0.00000 3.20 2.26 0.0023 0.0011 13 0.00000 0.00000 -3.98 0.56 0.0125 0.0015 14 0.00004 0.00000 -6.39 0.04 0.2569 0.0020 15 0.00000 0.00000 -4.36 3.84 0.0074 0.0028 16 0.00000 0.00000 1.83 6.75 0.0026 0.0021 The magnetic center is at X = -71.5 +- 0.6 microns Y = 63.8 +- 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: 03-15-1995 Time: 11:02:43 Magnet Name: 128 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.1009 +- 3.550039E-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 0.00010 0.00000 127.95 0.13 0.2742 0.0023 2 0.03500 0.00002 44.99 0.00 100.0000 0.0000 3 0.00003 0.00000 33.40 0.17 0.0809 0.0007 4 0.00001 0.00000 30.76 1.91 0.0155 0.0021 5 0.00001 0.00000 15.08 0.40 0.0176 0.0012 6 0.00007 0.00000 15.21 0.11 0.2070 0.0010 7 0.00000 0.00000 -12.95 18.81 0.0029 0.0015 8 0.00000 0.00000 -0.27 2.32 0.0042 0.0009 9 0.00000 0.00000 -6.41 1.06 0.0093 0.0011 10 0.00011 0.00000 -9.05 0.01 0.3024 0.0003 11 0.00000 0.00000 -10.22 2.42 0.0022 0.0008 12 0.00000 0.00000 -0.27 1.13 0.0059 0.0008 13 0.00000 0.00000 -3.22 0.61 0.0131 0.0010 14 0.00009 0.00000 -6.42 0.04 0.2545 0.0013 15 0.00000 0.00000 -1.72 4.32 0.0066 0.0023 16 0.00000 0.00000 4.89 8.33 0.0070 0.0015 The magnetic center is at X = -96.6 +- 0.8 microns Y = 75.3 +- 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: 03-15-1995 Time: 11:08:59 Magnet Name: 128 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06355 +- 8.572402E-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 128.05 0.16 0.2993 0.0013 2 0.06891 0.00003 44.99 0.00 100.0000 0.0000 3 0.00005 0.00000 34.09 0.29 0.0723 0.0016 4 0.00001 0.00000 18.05 2.46 0.0125 0.0016 5 0.00001 0.00000 16.01 1.31 0.0188 0.0016 6 0.00014 0.00000 15.14 0.03 0.2087 0.0014 7 0.00000 0.00000 10.16 19.22 0.0030 0.0013 8 0.00000 0.00000 3.31 5.17 0.0011 0.0004 9 0.00001 0.00000 -6.74 0.48 0.0088 0.0017 10 0.00021 0.00000 -9.03 0.02 0.3023 0.0012 11 0.00000 0.00000 -6.00 4.05 0.0021 0.0015 12 0.00000 0.00000 3.96 3.96 0.0035 0.0008 13 0.00001 0.00000 -3.52 0.39 0.0120 0.0012 14 0.00018 0.00000 -6.43 0.01 0.2570 0.0008 15 0.00000 0.00000 3.11 1.34 0.0032 0.0009 16 0.00000 0.00000 2.58 4.62 0.0024 0.0009 The magnetic center is at X = -105.3 +- 0.6 microns Y = 82.4 +- 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: 03-15-1995 Time: 11:15:19 Magnet Name: 128 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.057 +- 1.935304E-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 0.00043 0.00000 127.86 0.22 0.3164 0.0016 2 0.13745 0.00003 44.99 0.00 100.0000 0.0000 3 0.00009 0.00000 34.64 0.54 0.0683 0.0029 4 0.00002 0.00000 17.84 0.74 0.0120 0.0011 5 0.00002 0.00000 16.73 1.32 0.0179 0.0019 6 0.00029 0.00000 15.16 0.07 0.2106 0.0017 7 0.00001 0.00000 -10.81 20.39 0.0041 0.0011 8 0.00000 0.00000 -18.42 4.84 0.0013 0.0008 9 0.00001 0.00000 -7.23 0.64 0.0087 0.0005 10 0.00042 0.00000 -9.04 0.02 0.3032 0.0009 11 0.00000 0.00000 -10.02 2.77 0.0028 0.0006 12 0.00000 0.00000 2.57 8.61 0.0027 0.0015 13 0.00001 0.00000 -3.59 0.73 0.0107 0.0010 14 0.00035 0.00000 -6.40 0.03 0.2552 0.0008 15 0.00001 0.00000 -5.56 2.35 0.0053 0.0014 16 0.00000 0.00000 2.20 6.46 0.0029 0.0007 The magnetic center is at X = -111.6 +- 0.6 microns Y = 86.7 +- 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: 03-15-1995 Time: 11:21:39 Magnet Name: 128 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0682 +- 8.707877E-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 0.00067 0.00000 129.53 0.22 0.3245 0.0008 2 0.20576 0.00006 44.97 0.00 100.0000 0.0000 3 0.00013 0.00000 33.76 0.29 0.0620 0.0008 4 0.00003 0.00000 14.07 2.05 0.0128 0.0015 5 0.00004 0.00000 17.21 1.51 0.0183 0.0019 6 0.00042 0.00000 15.20 0.04 0.2036 0.0016 7 0.00001 0.00000 -21.06 3.63 0.0035 0.0024 8 0.00000 0.00000 -8.59 13.48 0.0013 0.0002 9 0.00002 0.00000 -7.63 0.76 0.0101 0.0010 10 0.00062 0.00000 -9.04 0.01 0.3006 0.0016 11 0.00001 0.00000 -12.14 2.60 0.0032 0.0012 12 0.00001 0.00000 0.74 9.48 0.0028 0.0012 13 0.00002 0.00000 -3.94 0.84 0.0115 0.0017 14 0.00053 0.00001 -6.39 0.05 0.2563 0.0028 15 0.00001 0.00000 1.01 6.40 0.0056 0.0021 16 0.00001 0.00001 0.60 1.53 0.0066 0.0026 The magnetic center is at X = -111.8 +- 0.5 microns Y = 92.3 +- 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: 03-15-1995 Time: 11:27:59 Magnet Name: 128 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3112 +- 8.584679E-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 0.00088 0.00001 131.08 0.38 0.3203 0.0022 2 0.27333 0.00009 44.97 0.00 100.0000 0.0000 3 0.00016 0.00000 33.63 0.69 0.0589 0.0005 4 0.00003 0.00001 15.89 2.94 0.0119 0.0023 5 0.00004 0.00001 17.50 0.37 0.0160 0.0021 6 0.00053 0.00001 15.20 0.07 0.1954 0.0021 7 0.00001 0.00000 1.70 22.95 0.0032 0.0014 8 0.00001 0.00000 1.22 5.00 0.0027 0.0010 9 0.00002 0.00000 -6.86 0.84 0.0088 0.0012 10 0.00084 0.00000 -9.06 0.01 0.3075 0.0016 11 0.00001 0.00000 -7.81 1.64 0.0030 0.0014 12 0.00001 0.00000 6.54 5.38 0.0018 0.0017 13 0.00003 0.00000 -3.02 0.66 0.0111 0.0016 14 0.00070 0.00000 -6.41 0.06 0.2553 0.0011 15 0.00001 0.00001 -3.28 4.43 0.0047 0.0019 16 0.00001 0.00001 -5.09 8.34 0.0037 0.0019 The magnetic center is at X = -107.8 +- 1.0 microns Y = 94.0 +- 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: 03-15-1995 Time: 11:34:18 Magnet Name: 128 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4108 +- 5.836362E-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 0.00103 0.00001 133.99 0.40 0.3036 0.0020 2 0.33844 0.00019 44.97 0.00 100.0000 0.0000 3 0.00015 0.00000 34.22 0.87 0.0455 0.0011 4 0.00005 0.00001 31.53 2.14 0.0137 0.0021 5 0.00005 0.00000 17.62 0.95 0.0135 0.0013 6 0.00057 0.00001 15.22 0.02 0.1682 0.0018 7 0.00001 0.00000 1.30 23.38 0.0039 0.0003 8 0.00002 0.00000 -0.02 1.65 0.0068 0.0011 9 0.00003 0.00000 -7.18 0.80 0.0078 0.0011 10 0.00106 0.00000 -9.06 0.00 0.3119 0.0012 11 0.00001 0.00000 -5.86 10.66 0.0019 0.0014 12 0.00001 0.00001 6.25 9.15 0.0036 0.0021 13 0.00004 0.00001 -2.86 0.92 0.0105 0.0017 14 0.00085 0.00000 -6.45 0.06 0.2510 0.0010 15 0.00002 0.00001 0.98 5.41 0.0057 0.0033 16 0.00002 0.00001 1.69 9.02 0.0047 0.0035 The magnetic center is at X = -97.6 +- 0.9 microns Y = 94.2 +- 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: 03-15-1995 Time: 11:40:38 Magnet Name: 128 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3965 +- 5.067664E-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 0.00119 0.00000 130.81 0.09 0.3061 0.0011 2 0.39022 0.00014 44.97 0.00 100.0000 0.0000 3 0.00021 0.00001 35.67 0.71 0.0527 0.0022 4 0.00004 0.00001 26.03 2.57 0.0097 0.0024 5 0.00005 0.00001 18.01 1.27 0.0128 0.0020 6 0.00048 0.00001 15.25 0.08 0.1226 0.0015 7 0.00002 0.00000 -10.01 19.14 0.0045 0.0006 8 0.00001 0.00000 -10.55 17.06 0.0037 0.0003 9 0.00003 0.00000 -6.45 1.32 0.0087 0.0009 10 0.00125 0.00000 -9.06 0.01 0.3208 0.0010 11 0.00001 0.00000 -8.76 1.89 0.0019 0.0007 12 0.00003 0.00001 0.49 1.19 0.0083 0.0017 13 0.00004 0.00001 -3.02 0.54 0.0113 0.0015 14 0.00098 0.00000 -6.46 0.00 0.2513 0.0012 15 0.00001 0.00000 -1.72 4.42 0.0033 0.0010 16 0.00002 0.00000 4.65 6.91 0.0058 0.0006 The magnetic center is at X = -103.5 +- 0.4 microns Y = 89.4 +- 0.4 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: 03-15-1995 Time: 11:46:59 Magnet Name: 128 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4 +- 5.401266E-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 0.00132 0.00000 128.35 0.18 0.3087 0.0007 2 0.42661 0.00012 44.97 0.00 100.0000 0.0000 3 0.00025 0.00001 36.54 1.02 0.0576 0.0019 4 0.00004 0.00001 25.51 1.64 0.0099 0.0017 5 0.00006 0.00001 18.40 2.31 0.0130 0.0017 6 0.00029 0.00001 15.56 0.19 0.0673 0.0016 7 0.00002 0.00000 -21.44 0.47 0.0043 0.0005 8 0.00003 0.00000 -10.65 19.14 0.0070 0.0009 9 0.00004 0.00001 -6.50 0.58 0.0101 0.0012 10 0.00142 0.00000 -9.06 0.02 0.3329 0.0006 11 0.00002 0.00000 -9.43 1.45 0.0038 0.0003 12 0.00003 0.00001 0.78 1.15 0.0080 0.0016 13 0.00005 0.00000 -3.30 0.45 0.0118 0.0005 14 0.00106 0.00001 -6.42 0.02 0.2489 0.0014 15 0.00001 0.00001 0.72 1.04 0.0032 0.0016 16 0.00002 0.00001 -0.16 0.46 0.0052 0.0012 The magnetic center is at X = -108.1 +- 0.4 microns Y = 85.6 +- 0.4 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 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)