SLAC Magnetic Measurements Date: 04-25-1995 Time: 08:35:21 Magnet Name (Serial #): 141 Bar Code Number: 371 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: bmd Run Number: 3 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: 04-25-1995 Time: 09:25:19 Magnet Name: 141 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 10.00083 +- 2.021008E-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 -20.54 0.30 0.5724 0.0054 2 0.01481 0.00000 -44.94 0.00 100.0000 0.0000 3 0.00002 0.00000 -44.29 0.35 0.1422 0.0057 4 0.00001 0.00000 -20.64 0.63 0.0615 0.0017 5 0.00000 0.00000 -21.86 1.50 0.0253 0.0032 6 0.00003 0.00000 -14.99 0.08 0.2191 0.0019 7 0.00000 0.00000 -2.11 1.21 0.0050 0.0004 8 0.00000 0.00000 -8.17 0.62 0.0043 0.0006 9 0.00000 0.00000 -15.64 1.35 0.0090 0.0007 10 0.00004 0.00000 9.05 0.01 0.3002 0.0011 11 0.00000 0.00000 4.39 12.64 0.0014 0.0005 12 0.00000 0.00000 -7.16 1.10 0.0044 0.0009 13 0.00000 0.00000 -11.60 1.35 0.0132 0.0022 14 0.00004 0.00000 6.50 0.02 0.2570 0.0015 15 0.00000 0.00000 5.12 2.09 0.0116 0.0034 16 0.00000 0.00000 -3.43 7.82 0.0070 0.0028 The magnetic center is at X = -89.7 +- 1.5 microns Y = 239.4 +- 2.3 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 ^ | S N --> x N S Date: 04-25-1995 Time: 09:31:25 Magnet Name: 141 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 25.10233 +- 3.684529E-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 0.00014 0.00000 -0.24 0.55 0.4111 0.0026 2 0.03488 0.00001 -44.94 0.00 100.0000 0.0000 3 0.00003 0.00000 -45.38 0.50 0.0783 0.0015 4 0.00002 0.00000 -22.64 0.73 0.0604 0.0033 5 0.00001 0.00000 -25.45 1.33 0.0219 0.0023 6 0.00008 0.00000 -14.99 0.04 0.2208 0.0018 7 0.00000 0.00000 -11.48 1.76 0.0043 0.0015 8 0.00000 0.00000 -18.67 1.26 0.0075 0.0018 9 0.00000 0.00000 -15.19 0.35 0.0094 0.0012 10 0.00010 0.00000 9.06 0.05 0.3003 0.0010 11 0.00000 0.00000 3.36 7.33 0.0023 0.0007 12 0.00000 0.00000 -2.54 0.54 0.0096 0.0029 13 0.00000 0.00000 -11.35 0.75 0.0107 0.0026 14 0.00009 0.00000 6.48 0.01 0.2558 0.0015 15 0.00000 0.00000 4.86 1.10 0.0132 0.0025 16 0.00000 0.00000 -0.32 5.64 0.0047 0.0030 The magnetic center is at X = -0.8 +- 1.7 microns Y = 183.6 +- 1.1 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 ^ | S N --> x N S Date: 04-25-1995 Time: 09:37:36 Magnet Name: 141 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 50.06757 +- 4.877557E-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 0.00025 0.00000 8.89 0.48 0.3615 0.0060 2 0.06874 0.00002 -44.94 0.00 100.0000 0.0000 3 0.00004 0.00000 -43.59 1.57 0.0547 0.0030 4 0.00004 0.00000 -21.20 0.76 0.0601 0.0029 5 0.00001 0.00000 -25.43 1.52 0.0174 0.0034 6 0.00015 0.00000 -14.96 0.06 0.2206 0.0015 7 0.00000 0.00000 -13.36 2.09 0.0049 0.0008 8 0.00000 0.00000 -10.27 0.54 0.0049 0.0013 9 0.00001 0.00000 -15.44 0.53 0.0100 0.0018 10 0.00021 0.00000 9.06 0.01 0.3012 0.0006 11 0.00000 0.00000 0.21 5.70 0.0014 0.0005 12 0.00000 0.00000 -8.81 1.77 0.0052 0.0040 13 0.00001 0.00000 -11.34 0.62 0.0080 0.0020 14 0.00017 0.00000 6.50 0.02 0.2523 0.0016 15 0.00001 0.00000 5.98 1.83 0.0078 0.0031 16 0.00001 0.00000 0.58 8.42 0.0077 0.0027 The magnetic center is at X = 24.9 +- 1.4 microns Y = 159.5 +- 2.6 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 ^ | S N --> x N S Date: 04-25-1995 Time: 09:43:52 Magnet Name: 141 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 100.0672 +- 6.157399E-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 0.00047 0.00001 12.63 0.73 0.3428 0.0047 2 0.13716 0.00003 -44.93 0.00 100.0000 0.0000 3 0.00007 0.00001 -41.31 1.18 0.0511 0.0041 4 0.00008 0.00000 -21.49 0.63 0.0610 0.0022 5 0.00003 0.00000 -24.58 0.74 0.0195 0.0029 6 0.00030 0.00000 -14.96 0.12 0.2198 0.0014 7 0.00001 0.00000 -13.74 2.35 0.0054 0.0004 8 0.00001 0.00000 -8.05 1.10 0.0051 0.0006 9 0.00001 0.00000 -14.92 0.26 0.0096 0.0010 10 0.00041 0.00000 9.04 0.02 0.3025 0.0006 11 0.00000 0.00000 4.63 7.00 0.0018 0.0001 12 0.00001 0.00000 -6.36 1.88 0.0052 0.0003 13 0.00002 0.00000 -12.26 0.87 0.0114 0.0006 14 0.00035 0.00000 6.52 0.04 0.2561 0.0022 15 0.00002 0.00000 5.36 0.31 0.0117 0.0009 16 0.00001 0.00000 -6.73 3.46 0.0072 0.0011 The magnetic center is at X = 33.5 +- 2.0 microns Y = 149.4 +- 2.1 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 ^ | S N --> x N S Date: 04-25-1995 Time: 09:50:07 Magnet Name: 141 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 150.0862 +- 5.750458E-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 0.00066 0.00001 12.70 0.83 0.3210 0.0051 2 0.20527 0.00003 -44.96 0.00 100.0000 0.0000 3 0.00010 0.00001 -41.30 2.20 0.0507 0.0042 4 0.00013 0.00001 -21.55 0.41 0.0610 0.0028 5 0.00004 0.00001 -25.67 0.82 0.0210 0.0026 6 0.00043 0.00000 -15.01 0.07 0.2118 0.0022 7 0.00001 0.00000 -14.56 2.17 0.0039 0.0017 8 0.00001 0.00000 -5.83 1.10 0.0049 0.0007 9 0.00002 0.00000 -15.07 0.45 0.0094 0.0009 10 0.00063 0.00000 9.03 0.01 0.3057 0.0007 11 0.00001 0.00000 1.56 4.03 0.0030 0.0016 12 0.00001 0.00000 -3.83 10.06 0.0032 0.0012 13 0.00002 0.00001 -5.59 10.29 0.0103 0.0025 14 0.00053 0.00000 6.49 0.02 0.2564 0.0017 15 0.00002 0.00001 4.29 1.21 0.0093 0.0043 16 0.00001 0.00001 0.40 8.17 0.0062 0.0027 The magnetic center is at X = 31.5 +- 2.1 microns Y = 139.9 +- 2.3 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 ^ | S N --> x N S Date: 04-25-1995 Time: 09:56:22 Magnet Name: 141 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 200.3358 +- 6.487229E-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 0.00085 0.00002 14.95 0.63 0.3105 0.0056 2 0.27299 0.00008 -44.96 0.00 100.0000 0.0000 3 0.00012 0.00001 -41.08 2.39 0.0430 0.0029 4 0.00016 0.00001 -24.92 0.36 0.0592 0.0022 5 0.00005 0.00001 -26.13 1.02 0.0182 0.0025 6 0.00056 0.00000 -14.95 0.09 0.2041 0.0011 7 0.00001 0.00000 -17.29 1.98 0.0051 0.0016 8 0.00003 0.00000 -2.73 0.94 0.0100 0.0004 9 0.00003 0.00000 -14.69 1.11 0.0103 0.0013 10 0.00084 0.00000 9.04 0.03 0.3091 0.0012 11 0.00000 0.00000 7.42 4.44 0.0012 0.0006 12 0.00001 0.00000 -7.46 2.25 0.0037 0.0012 13 0.00004 0.00000 -11.00 0.65 0.0133 0.0016 14 0.00070 0.00000 6.47 0.02 0.2560 0.0006 15 0.00003 0.00001 5.05 1.10 0.0109 0.0019 16 0.00001 0.00000 -2.34 7.45 0.0039 0.0009 The magnetic center is at X = 35.8 +- 1.6 microns Y = 134.0 +- 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 ^ | S N --> x N S Date: 04-25-1995 Time: 10:02:39 Magnet Name: 141 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 250.4405 +- 7.083432E-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 0.00002 19.06 0.81 0.3036 0.0058 2 0.33802 0.00007 -44.96 0.00 100.0000 0.0000 3 0.00011 0.00001 -41.79 3.62 0.0330 0.0028 4 0.00019 0.00000 -23.31 0.62 0.0570 0.0013 5 0.00006 0.00000 -25.06 1.81 0.0188 0.0014 6 0.00061 0.00000 -15.02 0.07 0.1797 0.0015 7 0.00002 0.00000 -15.51 1.83 0.0047 0.0012 8 0.00001 0.00000 -17.63 2.57 0.0041 0.0009 9 0.00003 0.00001 -15.33 0.73 0.0090 0.0015 10 0.00105 0.00000 9.02 0.02 0.3119 0.0007 11 0.00001 0.00000 0.98 5.46 0.0025 0.0005 12 0.00004 0.00001 -2.72 0.33 0.0112 0.0029 13 0.00004 0.00000 -5.57 11.11 0.0110 0.0013 14 0.00086 0.00000 6.45 0.02 0.2553 0.0010 15 0.00003 0.00001 5.90 2.06 0.0102 0.0020 16 0.00003 0.00002 -0.78 7.43 0.0084 0.0053 The magnetic center is at X = 44.3 +- 2.0 microns Y = 128.2 +- 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 ^ | S N --> x N S Date: 04-25-1995 Time: 10:08:56 Magnet Name: 141 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 300.4312 +- 4.623187E-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 0.00002 22.33 0.86 0.3390 0.0044 2 0.38967 0.00001 -44.96 0.00 100.0000 0.0000 3 0.00014 0.00002 -54.31 2.87 0.0369 0.0042 4 0.00021 0.00001 -22.25 0.27 0.0547 0.0031 5 0.00008 0.00000 -26.05 0.98 0.0195 0.0010 6 0.00049 0.00000 -14.96 0.14 0.1265 0.0012 7 0.00002 0.00000 -15.94 1.25 0.0054 0.0009 8 0.00002 0.00000 -19.12 1.39 0.0056 0.0007 9 0.00004 0.00001 -14.69 0.59 0.0105 0.0019 10 0.00125 0.00000 9.03 0.02 0.3216 0.0008 11 0.00001 0.00000 0.96 8.18 0.0017 0.0009 12 0.00002 0.00001 -5.20 0.58 0.0056 0.0028 13 0.00004 0.00001 -10.83 0.77 0.0091 0.0022 14 0.00099 0.00001 6.44 0.01 0.2552 0.0015 15 0.00004 0.00000 5.71 0.24 0.0098 0.0009 16 0.00004 0.00001 0.54 4.93 0.0097 0.0027 The magnetic center is at X = 57.5 +- 2.2 microns Y = 140.1 +- 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 ^ | S N --> x N S Date: 04-25-1995 Time: 10:15:12 Magnet Name: 141 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 350.4411 +- 9.413572E-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 0.00153 0.00002 24.24 0.55 0.3586 0.0049 2 0.42595 0.00005 -44.96 0.00 100.0000 0.0000 3 0.00019 0.00002 0.09 58.51 0.0438 0.0057 4 0.00022 0.00001 -22.21 0.50 0.0522 0.0023 5 0.00007 0.00001 -26.60 0.42 0.0167 0.0027 6 0.00029 0.00001 -14.96 0.23 0.0689 0.0014 7 0.00002 0.00001 -13.68 1.13 0.0058 0.0015 8 0.00001 0.00000 -16.18 3.00 0.0028 0.0008 9 0.00004 0.00001 -14.07 0.64 0.0104 0.0022 10 0.00142 0.00000 9.03 0.03 0.3328 0.0011 11 0.00001 0.00000 -10.00 4.89 0.0012 0.0009 12 0.00002 0.00001 -6.43 2.72 0.0039 0.0012 13 0.00004 0.00000 -11.71 1.27 0.0090 0.0008 14 0.00108 0.00001 6.44 0.03 0.2546 0.0021 15 0.00004 0.00000 6.51 1.03 0.0093 0.0009 16 0.00005 0.00002 -2.12 2.14 0.0107 0.0053 The magnetic center is at X = 65.8 +- 1.7 microns Y = 146.0 +- 2.1 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 ^ | S N --> x N S 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)