SLAC Magnetic Measurements Date: 04-11-1995 Time: 12:24:47 Magnet Name (Serial #): 142 Bar Code Number: 390 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: 04-11-1995 Time: 13:11:56 Magnet Name: 142 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00512 +- 3.363426E-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 -176.24 0.62 0.2863 0.0036 2 0.01486 0.00000 45.02 0.00 100.0000 0.0000 3 0.00001 0.00000 7.59 0.53 0.0847 0.0030 4 0.00000 0.00000 -14.71 3.61 0.0092 0.0020 5 0.00000 0.00000 18.76 0.87 0.0154 0.0013 6 0.00003 0.00000 15.07 0.06 0.2228 0.0024 7 0.00000 0.00000 17.13 0.78 0.0074 0.0012 8 0.00000 0.00000 0.01 12.97 0.0046 0.0016 9 0.00000 0.00000 -4.49 1.55 0.0066 0.0008 10 0.00004 0.00000 -9.00 0.01 0.3021 0.0011 11 0.00000 0.00000 -0.22 10.17 0.0016 0.0015 12 0.00000 0.00000 -9.58 0.16 0.0053 0.0009 13 0.00000 0.00000 -3.02 1.84 0.0101 0.0022 14 0.00004 0.00000 -6.39 0.02 0.2573 0.0013 15 0.00000 0.00000 -3.14 1.34 0.0072 0.0039 16 0.00000 0.00000 2.89 7.50 0.0066 0.0028 The magnetic center is at X = 8.4 +- 1.4 microns Y = 127.6 +- 1.6 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: 04-11-1995 Time: 13:18:01 Magnet Name: 142 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10912 +- 2.751495E-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 156.82 0.15 0.2956 0.0039 2 0.03497 0.00000 45.02 0.00 100.0000 0.0000 3 0.00002 0.00000 18.27 1.10 0.0632 0.0041 4 0.00000 0.00000 -28.49 2.64 0.0126 0.0023 5 0.00001 0.00000 15.01 0.87 0.0183 0.0008 6 0.00008 0.00000 15.09 0.13 0.2239 0.0015 7 0.00000 0.00000 13.77 1.93 0.0074 0.0021 8 0.00000 0.00000 -19.79 1.59 0.0096 0.0010 9 0.00000 0.00000 -3.90 1.94 0.0080 0.0016 10 0.00010 0.00000 -9.01 0.05 0.3000 0.0010 11 0.00000 0.00000 5.06 3.29 0.0025 0.0012 12 0.00000 0.00000 -3.07 4.95 0.0063 0.0022 13 0.00000 0.00000 -3.02 0.96 0.0093 0.0011 14 0.00009 0.00000 -6.39 0.04 0.2557 0.0015 15 0.00000 0.00000 -3.81 1.94 0.0053 0.0004 16 0.00000 0.00000 3.24 6.85 0.0067 0.0025 The magnetic center is at X = -52.0 +- 0.8 microns Y = 121.4 +- 1.6 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: 04-11-1995 Time: 13:24:14 Magnet Name: 142 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.0722 +- 4.947428E-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 0.00023 0.00000 150.17 0.53 0.3320 0.0016 2 0.06890 0.00001 45.02 0.00 100.0000 0.0000 3 0.00005 0.00000 20.35 1.16 0.0664 0.0021 4 0.00001 0.00000 -22.11 2.46 0.0143 0.0019 5 0.00001 0.00000 16.60 1.31 0.0183 0.0012 6 0.00015 0.00000 15.05 0.06 0.2236 0.0008 7 0.00000 0.00000 15.99 2.04 0.0059 0.0018 8 0.00000 0.00000 -9.39 3.90 0.0042 0.0017 9 0.00000 0.00000 -4.73 1.69 0.0051 0.0017 10 0.00021 0.00000 -8.99 0.03 0.3030 0.0008 11 0.00000 0.00000 -1.28 12.21 0.0014 0.0015 12 0.00000 0.00000 -7.26 2.02 0.0062 0.0023 13 0.00001 0.00000 -3.35 0.88 0.0121 0.0023 14 0.00018 0.00000 -6.36 0.04 0.2545 0.0010 15 0.00000 0.00000 -5.59 2.31 0.0043 0.0020 16 0.00000 0.00000 6.06 7.28 0.0040 0.0024 The magnetic center is at X = -73.8 +- 1.2 microns Y = 128.7 +- 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: 04-11-1995 Time: 13:30:30 Magnet Name: 142 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0665 +- 9.853593E-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 0.00049 0.00000 149.00 0.27 0.3574 0.0027 2 0.13747 0.00002 45.02 0.00 100.0000 0.0000 3 0.00010 0.00000 19.06 0.46 0.0699 0.0030 4 0.00002 0.00000 -23.43 1.82 0.0158 0.0017 5 0.00003 0.00000 16.05 1.08 0.0196 0.0031 6 0.00031 0.00000 15.11 0.08 0.2227 0.0018 7 0.00001 0.00000 13.45 1.29 0.0056 0.0013 8 0.00000 0.00000 -7.46 2.71 0.0033 0.0008 9 0.00001 0.00000 -3.97 0.45 0.0068 0.0013 10 0.00042 0.00000 -8.98 0.01 0.3025 0.0002 11 0.00000 0.00000 0.24 3.99 0.0012 0.0006 12 0.00001 0.00000 -7.13 2.12 0.0041 0.0011 13 0.00002 0.00000 -2.05 1.57 0.0128 0.0012 14 0.00035 0.00000 -6.39 0.03 0.2541 0.0015 15 0.00001 0.00000 -6.41 0.93 0.0071 0.0008 16 0.00001 0.00000 -2.74 7.12 0.0052 0.0015 The magnetic center is at X = -82.2 +- 0.9 microns Y = 136.8 +- 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 ^ | N S --> x S N Date: 04-11-1995 Time: 13:36:46 Magnet Name: 142 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0822 +- 3.589871E-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 0.00072 0.00000 148.65 0.35 0.3515 0.0018 2 0.20574 0.00002 44.99 0.00 100.0000 0.0000 3 0.00013 0.00000 19.05 0.74 0.0648 0.0017 4 0.00003 0.00001 -22.54 2.01 0.0149 0.0026 5 0.00004 0.00001 16.24 2.08 0.0175 0.0042 6 0.00044 0.00000 15.04 0.07 0.2143 0.0014 7 0.00001 0.00000 13.69 6.22 0.0051 0.0008 8 0.00001 0.00000 -10.30 5.50 0.0037 0.0013 9 0.00001 0.00000 -3.28 0.70 0.0068 0.0022 10 0.00063 0.00000 -9.00 0.02 0.3062 0.0010 11 0.00000 0.00000 5.55 5.00 0.0023 0.0008 12 0.00001 0.00000 -10.50 1.48 0.0067 0.0023 13 0.00002 0.00001 -3.53 1.36 0.0103 0.0043 14 0.00052 0.00000 -6.41 0.03 0.2543 0.0011 15 0.00002 0.00000 -2.91 0.67 0.0080 0.0011 16 0.00001 0.00000 1.89 7.99 0.0062 0.0023 The magnetic center is at X = -81.7 +- 0.9 microns Y = 134.1 +- 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: 04-11-1995 Time: 13:43:02 Magnet Name: 142 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3325 +- 3.864723E-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 0.00097 0.00001 147.05 0.36 0.3548 0.0020 2 0.27349 0.00004 44.99 0.00 100.0000 0.0000 3 0.00018 0.00001 20.21 0.77 0.0661 0.0020 4 0.00006 0.00001 -34.72 1.77 0.0215 0.0024 5 0.00005 0.00001 17.07 1.84 0.0189 0.0022 6 0.00056 0.00001 15.10 0.09 0.2065 0.0023 7 0.00001 0.00000 13.90 6.13 0.0038 0.0012 8 0.00003 0.00000 -2.71 1.07 0.0103 0.0009 9 0.00002 0.00001 -4.13 1.01 0.0059 0.0026 10 0.00084 0.00001 -9.02 0.04 0.3089 0.0019 11 0.00001 0.00001 -2.27 8.14 0.0032 0.0024 12 0.00001 0.00001 -2.32 10.05 0.0041 0.0024 13 0.00003 0.00000 -3.10 2.00 0.0095 0.0012 14 0.00070 0.00000 -6.40 0.02 0.2546 0.0011 15 0.00002 0.00001 -4.65 1.83 0.0081 0.0021 16 0.00002 0.00000 4.47 8.16 0.0065 0.0016 The magnetic center is at X = -86.2 +- 1.0 microns Y = 133.0 +- 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: 04-11-1995 Time: 13:49:18 Magnet Name: 142 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4367 +- 7.488475E-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 0.00120 0.00001 145.40 0.60 0.3558 0.0028 2 0.33852 0.00007 44.99 0.00 100.0000 0.0000 3 0.00024 0.00001 22.15 0.53 0.0702 0.0027 4 0.00005 0.00001 -31.72 1.75 0.0157 0.0027 5 0.00005 0.00001 15.92 1.12 0.0160 0.0028 6 0.00063 0.00001 15.15 0.11 0.1847 0.0026 7 0.00001 0.00000 17.86 4.71 0.0039 0.0014 8 0.00001 0.00000 -18.44 1.94 0.0038 0.0008 9 0.00002 0.00000 -5.45 1.23 0.0057 0.0014 10 0.00106 0.00001 -9.03 0.02 0.3123 0.0020 11 0.00001 0.00000 -0.65 5.16 0.0021 0.0011 12 0.00002 0.00001 -2.50 1.13 0.0069 0.0018 13 0.00003 0.00002 -2.46 0.99 0.0096 0.0046 14 0.00085 0.00000 -6.35 0.02 0.2522 0.0012 15 0.00002 0.00001 -1.85 2.58 0.0072 0.0041 16 0.00002 0.00001 5.61 2.49 0.0065 0.0027 The magnetic center is at X = -90.2 +- 1.5 microns Y = 130.8 +- 1.4 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: 04-11-1995 Time: 13:55:35 Magnet Name: 142 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4229 +- 5.185744E-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 0.00134 0.00001 142.59 0.51 0.3428 0.0024 2 0.39028 0.00002 44.99 0.00 100.0000 0.0000 3 0.00026 0.00000 24.97 0.80 0.0678 0.0007 4 0.00005 0.00001 -25.93 2.97 0.0123 0.0024 5 0.00007 0.00000 15.66 0.59 0.0178 0.0010 6 0.00051 0.00001 15.18 0.21 0.1310 0.0016 7 0.00001 0.00000 11.44 6.36 0.0038 0.0012 8 0.00002 0.00000 -18.96 1.54 0.0049 0.0012 9 0.00003 0.00001 -4.53 0.52 0.0065 0.0018 10 0.00126 0.00001 -8.99 0.01 0.3218 0.0015 11 0.00001 0.00001 6.25 8.44 0.0023 0.0014 12 0.00003 0.00001 -3.16 2.16 0.0074 0.0018 13 0.00003 0.00001 -2.59 1.09 0.0076 0.0036 14 0.00100 0.00000 -6.42 0.03 0.2562 0.0009 15 0.00004 0.00001 -4.50 1.69 0.0102 0.0025 16 0.00002 0.00000 3.57 5.06 0.0040 0.0012 The magnetic center is at X = -93.0 +- 1.3 microns Y = 121.6 +- 1.2 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: 04-11-1995 Time: 14:01:52 Magnet Name: 142 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4306 +- 1.884816E-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 0.00145 0.00002 140.52 0.20 0.3402 0.0041 2 0.42665 0.00006 44.99 0.00 100.0000 0.0000 3 0.00031 0.00001 27.32 0.73 0.0725 0.0013 4 0.00005 0.00001 -28.69 3.29 0.0117 0.0026 5 0.00007 0.00001 13.97 1.13 0.0173 0.0019 6 0.00032 0.00001 15.43 0.26 0.0740 0.0014 7 0.00001 0.00000 7.67 6.07 0.0024 0.0010 8 0.00001 0.00001 -11.56 2.60 0.0023 0.0013 9 0.00003 0.00000 -4.14 1.97 0.0065 0.0006 10 0.00142 0.00001 -9.02 0.01 0.3326 0.0026 11 0.00002 0.00000 3.42 1.38 0.0036 0.0003 12 0.00001 0.00001 -3.44 7.14 0.0028 0.0014 13 0.00004 0.00000 -1.87 1.20 0.0101 0.0007 14 0.00108 0.00001 -6.45 0.01 0.2531 0.0022 15 0.00003 0.00001 -4.54 2.71 0.0076 0.0022 16 0.00003 0.00001 4.45 2.43 0.0078 0.0034 The magnetic center is at X = -96.6 +- 1.2 microns Y = 117.3 +- 1.4 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)