SLAC Magnetic Measurements Date: 03-03-1995 Time: 10:15:23 Magnet Name (Serial #): 119 Bar Code Number: 236 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: bmd 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: 03-03-1995 Time: 11:02:27 Magnet Name: 119 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00012 +- 4.694059E-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 -16.38 0.11 0.5230 0.0012 2 0.01490 0.00000 -45.04 0.00 100.0000 0.0000 3 0.00001 0.00000 -24.30 0.57 0.0811 0.0007 4 0.00000 0.00000 12.09 0.53 0.0309 0.0021 5 0.00000 0.00000 -18.95 0.98 0.0137 0.0010 6 0.00003 0.00000 -14.82 0.07 0.2213 0.0016 7 0.00000 0.00000 16.94 5.16 0.0031 0.0004 8 0.00000 0.00000 6.70 4.89 0.0031 0.0009 9 0.00000 0.00000 -17.72 0.24 0.0112 0.0010 10 0.00004 0.00000 8.95 0.03 0.3013 0.0011 11 0.00000 0.00000 5.16 2.43 0.0027 0.0016 12 0.00000 0.00000 7.63 1.93 0.0043 0.0021 13 0.00000 0.00000 -0.10 13.40 0.0137 0.0015 14 0.00004 0.00000 6.42 0.02 0.2561 0.0026 15 0.00000 0.00000 3.87 9.22 0.0057 0.0045 16 0.00000 0.00000 -1.56 5.91 0.0045 0.0030 The magnetic center is at X = -65.9 +- 0.5 microns Y = 224.1 +- 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 ^ | S N --> x N S Date: 03-03-1995 Time: 11:08:31 Magnet Name: 119 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.09928 +- 2.113438E-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 0.00016 0.00000 0.82 0.28 0.4670 0.0009 2 0.03499 0.00001 -45.04 0.00 100.0000 0.0000 3 0.00001 0.00000 -28.62 0.95 0.0421 0.0035 4 0.00001 0.00000 15.80 0.94 0.0284 0.0010 5 0.00000 0.00000 -19.40 1.17 0.0100 0.0016 6 0.00008 0.00000 -14.87 0.05 0.2267 0.0007 7 0.00000 0.00000 1.67 12.28 0.0021 0.0006 8 0.00000 0.00000 20.10 1.36 0.0082 0.0009 9 0.00000 0.00000 -18.17 0.66 0.0113 0.0020 10 0.00011 0.00000 8.95 0.02 0.3018 0.0016 11 0.00000 0.00000 6.25 1.93 0.0034 0.0014 12 0.00000 0.00000 4.13 2.52 0.0049 0.0011 13 0.00000 0.00000 -13.41 0.40 0.0121 0.0012 14 0.00009 0.00000 6.40 0.02 0.2552 0.0021 15 0.00000 0.00000 3.85 8.57 0.0093 0.0043 16 0.00000 0.00000 -0.75 4.40 0.0056 0.0008 The magnetic center is at X = 3.0 +- 1.0 microns Y = 208.6 +- 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 ^ | S N --> x N S Date: 03-03-1995 Time: 11:14:42 Magnet Name: 119 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06142 +- 3.671485E-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 0.00031 0.00000 6.78 0.31 0.4531 0.0025 2 0.06891 0.00001 -45.04 0.00 100.0000 0.0000 3 0.00003 0.00000 -30.04 1.14 0.0390 0.0005 4 0.00002 0.00000 14.63 0.64 0.0303 0.0029 5 0.00001 0.00000 -19.28 2.24 0.0094 0.0011 6 0.00016 0.00000 -14.84 0.04 0.2277 0.0007 7 0.00000 0.00000 -11.96 9.08 0.0019 0.0009 8 0.00000 0.00000 9.16 2.37 0.0021 0.0011 9 0.00001 0.00000 -17.50 0.58 0.0115 0.0010 10 0.00021 0.00000 8.97 0.03 0.3041 0.0006 11 0.00000 0.00000 7.52 3.45 0.0030 0.0014 12 0.00000 0.00000 10.99 3.63 0.0038 0.0013 13 0.00001 0.00000 -6.28 11.54 0.0120 0.0015 14 0.00018 0.00000 6.41 0.03 0.2551 0.0008 15 0.00001 0.00000 3.28 8.51 0.0087 0.0019 16 0.00000 0.00000 -2.09 6.77 0.0052 0.0012 The magnetic center is at X = 23.9 +- 1.1 microns Y = 200.9 +- 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: 03-03-1995 Time: 11:20:57 Magnet Name: 119 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0531 +- 1.449655E-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 0.00061 0.00000 9.72 0.23 0.4451 0.0030 2 0.13752 0.00003 -45.04 0.00 100.0000 0.0000 3 0.00005 0.00000 -30.56 1.46 0.0382 0.0009 4 0.00004 0.00000 14.04 0.44 0.0312 0.0017 5 0.00001 0.00000 -17.68 2.46 0.0092 0.0015 6 0.00032 0.00000 -14.85 0.06 0.2292 0.0010 7 0.00000 0.00000 3.15 10.92 0.0014 0.0007 8 0.00000 0.00000 5.37 3.06 0.0031 0.0007 9 0.00002 0.00000 -17.38 0.42 0.0113 0.0006 10 0.00042 0.00000 8.97 0.03 0.3041 0.0012 11 0.00001 0.00000 8.23 1.61 0.0039 0.0008 12 0.00001 0.00000 6.97 7.24 0.0044 0.0012 13 0.00002 0.00000 -13.29 0.45 0.0116 0.0022 14 0.00035 0.00000 6.40 0.02 0.2565 0.0025 15 0.00001 0.00001 7.76 3.35 0.0070 0.0044 16 0.00001 0.00000 1.40 8.04 0.0042 0.0027 The magnetic center is at X = 33.5 +- 0.8 microns Y = 196.0 +- 1.3 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: 03-03-1995 Time: 11:27:11 Magnet Name: 119 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0639 +- 3.258386E-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 0.00092 0.00001 12.02 0.41 0.4482 0.0034 2 0.20578 0.00007 -45.06 0.00 100.0000 0.0000 3 0.00006 0.00001 -32.83 2.58 0.0295 0.0025 4 0.00006 0.00000 13.62 0.85 0.0307 0.0017 5 0.00002 0.00000 -20.70 3.28 0.0075 0.0020 6 0.00046 0.00000 -14.91 0.03 0.2213 0.0011 7 0.00000 0.00000 -9.05 10.82 0.0019 0.0006 8 0.00000 0.00000 8.94 4.08 0.0019 0.0005 9 0.00002 0.00000 -16.99 0.66 0.0111 0.0014 10 0.00064 0.00000 8.94 0.03 0.3087 0.0015 11 0.00001 0.00000 0.99 6.98 0.0030 0.0009 12 0.00001 0.00000 10.22 1.29 0.0060 0.0014 13 0.00003 0.00000 6.89 11.51 0.0134 0.0023 14 0.00052 0.00000 6.41 0.02 0.2547 0.0011 15 0.00001 0.00000 4.55 9.42 0.0050 0.0017 16 0.00001 0.00001 -5.83 3.18 0.0056 0.0028 The magnetic center is at X = 41.7 +- 1.4 microns Y = 195.8 +- 1.5 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: 03-03-1995 Time: 11:33:25 Magnet Name: 119 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3047 +- 1.237703E-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 0.00123 0.00001 14.21 0.34 0.4498 0.0023 2 0.27357 0.00005 -45.06 0.00 100.0000 0.0000 3 0.00006 0.00001 -33.79 1.86 0.0215 0.0023 4 0.00007 0.00000 19.76 0.48 0.0244 0.0016 5 0.00002 0.00000 -18.53 4.93 0.0068 0.0015 6 0.00058 0.00001 -14.90 0.08 0.2110 0.0021 7 0.00001 0.00000 -2.29 16.42 0.0029 0.0008 8 0.00002 0.00000 2.70 0.90 0.0090 0.0007 9 0.00003 0.00000 -18.01 0.64 0.0106 0.0010 10 0.00085 0.00000 8.91 0.04 0.3099 0.0018 11 0.00001 0.00000 7.60 1.63 0.0037 0.0016 12 0.00001 0.00001 6.58 4.58 0.0041 0.0022 13 0.00003 0.00000 -12.98 0.79 0.0112 0.0013 14 0.00070 0.00000 6.37 0.03 0.2549 0.0009 15 0.00002 0.00001 4.65 8.22 0.0080 0.0019 16 0.00002 0.00001 1.77 9.38 0.0055 0.0031 The magnetic center is at X = 49.3 +- 1.2 microns Y = 194.8 +- 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 ^ | S N --> x N S Date: 03-03-1995 Time: 11:39:39 Magnet Name: 119 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.402 +- 6.636696E-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 0.00152 0.00001 16.47 0.37 0.4493 0.0034 2 0.33843 0.00004 -45.06 0.00 100.0000 0.0000 3 0.00004 0.00000 -36.50 5.76 0.0128 0.0014 4 0.00009 0.00001 16.59 0.70 0.0277 0.0016 5 0.00002 0.00001 -22.80 4.82 0.0044 0.0018 6 0.00063 0.00001 -14.88 0.09 0.1861 0.0021 7 0.00001 0.00000 -3.46 5.16 0.0017 0.0004 8 0.00003 0.00001 19.86 0.52 0.0093 0.0016 9 0.00004 0.00000 -17.35 0.78 0.0118 0.0010 10 0.00106 0.00000 8.95 0.02 0.3141 0.0012 11 0.00001 0.00001 5.45 0.79 0.0036 0.0016 12 0.00002 0.00001 2.47 0.60 0.0064 0.0024 13 0.00004 0.00000 6.62 11.57 0.0127 0.0008 14 0.00086 0.00001 6.40 0.01 0.2551 0.0015 15 0.00002 0.00000 -0.04 10.94 0.0074 0.0014 16 0.00002 0.00001 -4.13 6.15 0.0047 0.0035 The magnetic center is at X = 56.9 +- 1.3 microns Y = 192.5 +- 1.5 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: 03-03-1995 Time: 11:45:53 Magnet Name: 119 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3841 +- 3.005633E-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 0.00174 0.00001 14.40 0.36 0.4471 0.0027 2 0.39025 0.00002 -45.06 0.00 100.0000 0.0000 3 0.00009 0.00001 -35.14 0.98 0.0228 0.0030 4 0.00011 0.00001 13.78 0.61 0.0286 0.0021 5 0.00003 0.00001 -23.52 2.12 0.0070 0.0014 6 0.00051 0.00001 -14.79 0.08 0.1302 0.0019 7 0.00001 0.00000 -6.09 6.49 0.0020 0.0005 8 0.00002 0.00000 15.60 0.90 0.0047 0.0006 9 0.00005 0.00000 -17.71 0.65 0.0121 0.0004 10 0.00127 0.00001 8.93 0.04 0.3266 0.0017 11 0.00002 0.00001 7.01 3.15 0.0044 0.0013 12 0.00002 0.00001 5.18 2.05 0.0051 0.0021 13 0.00005 0.00000 -6.37 11.48 0.0133 0.0011 14 0.00100 0.00001 6.37 0.03 0.2570 0.0016 15 0.00002 0.00001 8.90 1.88 0.0057 0.0023 16 0.00002 0.00001 -1.30 1.41 0.0053 0.0030 The magnetic center is at X = 49.7 +- 1.3 microns Y = 193.4 +- 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 ^ | S N --> x N S Date: 03-03-1995 Time: 11:52:08 Magnet Name: 119 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3866 +- 7.595751E-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 0.00189 0.00002 12.81 0.08 0.4433 0.0047 2 0.42647 0.00002 -45.07 0.00 100.0000 0.0000 3 0.00013 0.00001 -34.43 1.71 0.0294 0.0018 4 0.00013 0.00001 13.91 1.32 0.0294 0.0019 5 0.00003 0.00000 -24.01 1.72 0.0081 0.0007 6 0.00031 0.00001 -14.52 0.15 0.0728 0.0012 7 0.00001 0.00000 0.74 8.66 0.0026 0.0011 8 0.00002 0.00000 16.91 2.11 0.0056 0.0011 9 0.00006 0.00000 -18.41 0.74 0.0134 0.0011 10 0.00142 0.00000 8.93 0.04 0.3337 0.0008 11 0.00002 0.00001 7.20 3.10 0.0051 0.0016 12 0.00002 0.00001 7.06 5.18 0.0050 0.0025 13 0.00005 0.00000 -6.55 11.71 0.0113 0.0008 14 0.00108 0.00001 6.40 0.03 0.2537 0.0020 15 0.00004 0.00002 9.81 0.53 0.0085 0.0043 16 0.00003 0.00001 -2.04 2.05 0.0075 0.0020 The magnetic center is at X = 43.9 +- 0.5 microns Y = 193.1 +- 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)