SLAC Magnetic Measurements Date: 04-06-1995 Time: 08:50:03 Magnet Name (Serial #): 112 Bar Code Number: 462 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: 04-06-1995 Time: 09:37:38 Magnet Name: 112 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00138 +- 2.676981E-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 0.00002 0.00000 -13.26 0.83 0.1080 0.0015 2 0.01494 0.00000 44.98 0.00 100.0000 0.0000 3 0.00001 0.00000 37.71 2.16 0.0365 0.0013 4 0.00000 0.00000 -24.48 1.04 0.0282 0.0013 5 0.00000 0.00000 20.13 2.10 0.0180 0.0024 6 0.00003 0.00000 15.13 0.04 0.2115 0.0018 7 0.00000 0.00000 20.90 2.16 0.0048 0.0012 8 0.00000 0.00000 -13.25 1.68 0.0041 0.0011 9 0.00000 0.00000 -10.57 0.71 0.0073 0.0012 10 0.00004 0.00000 -9.03 0.01 0.2985 0.0014 11 0.00000 0.00000 -0.47 8.24 0.0015 0.0007 12 0.00000 0.00000 -9.19 2.09 0.0028 0.0002 13 0.00000 0.00000 -5.95 2.50 0.0077 0.0043 14 0.00004 0.00000 -6.51 0.01 0.2554 0.0026 15 0.00000 0.00000 4.87 4.45 0.0060 0.0031 16 0.00000 0.00000 3.51 7.18 0.0073 0.0026 The magnetic center is at X = 11.1 +- 0.7 microns Y = -47.0 +- 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: 04-06-1995 Time: 09:43:43 Magnet Name: 112 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10287 +- 5.255334E-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 71.94 1.09 0.1505 0.0028 2 0.03499 0.00001 44.97 0.00 100.0000 0.0000 3 0.00002 0.00000 34.90 1.26 0.0585 0.0026 4 0.00001 0.00000 -26.33 0.97 0.0316 0.0018 5 0.00001 0.00000 19.45 1.05 0.0194 0.0030 6 0.00008 0.00000 15.13 0.07 0.2172 0.0024 7 0.00000 0.00000 19.77 3.20 0.0041 0.0009 8 0.00000 0.00000 -19.43 0.87 0.0095 0.0015 9 0.00000 0.00000 -10.82 0.63 0.0070 0.0011 10 0.00010 0.00000 -9.07 0.04 0.2981 0.0014 11 0.00000 0.00000 2.55 10.02 0.0030 0.0006 12 0.00000 0.00000 -0.73 1.79 0.0062 0.0013 13 0.00000 0.00000 -5.32 2.23 0.0093 0.0031 14 0.00009 0.00000 -6.47 0.04 0.2569 0.0011 15 0.00000 0.00000 0.25 8.61 0.0060 0.0031 16 0.00000 0.00000 2.34 1.96 0.0053 0.0021 The magnetic center is at X = -63.9 +- 1.3 microns Y = -20.8 +- 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 ^ | N S --> x S N Date: 04-06-1995 Time: 09:49:55 Magnet Name: 112 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06591 +- 7.958902E-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 83.28 0.81 0.2024 0.0009 2 0.06889 0.00000 44.97 0.00 100.0000 0.0000 3 0.00004 0.00000 34.91 0.74 0.0629 0.0029 4 0.00002 0.00000 -24.54 0.85 0.0328 0.0013 5 0.00001 0.00000 19.54 0.77 0.0203 0.0036 6 0.00015 0.00000 15.12 0.09 0.2170 0.0020 7 0.00000 0.00000 9.49 17.02 0.0031 0.0015 8 0.00000 0.00000 -14.60 2.37 0.0039 0.0009 9 0.00000 0.00000 -10.92 0.99 0.0066 0.0022 10 0.00021 0.00000 -9.04 0.02 0.2995 0.0004 11 0.00000 0.00000 -4.04 10.26 0.0027 0.0004 12 0.00000 0.00000 0.37 13.21 0.0043 0.0017 13 0.00000 0.00000 -6.65 0.99 0.0071 0.0030 14 0.00018 0.00000 -6.46 0.03 0.2550 0.0015 15 0.00000 0.00000 1.09 7.11 0.0036 0.0008 16 0.00001 0.00000 -0.43 8.69 0.0079 0.0064 The magnetic center is at X = -89.8 +- 0.4 microns Y = -10.6 +- 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 ^ | N S --> x S N Date: 04-06-1995 Time: 09:56:10 Magnet Name: 112 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0632 +- 2.57711E-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 86.33 0.49 0.2253 0.0021 2 0.13746 0.00001 44.97 0.00 100.0000 0.0000 3 0.00009 0.00000 35.75 0.49 0.0650 0.0008 4 0.00005 0.00000 -24.62 0.56 0.0328 0.0019 5 0.00003 0.00000 19.15 1.59 0.0188 0.0022 6 0.00030 0.00000 15.11 0.07 0.2178 0.0020 7 0.00001 0.00000 22.28 2.13 0.0038 0.0012 8 0.00000 0.00000 -9.67 5.47 0.0025 0.0011 9 0.00001 0.00000 -9.83 0.76 0.0075 0.0011 10 0.00042 0.00000 -9.04 0.02 0.3024 0.0012 11 0.00000 0.00000 -5.96 6.68 0.0021 0.0005 12 0.00000 0.00000 -3.73 9.94 0.0028 0.0011 13 0.00001 0.00000 -6.91 1.41 0.0080 0.0027 14 0.00035 0.00001 -6.47 0.04 0.2559 0.0044 15 0.00001 0.00000 1.21 8.12 0.0040 0.0021 16 0.00001 0.00000 -2.20 6.67 0.0041 0.0015 The magnetic center is at X = -100.4 +- 0.9 microns Y = -6.4 +- 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: 04-06-1995 Time: 10:02:24 Magnet Name: 112 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0785 +- 6.404603E-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 0.00000 85.97 0.29 0.2286 0.0018 2 0.20572 0.00005 44.95 0.00 100.0000 0.0000 3 0.00014 0.00000 35.84 0.36 0.0659 0.0015 4 0.00007 0.00000 -24.38 0.44 0.0317 0.0022 5 0.00004 0.00000 19.44 0.91 0.0197 0.0024 6 0.00043 0.00001 15.03 0.07 0.2092 0.0031 7 0.00001 0.00000 11.41 20.91 0.0037 0.0015 8 0.00001 0.00000 -13.10 1.64 0.0037 0.0006 9 0.00002 0.00000 -8.53 1.02 0.0086 0.0016 10 0.00063 0.00000 -9.06 0.02 0.3039 0.0006 11 0.00000 0.00000 2.70 5.14 0.0020 0.0006 12 0.00001 0.00001 -5.72 11.77 0.0062 0.0025 13 0.00002 0.00001 -6.73 1.71 0.0118 0.0026 14 0.00052 0.00001 -6.49 0.02 0.2548 0.0027 15 0.00001 0.00000 5.81 3.94 0.0044 0.0010 16 0.00002 0.00000 -0.53 8.29 0.0076 0.0022 The magnetic center is at X = -101.9 +- 0.8 microns Y = -7.2 +- 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: 04-06-1995 Time: 10:08:39 Magnet Name: 112 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.325 +- 9.587876E-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 0.00062 0.00000 84.08 0.55 0.2265 0.0018 2 0.27342 0.00001 44.95 0.00 100.0000 0.0000 3 0.00017 0.00000 36.19 0.42 0.0637 0.0018 4 0.00010 0.00001 -29.57 0.59 0.0355 0.0025 5 0.00005 0.00000 18.87 1.46 0.0200 0.0013 6 0.00055 0.00000 15.05 0.09 0.2003 0.0018 7 0.00001 0.00001 12.36 10.51 0.0038 0.0019 8 0.00002 0.00000 -4.30 0.35 0.0085 0.0007 9 0.00002 0.00000 -9.79 1.21 0.0073 0.0010 10 0.00084 0.00000 -9.05 0.03 0.3073 0.0012 11 0.00001 0.00000 -0.85 5.61 0.0021 0.0002 12 0.00001 0.00000 -5.52 9.11 0.0050 0.0013 13 0.00002 0.00001 -6.39 0.76 0.0089 0.0031 14 0.00070 0.00001 -6.48 0.04 0.2553 0.0027 15 0.00001 0.00000 0.75 6.73 0.0052 0.0012 16 0.00002 0.00001 0.43 9.57 0.0090 0.0047 The magnetic center is at X = -100.6 +- 0.8 microns Y = -10.4 +- 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: 04-06-1995 Time: 10:14:56 Magnet Name: 112 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4268 +- 1.458911E-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 0.00074 0.00000 83.33 0.37 0.2196 0.0010 2 0.33841 0.00007 44.95 0.00 100.0000 0.0000 3 0.00020 0.00001 36.04 0.73 0.0595 0.0022 4 0.00011 0.00001 -27.10 0.80 0.0314 0.0022 5 0.00006 0.00001 19.06 1.11 0.0183 0.0023 6 0.00060 0.00001 15.12 0.03 0.1777 0.0019 7 0.00001 0.00001 19.71 2.23 0.0038 0.0016 8 0.00002 0.00000 -18.89 2.10 0.0073 0.0011 9 0.00003 0.00000 -11.36 1.10 0.0078 0.0011 10 0.00105 0.00000 -9.08 0.02 0.3097 0.0012 11 0.00000 0.00000 -4.31 6.13 0.0012 0.0013 12 0.00002 0.00001 -1.86 2.40 0.0050 0.0032 13 0.00002 0.00001 -7.12 1.29 0.0068 0.0023 14 0.00086 0.00001 -6.45 0.01 0.2549 0.0016 15 0.00001 0.00001 -1.41 3.55 0.0017 0.0019 16 0.00002 0.00001 -3.93 6.87 0.0053 0.0032 The magnetic center is at X = -97.4 +- 0.5 microns Y = -11.4 +- 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: 04-06-1995 Time: 10:21:11 Magnet Name: 112 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4144 +- 5.120228E-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 0.00080 0.00001 86.66 0.20 0.2048 0.0015 2 0.39038 0.00009 44.95 0.00 100.0000 0.0000 3 0.00020 0.00001 34.00 0.38 0.0515 0.0017 4 0.00012 0.00001 -24.77 0.78 0.0296 0.0016 5 0.00007 0.00001 20.36 0.99 0.0173 0.0013 6 0.00049 0.00001 15.12 0.11 0.1247 0.0015 7 0.00001 0.00001 12.30 14.92 0.0034 0.0020 8 0.00003 0.00000 -16.70 0.66 0.0074 0.0003 9 0.00003 0.00001 -8.91 1.00 0.0072 0.0014 10 0.00126 0.00001 -9.06 0.02 0.3217 0.0015 11 0.00001 0.00000 -6.78 9.82 0.0017 0.0006 12 0.00001 0.00001 -4.26 5.24 0.0031 0.0025 13 0.00004 0.00002 -6.95 1.13 0.0109 0.0042 14 0.00099 0.00001 -6.51 0.02 0.2549 0.0020 15 0.00002 0.00000 6.55 3.03 0.0056 0.0010 16 0.00001 0.00001 1.05 6.05 0.0029 0.0019 The magnetic center is at X = -91.3 +- 0.7 microns Y = -5.3 +- 0.3 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 ^ | N S --> x S N Date: 04-06-1995 Time: 10:27:28 Magnet Name: 112 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4213 +- 6.534611E-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 0.00081 0.00000 88.48 0.53 0.1892 0.0009 2 0.42682 0.00006 44.95 0.00 100.0000 0.0000 3 0.00018 0.00001 33.42 0.44 0.0420 0.0014 4 0.00012 0.00001 -25.60 0.94 0.0289 0.0022 5 0.00007 0.00001 20.28 0.64 0.0166 0.0020 6 0.00028 0.00001 15.31 0.26 0.0652 0.0015 7 0.00002 0.00001 18.77 3.23 0.0045 0.0012 8 0.00003 0.00000 -16.84 0.74 0.0059 0.0005 9 0.00003 0.00000 -9.10 1.78 0.0069 0.0011 10 0.00141 0.00001 -9.07 0.02 0.3294 0.0020 11 0.00000 0.00000 4.73 3.50 0.0009 0.0006 12 0.00003 0.00001 -5.88 10.56 0.0060 0.0033 13 0.00004 0.00001 -5.87 1.16 0.0090 0.0019 14 0.00107 0.00001 -6.46 0.05 0.2502 0.0019 15 0.00001 0.00001 5.17 3.03 0.0034 0.0016 16 0.00004 0.00001 0.92 1.47 0.0105 0.0031 The magnetic center is at X = -84.5 +- 0.4 microns Y = -2.2 +- 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 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)