SLAC Magnetic Measurements Date: 04-04-1995 Time: 12:39:50 Magnet Name (Serial #): 126 Bar Code Number: 402 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: 04-04-1995 Time: 13:27:07 Magnet Name: 126 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00137 +- 2.972127E-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 148.26 0.38 0.1775 0.0034 2 0.01489 0.00000 44.99 0.00 100.0000 0.0000 3 0.00001 0.00000 23.40 0.68 0.0949 0.0012 4 0.00000 0.00000 -33.75 1.67 0.0193 0.0014 5 0.00000 0.00000 17.40 0.50 0.0287 0.0026 6 0.00003 0.00000 15.04 0.04 0.2202 0.0011 7 0.00000 0.00000 10.52 3.54 0.0028 0.0011 8 0.00000 0.00000 -3.94 3.04 0.0046 0.0004 9 0.00000 0.00000 -4.33 2.05 0.0035 0.0007 10 0.00004 0.00000 -9.01 0.05 0.3004 0.0018 11 0.00000 0.00000 11.12 1.69 0.0024 0.0012 12 0.00000 0.00000 -6.91 3.66 0.0038 0.0010 13 0.00000 0.00000 -4.10 0.64 0.0102 0.0018 14 0.00004 0.00000 -6.44 0.01 0.2573 0.0029 15 0.00000 0.00000 -4.24 4.36 0.0026 0.0017 16 0.00000 0.00000 -0.28 5.54 0.0067 0.0026 The magnetic center is at X = -41.7 +- 0.9 microns Y = 67.4 +- 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: 04-04-1995 Time: 13:33:13 Magnet Name: 126 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10307 +- 6.304408E-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 150.05 0.41 0.2799 0.0027 2 0.03493 0.00001 44.99 0.00 100.0000 0.0000 3 0.00003 0.00000 15.76 0.52 0.0764 0.0020 4 0.00001 0.00000 -36.01 1.26 0.0261 0.0019 5 0.00001 0.00000 18.05 0.77 0.0261 0.0026 6 0.00008 0.00000 14.99 0.05 0.2229 0.0013 7 0.00000 0.00000 11.82 1.51 0.0053 0.0004 8 0.00000 0.00000 11.28 18.95 0.0080 0.0012 9 0.00000 0.00000 -6.18 1.40 0.0053 0.0008 10 0.00010 0.00000 -9.05 0.04 0.2996 0.0012 11 0.00000 0.00000 -1.21 6.29 0.0030 0.0006 12 0.00000 0.00000 0.32 1.15 0.0068 0.0019 13 0.00000 0.00000 -2.82 1.61 0.0105 0.0030 14 0.00009 0.00000 -6.46 0.05 0.2547 0.0020 15 0.00000 0.00000 4.34 4.68 0.0038 0.0013 16 0.00000 0.00000 2.37 5.11 0.0074 0.0009 The magnetic center is at X = -62.4 +- 1.0 microns Y = 108.3 +- 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: 04-04-1995 Time: 13:39:23 Magnet Name: 126 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06671 +- 3.268753E-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 0.00022 0.00000 149.17 0.50 0.3176 0.0021 2 0.06881 0.00001 44.98 0.00 100.0000 0.0000 3 0.00005 0.00000 13.20 0.68 0.0712 0.0027 4 0.00002 0.00000 -34.54 1.17 0.0227 0.0015 5 0.00002 0.00000 17.83 0.72 0.0244 0.0026 6 0.00015 0.00000 15.04 0.05 0.2229 0.0009 7 0.00000 0.00000 13.27 1.70 0.0044 0.0007 8 0.00000 0.00000 -0.30 3.07 0.0019 0.0007 9 0.00000 0.00000 -5.94 3.39 0.0033 0.0009 10 0.00021 0.00000 -9.02 0.03 0.2995 0.0020 11 0.00000 0.00000 6.13 6.00 0.0023 0.0009 12 0.00000 0.00000 -2.37 10.68 0.0048 0.0016 13 0.00001 0.00000 -4.42 0.77 0.0120 0.0028 14 0.00018 0.00000 -6.43 0.02 0.2551 0.0016 15 0.00000 0.00000 3.65 4.92 0.0041 0.0007 16 0.00000 0.00000 4.63 4.95 0.0048 0.0029 The magnetic center is at X = -72.7 +- 1.2 microns Y = 121.8 +- 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: 04-04-1995 Time: 13:45:39 Magnet Name: 126 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0619 +- 4.921107E-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 0.00046 0.00000 146.54 0.47 0.3370 0.0010 2 0.13731 0.00002 44.98 0.00 100.0000 0.0000 3 0.00010 0.00000 13.42 0.81 0.0718 0.0016 4 0.00003 0.00000 -34.07 1.09 0.0216 0.0017 5 0.00004 0.00000 18.86 1.28 0.0255 0.0017 6 0.00031 0.00000 14.97 0.07 0.2234 0.0012 7 0.00001 0.00000 13.43 1.07 0.0043 0.0012 8 0.00000 0.00000 -5.64 9.00 0.0024 0.0015 9 0.00001 0.00000 -1.28 8.91 0.0040 0.0017 10 0.00042 0.00000 -9.02 0.02 0.3024 0.0011 11 0.00000 0.00000 -3.53 6.45 0.0016 0.0013 12 0.00000 0.00000 3.70 11.19 0.0035 0.0022 13 0.00002 0.00001 -3.83 1.21 0.0120 0.0037 14 0.00035 0.00000 -6.47 0.03 0.2557 0.0014 15 0.00000 0.00000 0.54 7.36 0.0016 0.0007 16 0.00001 0.00000 1.09 6.71 0.0052 0.0005 The magnetic center is at X = -83.0 +- 1.1 microns Y = 125.6 +- 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 Date: 04-04-1995 Time: 13:51:53 Magnet Name: 126 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0774 +- 1.001458E-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 0.00069 0.00001 145.65 0.15 0.3377 0.0027 2 0.20550 0.00003 44.96 0.00 100.0000 0.0000 3 0.00015 0.00000 13.75 1.14 0.0706 0.0012 4 0.00005 0.00000 -33.71 1.62 0.0224 0.0008 5 0.00005 0.00001 17.94 0.65 0.0258 0.0029 6 0.00044 0.00000 15.01 0.13 0.2155 0.0016 7 0.00001 0.00000 14.82 2.69 0.0045 0.0012 8 0.00000 0.00000 -0.29 3.61 0.0024 0.0009 9 0.00001 0.00000 -7.06 3.09 0.0030 0.0008 10 0.00063 0.00000 -9.03 0.03 0.3060 0.0016 11 0.00001 0.00000 11.95 2.22 0.0028 0.0004 12 0.00001 0.00000 -3.94 11.10 0.0035 0.0016 13 0.00002 0.00000 -3.29 0.68 0.0119 0.0008 14 0.00052 0.00000 -6.48 0.04 0.2547 0.0023 15 0.00001 0.00000 5.25 7.48 0.0039 0.0015 16 0.00001 0.00000 -2.28 8.19 0.0036 0.0018 The magnetic center is at X = -85.1 +- 0.7 microns Y = 124.5 +- 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: 04-04-1995 Time: 13:58:08 Magnet Name: 126 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3244 +- 5.846824E-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 0.00000 146.27 0.32 0.3353 0.0016 2 0.27306 0.00004 44.96 0.00 100.0000 0.0000 3 0.00018 0.00001 12.57 0.25 0.0668 0.0031 4 0.00010 0.00001 -37.62 0.43 0.0351 0.0026 5 0.00007 0.00001 19.14 1.30 0.0248 0.0020 6 0.00057 0.00001 14.99 0.08 0.2097 0.0018 7 0.00001 0.00000 15.83 3.98 0.0032 0.0012 8 0.00003 0.00000 -0.52 0.62 0.0102 0.0002 9 0.00001 0.00001 -3.56 1.73 0.0050 0.0020 10 0.00084 0.00000 -9.06 0.04 0.3073 0.0017 11 0.00001 0.00000 8.13 3.96 0.0031 0.0011 12 0.00001 0.00000 -3.16 7.65 0.0032 0.0013 13 0.00003 0.00001 -3.68 1.57 0.0099 0.0024 14 0.00070 0.00000 -6.46 0.01 0.2557 0.0015 15 0.00001 0.00001 -0.71 2.89 0.0042 0.0024 16 0.00001 0.00000 -3.64 6.94 0.0032 0.0016 The magnetic center is at X = -83.2 +- 0.8 microns Y = 124.6 +- 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 Date: 04-04-1995 Time: 14:04:25 Magnet Name: 126 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.426 +- 7.619852E-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 0.00109 0.00001 144.13 0.48 0.3237 0.0021 2 0.33789 0.00013 44.96 0.00 100.0000 0.0000 3 0.00022 0.00000 14.18 0.61 0.0649 0.0014 4 0.00010 0.00001 -36.20 0.87 0.0283 0.0020 5 0.00008 0.00000 18.11 0.80 0.0249 0.0006 6 0.00063 0.00001 15.00 0.13 0.1865 0.0016 7 0.00002 0.00000 13.04 1.78 0.0049 0.0009 8 0.00001 0.00000 -20.67 1.43 0.0036 0.0010 9 0.00001 0.00001 -7.19 2.34 0.0038 0.0016 10 0.00104 0.00000 -9.06 0.03 0.3090 0.0012 11 0.00001 0.00001 5.89 6.05 0.0028 0.0018 12 0.00003 0.00000 -1.11 0.48 0.0094 0.0011 13 0.00004 0.00000 -3.08 0.81 0.0115 0.0008 14 0.00086 0.00000 -6.47 0.02 0.2531 0.0013 15 0.00001 0.00000 -4.70 2.33 0.0024 0.0007 16 0.00003 0.00001 -9.11 1.31 0.0094 0.0015 The magnetic center is at X = -84.7 +- 1.1 microns Y = 117.2 +- 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: 04-04-1995 Time: 14:10:41 Magnet Name: 126 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4133 +- 7.186225E-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 0.00108 0.00001 134.73 0.34 0.2767 0.0016 2 0.38992 0.00003 44.96 0.00 100.0000 0.0000 3 0.00018 0.00000 24.88 0.85 0.0463 0.0008 4 0.00009 0.00001 -33.71 1.30 0.0243 0.0021 5 0.00008 0.00001 16.81 1.19 0.0208 0.0018 6 0.00053 0.00001 15.09 0.14 0.1350 0.0017 7 0.00001 0.00000 7.05 2.12 0.0038 0.0011 8 0.00002 0.00000 20.73 1.06 0.0059 0.0008 9 0.00001 0.00000 -7.88 2.12 0.0036 0.0008 10 0.00125 0.00001 -9.06 0.03 0.3199 0.0014 11 0.00001 0.00000 1.51 8.69 0.0031 0.0012 12 0.00002 0.00001 -1.40 2.02 0.0043 0.0031 13 0.00003 0.00001 -2.45 1.36 0.0081 0.0017 14 0.00100 0.00001 -6.49 0.03 0.2558 0.0019 15 0.00001 0.00001 1.88 6.66 0.0038 0.0023 16 0.00002 0.00000 -0.64 2.27 0.0050 0.0013 The magnetic center is at X = -87.8 +- 0.7 microns Y = 87.0 +- 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: 04-04-1995 Time: 14:16:57 Magnet Name: 126 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4202 +- 9.594855E-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 0.00109 0.00000 128.04 0.56 0.2562 0.0008 2 0.42635 0.00004 44.96 0.00 100.0000 0.0000 3 0.00021 0.00001 33.15 0.68 0.0482 0.0013 4 0.00011 0.00001 -33.57 1.30 0.0254 0.0021 5 0.00009 0.00001 16.67 0.99 0.0220 0.0013 6 0.00033 0.00001 15.04 0.18 0.0764 0.0019 7 0.00002 0.00000 6.66 1.37 0.0051 0.0011 8 0.00001 0.00001 0.44 21.12 0.0032 0.0012 9 0.00002 0.00001 -8.05 0.78 0.0037 0.0012 10 0.00141 0.00000 -9.03 0.02 0.3309 0.0007 11 0.00001 0.00001 6.60 11.99 0.0021 0.0013 12 0.00002 0.00001 -7.32 4.27 0.0039 0.0018 13 0.00005 0.00001 -3.99 0.83 0.0111 0.0016 14 0.00108 0.00001 -6.46 0.02 0.2523 0.0013 15 0.00002 0.00001 -0.72 6.61 0.0035 0.0023 16 0.00003 0.00000 -3.76 3.86 0.0061 0.0012 The magnetic center is at X = -90.1 +- 0.7 microns Y = 70.5 +- 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 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)