SLAC Magnetic Measurements Date: 03-20-1995 Time: 10:12:40 Magnet Name (Serial #): 178 Bar Code Number: 518 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: 03-20-1995 Time: 11:00:09 Magnet Name: 178 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00369 +- 4.650769E-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 -117.34 1.14 0.2866 0.0043 2 0.01486 0.00000 44.96 0.00 100.0000 0.0000 3 0.00001 0.00000 15.76 0.92 0.0997 0.0067 4 0.00000 0.00000 0.77 4.19 0.0074 0.0017 5 0.00000 0.00000 19.01 0.87 0.0177 0.0011 6 0.00003 0.00000 15.13 0.05 0.2153 0.0005 7 0.00000 0.00000 22.51 1.78 0.0050 0.0007 8 0.00000 0.00000 1.34 18.51 0.0025 0.0010 9 0.00000 0.00000 1.40 5.45 0.0035 0.0024 10 0.00004 0.00000 -9.06 0.04 0.2972 0.0008 11 0.00000 0.00000 -4.13 6.57 0.0025 0.0015 12 0.00000 0.00000 10.58 4.18 0.0038 0.0013 13 0.00000 0.00000 2.74 3.52 0.0087 0.0040 14 0.00004 0.00000 -6.41 0.02 0.2551 0.0013 15 0.00000 0.00000 -1.61 6.15 0.0072 0.0022 16 0.00000 0.00000 -0.08 4.77 0.0035 0.0021 The magnetic center is at X = 113.7 +- 2.1 microns Y = 58.8 +- 2.4 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: 03-20-1995 Time: 11:06:15 Magnet Name: 178 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.1066 +- 6.215514E-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 0.00009 0.00000 -126.63 1.13 0.2562 0.0048 2 0.03497 0.00001 44.96 0.00 100.0000 0.0000 3 0.00002 0.00000 17.86 1.68 0.0540 0.0042 4 0.00000 0.00000 -25.56 4.44 0.0052 0.0018 5 0.00001 0.00000 17.08 1.20 0.0144 0.0011 6 0.00008 0.00000 15.11 0.07 0.2213 0.0009 7 0.00000 0.00000 14.83 3.75 0.0045 0.0009 8 0.00000 0.00000 10.78 19.10 0.0102 0.0010 9 0.00000 0.00000 4.46 2.26 0.0043 0.0013 10 0.00010 0.00000 -9.02 0.03 0.2974 0.0024 11 0.00000 0.00000 -3.52 9.27 0.0025 0.0013 12 0.00000 0.00000 -1.08 3.28 0.0060 0.0013 13 0.00000 0.00000 3.24 7.72 0.0070 0.0047 14 0.00009 0.00000 -6.47 0.05 0.2546 0.0027 15 0.00000 0.00000 -2.10 3.74 0.0113 0.0031 16 0.00000 0.00000 -4.00 7.95 0.0066 0.0028 The magnetic center is at X = 91.8 +- 2.2 microns Y = 68.3 +- 2.2 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: 03-20-1995 Time: 11:12:26 Magnet Name: 178 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06837 +- 4.22468E-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 0.00017 0.00000 -134.97 0.96 0.2436 0.0028 2 0.06885 0.00001 44.96 0.00 100.0000 0.0000 3 0.00003 0.00000 19.32 1.35 0.0486 0.0040 4 0.00001 0.00000 -14.93 2.92 0.0089 0.0024 5 0.00001 0.00000 17.10 0.88 0.0147 0.0013 6 0.00015 0.00000 15.10 0.04 0.2206 0.0011 7 0.00000 0.00000 13.49 2.08 0.0043 0.0014 8 0.00000 0.00000 16.65 3.52 0.0024 0.0011 9 0.00000 0.00000 6.98 2.22 0.0044 0.0009 10 0.00021 0.00000 -9.06 0.02 0.2992 0.0007 11 0.00000 0.00000 8.89 4.66 0.0018 0.0002 12 0.00000 0.00000 -5.55 11.83 0.0058 0.0013 13 0.00000 0.00000 6.45 3.78 0.0069 0.0025 14 0.00017 0.00000 -6.45 0.03 0.2502 0.0012 15 0.00000 0.00000 1.50 5.73 0.0071 0.0044 16 0.00001 0.00000 8.41 1.61 0.0076 0.0028 The magnetic center is at X = 77.0 +- 1.6 microns Y = 76.9 +- 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: 03-20-1995 Time: 11:18:42 Magnet Name: 178 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0611 +- 4.16379E-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 0.00033 0.00001 -140.22 1.00 0.2436 0.0056 2 0.13738 0.00002 44.96 0.00 100.0000 0.0000 3 0.00006 0.00000 19.78 1.69 0.0462 0.0033 4 0.00001 0.00000 -15.99 4.18 0.0090 0.0013 5 0.00002 0.00000 17.53 0.89 0.0138 0.0008 6 0.00030 0.00000 15.10 0.10 0.2214 0.0014 7 0.00001 0.00000 11.86 1.85 0.0041 0.0012 8 0.00000 0.00000 2.50 17.06 0.0024 0.0008 9 0.00000 0.00000 2.47 1.76 0.0031 0.0010 10 0.00041 0.00000 -9.04 0.02 0.3015 0.0015 11 0.00000 0.00000 -0.40 10.40 0.0022 0.0013 12 0.00001 0.00000 2.92 11.00 0.0052 0.0005 13 0.00001 0.00001 2.28 2.17 0.0093 0.0037 14 0.00035 0.00000 -6.46 0.04 0.2549 0.0032 15 0.00001 0.00000 4.51 4.74 0.0059 0.0027 16 0.00001 0.00000 1.60 5.17 0.0085 0.0027 The magnetic center is at X = 69.6 +- 2.2 microns Y = 83.6 +- 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 ^ | N S --> x S N Date: 03-20-1995 Time: 11:24:57 Magnet Name: 178 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0737 +- 3.879005E-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 0.00052 0.00001 -140.08 0.75 0.2533 0.0057 2 0.20565 0.00005 44.93 0.00 100.0000 0.0000 3 0.00008 0.00001 17.19 1.66 0.0376 0.0039 4 0.00002 0.00000 -16.88 1.35 0.0106 0.0012 5 0.00003 0.00000 17.78 2.37 0.0125 0.0016 6 0.00044 0.00000 15.13 0.10 0.2123 0.0010 7 0.00001 0.00000 12.02 3.91 0.0035 0.0010 8 0.00000 0.00000 15.10 9.77 0.0020 0.0005 9 0.00001 0.00000 4.64 2.13 0.0035 0.0011 10 0.00062 0.00000 -9.08 0.04 0.3026 0.0017 11 0.00001 0.00000 -6.00 5.69 0.0033 0.0009 12 0.00001 0.00000 1.41 11.21 0.0056 0.0021 13 0.00001 0.00000 -0.90 5.44 0.0049 0.0023 14 0.00052 0.00001 -6.48 0.02 0.2552 0.0027 15 0.00002 0.00001 -1.15 2.94 0.0106 0.0046 16 0.00002 0.00001 1.19 8.85 0.0091 0.0063 The magnetic center is at X = 72.6 +- 2.0 microns Y = 86.8 +- 2.2 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: 03-20-1995 Time: 11:31:11 Magnet Name: 178 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3211 +- 6.363117E-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 0.00071 0.00002 -142.36 0.52 0.2606 0.0064 2 0.27341 0.00007 44.93 0.00 100.0000 0.0000 3 0.00012 0.00001 14.05 2.71 0.0440 0.0025 4 0.00004 0.00000 -33.35 2.50 0.0158 0.0014 5 0.00003 0.00001 18.25 2.54 0.0125 0.0019 6 0.00056 0.00000 15.08 0.05 0.2034 0.0010 7 0.00001 0.00000 13.06 2.76 0.0040 0.0012 8 0.00002 0.00000 0.18 1.30 0.0069 0.0009 9 0.00001 0.00001 3.42 1.96 0.0042 0.0026 10 0.00084 0.00000 -9.07 0.02 0.3055 0.0012 11 0.00001 0.00000 -5.33 5.00 0.0020 0.0010 12 0.00001 0.00000 4.58 6.77 0.0030 0.0017 13 0.00002 0.00001 2.13 2.85 0.0069 0.0040 14 0.00070 0.00000 -6.47 0.04 0.2549 0.0017 15 0.00002 0.00001 1.01 5.91 0.0060 0.0032 16 0.00003 0.00001 1.35 7.38 0.0106 0.0045 The magnetic center is at X = 71.1 +- 2.0 microns Y = 92.2 +- 2.4 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: 03-20-1995 Time: 11:37:28 Magnet Name: 178 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4238 +- 1.421711E-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 0.00094 0.00001 -141.75 1.07 0.2788 0.0043 2 0.33845 0.00004 44.93 0.00 100.0000 0.0000 3 0.00015 0.00002 8.26 1.96 0.0431 0.0057 4 0.00005 0.00001 -27.52 1.97 0.0135 0.0018 5 0.00004 0.00001 16.84 3.24 0.0114 0.0026 6 0.00062 0.00000 15.18 0.10 0.1819 0.0006 7 0.00001 0.00000 14.64 4.79 0.0028 0.0011 8 0.00002 0.00000 -11.13 17.82 0.0065 0.0007 9 0.00002 0.00001 3.74 4.13 0.0050 0.0023 10 0.00104 0.00000 -9.07 0.02 0.3086 0.0012 11 0.00001 0.00000 2.73 7.77 0.0018 0.0006 12 0.00002 0.00000 -1.94 1.40 0.0062 0.0009 13 0.00003 0.00001 1.43 4.15 0.0093 0.0040 14 0.00086 0.00000 -6.49 0.02 0.2532 0.0013 15 0.00002 0.00001 3.38 6.28 0.0066 0.0031 16 0.00002 0.00001 3.93 8.46 0.0071 0.0028 The magnetic center is at X = 77.1 +- 2.2 microns Y = 97.8 +- 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 ^ | N S --> x S N Date: 03-20-1995 Time: 11:43:44 Magnet Name: 178 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4058 +- 8.647844E-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 0.00106 0.00001 -138.12 0.70 0.2703 0.0014 2 0.39040 0.00007 44.93 0.00 100.0000 0.0000 3 0.00012 0.00001 10.29 0.69 0.0300 0.0029 4 0.00005 0.00001 -24.28 2.28 0.0136 0.0014 5 0.00004 0.00001 16.15 1.60 0.0101 0.0034 6 0.00051 0.00001 15.31 0.07 0.1297 0.0014 7 0.00001 0.00001 11.46 3.35 0.0034 0.0015 8 0.00003 0.00000 21.48 0.32 0.0077 0.0002 9 0.00001 0.00001 6.45 3.95 0.0029 0.0014 10 0.00124 0.00001 -9.08 0.04 0.3186 0.0014 11 0.00001 0.00000 -4.07 8.73 0.0016 0.0006 12 0.00002 0.00001 -5.72 5.92 0.0047 0.0021 13 0.00004 0.00002 2.14 1.63 0.0097 0.0039 14 0.00099 0.00002 -6.47 0.04 0.2533 0.0041 15 0.00002 0.00001 -0.09 5.62 0.0054 0.0025 16 0.00003 0.00001 1.70 4.44 0.0086 0.0033 The magnetic center is at X = 80.6 +- 1.2 microns Y = 89.9 +- 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 ^ | N S --> x S N Date: 03-20-1995 Time: 11:50:00 Magnet Name: 178 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4096 +- 7.313084E-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 0.00117 0.00001 -136.57 0.23 0.2744 0.0025 2 0.42689 0.00009 44.93 0.00 100.0000 0.0000 3 0.00011 0.00001 7.32 2.64 0.0251 0.0023 4 0.00007 0.00001 -25.41 2.06 0.0161 0.0019 5 0.00005 0.00000 17.65 1.19 0.0107 0.0007 6 0.00031 0.00001 15.56 0.21 0.0727 0.0013 7 0.00002 0.00000 14.03 3.26 0.0039 0.0007 8 0.00002 0.00000 0.41 20.93 0.0057 0.0010 9 0.00002 0.00000 3.48 0.98 0.0044 0.0008 10 0.00140 0.00000 -9.10 0.01 0.3290 0.0007 11 0.00001 0.00000 -0.81 5.04 0.0028 0.0007 12 0.00001 0.00001 6.30 7.54 0.0023 0.0016 13 0.00003 0.00001 0.57 2.63 0.0059 0.0024 14 0.00107 0.00001 -6.50 0.03 0.2517 0.0032 15 0.00001 0.00000 2.43 4.38 0.0031 0.0010 16 0.00004 0.00001 -2.53 3.97 0.0089 0.0026 The magnetic center is at X = 84.3 +- 0.8 microns Y = 89.0 +- 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 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)