SLAC Magnetic Measurements Date: 03-24-1995 Time: 14:07:27 Magnet Name (Serial #): 123 Bar Code Number: 466 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl Run Number: 2 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: 03-24-1995 Time: 14:54:34 Magnet Name: 123 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00165 +- 4.907347E-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 0.00001 0.00000 73.95 4.84 0.0860 0.0033 2 0.01487 0.00000 44.97 0.00 100.0000 0.0000 3 0.00001 0.00000 25.16 1.38 0.0608 0.0033 4 0.00001 0.00000 19.40 0.93 0.0485 0.0009 5 0.00000 0.00000 8.26 0.95 0.0254 0.0018 6 0.00003 0.00000 15.16 0.09 0.2201 0.0013 7 0.00000 0.00000 9.94 1.83 0.0066 0.0012 8 0.00000 0.00000 13.33 1.66 0.0048 0.0001 9 0.00000 0.00000 -9.25 2.76 0.0034 0.0017 10 0.00004 0.00000 -9.09 0.01 0.3002 0.0017 11 0.00000 0.00000 -5.77 8.47 0.0022 0.0010 12 0.00000 0.00000 12.47 0.85 0.0062 0.0009 13 0.00000 0.00000 -0.95 2.15 0.0078 0.0023 14 0.00004 0.00000 -6.42 0.01 0.2583 0.0019 15 0.00000 0.00000 -8.63 1.07 0.0107 0.0034 16 0.00000 0.00000 4.21 2.28 0.0069 0.0029 The magnetic center is at X = -36.9 +- 1.7 microns Y = -10.6 +- 3.1 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: 03-24-1995 Time: 15:00:40 Magnet Name: 123 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10333 +- 3.625543E-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 101.29 1.67 0.2547 0.0019 2 0.03495 0.00001 44.96 0.00 100.0000 0.0000 3 0.00003 0.00000 25.62 1.42 0.0917 0.0032 4 0.00002 0.00000 20.98 0.73 0.0439 0.0025 5 0.00001 0.00000 10.01 0.59 0.0263 0.0014 6 0.00008 0.00000 15.21 0.11 0.2240 0.0011 7 0.00000 0.00000 9.50 3.51 0.0049 0.0011 8 0.00000 0.00000 18.94 0.76 0.0120 0.0019 9 0.00000 0.00000 -8.39 3.30 0.0052 0.0021 10 0.00011 0.00000 -9.05 0.03 0.3022 0.0015 11 0.00000 0.00000 2.50 6.97 0.0026 0.0012 12 0.00000 0.00000 1.60 2.76 0.0043 0.0008 13 0.00000 0.00000 -1.28 5.05 0.0056 0.0023 14 0.00009 0.00000 -6.43 0.02 0.2552 0.0022 15 0.00000 0.00000 -6.36 0.75 0.0126 0.0033 16 0.00000 0.00000 1.85 1.73 0.0074 0.0027 The magnetic center is at X = -111.6 +- 1.1 microns Y = 22.3 +- 3.3 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: 03-24-1995 Time: 15:06:51 Magnet Name: 123 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.06601 +- 1.786403E-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 104.27 1.25 0.3131 0.0045 2 0.06882 0.00002 44.96 0.00 100.0000 0.0000 3 0.00007 0.00000 25.56 1.13 0.0998 0.0044 4 0.00003 0.00000 18.73 1.00 0.0438 0.0024 5 0.00002 0.00000 10.53 0.50 0.0253 0.0029 6 0.00015 0.00000 15.19 0.05 0.2233 0.0013 7 0.00000 0.00000 9.43 5.63 0.0048 0.0008 8 0.00000 0.00000 13.08 1.58 0.0044 0.0019 9 0.00000 0.00000 -8.98 1.51 0.0057 0.0011 10 0.00021 0.00000 -9.06 0.02 0.3021 0.0011 11 0.00000 0.00000 8.63 6.11 0.0022 0.0005 12 0.00000 0.00000 13.16 1.71 0.0054 0.0004 13 0.00000 0.00000 -1.52 2.39 0.0072 0.0017 14 0.00017 0.00000 -6.45 0.03 0.2517 0.0009 15 0.00001 0.00000 -7.43 0.86 0.0131 0.0055 16 0.00001 0.00000 6.18 1.74 0.0116 0.0042 The magnetic center is at X = -135.5 +- 2.1 microns Y = 34.5 +- 3.0 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: 03-24-1995 Time: 15:13:07 Magnet Name: 123 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0593 +- 7.309701E-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 105.90 1.16 0.3400 0.0026 2 0.13732 0.00001 44.96 0.00 100.0000 0.0000 3 0.00014 0.00000 25.07 1.20 0.1018 0.0023 4 0.00006 0.00000 18.07 0.45 0.0433 0.0023 5 0.00003 0.00000 10.89 0.28 0.0251 0.0018 6 0.00031 0.00000 15.17 0.05 0.2249 0.0017 7 0.00001 0.00000 9.40 1.50 0.0054 0.0014 8 0.00001 0.00000 12.91 1.84 0.0043 0.0010 9 0.00001 0.00000 -8.77 0.73 0.0070 0.0021 10 0.00042 0.00000 -9.06 0.01 0.3048 0.0014 11 0.00000 0.00000 -3.44 10.51 0.0030 0.0011 12 0.00001 0.00000 2.87 12.46 0.0041 0.0028 13 0.00001 0.00000 -3.63 2.03 0.0083 0.0021 14 0.00035 0.00000 -6.42 0.03 0.2569 0.0008 15 0.00001 0.00000 -7.29 0.58 0.0104 0.0022 16 0.00001 0.00000 3.29 3.96 0.0063 0.0031 The magnetic center is at X = -146.1 +- 1.4 microns Y = 41.6 +- 3.0 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: 03-24-1995 Time: 15:19:22 Magnet Name: 123 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0723 +- 6.540843E-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 0.00001 106.58 0.99 0.3462 0.0044 2 0.20555 0.00003 44.94 0.00 100.0000 0.0000 3 0.00021 0.00001 24.50 0.79 0.1007 0.0057 4 0.00009 0.00000 17.40 0.65 0.0418 0.0022 5 0.00005 0.00001 11.26 0.79 0.0266 0.0026 6 0.00044 0.00000 15.12 0.04 0.2153 0.0021 7 0.00001 0.00000 9.53 2.88 0.0058 0.0010 8 0.00001 0.00000 11.64 3.23 0.0049 0.0018 9 0.00001 0.00000 -9.36 1.23 0.0058 0.0020 10 0.00063 0.00000 -9.07 0.01 0.3084 0.0012 11 0.00000 0.00000 -5.75 8.75 0.0022 0.0002 12 0.00002 0.00000 6.69 12.27 0.0080 0.0018 13 0.00002 0.00001 -4.95 0.79 0.0093 0.0025 14 0.00052 0.00000 -6.45 0.03 0.2550 0.0023 15 0.00002 0.00001 -5.88 1.31 0.0111 0.0038 16 0.00002 0.00001 1.92 6.22 0.0074 0.0024 The magnetic center is at X = -148.2 +- 2.0 microns Y = 44.1 +- 2.6 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: 03-24-1995 Time: 15:25:38 Magnet Name: 123 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3176 +- 3.16229E-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 0.00096 0.00001 107.31 0.83 0.3514 0.0053 2 0.27326 0.00006 44.94 0.00 100.0000 0.0000 3 0.00028 0.00001 23.99 0.58 0.1015 0.0053 4 0.00010 0.00000 22.26 0.90 0.0355 0.0017 5 0.00007 0.00000 11.38 0.72 0.0267 0.0017 6 0.00057 0.00000 15.18 0.10 0.2085 0.0016 7 0.00001 0.00000 7.16 3.87 0.0044 0.0006 8 0.00002 0.00000 3.82 0.83 0.0083 0.0002 9 0.00001 0.00001 -5.48 1.25 0.0043 0.0025 10 0.00084 0.00000 -9.07 0.01 0.3091 0.0008 11 0.00000 0.00000 7.50 3.04 0.0018 0.0010 12 0.00001 0.00000 6.19 10.72 0.0031 0.0011 13 0.00002 0.00001 -5.07 3.38 0.0062 0.0032 14 0.00070 0.00000 -6.51 0.01 0.2560 0.0012 15 0.00003 0.00001 -7.55 0.73 0.0114 0.0051 16 0.00004 0.00001 3.33 7.86 0.0130 0.0047 The magnetic center is at X = -149.8 +- 2.4 microns Y = 46.7 +- 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: 03-24-1995 Time: 15:31:54 Magnet Name: 123 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4169 +- 5.385077E-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 0.00112 0.00001 107.61 0.22 0.3324 0.0021 2 0.33829 0.00002 44.94 0.00 100.0000 0.0000 3 0.00030 0.00001 24.23 0.65 0.0888 0.0021 4 0.00011 0.00001 19.80 0.80 0.0327 0.0024 5 0.00009 0.00000 11.87 0.68 0.0255 0.0010 6 0.00063 0.00001 15.23 0.06 0.1862 0.0015 7 0.00001 0.00001 11.65 0.65 0.0041 0.0020 8 0.00002 0.00000 18.38 1.46 0.0063 0.0007 9 0.00001 0.00000 -7.30 1.82 0.0038 0.0009 10 0.00106 0.00000 -9.11 0.04 0.3119 0.0011 11 0.00000 0.00000 10.78 6.91 0.0014 0.0010 12 0.00002 0.00001 2.59 4.35 0.0050 0.0028 13 0.00003 0.00001 -6.70 1.32 0.0083 0.0030 14 0.00086 0.00001 -6.48 0.03 0.2551 0.0017 15 0.00004 0.00001 -5.86 1.06 0.0113 0.0042 16 0.00003 0.00001 3.73 8.85 0.0082 0.0036 The magnetic center is at X = -141.5 +- 0.9 microns Y = 44.9 +- 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: 03-24-1995 Time: 15:38:09 Magnet Name: 123 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4039 +- 8.946909E-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 0.00111 0.00002 112.57 1.05 0.2854 0.0051 2 0.39032 0.00003 44.94 0.00 100.0000 0.0000 3 0.00026 0.00002 19.64 1.44 0.0659 0.0053 4 0.00012 0.00001 15.68 0.79 0.0310 0.0026 5 0.00009 0.00001 9.99 0.69 0.0243 0.0022 6 0.00052 0.00001 15.24 0.08 0.1341 0.0018 7 0.00002 0.00001 8.65 1.33 0.0050 0.0018 8 0.00003 0.00001 19.20 1.11 0.0074 0.0015 9 0.00002 0.00001 -5.96 0.68 0.0057 0.0018 10 0.00126 0.00001 -9.08 0.02 0.3225 0.0013 11 0.00001 0.00000 5.98 9.03 0.0024 0.0009 12 0.00001 0.00000 2.44 8.81 0.0032 0.0013 13 0.00002 0.00001 -7.30 1.80 0.0060 0.0032 14 0.00100 0.00001 -6.51 0.04 0.2550 0.0024 15 0.00003 0.00001 -7.21 0.81 0.0086 0.0026 16 0.00004 0.00001 4.77 1.01 0.0101 0.0024 The magnetic center is at X = -117.7 +- 2.3 microns Y = 48.9 +- 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: 03-24-1995 Time: 15:44:25 Magnet Name: 123 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4091 +- 1.026203E-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 0.00108 0.00002 113.12 1.08 0.2534 0.0054 2 0.42675 0.00006 44.94 0.00 100.0000 0.0000 3 0.00020 0.00002 18.19 1.84 0.0478 0.0041 4 0.00012 0.00001 15.78 1.66 0.0284 0.0019 5 0.00009 0.00001 10.09 0.61 0.0222 0.0022 6 0.00033 0.00000 15.49 0.15 0.0762 0.0011 7 0.00003 0.00000 10.66 1.15 0.0064 0.0001 8 0.00002 0.00000 19.00 1.22 0.0046 0.0002 9 0.00002 0.00001 -8.43 1.27 0.0053 0.0014 10 0.00143 0.00001 -9.09 0.01 0.3341 0.0016 11 0.00001 0.00000 0.54 10.27 0.0019 0.0006 12 0.00002 0.00001 -1.06 12.20 0.0044 0.0013 13 0.00004 0.00002 -4.64 2.67 0.0093 0.0038 14 0.00108 0.00001 -6.46 0.02 0.2542 0.0024 15 0.00004 0.00002 -7.97 1.42 0.0093 0.0042 16 0.00004 0.00001 3.04 1.11 0.0105 0.0024 The magnetic center is at X = -104.1 +- 2.4 microns Y = 44.4 +- 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 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)