SLAC Magnetic Measurements Date: 01-16-1996 Time: 10:47:53 Magnet Name (Serial #): 107 Bar Code Number: 468 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: dan Run Number: 1 Comment: none 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: 01-16-1996 Time: 11:36:39 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00765 +- 1.192511E-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 0.00004 0.00000 45.15 0.29 0.2375 0.0016 2 0.01490 0.00000 -45.11 0.00 100.0000 0.0000 3 0.00001 0.00000 -4.52 0.56 0.0756 0.0024 4 0.00000 0.00000 -23.04 1.45 0.0214 0.0021 5 0.00000 0.00000 -24.78 2.37 0.0154 0.0032 6 0.00003 0.00000 -15.10 0.05 0.2109 0.0026 7 0.00000 0.00000 -8.81 2.89 0.0036 0.0019 8 0.00000 0.00000 -7.86 2.60 0.0024 0.0006 9 0.00000 0.00000 -11.67 1.87 0.0043 0.0010 10 0.00004 0.00000 8.90 0.03 0.2971 0.0015 11 0.00000 0.00000 -1.32 6.94 0.0020 0.0009 12 0.00000 0.00000 -0.45 10.11 0.0025 0.0012 13 0.00000 0.00000 -12.38 1.02 0.0109 0.0024 14 0.00004 0.00000 6.31 0.02 0.2533 0.0025 15 0.00000 0.00000 -6.64 4.19 0.0048 0.0016 16 0.00000 0.00000 1.11 2.91 0.0062 0.0023 The magnetic center is at X = 75.2 +- 0.6 microns Y = 74.8 +- 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 ^ | S N --> x N S Date: 01-16-1996 Time: 11:42:44 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.12238 +- 9.903047E-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 52.05 0.49 0.2699 0.0016 2 0.03491 0.00000 -45.11 0.00 100.0000 0.0000 3 0.00002 0.00000 -10.02 0.67 0.0685 0.0029 4 0.00001 0.00000 -26.65 1.35 0.0206 0.0026 5 0.00001 0.00000 -24.09 1.72 0.0145 0.0031 6 0.00008 0.00000 -15.00 0.11 0.2167 0.0032 7 0.00000 0.00000 -8.39 3.83 0.0052 0.0018 8 0.00000 0.00000 -20.44 0.95 0.0074 0.0018 9 0.00000 0.00000 -12.24 0.57 0.0050 0.0023 10 0.00010 0.00000 8.87 0.04 0.2963 0.0018 11 0.00000 0.00000 -5.69 6.14 0.0027 0.0016 12 0.00000 0.00000 1.76 1.55 0.0089 0.0023 13 0.00000 0.00000 -12.08 1.35 0.0099 0.0043 14 0.00009 0.00000 6.29 0.03 0.2514 0.0004 15 0.00000 0.00000 6.52 7.19 0.0048 0.0021 16 0.00000 0.00000 -0.94 1.33 0.0105 0.0032 The magnetic center is at X = 95.1 +- 0.9 microns Y = 74.1 +- 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 ^ | S N --> x N S Date: 01-16-1996 Time: 11:48:56 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.10065 +- 1.575292E-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 0.00019 0.00000 54.91 0.22 0.2804 0.0008 2 0.06885 0.00001 -45.11 0.00 100.0000 0.0000 3 0.00005 0.00000 -12.58 0.45 0.0681 0.0025 4 0.00001 0.00000 -22.28 2.34 0.0192 0.0031 5 0.00001 0.00000 -23.96 1.08 0.0158 0.0023 6 0.00015 0.00000 -14.97 0.02 0.2172 0.0026 7 0.00000 0.00000 -6.53 3.57 0.0030 0.0015 8 0.00000 0.00000 -8.29 3.32 0.0018 0.0004 9 0.00000 0.00000 -13.28 2.16 0.0062 0.0008 10 0.00021 0.00000 8.88 0.04 0.2980 0.0023 11 0.00000 0.00000 -6.75 3.90 0.0023 0.0008 12 0.00000 0.00000 -3.12 7.64 0.0020 0.0008 13 0.00001 0.00000 -11.43 1.04 0.0106 0.0030 14 0.00017 0.00000 6.33 0.02 0.2504 0.0021 15 0.00000 0.00000 -8.37 0.92 0.0051 0.0031 16 0.00000 0.00000 -0.88 5.69 0.0059 0.0018 The magnetic center is at X = 102.5 +- 0.4 microns Y = 72.0 +- 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: 01-16-1996 Time: 11:55:11 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.1317 +- 6.528819E-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 0.00038 0.00000 56.57 0.19 0.2802 0.0013 2 0.13736 0.00004 -45.11 0.00 100.0000 0.0000 3 0.00010 0.00001 -13.95 0.67 0.0694 0.0051 4 0.00003 0.00000 -22.20 2.21 0.0186 0.0029 5 0.00002 0.00000 -23.99 1.50 0.0158 0.0033 6 0.00030 0.00000 -15.05 0.06 0.2178 0.0026 7 0.00000 0.00000 1.64 5.60 0.0032 0.0020 8 0.00000 0.00000 -4.78 2.59 0.0030 0.0004 9 0.00001 0.00000 -15.07 1.08 0.0049 0.0009 10 0.00041 0.00000 8.86 0.02 0.2997 0.0013 11 0.00000 0.00000 4.87 8.51 0.0025 0.0012 12 0.00000 0.00000 4.22 6.27 0.0035 0.0022 13 0.00001 0.00001 -10.29 1.60 0.0087 0.0037 14 0.00034 0.00000 6.30 0.01 0.2501 0.0031 15 0.00001 0.00000 0.15 11.00 0.0069 0.0024 16 0.00001 0.00001 -0.39 4.62 0.0097 0.0042 The magnetic center is at X = 104.4 +- 0.5 microns Y = 69.0 +- 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: 01-16-1996 Time: 12:01:26 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.1822 +- 7.730576E-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 0.00000 57.55 0.41 0.2511 0.0016 2 0.20558 0.00005 -45.13 0.00 100.0000 0.0000 3 0.00014 0.00000 -15.64 0.58 0.0685 0.0018 4 0.00004 0.00000 -22.49 2.71 0.0182 0.0023 5 0.00003 0.00001 -23.64 0.82 0.0165 0.0038 6 0.00043 0.00001 -15.12 0.05 0.2088 0.0024 7 0.00001 0.00000 1.78 2.05 0.0026 0.0013 8 0.00001 0.00000 -8.67 3.53 0.0036 0.0012 9 0.00001 0.00000 -14.03 2.25 0.0047 0.0002 10 0.00062 0.00001 8.87 0.03 0.3035 0.0029 11 0.00001 0.00000 -2.23 5.29 0.0035 0.0012 12 0.00001 0.00000 4.48 10.27 0.0049 0.0019 13 0.00002 0.00001 -10.95 1.03 0.0084 0.0025 14 0.00051 0.00001 6.34 0.05 0.2502 0.0046 15 0.00001 0.00001 1.17 10.29 0.0048 0.0028 16 0.00002 0.00001 3.82 6.17 0.0090 0.0033 The magnetic center is at X = 94.6 +- 0.8 microns Y = 60.2 +- 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 ^ | S N --> x N S Date: 01-16-1996 Time: 12:07:41 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.4621 +- 7.869009E-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 0.00068 0.00000 54.72 0.21 0.2494 0.0016 2 0.27317 0.00007 -45.13 0.00 100.0000 0.0000 3 0.00019 0.00001 -17.37 0.33 0.0682 0.0023 4 0.00007 0.00001 -33.03 1.68 0.0244 0.0035 5 0.00004 0.00001 -23.18 1.43 0.0140 0.0029 6 0.00055 0.00001 -15.09 0.06 0.2017 0.0026 7 0.00001 0.00000 -0.59 5.52 0.0035 0.0011 8 0.00003 0.00000 -2.29 0.57 0.0093 0.0014 9 0.00001 0.00000 -15.37 1.10 0.0045 0.0015 10 0.00083 0.00000 8.90 0.02 0.3044 0.0009 11 0.00001 0.00000 1.04 8.82 0.0034 0.0006 12 0.00001 0.00000 9.30 8.45 0.0032 0.0007 13 0.00003 0.00001 -11.13 1.27 0.0121 0.0036 14 0.00070 0.00001 6.31 0.04 0.2546 0.0028 15 0.00002 0.00000 -4.16 9.10 0.0057 0.0017 16 0.00001 0.00001 -1.53 6.51 0.0051 0.0021 The magnetic center is at X = 90.9 +- 0.6 microns Y = 64.3 +- 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: 01-16-1996 Time: 12:13:57 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.5911 +- 1.241249E-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 0.00085 0.00001 47.60 0.50 0.2518 0.0015 2 0.33781 0.00004 -45.13 0.00 100.0000 0.0000 3 0.00024 0.00001 -21.48 0.47 0.0696 0.0018 4 0.00006 0.00001 -29.03 2.35 0.0166 0.0028 5 0.00005 0.00001 -22.66 1.63 0.0150 0.0023 6 0.00060 0.00001 -15.02 0.16 0.1788 0.0028 7 0.00001 0.00000 -0.35 3.92 0.0043 0.0013 8 0.00001 0.00000 0.46 21.65 0.0043 0.0006 9 0.00002 0.00000 -14.17 1.47 0.0049 0.0004 10 0.00104 0.00000 8.87 0.03 0.3088 0.0012 11 0.00000 0.00000 2.98 10.38 0.0013 0.0004 12 0.00003 0.00000 0.47 1.37 0.0076 0.0009 13 0.00002 0.00000 -11.66 0.44 0.0059 0.0012 14 0.00085 0.00001 6.25 0.06 0.2505 0.0025 15 0.00003 0.00001 -4.48 9.18 0.0080 0.0035 16 0.00002 0.00001 -1.63 5.17 0.0065 0.0029 The magnetic center is at X = 83.1 +- 0.8 microns Y = 75.8 +- 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 ^ | S N --> x N S Date: 01-16-1996 Time: 12:20:14 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.604 +- 4.748451E-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 0.00099 0.00000 49.25 0.11 0.2544 0.0011 2 0.38933 0.00014 -45.13 0.00 100.0000 0.0000 3 0.00026 0.00001 -19.90 0.56 0.0669 0.0025 4 0.00006 0.00001 -22.43 2.98 0.0164 0.0025 5 0.00005 0.00001 -23.92 1.99 0.0139 0.0019 6 0.00050 0.00001 -15.04 0.15 0.1284 0.0021 7 0.00002 0.00001 1.31 3.19 0.0040 0.0020 8 0.00001 0.00000 -9.54 17.32 0.0036 0.0005 9 0.00002 0.00000 -14.41 1.08 0.0040 0.0007 10 0.00124 0.00001 8.88 0.02 0.3197 0.0013 11 0.00001 0.00000 4.72 2.43 0.0029 0.0011 12 0.00002 0.00001 -2.00 7.58 0.0041 0.0025 13 0.00003 0.00000 -11.54 1.53 0.0070 0.0011 14 0.00098 0.00000 6.31 0.03 0.2520 0.0011 15 0.00003 0.00001 -5.17 9.17 0.0067 0.0018 16 0.00003 0.00001 -0.63 3.02 0.0079 0.0036 The magnetic center is at X = 86.1 +- 0.4 microns Y = 74.2 +- 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: 01-16-1996 Time: 12:26:30 Magnet Name: 107 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.6344 +- 1.717072E-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 0.00107 0.00001 48.59 0.72 0.2511 0.0026 2 0.42523 0.00008 -45.13 0.00 100.0000 0.0000 3 0.00029 0.00001 -20.09 0.51 0.0690 0.0024 4 0.00007 0.00001 -22.93 1.84 0.0156 0.0022 5 0.00006 0.00001 -22.94 1.63 0.0146 0.0021 6 0.00031 0.00001 -14.90 0.31 0.0719 0.0014 7 0.00001 0.00001 -1.39 3.93 0.0032 0.0014 8 0.00001 0.00001 -1.03 17.04 0.0027 0.0014 9 0.00002 0.00000 -14.44 1.51 0.0056 0.0004 10 0.00139 0.00001 8.89 0.03 0.3277 0.0022 11 0.00001 0.00001 0.40 8.27 0.0021 0.0012 12 0.00002 0.00000 4.32 9.43 0.0037 0.0011 13 0.00003 0.00001 -3.65 9.73 0.0067 0.0019 14 0.00107 0.00001 6.31 0.05 0.2510 0.0022 15 0.00003 0.00001 -5.58 9.44 0.0070 0.0024 16 0.00005 0.00000 0.26 0.79 0.0108 0.0011 The magnetic center is at X = 84.1 +- 1.3 microns Y = 74.2 +- 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 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)