SLAC Magnetic Measurements Date: 04-26-1995 Time: 06:24:43 Magnet Name (Serial #): 134 Bar Code Number: 349 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl Run Number: 3 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: 04-26-1995 Time: 07:12:00 Magnet Name: 134 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 10.00136 +- 2.719958E-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 -141.88 0.54 0.3481 0.0056 2 0.01486 0.00000 45.03 0.00 100.0000 0.0000 3 0.00002 0.00000 30.66 0.62 0.1047 0.0063 4 0.00001 0.00000 30.01 3.04 0.0422 0.0078 5 0.00000 0.00000 11.58 6.84 0.0135 0.0069 6 0.00003 0.00000 15.31 0.38 0.2276 0.0109 7 0.00000 0.00000 2.32 11.03 0.0070 0.0034 8 0.00000 0.00000 9.38 9.60 0.0085 0.0034 9 0.00000 0.00000 3.23 1.22 0.0111 0.0007 10 0.00004 0.00000 -8.95 0.03 0.2979 0.0013 11 0.00000 0.00000 2.74 5.95 0.0021 0.0013 12 0.00000 0.00000 8.63 3.26 0.0096 0.0031 13 0.00000 0.00000 1.91 0.80 0.0215 0.0047 14 0.00004 0.00000 -6.37 0.05 0.2587 0.0027 15 0.00000 0.00000 -7.73 2.12 0.0125 0.0030 16 0.00000 0.00000 2.92 4.55 0.0037 0.0027 The magnetic center is at X = 96.0 +- 1.9 microns Y = 122.3 +- 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: 04-26-1995 Time: 07:18:06 Magnet Name: 134 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 25.10349 +- 6.013467E-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 -154.70 0.36 0.4007 0.0042 2 0.03496 0.00000 45.03 0.00 100.0000 0.0000 3 0.00003 0.00000 26.84 0.91 0.0804 0.0038 4 0.00002 0.00000 32.33 0.88 0.0450 0.0031 5 0.00001 0.00000 9.41 1.30 0.0161 0.0047 6 0.00008 0.00000 15.05 0.07 0.2271 0.0062 7 0.00000 0.00000 -1.41 7.53 0.0042 0.0025 8 0.00000 0.00000 18.18 2.61 0.0110 0.0043 9 0.00000 0.00000 3.72 0.39 0.0121 0.0011 10 0.00010 0.00000 -8.97 0.05 0.2985 0.0017 11 0.00000 0.00000 0.03 3.35 0.0041 0.0007 12 0.00000 0.00000 2.22 1.74 0.0127 0.0027 13 0.00001 0.00000 2.01 0.33 0.0251 0.0037 14 0.00009 0.00000 -6.46 0.07 0.2568 0.0012 15 0.00000 0.00000 -6.89 2.36 0.0135 0.0058 16 0.00000 0.00000 2.11 4.33 0.0050 0.0027 The magnetic center is at X = 76.5 +- 1.3 microns Y = 161.8 +- 1.7 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: 04-26-1995 Time: 07:24:18 Magnet Name: 134 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 50.06894 +- 3.141398E-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 0.00029 0.00000 -160.65 0.21 0.4214 0.0047 2 0.06886 0.00001 45.03 0.00 100.0000 0.0000 3 0.00006 0.00000 26.02 1.10 0.0842 0.0034 4 0.00003 0.00000 29.52 0.54 0.0386 0.0018 5 0.00001 0.00000 7.79 1.38 0.0148 0.0033 6 0.00015 0.00000 15.10 0.08 0.2250 0.0039 7 0.00000 0.00000 9.92 8.38 0.0024 0.0012 8 0.00001 0.00000 11.46 2.86 0.0078 0.0001 9 0.00001 0.00000 4.43 0.29 0.0119 0.0017 10 0.00021 0.00000 -8.93 0.05 0.2993 0.0014 11 0.00000 0.00000 -1.11 2.20 0.0044 0.0008 12 0.00001 0.00000 5.59 2.49 0.0098 0.0018 13 0.00001 0.00000 1.34 1.08 0.0210 0.0052 14 0.00018 0.00000 -6.44 0.02 0.2574 0.0038 15 0.00001 0.00000 -6.34 1.80 0.0126 0.0041 16 0.00000 0.00000 1.74 8.47 0.0038 0.0009 The magnetic center is at X = 62.3 +- 0.9 microns Y = 177.6 +- 2.0 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: 04-26-1995 Time: 07:30:34 Magnet Name: 134 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 100.0676 +- 5.432429E-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 0.00058 0.00001 -162.83 0.63 0.4217 0.0067 2 0.13735 0.00002 45.03 0.00 100.0000 0.0000 3 0.00011 0.00000 26.81 0.75 0.0826 0.0034 4 0.00005 0.00000 30.14 0.82 0.0383 0.0023 5 0.00002 0.00000 8.84 1.22 0.0132 0.0023 6 0.00031 0.00000 15.05 0.07 0.2276 0.0013 7 0.00001 0.00000 7.48 1.92 0.0040 0.0011 8 0.00000 0.00000 2.86 8.29 0.0021 0.0009 9 0.00001 0.00000 3.46 0.78 0.0109 0.0010 10 0.00041 0.00000 -8.95 0.02 0.3017 0.0005 11 0.00001 0.00000 -1.21 2.93 0.0036 0.0010 12 0.00000 0.00000 2.33 10.51 0.0030 0.0017 13 0.00003 0.00000 1.43 0.96 0.0243 0.0029 14 0.00035 0.00000 -6.40 0.05 0.2528 0.0019 15 0.00002 0.00001 -6.78 1.25 0.0110 0.0047 16 0.00001 0.00000 -0.04 7.86 0.0053 0.0017 The magnetic center is at X = 55.6 +- 2.2 microns Y = 179.9 +- 2.9 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: 04-26-1995 Time: 07:36:49 Magnet Name: 134 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 150.0867 +- 7.293957E-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 0.00083 0.00001 -164.07 0.78 0.4052 0.0057 2 0.20556 0.00004 45.01 0.00 100.0000 0.0000 3 0.00016 0.00001 28.20 1.50 0.0784 0.0057 4 0.00008 0.00001 29.46 0.80 0.0376 0.0035 5 0.00003 0.00000 8.34 1.27 0.0132 0.0021 6 0.00045 0.00000 15.07 0.06 0.2179 0.0022 7 0.00001 0.00000 8.90 6.28 0.0034 0.0020 8 0.00001 0.00000 5.18 10.15 0.0038 0.0017 9 0.00002 0.00000 4.82 0.89 0.0119 0.0007 10 0.00063 0.00000 -8.95 0.02 0.3043 0.0013 11 0.00001 0.00000 3.83 4.66 0.0026 0.0005 12 0.00001 0.00000 10.79 2.82 0.0072 0.0021 13 0.00004 0.00001 1.58 0.80 0.0184 0.0043 14 0.00053 0.00001 -6.44 0.02 0.2581 0.0026 15 0.00002 0.00001 -6.32 1.54 0.0099 0.0030 16 0.00001 0.00000 -1.69 5.52 0.0045 0.0023 The magnetic center is at X = 49.7 +- 2.5 microns Y = 174.0 +- 2.5 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: 04-26-1995 Time: 07:43:04 Magnet Name: 134 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 200.336 +- 1.274406E-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 0.00112 0.00002 -163.66 0.57 0.4108 0.0062 2 0.27312 0.00009 45.01 0.00 100.0000 0.0000 3 0.00020 0.00001 27.67 0.65 0.0733 0.0031 4 0.00012 0.00000 33.84 0.52 0.0444 0.0018 5 0.00003 0.00001 8.19 1.57 0.0122 0.0034 6 0.00057 0.00000 15.09 0.06 0.2090 0.0012 7 0.00000 0.00000 1.79 17.24 0.0017 0.0016 8 0.00002 0.00001 5.29 3.18 0.0066 0.0023 9 0.00003 0.00001 4.41 0.75 0.0119 0.0019 10 0.00084 0.00001 -8.97 0.03 0.3067 0.0029 11 0.00001 0.00000 -5.70 2.34 0.0027 0.0015 12 0.00001 0.00001 1.25 9.85 0.0049 0.0026 13 0.00006 0.00001 1.06 0.29 0.0223 0.0038 14 0.00070 0.00001 -6.45 0.04 0.2568 0.0029 15 0.00002 0.00001 -7.16 1.10 0.0077 0.0026 16 0.00002 0.00001 -2.09 6.97 0.0064 0.0046 The magnetic center is at X = 51.6 +- 1.9 microns Y = 176.1 +- 2.7 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: 04-26-1995 Time: 07:49:21 Magnet Name: 134 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 250.4413 +- 1.58871E-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 0.00142 0.00002 -162.63 0.41 0.4199 0.0067 2 0.33811 0.00006 45.01 0.00 100.0000 0.0000 3 0.00023 0.00001 26.75 1.70 0.0693 0.0037 4 0.00013 0.00001 32.19 0.99 0.0397 0.0016 5 0.00004 0.00001 8.13 2.92 0.0125 0.0021 6 0.00063 0.00000 15.05 0.07 0.1856 0.0012 7 0.00001 0.00000 9.66 5.77 0.0029 0.0002 8 0.00002 0.00000 19.31 1.48 0.0067 0.0014 9 0.00004 0.00000 3.83 0.59 0.0124 0.0013 10 0.00105 0.00000 -8.98 0.01 0.3103 0.0014 11 0.00001 0.00000 -0.31 4.19 0.0039 0.0005 12 0.00003 0.00001 2.50 2.47 0.0085 0.0034 13 0.00007 0.00001 1.86 1.00 0.0203 0.0020 14 0.00087 0.00001 -6.42 0.08 0.2560 0.0027 15 0.00004 0.00001 -5.98 0.73 0.0107 0.0040 16 0.00003 0.00001 -3.14 6.43 0.0084 0.0039 The magnetic center is at X = 56.0 +- 1.6 microns Y = 179.0 +- 2.9 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: 04-26-1995 Time: 07:55:36 Magnet Name: 134 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 300.4315 +- 4.645794E-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 0.00172 0.00002 -161.16 0.53 0.4413 0.0058 2 0.38992 0.00005 45.01 0.00 100.0000 0.0000 3 0.00023 0.00001 23.40 1.50 0.0599 0.0022 4 0.00014 0.00001 31.79 0.76 0.0352 0.0016 5 0.00004 0.00002 7.34 3.89 0.0114 0.0044 6 0.00052 0.00001 15.04 0.04 0.1333 0.0014 7 0.00001 0.00000 9.45 11.53 0.0022 0.0005 8 0.00003 0.00000 19.58 0.89 0.0087 0.0009 9 0.00004 0.00001 4.11 0.61 0.0115 0.0014 10 0.00126 0.00001 -8.95 0.01 0.3228 0.0017 11 0.00001 0.00001 -1.86 3.36 0.0037 0.0015 12 0.00002 0.00001 -0.49 0.90 0.0062 0.0015 13 0.00009 0.00000 2.40 0.90 0.0235 0.0011 14 0.00100 0.00001 -6.46 0.03 0.2564 0.0015 15 0.00004 0.00001 -7.57 1.64 0.0109 0.0034 16 0.00003 0.00001 0.34 0.97 0.0072 0.0031 The magnetic center is at X = 63.7 +- 1.9 microns Y = 186.5 +- 2.5 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: 04-26-1995 Time: 08:01:52 Magnet Name: 134 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 350.4407 +- 1.274177E-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 0.00195 0.00003 -161.29 0.54 0.4580 0.0064 2 0.42630 0.00006 45.01 0.00 100.0000 0.0000 3 0.00028 0.00002 20.46 1.48 0.0647 0.0057 4 0.00014 0.00001 31.85 1.03 0.0334 0.0030 5 0.00005 0.00000 7.18 1.47 0.0127 0.0007 6 0.00032 0.00001 15.19 0.21 0.0744 0.0019 7 0.00002 0.00001 8.51 3.43 0.0035 0.0014 8 0.00002 0.00000 19.69 1.41 0.0054 0.0004 9 0.00006 0.00000 3.83 0.49 0.0147 0.0006 10 0.00140 0.00000 -8.94 0.01 0.3294 0.0009 11 0.00001 0.00001 -0.18 3.56 0.0034 0.0013 12 0.00002 0.00001 5.12 3.62 0.0045 0.0018 13 0.00008 0.00001 1.69 1.24 0.0184 0.0030 14 0.00109 0.00002 -6.43 0.04 0.2550 0.0039 15 0.00003 0.00001 -6.34 1.26 0.0074 0.0021 16 0.00004 0.00001 0.46 2.18 0.0103 0.0021 The magnetic center is at X = 65.6 +- 2.1 microns Y = 193.7 +- 2.8 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)