SLAC Magnetic Measurements Date: 03-07-1995 Time: 14:37:06 Magnet Name (Serial #): 194 Bar Code Number: 553 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: 03-07-1995 Time: 15:24:44 Magnet Name: 194 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00118 +- 5.368435E-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 -165.99 0.31 0.3131 0.0009 2 0.01490 0.00000 44.96 0.00 100.0000 0.0000 3 0.00002 0.00000 21.56 0.40 0.1493 0.0023 4 0.00000 0.00000 4.00 30.90 0.0041 0.0008 5 0.00000 0.00000 16.53 1.21 0.0252 0.0022 6 0.00003 0.00000 15.19 0.09 0.2175 0.0028 7 0.00000 0.00000 18.55 3.99 0.0038 0.0008 8 0.00000 0.00000 -10.07 18.37 0.0040 0.0007 9 0.00000 0.00000 0.15 1.06 0.0071 0.0007 10 0.00004 0.00000 -9.09 0.03 0.3006 0.0013 11 0.00000 0.00000 5.45 9.21 0.0024 0.0014 12 0.00000 0.00000 -5.46 8.47 0.0039 0.0021 13 0.00000 0.00000 -1.17 0.90 0.0088 0.0025 14 0.00004 0.00000 -6.46 0.02 0.2618 0.0012 15 0.00000 0.00000 -2.63 3.23 0.0081 0.0020 16 0.00000 0.00000 -0.17 3.61 0.0051 0.0027 The magnetic center is at X = 33.9 +- 0.7 microns Y = 135.7 +- 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 ^ | N S --> x S N Date: 03-07-1995 Time: 15:30:48 Magnet Name: 194 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10149 +- 4.974854E-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 0.00011 0.00000 -165.83 0.24 0.3124 0.0013 2 0.03494 0.00001 44.96 0.00 100.0000 0.0000 3 0.00003 0.00000 22.58 0.53 0.0762 0.0018 4 0.00000 0.00000 -36.26 3.85 0.0080 0.0026 5 0.00001 0.00000 14.71 1.38 0.0214 0.0028 6 0.00008 0.00000 15.14 0.09 0.2206 0.0017 7 0.00000 0.00000 11.74 1.80 0.0072 0.0007 8 0.00000 0.00000 -21.24 0.80 0.0089 0.0009 9 0.00000 0.00000 0.04 0.56 0.0078 0.0011 10 0.00011 0.00000 -9.07 0.04 0.3017 0.0017 11 0.00000 0.00000 -4.64 7.40 0.0018 0.0007 12 0.00000 0.00000 -7.33 2.62 0.0053 0.0015 13 0.00000 0.00000 -0.79 1.08 0.0064 0.0009 14 0.00009 0.00000 -6.41 0.02 0.2585 0.0014 15 0.00000 0.00000 -5.13 0.57 0.0131 0.0026 16 0.00000 0.00000 -1.44 1.64 0.0089 0.0025 The magnetic center is at X = 34.2 +- 0.6 microns Y = 135.3 +- 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: 03-07-1995 Time: 15:36:58 Magnet Name: 194 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06272 +- 8.275476E-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 -170.23 0.13 0.3214 0.0013 2 0.06883 0.00000 44.96 0.00 100.0000 0.0000 3 0.00004 0.00000 23.75 0.45 0.0625 0.0013 4 0.00001 0.00000 -28.72 2.78 0.0085 0.0019 5 0.00001 0.00000 14.06 1.45 0.0181 0.0016 6 0.00015 0.00000 15.26 0.10 0.2210 0.0018 7 0.00001 0.00000 11.69 0.75 0.0082 0.0009 8 0.00000 0.00000 -7.19 9.28 0.0014 0.0009 9 0.00000 0.00000 0.42 1.78 0.0066 0.0015 10 0.00021 0.00000 -9.06 0.03 0.3036 0.0023 11 0.00000 0.00000 -1.66 12.77 0.0035 0.0016 12 0.00000 0.00000 -8.87 2.02 0.0068 0.0023 13 0.00001 0.00000 -1.05 0.91 0.0089 0.0004 14 0.00018 0.00000 -6.44 0.03 0.2559 0.0021 15 0.00001 0.00000 -2.73 1.77 0.0075 0.0028 16 0.00000 0.00000 5.64 7.83 0.0068 0.0017 The magnetic center is at X = 24.4 +- 0.3 microns Y = 141.5 +- 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: 03-07-1995 Time: 15:43:13 Magnet Name: 194 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0543 +- 5.216381E-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 -174.20 0.14 0.3338 0.0015 2 0.13732 0.00003 44.96 0.00 100.0000 0.0000 3 0.00009 0.00000 23.87 0.23 0.0651 0.0011 4 0.00001 0.00000 -29.34 3.45 0.0106 0.0020 5 0.00002 0.00000 14.79 1.04 0.0178 0.0021 6 0.00030 0.00000 15.20 0.11 0.2205 0.0017 7 0.00001 0.00000 13.04 1.33 0.0081 0.0016 8 0.00000 0.00000 -12.35 4.35 0.0023 0.0009 9 0.00001 0.00000 0.02 1.06 0.0061 0.0007 10 0.00042 0.00000 -9.07 0.04 0.3041 0.0018 11 0.00000 0.00000 -7.55 8.60 0.0019 0.0013 12 0.00001 0.00000 -10.62 0.39 0.0076 0.0016 13 0.00001 0.00000 -1.19 0.74 0.0071 0.0013 14 0.00035 0.00000 -6.41 0.01 0.2582 0.0011 15 0.00001 0.00001 -3.88 2.38 0.0100 0.0049 16 0.00001 0.00000 1.62 6.78 0.0043 0.0015 The magnetic center is at X = 15.1 +- 0.4 microns Y = 148.3 +- 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: 03-07-1995 Time: 15:49:27 Magnet Name: 194 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0649 +- 2.219092E-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 -174.21 0.18 0.3326 0.0020 2 0.20547 0.00001 44.93 0.00 100.0000 0.0000 3 0.00013 0.00000 23.52 0.33 0.0635 0.0020 4 0.00002 0.00000 -28.40 4.27 0.0112 0.0019 5 0.00003 0.00000 14.16 1.06 0.0168 0.0012 6 0.00044 0.00000 15.26 0.07 0.2117 0.0009 7 0.00002 0.00000 12.14 2.10 0.0073 0.0014 8 0.00001 0.00000 -18.05 1.45 0.0035 0.0014 9 0.00002 0.00000 0.47 1.55 0.0079 0.0005 10 0.00063 0.00000 -9.10 0.02 0.3051 0.0021 11 0.00000 0.00000 -9.33 5.45 0.0019 0.0013 12 0.00001 0.00000 -11.62 0.56 0.0061 0.0013 13 0.00001 0.00000 -1.15 0.51 0.0069 0.0004 14 0.00053 0.00000 -6.46 0.02 0.2576 0.0020 15 0.00002 0.00001 -3.08 0.96 0.0114 0.0043 16 0.00001 0.00000 3.65 7.50 0.0049 0.0019 The magnetic center is at X = 15.0 +- 0.5 microns Y = 147.8 +- 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 ^ | N S --> x S N Date: 03-07-1995 Time: 15:55:41 Magnet Name: 194 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3072 +- 5.596565E-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 0.00089 0.00000 -173.29 0.27 0.3277 0.0010 2 0.27308 0.00006 44.93 0.00 100.0000 0.0000 3 0.00015 0.00000 23.76 0.56 0.0559 0.0010 4 0.00006 0.00001 -37.61 1.18 0.0216 0.0024 5 0.00004 0.00000 14.61 0.92 0.0159 0.0017 6 0.00056 0.00000 15.20 0.05 0.2050 0.0009 7 0.00002 0.00000 13.00 1.81 0.0077 0.0018 8 0.00002 0.00000 -2.31 1.06 0.0069 0.0007 9 0.00002 0.00001 -0.46 1.49 0.0068 0.0027 10 0.00084 0.00001 -9.09 0.04 0.3077 0.0022 11 0.00001 0.00000 -6.14 3.09 0.0022 0.0014 12 0.00001 0.00001 -8.35 2.50 0.0052 0.0020 13 0.00002 0.00001 0.06 0.78 0.0060 0.0025 14 0.00070 0.00000 -6.50 0.03 0.2573 0.0011 15 0.00003 0.00001 -3.34 2.35 0.0095 0.0038 16 0.00002 0.00001 -5.24 9.30 0.0071 0.0025 The magnetic center is at X = 17.1 +- 0.7 microns Y = 145.4 +- 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 ^ | N S --> x S N Date: 03-07-1995 Time: 16:01:55 Magnet Name: 194 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4053 +- 2.57711E-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 0.00107 0.00000 -171.42 0.09 0.3160 0.0010 2 0.33797 0.00005 44.93 0.00 100.0000 0.0000 3 0.00017 0.00001 25.65 0.39 0.0504 0.0017 4 0.00005 0.00001 -34.72 1.78 0.0160 0.0029 5 0.00005 0.00001 13.20 0.75 0.0144 0.0020 6 0.00061 0.00000 15.34 0.12 0.1801 0.0008 7 0.00002 0.00000 9.97 1.23 0.0062 0.0013 8 0.00003 0.00000 -10.27 18.57 0.0095 0.0009 9 0.00003 0.00000 0.10 1.26 0.0082 0.0009 10 0.00105 0.00001 -9.16 0.06 0.3122 0.0021 11 0.00001 0.00000 -7.73 3.62 0.0035 0.0004 12 0.00002 0.00001 -3.81 2.92 0.0068 0.0031 13 0.00003 0.00000 -1.73 0.38 0.0091 0.0014 14 0.00087 0.00000 -6.48 0.02 0.2563 0.0014 15 0.00002 0.00001 -4.74 2.82 0.0060 0.0028 16 0.00002 0.00001 3.54 3.28 0.0063 0.0021 The magnetic center is at X = 21.1 +- 0.2 microns Y = 139.6 +- 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 ^ | N S --> x S N Date: 03-07-1995 Time: 16:08:09 Magnet Name: 194 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3882 +- 2.211209E-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 0.00120 0.00000 -175.09 0.10 0.3073 0.0012 2 0.38977 0.00008 44.93 0.00 100.0000 0.0000 3 0.00024 0.00001 27.70 0.72 0.0606 0.0019 4 0.00005 0.00001 -30.21 1.97 0.0118 0.0020 5 0.00006 0.00001 13.68 1.52 0.0147 0.0023 6 0.00049 0.00000 15.41 0.22 0.1267 0.0009 7 0.00002 0.00000 10.79 0.70 0.0055 0.0005 8 0.00003 0.00000 -20.49 0.26 0.0071 0.0004 9 0.00002 0.00000 -0.43 1.13 0.0062 0.0003 10 0.00126 0.00001 -9.09 0.04 0.3241 0.0037 11 0.00001 0.00000 -11.44 3.37 0.0028 0.0009 12 0.00002 0.00001 -5.45 2.86 0.0050 0.0015 13 0.00003 0.00001 0.98 1.16 0.0090 0.0023 14 0.00101 0.00001 -6.48 0.07 0.2594 0.0019 15 0.00003 0.00002 -8.52 1.95 0.0071 0.0043 16 0.00001 0.00001 3.63 4.89 0.0036 0.0017 The magnetic center is at X = 11.7 +- 0.2 microns Y = 136.7 +- 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: 03-07-1995 Time: 16:14:24 Magnet Name: 194 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3905 +- 1.602827E-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 0.00126 0.00000 -177.30 0.42 0.2953 0.0006 2 0.42616 0.00008 44.93 0.00 100.0000 0.0000 3 0.00029 0.00001 29.02 0.28 0.0677 0.0027 4 0.00005 0.00001 -31.80 2.52 0.0116 0.0017 5 0.00006 0.00001 11.87 2.04 0.0135 0.0021 6 0.00030 0.00001 15.88 0.19 0.0704 0.0020 7 0.00002 0.00000 8.13 1.68 0.0044 0.0007 8 0.00003 0.00000 -20.78 0.80 0.0067 0.0006 9 0.00004 0.00000 -1.18 1.00 0.0087 0.0009 10 0.00142 0.00001 -9.09 0.05 0.3337 0.0024 11 0.00001 0.00000 -3.00 2.98 0.0019 0.0009 12 0.00005 0.00001 -9.47 1.87 0.0107 0.0020 13 0.00003 0.00001 0.16 0.09 0.0068 0.0015 14 0.00108 0.00000 -6.50 0.02 0.2542 0.0010 15 0.00003 0.00001 -5.92 1.52 0.0069 0.0034 16 0.00002 0.00002 -0.04 2.91 0.0056 0.0038 The magnetic center is at X = 6.2 +- 1.0 microns Y = 131.8 +- 0.3 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 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)