SLAC Magnetic Measurements Date: 04-14-1995 Time: 08:56:42 Magnet Name (Serial #): 149 Bar Code Number: 235 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: 04-14-1995 Time: 09:43:48 Magnet Name: 149 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00025 +- 5.770455E-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 0.00008 0.00000 -25.48 0.13 0.5418 0.0022 2 0.01484 0.00000 -44.97 0.00 100.0000 0.0000 3 0.00002 0.00000 -32.71 0.16 0.1186 0.0010 4 0.00001 0.00000 -23.86 1.17 0.0391 0.0022 5 0.00000 0.00000 -22.14 0.71 0.0236 0.0016 6 0.00003 0.00000 -15.00 0.08 0.2171 0.0020 7 0.00000 0.00000 -18.68 1.70 0.0063 0.0014 8 0.00000 0.00000 1.62 3.03 0.0032 0.0007 9 0.00000 0.00000 -16.95 0.70 0.0116 0.0020 10 0.00004 0.00000 9.00 0.02 0.3025 0.0011 11 0.00000 0.00000 2.29 10.18 0.0014 0.0005 12 0.00000 0.00000 -0.48 1.00 0.0032 0.0009 13 0.00000 0.00000 -12.01 0.79 0.0128 0.0005 14 0.00004 0.00000 6.48 0.03 0.2567 0.0014 15 0.00000 0.00000 5.71 0.40 0.0077 0.0023 16 0.00000 0.00000 -6.05 1.62 0.0078 0.0034 The magnetic center is at X = -104.1 +- 0.7 microns Y = 218.5 +- 1.0 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 ^ | S N --> x N S Date: 04-14-1995 Time: 09:49:54 Magnet Name: 149 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10189 +- 4.100966E-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 -10.33 0.28 0.4760 0.0018 2 0.03488 0.00000 -44.97 0.00 100.0000 0.0000 3 0.00004 0.00000 -38.15 0.27 0.1066 0.0016 4 0.00001 0.00000 -26.85 0.69 0.0346 0.0018 5 0.00001 0.00000 -19.65 1.36 0.0194 0.0026 6 0.00008 0.00000 -14.92 0.04 0.2222 0.0013 7 0.00000 0.00000 -15.10 0.85 0.0075 0.0001 8 0.00000 0.00000 11.54 17.91 0.0044 0.0010 9 0.00000 0.00000 -16.82 0.50 0.0118 0.0016 10 0.00011 0.00000 9.01 0.03 0.3020 0.0029 11 0.00000 0.00000 1.34 11.08 0.0025 0.0012 12 0.00000 0.00000 -0.37 0.84 0.0107 0.0015 13 0.00000 0.00000 -5.90 11.39 0.0141 0.0018 14 0.00009 0.00000 6.46 0.03 0.2575 0.0016 15 0.00000 0.00000 4.47 1.72 0.0079 0.0029 16 0.00000 0.00000 -3.25 2.06 0.0089 0.0041 The magnetic center is at X = -38.1 +- 1.0 microns Y = 209.2 +- 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: 04-14-1995 Time: 09:56:06 Magnet Name: 149 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.0668 +- 7.811146E-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 0.00031 0.00000 -5.61 0.30 0.4526 0.0012 2 0.06871 0.00001 -44.97 0.00 100.0000 0.0000 3 0.00007 0.00000 -38.88 0.22 0.1064 0.0005 4 0.00002 0.00000 -25.60 0.89 0.0316 0.0032 5 0.00001 0.00000 -20.15 1.10 0.0178 0.0019 6 0.00015 0.00000 -14.89 0.04 0.2227 0.0012 7 0.00000 0.00000 -16.22 1.47 0.0065 0.0012 8 0.00000 0.00000 -1.01 3.11 0.0029 0.0017 9 0.00001 0.00000 -16.85 1.30 0.0115 0.0013 10 0.00021 0.00000 8.98 0.01 0.3043 0.0011 11 0.00000 0.00000 3.80 10.08 0.0021 0.0008 12 0.00000 0.00000 0.05 3.58 0.0047 0.0012 13 0.00001 0.00000 -5.99 11.01 0.0130 0.0010 14 0.00017 0.00000 6.49 0.03 0.2518 0.0010 15 0.00001 0.00000 5.80 1.44 0.0105 0.0030 16 0.00001 0.00000 -2.58 7.64 0.0086 0.0011 The magnetic center is at X = -19.7 +- 1.1 microns Y = 201.2 +- 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: 04-14-1995 Time: 10:02:22 Magnet Name: 149 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.064 +- 4.636074E-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 0.00060 0.00000 -2.36 0.14 0.4379 0.0020 2 0.13712 0.00002 -44.97 0.00 100.0000 0.0000 3 0.00015 0.00000 -39.23 0.27 0.1071 0.0024 4 0.00004 0.00000 -26.61 0.56 0.0300 0.0024 5 0.00002 0.00000 -19.13 1.85 0.0170 0.0016 6 0.00031 0.00000 -14.87 0.04 0.2247 0.0014 7 0.00001 0.00000 -16.39 0.70 0.0075 0.0010 8 0.00001 0.00000 -1.39 1.16 0.0042 0.0010 9 0.00002 0.00000 -16.30 0.78 0.0132 0.0022 10 0.00042 0.00000 9.04 0.04 0.3056 0.0023 11 0.00000 0.00000 -2.69 6.91 0.0019 0.0009 12 0.00001 0.00000 -2.52 7.13 0.0044 0.0008 13 0.00002 0.00000 -6.06 10.92 0.0151 0.0017 14 0.00035 0.00000 6.46 0.02 0.2559 0.0014 15 0.00001 0.00001 4.16 1.12 0.0086 0.0043 16 0.00001 0.00000 -1.98 1.27 0.0057 0.0024 The magnetic center is at X = -8.1 +- 0.5 microns Y = 195.4 +- 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: 04-14-1995 Time: 10:08:36 Magnet Name: 149 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0807 +- 7.26437E-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 0.00086 0.00000 0.07 0.34 0.4195 0.0017 2 0.20528 0.00001 -44.99 0.00 100.0000 0.0000 3 0.00022 0.00000 -39.33 0.60 0.1066 0.0006 4 0.00006 0.00000 -25.27 0.85 0.0276 0.0019 5 0.00004 0.00001 -18.29 1.86 0.0171 0.0025 6 0.00044 0.00000 -14.89 0.06 0.2136 0.0009 7 0.00002 0.00000 -16.50 1.20 0.0075 0.0005 8 0.00001 0.00000 -1.55 2.47 0.0031 0.0009 9 0.00002 0.00000 -17.07 1.32 0.0118 0.0008 10 0.00063 0.00000 9.00 0.01 0.3065 0.0004 11 0.00000 0.00000 -0.11 7.20 0.0024 0.0008 12 0.00001 0.00000 -12.25 2.07 0.0035 0.0004 13 0.00003 0.00000 -11.73 1.51 0.0156 0.0009 14 0.00052 0.00000 6.45 0.04 0.2542 0.0010 15 0.00003 0.00001 4.41 0.95 0.0131 0.0055 16 0.00001 0.00000 -3.26 7.07 0.0049 0.0018 The magnetic center is at X = 0.2 +- 1.1 microns Y = 187.4 +- 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: 04-14-1995 Time: 10:14:51 Magnet Name: 149 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3284 +- 6.781584E-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 0.00000 1.14 0.19 0.4098 0.0015 2 0.27288 0.00002 -44.99 0.00 100.0000 0.0000 3 0.00028 0.00001 -38.87 0.17 0.1033 0.0038 4 0.00009 0.00001 -32.27 0.88 0.0344 0.0022 5 0.00004 0.00001 -19.91 2.00 0.0158 0.0027 6 0.00056 0.00000 -14.79 0.04 0.2052 0.0003 7 0.00002 0.00000 -17.36 1.83 0.0071 0.0018 8 0.00003 0.00000 -0.93 0.46 0.0125 0.0007 9 0.00003 0.00000 -16.42 1.20 0.0117 0.0006 10 0.00085 0.00000 9.00 0.01 0.3110 0.0017 11 0.00000 0.00000 -1.48 8.29 0.0018 0.0005 12 0.00001 0.00000 -7.41 3.07 0.0029 0.0011 13 0.00003 0.00001 -6.00 11.38 0.0125 0.0029 14 0.00070 0.00000 6.43 0.01 0.2554 0.0005 15 0.00002 0.00001 4.77 1.07 0.0084 0.0023 16 0.00002 0.00001 -7.45 1.00 0.0075 0.0040 The magnetic center is at X = 3.7 +- 0.6 microns Y = 183.0 +- 0.7 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 ^ | S N --> x N S Date: 04-14-1995 Time: 10:21:07 Magnet Name: 149 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4318 +- 1.336321E-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 0.00132 0.00000 1.88 0.23 0.3918 0.0007 2 0.33777 0.00007 -44.99 0.00 100.0000 0.0000 3 0.00033 0.00001 -37.78 0.20 0.0981 0.0023 4 0.00010 0.00001 -30.47 0.55 0.0304 0.0026 5 0.00005 0.00001 -20.50 2.19 0.0148 0.0034 6 0.00062 0.00001 -14.83 0.08 0.1834 0.0023 7 0.00002 0.00000 -17.16 1.38 0.0069 0.0008 8 0.00001 0.00000 11.87 10.10 0.0015 0.0009 9 0.00004 0.00000 -16.06 0.37 0.0127 0.0013 10 0.00107 0.00000 9.01 0.03 0.3162 0.0006 11 0.00001 0.00000 1.04 7.70 0.0018 0.0007 12 0.00003 0.00001 0.39 1.05 0.0100 0.0015 13 0.00004 0.00001 -6.00 11.16 0.0118 0.0028 14 0.00085 0.00000 6.45 0.03 0.2530 0.0003 15 0.00004 0.00001 5.65 0.88 0.0109 0.0023 16 0.00002 0.00001 -4.08 6.19 0.0069 0.0029 The magnetic center is at X = 5.7 +- 0.7 microns Y = 174.9 +- 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 ^ | S N --> x N S Date: 04-14-1995 Time: 10:27:23 Magnet Name: 149 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4202 +- 9.091473E-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 0.00144 0.00001 2.26 0.19 0.3695 0.0017 2 0.38955 0.00016 -44.99 0.00 100.0000 0.0000 3 0.00036 0.00001 -36.36 0.37 0.0934 0.0028 4 0.00010 0.00001 -28.28 1.61 0.0267 0.0028 5 0.00006 0.00002 -21.62 1.78 0.0157 0.0039 6 0.00050 0.00001 -14.74 0.15 0.1277 0.0020 7 0.00003 0.00001 -18.57 0.70 0.0080 0.0014 8 0.00001 0.00000 14.74 2.75 0.0023 0.0005 9 0.00005 0.00001 -16.68 0.93 0.0133 0.0020 10 0.00127 0.00001 9.00 0.01 0.3265 0.0018 11 0.00001 0.00000 -4.93 5.51 0.0018 0.0008 12 0.00003 0.00000 0.27 1.93 0.0073 0.0011 13 0.00005 0.00001 -12.58 0.49 0.0131 0.0030 14 0.00099 0.00001 6.46 0.03 0.2537 0.0019 15 0.00004 0.00001 4.49 1.05 0.0112 0.0018 16 0.00005 0.00001 -2.79 1.41 0.0122 0.0027 The magnetic center is at X = 6.5 +- 0.6 microns Y = 164.9 +- 0.7 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 ^ | S N --> x N S Date: 04-14-1995 Time: 10:33:38 Magnet Name: 149 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4281 +- 5.412032E-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 0.00148 0.00000 2.36 0.39 0.3479 0.0011 2 0.42598 0.00008 -44.99 0.00 100.0000 0.0000 3 0.00039 0.00001 -34.33 0.40 0.0904 0.0029 4 0.00011 0.00001 -28.86 0.79 0.0258 0.0019 5 0.00007 0.00001 -23.69 1.46 0.0161 0.0025 6 0.00030 0.00001 -14.33 0.20 0.0694 0.0020 7 0.00003 0.00001 -19.53 2.29 0.0077 0.0013 8 0.00002 0.00000 -0.46 6.14 0.0036 0.0011 9 0.00006 0.00000 -16.57 0.89 0.0131 0.0009 10 0.00143 0.00001 9.00 0.01 0.3362 0.0023 11 0.00001 0.00001 1.28 4.80 0.0028 0.0013 12 0.00003 0.00001 0.47 4.01 0.0061 0.0018 13 0.00005 0.00001 -11.99 1.13 0.0126 0.0024 14 0.00107 0.00001 6.44 0.01 0.2513 0.0019 15 0.00004 0.00002 5.76 1.30 0.0088 0.0037 16 0.00004 0.00001 -2.30 1.37 0.0102 0.0035 The magnetic center is at X = 6.4 +- 1.1 microns Y = 155.3 +- 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 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)