SLAC Magnetic Measurements Date: 03-10-1995 Time: 10:35:08 Magnet Name (Serial #): 190 Bar Code Number: 590 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: 03-10-1995 Time: 11:25:31 Magnet Name: 190 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00137 +- 3.536518E-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 0.00003 0.00000 134.54 2.00 0.2042 0.0027 2 0.01483 0.00000 44.96 0.00 100.0000 0.0000 3 0.00001 0.00000 24.55 0.73 0.0711 0.0019 4 0.00000 0.00000 -26.33 1.27 0.0133 0.0035 5 0.00000 0.00000 16.71 3.49 0.0226 0.0042 6 0.00003 0.00000 15.09 0.10 0.2213 0.0017 7 0.00000 0.00000 12.37 17.55 0.0039 0.0011 8 0.00000 0.00000 -8.82 4.63 0.0051 0.0017 9 0.00000 0.00000 -5.26 1.33 0.0080 0.0008 10 0.00004 0.00000 -9.05 0.04 0.3013 0.0011 11 0.00000 0.00000 -11.64 3.05 0.0031 0.0017 12 0.00000 0.00000 6.86 3.72 0.0056 0.0026 13 0.00000 0.00000 -2.84 0.90 0.0081 0.0019 14 0.00004 0.00000 -6.50 0.08 0.2482 0.0057 15 0.00000 0.00000 -2.27 8.01 0.0067 0.0021 16 0.00000 0.00000 -0.50 5.59 0.0051 0.0017 The magnetic center is at X = -65.0 +- 2.4 microns Y = 64.0 +- 2.4 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: 03-10-1995 Time: 11:31:40 Magnet Name: 190 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10285 +- 4.43765E-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 130.51 0.68 0.2425 0.0018 2 0.03492 0.00001 44.96 0.00 100.0000 0.0000 3 0.00002 0.00000 34.80 0.40 0.0688 0.0018 4 0.00001 0.00000 -35.18 1.22 0.0249 0.0024 5 0.00001 0.00000 16.43 0.71 0.0208 0.0021 6 0.00008 0.00000 15.10 0.07 0.2220 0.0021 7 0.00000 0.00000 15.45 6.34 0.0025 0.0014 8 0.00000 0.00000 -4.06 2.97 0.0045 0.0017 9 0.00000 0.00000 -6.84 0.38 0.0099 0.0014 10 0.00010 0.00000 -9.05 0.01 0.3005 0.0009 11 0.00000 0.00000 -9.46 0.94 0.0031 0.0012 12 0.00000 0.00000 1.04 1.10 0.0063 0.0034 13 0.00000 0.00000 -2.84 1.03 0.0096 0.0016 14 0.00009 0.00000 -6.47 0.07 0.2485 0.0033 15 0.00000 0.00000 -0.11 4.92 0.0051 0.0021 16 0.00000 0.00000 2.09 8.98 0.0053 0.0016 The magnetic center is at X = -82.4 +- 1.0 microns Y = 70.4 +- 1.1 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: 03-10-1995 Time: 11:37:55 Magnet Name: 190 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06458 +- 3.675298E-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 0.00018 0.00000 131.57 0.32 0.2678 0.0022 2 0.06878 0.00003 44.96 0.00 100.0000 0.0000 3 0.00005 0.00000 35.44 0.13 0.0701 0.0006 4 0.00001 0.00000 -28.37 2.47 0.0194 0.0026 5 0.00001 0.00000 17.50 0.52 0.0192 0.0017 6 0.00015 0.00000 15.03 0.08 0.2235 0.0020 7 0.00000 0.00000 16.07 4.85 0.0033 0.0020 8 0.00000 0.00000 -4.31 3.40 0.0022 0.0013 9 0.00001 0.00000 -6.36 1.30 0.0089 0.0012 10 0.00021 0.00000 -9.03 0.02 0.2997 0.0013 11 0.00000 0.00000 -10.85 3.57 0.0034 0.0011 12 0.00000 0.00000 3.30 1.23 0.0061 0.0016 13 0.00001 0.00000 -3.99 0.60 0.0090 0.0009 14 0.00017 0.00000 -6.46 0.10 0.2491 0.0033 15 0.00000 0.00000 -1.43 4.84 0.0036 0.0021 16 0.00000 0.00000 -0.17 6.20 0.0039 0.0011 The magnetic center is at X = -89.5 +- 0.9 microns Y = 79.4 +- 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 ^ | N S --> x S N Date: 03-10-1995 Time: 11:44:15 Magnet Name: 190 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0565 +- 4.993758E-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 131.77 0.26 0.2777 0.0010 2 0.13726 0.00003 44.95 0.00 100.0000 0.0000 3 0.00010 0.00000 36.17 0.52 0.0705 0.0012 4 0.00003 0.00000 -27.86 2.58 0.0204 0.0015 5 0.00003 0.00000 16.71 0.68 0.0213 0.0014 6 0.00031 0.00000 15.13 0.05 0.2247 0.0005 7 0.00000 0.00000 14.10 6.24 0.0016 0.0007 8 0.00000 0.00000 -14.67 3.14 0.0025 0.0013 9 0.00001 0.00000 -7.67 0.43 0.0085 0.0009 10 0.00042 0.00000 -9.06 0.01 0.3025 0.0012 11 0.00000 0.00000 -11.91 3.84 0.0030 0.0016 12 0.00000 0.00000 3.18 4.98 0.0036 0.0018 13 0.00002 0.00000 -3.48 0.59 0.0124 0.0034 14 0.00034 0.00000 -6.42 0.06 0.2505 0.0029 15 0.00001 0.00000 -3.71 1.99 0.0048 0.0031 16 0.00001 0.00000 -3.23 5.61 0.0043 0.0002 The magnetic center is at X = -92.5 +- 0.5 microns Y = 82.6 +- 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: 03-10-1995 Time: 11:50:33 Magnet Name: 190 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0691 +- 1.954346E-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 0.00055 0.00000 131.72 0.13 0.2700 0.0008 2 0.20550 0.00006 44.93 0.00 100.0000 0.0000 3 0.00015 0.00001 36.93 0.99 0.0707 0.0038 4 0.00005 0.00000 -26.57 1.97 0.0225 0.0024 5 0.00004 0.00000 16.18 1.66 0.0217 0.0019 6 0.00045 0.00000 15.08 0.12 0.2180 0.0008 7 0.00000 0.00000 10.24 9.49 0.0022 0.0005 8 0.00001 0.00000 -7.86 6.80 0.0031 0.0007 9 0.00002 0.00000 -6.16 1.11 0.0084 0.0011 10 0.00062 0.00000 -9.04 0.04 0.3021 0.0023 11 0.00001 0.00000 -2.41 10.29 0.0031 0.0009 12 0.00001 0.00001 2.59 10.16 0.0056 0.0027 13 0.00002 0.00000 -3.62 0.86 0.0104 0.0006 14 0.00052 0.00001 -6.49 0.11 0.2545 0.0026 15 0.00001 0.00000 3.45 2.14 0.0055 0.0009 16 0.00002 0.00001 -0.18 0.64 0.0083 0.0025 The magnetic center is at X = -90.0 +- 0.3 microns Y = 80.3 +- 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 Date: 03-10-1995 Time: 11:56:51 Magnet Name: 190 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3115 +- 5.73982E-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 0.00072 0.00000 131.18 0.28 0.2645 0.0007 2 0.27323 0.00003 44.93 0.00 100.0000 0.0000 3 0.00019 0.00000 38.66 0.46 0.0704 0.0017 4 0.00006 0.00000 -26.25 1.51 0.0232 0.0008 5 0.00005 0.00000 16.58 0.84 0.0196 0.0016 6 0.00057 0.00000 15.11 0.07 0.2079 0.0008 7 0.00001 0.00000 6.41 5.85 0.0022 0.0008 8 0.00001 0.00000 -5.34 2.57 0.0050 0.0014 9 0.00002 0.00000 -7.48 0.69 0.0085 0.0005 10 0.00084 0.00000 -9.06 0.01 0.3066 0.0014 11 0.00001 0.00000 -6.80 4.24 0.0037 0.0007 12 0.00001 0.00000 0.59 9.88 0.0038 0.0008 13 0.00002 0.00001 -2.81 1.17 0.0090 0.0022 14 0.00070 0.00001 -6.47 0.08 0.2546 0.0019 15 0.00001 0.00001 1.49 6.71 0.0052 0.0035 16 0.00001 0.00001 4.29 5.59 0.0049 0.0028 The magnetic center is at X = -88.9 +- 0.4 microns Y = 77.8 +- 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: 03-10-1995 Time: 12:03:12 Magnet Name: 190 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4106 +- 3.543359E-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 0.00085 0.00000 130.37 0.06 0.2510 0.0012 2 0.33835 0.00011 44.93 0.00 100.0000 0.0000 3 0.00024 0.00001 40.19 0.37 0.0704 0.0023 4 0.00011 0.00001 -31.98 1.00 0.0316 0.0021 5 0.00007 0.00000 15.65 1.08 0.0196 0.0011 6 0.00061 0.00001 15.11 0.06 0.1811 0.0016 7 0.00001 0.00000 9.14 8.52 0.0020 0.0009 8 0.00002 0.00000 -5.56 1.49 0.0056 0.0004 9 0.00003 0.00000 -6.67 1.05 0.0088 0.0010 10 0.00105 0.00000 -9.07 0.02 0.3116 0.0009 11 0.00001 0.00000 -10.58 1.80 0.0032 0.0006 12 0.00002 0.00001 1.45 1.53 0.0060 0.0017 13 0.00004 0.00001 -2.62 0.96 0.0104 0.0015 14 0.00085 0.00001 -6.49 0.05 0.2502 0.0019 15 0.00002 0.00001 -1.10 3.15 0.0053 0.0021 16 0.00002 0.00001 7.66 2.91 0.0069 0.0030 The magnetic center is at X = -85.4 +- 0.5 microns Y = 72.6 +- 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: 03-10-1995 Time: 12:09:32 Magnet Name: 190 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3941 +- 6.722531E-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 0.00091 0.00000 130.82 0.30 0.2340 0.0011 2 0.39036 0.00007 44.93 0.00 100.0000 0.0000 3 0.00027 0.00001 42.02 0.28 0.0684 0.0014 4 0.00011 0.00001 -29.29 0.95 0.0289 0.0024 5 0.00008 0.00000 15.43 0.99 0.0199 0.0012 6 0.00054 0.00001 15.19 0.12 0.1373 0.0018 7 0.00001 0.00000 4.65 8.69 0.0027 0.0011 8 0.00002 0.00000 -19.33 1.84 0.0064 0.0012 9 0.00003 0.00001 -6.19 0.45 0.0089 0.0014 10 0.00125 0.00000 -9.07 0.01 0.3197 0.0007 11 0.00001 0.00000 -1.38 10.27 0.0038 0.0007 12 0.00003 0.00000 0.78 1.76 0.0079 0.0010 13 0.00003 0.00000 -3.75 1.70 0.0089 0.0006 14 0.00098 0.00001 -6.52 0.06 0.2504 0.0017 15 0.00001 0.00001 2.86 6.32 0.0035 0.0020 16 0.00002 0.00001 7.85 3.03 0.0043 0.0034 The magnetic center is at X = -79.1 +- 0.5 microns Y = 68.3 +- 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 ^ | N S --> x S N Date: 03-10-1995 Time: 12:15:53 Magnet Name: 190 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.397 +- 6.696505E-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 0.00094 0.00000 129.31 0.62 0.2196 0.0012 2 0.42659 0.00014 44.93 0.00 100.0000 0.0000 3 0.00028 0.00000 43.97 0.70 0.0659 0.0006 4 0.00013 0.00001 -28.60 0.91 0.0308 0.0019 5 0.00008 0.00001 14.35 1.18 0.0182 0.0021 6 0.00034 0.00001 15.38 0.23 0.0803 0.0016 7 0.00001 0.00000 4.13 4.90 0.0030 0.0006 8 0.00003 0.00000 -18.98 1.22 0.0076 0.0007 9 0.00004 0.00000 -6.81 0.75 0.0102 0.0008 10 0.00142 0.00000 -9.06 0.02 0.3320 0.0009 11 0.00001 0.00001 -10.09 1.13 0.0025 0.0012 12 0.00002 0.00001 0.54 0.88 0.0048 0.0024 13 0.00004 0.00001 -2.99 0.44 0.0095 0.0013 14 0.00106 0.00001 -6.51 0.07 0.2485 0.0018 15 0.00002 0.00001 3.19 3.29 0.0049 0.0022 16 0.00004 0.00001 1.66 1.31 0.0088 0.0012 The magnetic center is at X = -75.9 +- 0.8 microns Y = 62.1 +- 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 ^ | 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)