SLAC Magnetic Measurements Date: 03-06-1995 Time: 07:44:31 Magnet Name (Serial #): 193 Bar Code Number: 598 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: 03-06-1995 Time: 08:32:00 Magnet Name: 193 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.995765 +- 3.483595E-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 0.00006 0.00000 -134.69 0.66 0.3963 0.0006 2 0.01486 0.00000 44.94 0.00 100.0000 0.0000 3 0.00000 0.00000 -10.54 21.25 0.0060 0.0025 4 0.00000 0.00000 20.15 1.63 0.0192 0.0010 5 0.00000 0.00000 13.59 1.17 0.0172 0.0015 6 0.00003 0.00000 15.12 0.07 0.2190 0.0016 7 0.00000 0.00000 15.51 1.93 0.0051 0.0012 8 0.00000 0.00000 10.52 5.84 0.0023 0.0014 9 0.00000 0.00000 -1.94 0.42 0.0098 0.0006 10 0.00004 0.00000 -9.04 0.04 0.2998 0.0015 11 0.00000 0.00000 -9.49 0.69 0.0026 0.0009 12 0.00000 0.00000 -6.35 7.04 0.0024 0.0007 13 0.00000 0.00000 -0.28 1.15 0.0094 0.0014 14 0.00004 0.00000 -6.51 0.01 0.2572 0.0011 15 0.00000 0.00000 -6.68 3.67 0.0034 0.0014 16 0.00000 0.00000 5.80 1.99 0.0025 0.0011 The magnetic center is at X = 125.8 +- 1.4 microns Y = 124.5 +- 1.5 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: 03-06-1995 Time: 08:38:04 Magnet Name: 193 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.09496 +- 2.311554E-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 0.00012 0.00000 -165.57 0.16 0.3537 0.0024 2 0.03492 0.00000 44.94 0.00 100.0000 0.0000 3 0.00001 0.00000 25.22 1.25 0.0418 0.0019 4 0.00001 0.00000 24.48 0.88 0.0185 0.0009 5 0.00001 0.00000 15.27 0.64 0.0174 0.0025 6 0.00008 0.00000 15.09 0.08 0.2203 0.0014 7 0.00000 0.00000 15.00 1.49 0.0036 0.0003 8 0.00000 0.00000 10.21 18.77 0.0078 0.0018 9 0.00000 0.00000 -2.60 0.52 0.0084 0.0005 10 0.00011 0.00000 -9.06 0.02 0.3012 0.0014 11 0.00000 0.00000 -1.86 9.06 0.0019 0.0003 12 0.00000 0.00000 -1.27 2.49 0.0044 0.0014 13 0.00000 0.00000 -0.68 0.70 0.0139 0.0010 14 0.00009 0.00000 -6.51 0.03 0.2563 0.0032 15 0.00000 0.00000 4.58 3.89 0.0043 0.0020 16 0.00000 0.00000 1.32 1.72 0.0092 0.0024 The magnetic center is at X = 39.4 +- 0.5 microns Y = 153.0 +- 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: 03-06-1995 Time: 08:44:15 Magnet Name: 193 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.05659 +- 2.541072E-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 0.00025 0.00000 -174.50 0.44 0.3641 0.0030 2 0.06876 0.00001 44.94 0.00 100.0000 0.0000 3 0.00003 0.00000 25.48 1.10 0.0463 0.0042 4 0.00001 0.00000 21.93 1.71 0.0168 0.0013 5 0.00001 0.00000 15.54 1.05 0.0184 0.0021 6 0.00015 0.00000 15.11 0.04 0.2212 0.0017 7 0.00000 0.00000 15.09 4.53 0.0026 0.0007 8 0.00000 0.00000 0.27 15.75 0.0020 0.0008 9 0.00001 0.00000 -2.30 0.80 0.0093 0.0016 10 0.00021 0.00000 -9.04 0.02 0.3004 0.0015 11 0.00000 0.00000 -7.54 2.25 0.0020 0.0008 12 0.00000 0.00000 -3.47 9.68 0.0023 0.0012 13 0.00001 0.00000 -2.06 0.33 0.0111 0.0014 14 0.00018 0.00000 -6.48 0.04 0.2559 0.0023 15 0.00000 0.00000 -1.66 1.55 0.0045 0.0019 16 0.00000 0.00000 4.97 5.25 0.0065 0.0025 The magnetic center is at X = 15.6 +- 1.2 microns Y = 161.9 +- 1.4 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: 03-06-1995 Time: 08:50:30 Magnet Name: 193 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0499 +- 1.582184E-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 0.00052 0.00000 -177.86 0.24 0.3761 0.0032 2 0.13720 0.00002 44.94 0.00 100.0000 0.0000 3 0.00006 0.00000 25.60 1.01 0.0434 0.0028 4 0.00002 0.00000 21.64 1.09 0.0162 0.0016 5 0.00003 0.00000 16.40 0.82 0.0185 0.0017 6 0.00030 0.00000 15.09 0.05 0.2216 0.0012 7 0.00000 0.00000 15.92 4.13 0.0020 0.0002 8 0.00000 0.00000 0.59 13.12 0.0017 0.0011 9 0.00001 0.00000 -2.54 0.60 0.0100 0.0007 10 0.00041 0.00000 -9.04 0.02 0.3022 0.0009 11 0.00000 0.00000 -4.89 10.85 0.0020 0.0008 12 0.00001 0.00000 6.76 5.57 0.0042 0.0029 13 0.00002 0.00000 -1.44 0.87 0.0148 0.0015 14 0.00035 0.00000 -6.52 0.02 0.2550 0.0017 15 0.00000 0.00000 2.11 7.71 0.0036 0.0017 16 0.00001 0.00000 -2.31 5.03 0.0044 0.0025 The magnetic center is at X = 6.3 +- 0.7 microns Y = 167.9 +- 1.4 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: 03-06-1995 Time: 08:56:43 Magnet Name: 193 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0607 +- 9.513522E-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 0.00074 0.00001 179.25 0.39 0.3615 0.0051 2 0.20528 0.00006 44.91 0.00 100.0000 0.0000 3 0.00009 0.00000 28.05 0.69 0.0438 0.0021 4 0.00003 0.00000 18.31 1.21 0.0145 0.0012 5 0.00004 0.00001 14.79 1.26 0.0185 0.0025 6 0.00044 0.00000 15.14 0.04 0.2140 0.0017 7 0.00001 0.00000 16.80 3.48 0.0025 0.0008 8 0.00000 0.00000 5.66 9.28 0.0021 0.0011 9 0.00002 0.00000 -2.63 1.54 0.0093 0.0008 10 0.00063 0.00000 -9.09 0.03 0.3054 0.0010 11 0.00001 0.00000 -9.09 2.71 0.0027 0.0008 12 0.00001 0.00000 5.46 11.45 0.0052 0.0017 13 0.00003 0.00000 -2.03 0.48 0.0123 0.0011 14 0.00053 0.00000 -6.51 0.04 0.2570 0.0012 15 0.00001 0.00000 0.53 4.36 0.0057 0.0024 16 0.00002 0.00001 -4.85 8.06 0.0079 0.0030 The magnetic center is at X = -2.1 +- 1.1 microns Y = 161.4 +- 2.3 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: 03-06-1995 Time: 09:02:57 Magnet Name: 193 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.2991 +- 2.323974E-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 0.00097 0.00001 177.74 0.42 0.3552 0.0049 2 0.27285 0.00003 44.91 0.00 100.0000 0.0000 3 0.00012 0.00001 30.63 1.07 0.0446 0.0031 4 0.00005 0.00001 33.34 1.09 0.0193 0.0027 5 0.00005 0.00000 15.77 0.75 0.0193 0.0018 6 0.00056 0.00000 15.09 0.07 0.2054 0.0016 7 0.00001 0.00000 12.19 3.01 0.0020 0.0011 8 0.00002 0.00000 1.75 1.77 0.0065 0.0003 9 0.00002 0.00000 -2.20 1.08 0.0077 0.0005 10 0.00083 0.00000 -9.10 0.01 0.3060 0.0010 11 0.00001 0.00000 -12.22 1.52 0.0025 0.0009 12 0.00001 0.00000 3.74 10.88 0.0027 0.0013 13 0.00004 0.00001 -1.18 0.53 0.0132 0.0025 14 0.00070 0.00001 -6.51 0.03 0.2553 0.0030 15 0.00001 0.00001 -1.10 5.75 0.0044 0.0021 16 0.00002 0.00001 -0.56 9.98 0.0076 0.0027 The magnetic center is at X = -6.2 +- 1.2 microns Y = 158.5 +- 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: 03-06-1995 Time: 09:09:12 Magnet Name: 193 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.3946 +- 7.350794E-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 0.00118 0.00001 176.56 0.20 0.3493 0.0034 2 0.33774 0.00008 44.91 0.00 100.0000 0.0000 3 0.00016 0.00001 31.18 1.14 0.0479 0.0023 4 0.00005 0.00001 29.70 0.83 0.0135 0.0017 5 0.00006 0.00000 14.43 1.82 0.0175 0.0008 6 0.00061 0.00001 15.16 0.09 0.1818 0.0028 7 0.00000 0.00000 6.37 4.40 0.0011 0.0002 8 0.00003 0.00000 10.39 18.61 0.0102 0.0014 9 0.00003 0.00000 -3.00 0.49 0.0088 0.0006 10 0.00104 0.00001 -9.09 0.04 0.3084 0.0020 11 0.00001 0.00000 -9.05 2.97 0.0023 0.0007 12 0.00002 0.00000 0.58 2.19 0.0053 0.0011 13 0.00005 0.00001 -1.39 0.64 0.0151 0.0021 14 0.00085 0.00001 -6.52 0.03 0.2527 0.0016 15 0.00001 0.00001 -2.25 8.32 0.0044 0.0018 16 0.00001 0.00000 4.59 6.60 0.0027 0.0014 The magnetic center is at X = -9.4 +- 0.5 microns Y = 155.7 +- 1.5 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: 03-06-1995 Time: 09:15:26 Magnet Name: 193 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3813 +- 5.86819E-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 0.00138 0.00002 174.84 0.26 0.3532 0.0041 2 0.38984 0.00006 44.91 0.00 100.0000 0.0000 3 0.00021 0.00001 30.84 1.11 0.0530 0.0021 4 0.00005 0.00001 20.59 2.23 0.0118 0.0015 5 0.00007 0.00001 13.92 0.72 0.0191 0.0015 6 0.00050 0.00001 15.30 0.07 0.1294 0.0017 7 0.00001 0.00000 -0.97 15.51 0.0016 0.0005 8 0.00003 0.00000 20.63 1.19 0.0065 0.0009 9 0.00004 0.00000 -2.56 1.23 0.0095 0.0010 10 0.00125 0.00000 -9.07 0.04 0.3210 0.0008 11 0.00001 0.00000 -3.59 11.06 0.0024 0.0006 12 0.00001 0.00001 2.31 4.26 0.0035 0.0019 13 0.00005 0.00000 -1.74 0.65 0.0125 0.0011 14 0.00100 0.00001 -6.55 0.03 0.2561 0.0026 15 0.00002 0.00001 2.73 5.84 0.0051 0.0014 16 0.00003 0.00001 1.54 1.61 0.0066 0.0026 The magnetic center is at X = -14.2 +- 0.7 microns Y = 157.1 +- 1.8 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: 03-06-1995 Time: 09:21:41 Magnet Name: 193 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3841 +- 9.789438E-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 0.00152 0.00002 173.95 0.50 0.3554 0.0045 2 0.42648 0.00008 44.91 0.00 100.0000 0.0000 3 0.00024 0.00001 30.84 1.30 0.0558 0.0025 4 0.00005 0.00000 20.52 0.94 0.0116 0.0005 5 0.00008 0.00001 14.61 1.53 0.0181 0.0027 6 0.00031 0.00000 15.62 0.33 0.0721 0.0005 7 0.00001 0.00000 -16.12 1.30 0.0028 0.0006 8 0.00003 0.00000 19.60 0.44 0.0072 0.0009 9 0.00004 0.00001 -3.16 0.60 0.0087 0.0016 10 0.00141 0.00001 -9.07 0.01 0.3316 0.0020 11 0.00001 0.00000 -11.79 3.37 0.0030 0.0009 12 0.00002 0.00001 -4.61 9.97 0.0037 0.0018 13 0.00004 0.00001 -1.21 1.21 0.0087 0.0015 14 0.00108 0.00001 -6.56 0.03 0.2537 0.0027 15 0.00002 0.00001 -4.32 3.40 0.0047 0.0022 16 0.00001 0.00001 -0.47 2.25 0.0033 0.0014 The magnetic center is at X = -16.7 +- 1.4 microns Y = 157.9 +- 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 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)