SLAC Magnetic Measurements Date: 03-30-1995 Time: 09:55:50 Magnet Name (Serial #): 176 Bar Code Number: 221 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl 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: 03-30-1995 Time: 10:42:56 Magnet Name: 176 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.999395 +- 2.932068E-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 -126.15 0.76 0.3116 0.0040 2 0.01493 0.00000 45.02 0.00 100.0000 0.0000 3 0.00000 0.00000 -47.80 4.23 0.0197 0.0039 4 0.00000 0.00000 20.91 0.78 0.0278 0.0018 5 0.00000 0.00000 9.92 2.56 0.0118 0.0019 6 0.00003 0.00000 15.23 0.06 0.2173 0.0021 7 0.00000 0.00000 12.41 1.00 0.0108 0.0014 8 0.00000 0.00000 13.13 4.85 0.0023 0.0010 9 0.00000 0.00000 1.62 2.58 0.0072 0.0026 10 0.00004 0.00000 -9.02 0.03 0.2964 0.0009 11 0.00000 0.00000 12.43 1.30 0.0023 0.0009 12 0.00000 0.00000 3.21 4.82 0.0038 0.0015 13 0.00000 0.00000 -1.10 3.22 0.0087 0.0011 14 0.00004 0.00000 -6.36 0.06 0.2577 0.0031 15 0.00000 0.00000 -2.79 1.60 0.0083 0.0032 16 0.00000 0.00000 7.01 1.61 0.0082 0.0016 The magnetic center is at X = 112.4 +- 1.8 microns Y = 82.1 +- 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: 03-30-1995 Time: 10:49:03 Magnet Name: 176 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.0996 +- 5.075859E-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 -176.67 0.78 0.3008 0.0025 2 0.03496 0.00001 45.02 0.00 100.0000 0.0000 3 0.00002 0.00000 26.36 0.85 0.0693 0.0058 4 0.00001 0.00000 25.20 1.45 0.0231 0.0021 5 0.00000 0.00000 14.69 2.02 0.0139 0.0018 6 0.00008 0.00000 15.22 0.08 0.2241 0.0014 7 0.00000 0.00000 13.84 2.55 0.0034 0.0007 8 0.00000 0.00000 11.09 19.05 0.0065 0.0015 9 0.00000 0.00000 -2.75 2.69 0.0101 0.0017 10 0.00010 0.00000 -9.01 0.03 0.2954 0.0015 11 0.00000 0.00000 -3.82 9.79 0.0018 0.0007 12 0.00000 0.00000 0.97 2.59 0.0076 0.0041 13 0.00001 0.00000 -0.90 0.43 0.0161 0.0022 14 0.00009 0.00000 -6.38 0.03 0.2556 0.0053 15 0.00000 0.00000 -8.14 2.58 0.0053 0.0037 16 0.00000 0.00000 0.99 7.54 0.0073 0.0023 The magnetic center is at X = 7.8 +- 1.8 microns Y = 134.1 +- 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: 03-30-1995 Time: 10:55:15 Magnet Name: 176 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06283 +- 3.942679E-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 0.00023 0.00000 171.34 0.82 0.3318 0.0058 2 0.06878 0.00000 45.02 0.00 100.0000 0.0000 3 0.00006 0.00000 27.21 0.97 0.0901 0.0035 4 0.00001 0.00000 21.35 1.60 0.0215 0.0019 5 0.00001 0.00000 15.86 1.34 0.0164 0.0018 6 0.00015 0.00000 15.22 0.10 0.2234 0.0018 7 0.00000 0.00000 15.06 3.18 0.0044 0.0011 8 0.00000 0.00000 7.17 3.60 0.0024 0.0011 9 0.00000 0.00000 0.49 2.87 0.0071 0.0009 10 0.00020 0.00000 -8.98 0.03 0.2969 0.0010 11 0.00000 0.00000 2.38 9.33 0.0035 0.0017 12 0.00000 0.00000 5.55 2.01 0.0049 0.0035 13 0.00001 0.00000 2.47 2.90 0.0118 0.0047 14 0.00018 0.00000 -6.33 0.02 0.2568 0.0033 15 0.00001 0.00000 -3.18 6.07 0.0100 0.0044 16 0.00000 0.00000 -5.42 6.43 0.0046 0.0009 The magnetic center is at X = -22.3 +- 2.1 microns Y = 146.5 +- 2.6 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: 03-30-1995 Time: 11:01:31 Magnet Name: 176 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0588 +- 8.820039E-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 0.00048 0.00001 167.47 0.61 0.3485 0.0041 2 0.13716 0.00003 45.02 0.00 100.0000 0.0000 3 0.00013 0.00001 27.16 0.55 0.0953 0.0064 4 0.00003 0.00000 20.42 1.47 0.0202 0.0013 5 0.00002 0.00000 15.98 2.13 0.0149 0.0012 6 0.00031 0.00000 15.22 0.07 0.2239 0.0019 7 0.00000 0.00000 13.60 6.04 0.0023 0.0008 8 0.00000 0.00000 4.36 3.62 0.0032 0.0008 9 0.00001 0.00000 -2.19 1.63 0.0094 0.0023 10 0.00041 0.00000 -8.97 0.03 0.3004 0.0014 11 0.00000 0.00000 0.67 9.95 0.0020 0.0004 12 0.00000 0.00000 4.58 2.65 0.0029 0.0008 13 0.00002 0.00000 0.23 1.40 0.0119 0.0036 14 0.00035 0.00000 -6.36 0.05 0.2572 0.0022 15 0.00001 0.00000 -3.12 2.41 0.0064 0.0026 16 0.00001 0.00000 -0.29 6.84 0.0069 0.0015 The magnetic center is at X = -33.8 +- 1.7 microns Y = 151.9 +- 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: 03-30-1995 Time: 11:07:46 Magnet Name: 176 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.073 +- 3.809353E-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 0.00001 167.89 0.80 0.3483 0.0063 2 0.20529 0.00003 45.00 0.00 100.0000 0.0000 3 0.00019 0.00001 26.64 1.05 0.0927 0.0027 4 0.00003 0.00000 18.58 0.55 0.0169 0.0016 5 0.00003 0.00000 16.87 1.44 0.0146 0.0018 6 0.00044 0.00000 15.15 0.09 0.2155 0.0023 7 0.00001 0.00000 11.41 16.99 0.0026 0.0016 8 0.00000 0.00000 3.65 3.89 0.0023 0.0005 9 0.00002 0.00001 -0.58 1.79 0.0074 0.0028 10 0.00062 0.00001 -9.04 0.01 0.3024 0.0026 11 0.00000 0.00000 -6.05 3.61 0.0018 0.0012 12 0.00002 0.00000 5.52 11.23 0.0077 0.0020 13 0.00002 0.00000 0.42 1.79 0.0088 0.0024 14 0.00052 0.00001 -6.36 0.04 0.2534 0.0049 15 0.00002 0.00001 -3.54 1.32 0.0078 0.0027 16 0.00002 0.00001 5.53 6.28 0.0085 0.0055 The magnetic center is at X = -32.6 +- 2.2 microns Y = 152.1 +- 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 Date: 03-30-1995 Time: 11:14:02 Magnet Name: 176 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3179 +- 1.663943E-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 0.00094 0.00002 167.13 0.62 0.3435 0.0063 2 0.27283 0.00007 45.00 0.00 100.0000 0.0000 3 0.00025 0.00001 27.34 0.97 0.0922 0.0036 4 0.00005 0.00001 31.87 1.51 0.0189 0.0020 5 0.00004 0.00001 17.70 1.75 0.0147 0.0019 6 0.00056 0.00000 15.22 0.08 0.2069 0.0017 7 0.00001 0.00001 -0.30 19.24 0.0029 0.0020 8 0.00003 0.00000 0.64 0.34 0.0102 0.0007 9 0.00002 0.00000 -0.69 2.26 0.0077 0.0007 10 0.00083 0.00000 -8.99 0.02 0.3057 0.0013 11 0.00001 0.00000 8.15 6.61 0.0027 0.0010 12 0.00001 0.00000 0.82 3.43 0.0051 0.0015 13 0.00004 0.00001 -0.41 0.94 0.0130 0.0039 14 0.00070 0.00001 -6.42 0.05 0.2567 0.0039 15 0.00001 0.00001 -7.60 1.54 0.0046 0.0020 16 0.00002 0.00001 2.29 7.44 0.0088 0.0022 The magnetic center is at X = -34.2 +- 1.7 microns Y = 149.6 +- 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: 03-30-1995 Time: 11:20:19 Magnet Name: 176 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4178 +- 1.185064E-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 0.00001 165.60 0.42 0.3326 0.0037 2 0.33766 0.00004 45.00 0.00 100.0000 0.0000 3 0.00032 0.00000 28.07 0.96 0.0956 0.0010 4 0.00004 0.00001 27.84 1.48 0.0129 0.0024 5 0.00005 0.00001 16.66 1.12 0.0144 0.0027 6 0.00062 0.00000 15.24 0.09 0.1830 0.0013 7 0.00001 0.00000 -0.78 15.18 0.0018 0.0012 8 0.00001 0.00000 -0.24 18.68 0.0025 0.0011 9 0.00003 0.00001 -1.04 1.45 0.0079 0.0017 10 0.00104 0.00000 -8.99 0.03 0.3092 0.0009 11 0.00001 0.00000 -5.23 7.22 0.0024 0.0009 12 0.00002 0.00000 -0.04 2.13 0.0073 0.0015 13 0.00004 0.00002 -0.18 1.81 0.0105 0.0048 14 0.00086 0.00001 -6.35 0.04 0.2539 0.0023 15 0.00003 0.00001 -3.60 3.27 0.0083 0.0024 16 0.00003 0.00001 7.90 2.97 0.0081 0.0042 The magnetic center is at X = -36.9 +- 1.1 microns Y = 143.9 +- 1.6 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: 03-30-1995 Time: 11:26:34 Magnet Name: 176 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4048 +- 7.321039E-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 0.00133 0.00001 170.51 0.40 0.3404 0.0037 2 0.38991 0.00005 45.00 0.00 100.0000 0.0000 3 0.00031 0.00001 26.06 1.06 0.0806 0.0029 4 0.00004 0.00001 25.45 4.25 0.0095 0.0023 5 0.00004 0.00001 17.43 1.14 0.0113 0.0028 6 0.00051 0.00001 15.36 0.11 0.1311 0.0024 7 0.00001 0.00000 -2.61 18.34 0.0028 0.0003 8 0.00002 0.00001 1.15 20.71 0.0041 0.0017 9 0.00003 0.00000 -1.21 0.58 0.0075 0.0003 10 0.00125 0.00000 -9.03 0.02 0.3196 0.0003 11 0.00001 0.00000 -5.00 7.51 0.0022 0.0002 12 0.00002 0.00001 -0.12 4.30 0.0056 0.0032 13 0.00004 0.00001 0.50 2.38 0.0097 0.0020 14 0.00099 0.00002 -6.39 0.02 0.2539 0.0058 15 0.00003 0.00001 -5.13 2.89 0.0073 0.0033 16 0.00003 0.00002 4.53 3.10 0.0088 0.0048 The magnetic center is at X = -25.1 +- 1.1 microns Y = 150.0 +- 1.6 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: 03-30-1995 Time: 11:32:50 Magnet Name: 176 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4111 +- 1.084448E-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 0.00152 0.00002 173.17 0.73 0.3557 0.0049 2 0.42663 0.00006 45.00 0.00 100.0000 0.0000 3 0.00032 0.00002 22.66 0.74 0.0758 0.0058 4 0.00003 0.00001 22.86 3.67 0.0075 0.0026 5 0.00005 0.00001 18.30 2.43 0.0114 0.0016 6 0.00031 0.00001 15.62 0.09 0.0735 0.0020 7 0.00002 0.00000 5.60 18.10 0.0037 0.0011 8 0.00001 0.00001 -7.61 15.05 0.0020 0.0012 9 0.00003 0.00000 -0.59 1.09 0.0077 0.0011 10 0.00141 0.00000 -9.02 0.02 0.3301 0.0003 11 0.00001 0.00000 4.57 4.81 0.0017 0.0003 12 0.00001 0.00000 2.04 9.18 0.0015 0.0011 13 0.00006 0.00001 0.28 1.00 0.0135 0.0015 14 0.00107 0.00000 -6.35 0.03 0.2501 0.0008 15 0.00002 0.00001 -4.49 6.29 0.0046 0.0024 16 0.00004 0.00001 3.56 2.13 0.0082 0.0030 The magnetic center is at X = -18.9 +- 2.0 microns Y = 157.8 +- 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 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)