SLAC Magnetic Measurements Date: 01-30-1995 Time: 13:24:47 Magnet Name: 2Q4-3 Project: PEP II Injection Line Test Stand: Rotating Coil Stand 2 Measurement Coil: DC100 Operator: Wendy Sibbring Run Number: 2 Comment: Standard Run Double Standardization Standardization Currents (A): 45.0 2.0 45.0 2.0 45.0 2.0 Test Currents (A): 3.0 9.0 15.0 21.0 24.0 27.0 30.0 33.0 36.0 40.0 45.0 40.0 30.0 20.0 10.0 HARMONICS MEASUREMENTS Date: 01-30-1995 Time: 14:01:23 Magnet Name: 2Q4-3 Project: PEP II Injection Line Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 23.99842 +- 4.21455E-05 A Coil Radius, Rcoil = .0189973 m Coil # Turns, Nturns = 30 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Gm) (Gm) (deg) (deg) (%) (%) --- -------+------- -------+------- -------+------- 1 0.046 0.002 44.35 2.55 0.068 0.004 2 68.499 0.016 -41.77 0.01 100.000 0.000 3 0.131 0.006 -7.44 0.92 0.191 0.009 4 0.065 0.009 -17.60 2.92 0.094 0.013 5 0.039 0.007 -19.39 1.78 0.056 0.010 6 0.258 0.042 12.41 24.51 0.377 0.062 7 0.065 0.016 -10.81 2.39 0.095 0.024 8 0.343 0.104 -10.75 18.67 0.501 0.152 9 0.032 0.005 13.51 1.08 0.047 0.008 10 0.105 0.006 10.44 0.24 0.153 0.008 11 0.006 0.004 4.53 5.59 0.008 0.005 12 0.008 0.003 -0.00 2.84 0.012 0.004 13 0.003 0.001 0.22 11.29 0.005 0.002 14 0.019 0.001 8.96 0.65 0.028 0.001 15 0.006 0.003 -1.41 7.03 0.009 0.004 16 0.007 0.002 5.81 0.50 0.010 0.003 The magnetic center is at X = 9.0 +- 0.6 microns Y = 9.2 +- 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: 01-30-1995 Time: 14:15:24 Magnet Name: 2Q4-3 Project: PEP II Injection Line Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 29.99735 +- 3.439844E-05 A Coil Radius, Rcoil = .0189973 m Coil # Turns, Nturns = 30 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Gm) (Gm) (deg) (deg) (%) (%) --- -------+------- -------+------- -------+------- 1 0.072 0.002 89.56 0.42 0.084 0.002 2 85.523 0.021 -41.76 0.01 100.000 0.000 3 0.173 0.005 -6.74 0.49 0.202 0.006 4 0.080 0.020 -16.47 1.44 0.093 0.023 5 0.042 0.008 -18.10 4.19 0.049 0.009 6 0.281 0.014 26.53 1.30 0.329 0.017 7 0.060 0.013 -9.76 1.99 0.070 0.015 8 0.337 0.048 -10.80 18.98 0.394 0.056 9 0.034 0.010 13.19 1.00 0.040 0.012 10 0.133 0.003 10.60 0.16 0.156 0.003 11 0.006 0.003 5.15 10.73 0.007 0.004 12 0.013 0.002 0.80 1.28 0.015 0.002 13 0.003 0.002 0.29 12.38 0.004 0.002 14 0.019 0.001 8.72 0.30 0.022 0.001 15 0.004 0.001 -3.50 7.12 0.005 0.001 16 0.008 0.002 4.85 0.65 0.009 0.002 The magnetic center is at X = 15.9 +- 0.4 microns Y = 0.1 +- 0.1 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 ^ | S N --> x N S Date: 01-30-1995 Time: 14:29:23 Magnet Name: 2Q4-3 Project: PEP II Injection Line Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 35.9966 +- 3.506618E-05 A Coil Radius, Rcoil = .0189973 m Coil # Turns, Nturns = 30 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Gm) (Gm) (deg) (deg) (%) (%) --- -------+------- -------+------- -------+------- 1 0.117 0.002 105.47 1.30 0.114 0.002 2 102.557 0.037 -41.76 0.00 100.000 0.000 3 0.212 0.007 -6.26 0.18 0.207 0.007 4 0.089 0.018 -16.07 0.90 0.087 0.017 5 0.062 0.011 -18.60 1.12 0.060 0.011 6 0.349 0.016 28.15 0.78 0.341 0.016 7 0.099 0.020 -9.38 1.21 0.097 0.019 8 0.464 0.040 -21.21 0.55 0.453 0.039 9 0.047 0.018 13.56 1.17 0.046 0.017 10 0.160 0.002 10.60 0.13 0.156 0.002 11 0.007 0.003 5.74 12.71 0.007 0.003 12 0.016 0.003 2.85 0.68 0.016 0.003 13 0.003 0.001 5.16 10.72 0.003 0.001 14 0.025 0.003 8.51 0.24 0.024 0.003 15 0.005 0.001 -7.87 2.87 0.005 0.001 16 0.011 0.001 4.80 1.12 0.011 0.001 The magnetic center is at X = 20.9 +- 0.4 microns Y = -5.8 +- 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 ^ | S N --> x N S SUMMARY OF THE CALCULATIONS AND CONVENTIONS USED Calculation of GL using a double coil (assumed flat): V2 = (Nturns * velocity * B2 * L)_1 + (Nturns * velocity * B2 * L)_2 = (Nturns1 * Rcoil1 * ang_freq * GL * Rcoil1) + (Nturns2 * Rcoil2 * ang_freq * GL * Rcoil2) = (Nturns1 * Rcoil1^2 + Nturns2 * Rcoil2^2) * ang_freq * GL If Nturns1 = Nturns2 == Nturns12, then V2 = Nturns12 * (Rcoil1^2 + Rcoil2^2) * ang_freq * GL Let Reff^2 = Rcoil1^2 + Rcoil2^2, then V2 = Nturns12 * Reff^2 * ang_freq * GL Or, GL = V2 / (Nturns12 * Reff^2 * ang_freq) Calculation of the harmonics: The integrated radial field for the n'th harmonic at the coil radius is given by BLn(th) = BLn * cos(n*(th - THspole)) The coil voltage is V = Nturns * v_theta * B_r * L Vn(th) = Nturns * velocity * BLn(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) Then, Vn = Nturns * Rcoil * ang_freq * BLn PhiVn = - n * THspole Or, BLn = Vn / (Nturns * Rcoil * ang_freq) THspole = - PhiVn / n Calculation of the magnetic center: Xcenter = - (1/GL) * BL1 * sin(THspole1) Ycenter = - (1/GL) * BL1 * cos(THspole1)