SLAC Magnetic Measurements Date: 01-24-1995 Time: 14:27:10 Magnet Name: 2Q4-32 Project: PEP II Injection Line Test Stand: Rotating Coil Stand 2 Measurement Coil: DC100 Operator: zw Run Number: 2 Comment: power leads not connected on previous run 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 FIELD HARMONICS Magnet Current, Imag = 23.99749 +- 9.603742E-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 0.326 0.001 31.21 0.18 0.474 0.001 2 68.781 0.012 -42.59 0.01 100.000 0.000 3 0.213 0.003 -4.16 0.37 0.310 0.005 4 0.010 0.005 1.40 5.93 0.015 0.007 5 0.018 0.004 23.28 2.92 0.026 0.006 6 0.188 0.016 16.51 0.61 0.273 0.024 7 0.050 0.008 -12.53 21.78 0.073 0.011 8 0.071 0.024 -11.57 0.91 0.103 0.035 9 0.045 0.010 -13.73 0.76 0.065 0.014 10 0.107 0.006 11.77 0.27 0.155 0.009 11 0.006 0.002 2.58 1.59 0.008 0.003 12 0.004 0.002 -5.69 11.96 0.006 0.003 13 0.004 0.001 -8.99 0.45 0.006 0.001 14 0.017 0.000 9.20 0.10 0.025 0.001 15 0.003 0.001 5.16 9.71 0.004 0.001 16 0.002 0.001 0.11 9.43 0.003 0.002 The magnetic center is at X = 46.6 +- 0.3 microns Y = 76.9 +- 0.2 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 ^ | S N --> x N S FIELD HARMONICS Magnet Current, Imag = 29.9973 +- 1.054274E-04 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 0.384 0.002 38.03 0.33 0.448 0.003 2 85.882 0.021 -42.59 0.01 100.000 0.000 3 0.272 0.005 -3.67 0.37 0.316 0.005 4 0.016 0.008 10.22 21.12 0.019 0.009 5 0.016 0.007 6.58 24.34 0.018 0.008 6 0.249 0.020 16.96 0.97 0.290 0.024 7 0.072 0.015 0.32 23.94 0.084 0.017 8 0.068 0.017 -10.66 2.76 0.080 0.020 9 0.068 0.022 -12.13 1.35 0.079 0.025 10 0.136 0.008 11.61 0.40 0.158 0.009 11 0.013 0.005 -7.27 11.17 0.015 0.006 12 0.005 0.003 -8.39 4.34 0.006 0.003 13 0.008 0.000 -8.99 1.02 0.009 0.000 14 0.019 0.002 9.67 0.56 0.022 0.002 15 0.002 0.000 1.29 9.51 0.002 0.000 16 0.005 0.001 2.66 8.46 0.006 0.001 The magnetic center is at X = 52.4 +- 0.5 microns Y = 67.0 +- 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 FIELD HARMONICS Magnet Current, Imag = 35.99648 +- 4.121815E-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 0.454 0.003 41.91 0.19 0.440 0.003 2 102.993 0.023 -42.59 0.01 100.000 0.000 3 0.327 0.003 -3.24 0.57 0.318 0.003 4 0.023 0.008 -2.85 20.57 0.022 0.007 5 0.028 0.009 -3.84 16.64 0.028 0.009 6 0.289 0.020 16.23 0.74 0.280 0.019 7 0.039 0.008 11.32 19.46 0.038 0.008 8 0.142 0.035 -10.48 2.81 0.138 0.034 9 0.085 0.029 -14.69 0.75 0.083 0.028 10 0.164 0.007 11.84 0.29 0.159 0.007 11 0.017 0.005 6.05 5.32 0.016 0.004 12 0.004 0.002 -7.57 4.57 0.004 0.002 13 0.007 0.001 -8.88 1.29 0.007 0.001 14 0.028 0.002 9.23 0.25 0.027 0.002 15 0.003 0.001 -0.74 9.45 0.003 0.000 16 0.005 0.001 5.65 4.26 0.005 0.001 The magnetic center is at X = 55.9 +- 0.4 microns Y = 62.3 +- 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 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)