SLAC Magnetic Measurements Date: 03-10-1995 Time: 07:35:10 Magnet Name: 2Q10-19 Project: PEP II Injection Line Test Stand: Rotating Coil Stand 2 Measurement Coil: DC100 Operator: STEVEN GARCIA Run Number: 1 Comment: STANDARD MEASUREMENT Standardization Currents (A): 160.0 2.0 160.0 2.0 160.0 2.0 Test Currents (A): 10.0 30.0 45.0 60.0 75.0 90.0 100.0 110.0 125.0 140.0 160.0 130.0 100.0 60.0 HARMONICS MEASUREMENTS Date: 03-10-1995 Time: 08:02:15 Magnet Name: 2Q10-19 Project: PEP II Injection Line Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 60.01224 +- 1.735373E-04 A Coil Radius, Rcoil = .0189973 m Coil # Turns, Nturns = 30 Average, # Rotations/Measurement = 8 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Gm) (Gm) (deg) (deg) (%) (%) --- -------+------- -------+------- -------+------- 1 4.390 0.016 103.44 0.20 1.210 0.005 2 362.722 0.118 -45.15 0.01 100.000 0.000 3 0.555 0.097 22.72 2.33 0.153 0.027 4 0.179 0.045 -29.03 2.31 0.049 0.012 5 0.474 0.043 -24.43 0.89 0.131 0.012 6 0.977 0.047 -17.50 0.63 0.269 0.013 7 0.680 0.057 16.09 0.53 0.187 0.016 8 0.863 0.109 15.97 0.88 0.238 0.030 9 0.215 0.016 -4.25 0.11 0.059 0.005 10 0.870 0.011 8.43 0.10 0.240 0.003 11 0.026 0.003 -11.75 2.68 0.007 0.001 12 0.051 0.009 7.25 12.81 0.014 0.002 13 0.036 0.005 -6.35 0.96 0.010 0.001 14 0.173 0.006 5.81 0.04 0.048 0.002 15 0.016 0.002 -6.61 0.88 0.004 0.001 16 0.007 0.003 -4.32 1.43 0.002 0.001 The magnetic center is at X = 223.6 +- 0.8 microns Y = -53.4 +- 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 ^ | S N --> x N S Date: 03-10-1995 Time: 08:18:56 Magnet Name: 2Q10-19 Project: PEP II Injection Line Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 99.99931 +- 2.087654E-04 A Coil Radius, Rcoil = .0189973 m Coil # Turns, Nturns = 30 Average, # Rotations/Measurement = 8 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Gm) (Gm) (deg) (deg) (%) (%) --- -------+------- -------+------- -------+------- 1 7.461 0.012 105.01 0.05 1.236 0.002 2 603.913 0.112 -45.14 0.01 100.000 0.000 3 0.791 0.065 22.78 1.64 0.131 0.011 4 0.423 0.060 -27.22 2.24 0.070 0.010 5 0.698 0.054 -24.16 0.85 0.116 0.009 6 1.694 0.106 -18.44 0.47 0.281 0.018 7 1.162 0.086 15.34 0.24 0.192 0.014 8 1.536 0.147 16.35 0.72 0.254 0.024 9 0.410 0.020 -3.94 0.56 0.068 0.003 10 1.450 0.018 8.40 0.11 0.240 0.003 11 0.023 0.005 -11.79 0.83 0.004 0.001 12 0.080 0.003 14.57 0.13 0.013 0.000 13 0.051 0.004 -5.75 0.43 0.008 0.001 14 0.299 0.008 5.84 0.10 0.049 0.001 15 0.024 0.004 -6.08 0.42 0.004 0.001 16 0.007 0.002 3.41 5.63 0.001 0.000 The magnetic center is at X = 226.7 +- 0.4 microns Y = -60.8 +- 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 Date: 03-10-1995 Time: 08:35:40 Magnet Name: 2Q10-19 Project: PEP II Injection Line Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 139.9969 +- 2.722101E-04 A Coil Radius, Rcoil = .0189973 m Coil # Turns, Nturns = 30 Average, # Rotations/Measurement = 8 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Gm) (Gm) (deg) (deg) (%) (%) --- -------+------- -------+------- -------+------- 1 10.434 0.009 105.71 0.18 1.237 0.001 2 843.427 0.172 -45.14 0.01 100.000 0.000 3 1.203 0.034 22.81 0.99 0.143 0.004 4 0.471 0.103 -28.45 1.73 0.056 0.012 5 0.931 0.069 -25.97 1.49 0.110 0.008 6 2.635 0.124 -17.26 0.23 0.312 0.015 7 1.753 0.036 15.66 0.66 0.208 0.004 8 2.204 0.049 15.04 0.77 0.261 0.006 9 0.579 0.052 -4.09 0.45 0.069 0.006 10 2.020 0.022 8.34 0.09 0.240 0.003 11 0.041 0.014 -11.39 1.16 0.005 0.002 12 0.108 0.004 6.52 12.42 0.013 0.000 13 0.071 0.004 -5.80 0.37 0.008 0.000 14 0.402 0.004 5.79 0.04 0.048 0.000 15 0.049 0.004 -6.00 0.46 0.006 0.000 16 0.017 0.004 4.74 2.62 0.002 0.001 The magnetic center is at X = 226.2 +- 0.3 microns Y = -63.6 +- 0.7 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 ^ | 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)