SLAC Magnetic Measurements Date: 07-02-1996 Time: 11:24:51 Magnet Name: 2Q4W-31 Project: PEP II Injection Line Test Stand: 1 Measurement Coil: DC100 Operator: J. BRATMAN Run Number: 3 Comment: STANDARD MEASUREMENT (180 AMPS) Standardization Currents (A): 180.0 2.0 180.0 2.0 180.0 2.0 180.0 2.0 180.0 2.0 180.0 2.0 Test Currents (A): 10.0 30.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 130.0 140.0 150.0 160.0 180.0 150.0 100.0 50.0 HARMONICS MEASUREMENTS Date: 07-02-1996 Time: 12:02:51 Magnet Name: 2Q4W-31 Project: PEP II Injection Line Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 49.99347 +- 4.706941E-05 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 1.772 0.002 154.84 0.03 1.236 0.002 2 143.432 0.029 44.43 0.00 100.000 0.000 3 0.070 0.007 48.75 2.12 0.049 0.005 4 0.133 0.011 16.84 1.41 0.093 0.008 5 0.059 0.031 18.78 1.54 0.041 0.021 6 0.127 0.008 -12.99 0.98 0.089 0.006 7 0.198 0.034 -20.63 3.24 0.138 0.024 8 0.038 0.013 -5.89 10.97 0.027 0.009 9 0.040 0.006 -8.63 1.86 0.028 0.004 10 0.282 0.004 -9.62 0.06 0.197 0.003 11 0.008 0.002 -3.27 4.26 0.005 0.001 12 0.004 0.001 8.99 4.18 0.003 0.001 13 0.007 0.001 -4.00 0.42 0.005 0.001 14 0.056 0.003 -6.83 0.16 0.039 0.002 15 0.005 0.003 -1.37 10.44 0.004 0.002 16 0.004 0.001 -5.82 7.46 0.003 0.001 The magnetic center is at X = -99.8 +- 0.2 microns Y = 212.5 +- 0.3 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: 07-02-1996 Time: 12:29:36 Magnet Name: 2Q4W-31 Project: PEP II Injection Line Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 109.969 +- 4.410555E-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 3.665 0.003 150.57 0.11 1.163 0.001 2 315.001 0.054 44.51 0.00 100.000 0.000 3 0.192 0.013 57.25 0.91 0.061 0.004 4 0.243 0.027 22.12 0.56 0.077 0.009 5 0.140 0.034 19.55 1.69 0.044 0.011 6 0.531 0.031 -15.12 0.55 0.169 0.010 7 0.401 0.055 -19.42 2.41 0.127 0.017 8 0.103 0.055 -1.77 3.86 0.033 0.018 9 0.067 0.024 -5.72 1.79 0.021 0.008 10 0.632 0.004 -9.54 0.09 0.201 0.001 11 0.012 0.004 0.06 2.63 0.004 0.001 12 0.008 0.003 9.90 3.69 0.002 0.001 13 0.018 0.003 -5.16 1.41 0.006 0.001 14 0.125 0.005 -7.12 0.12 0.040 0.002 15 0.005 0.004 -0.36 6.64 0.001 0.001 16 0.009 0.004 -0.99 2.53 0.003 0.001 The magnetic center is at X = -108.6 +- 0.4 microns Y = 192.5 +- 0.3 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: 07-02-1996 Time: 12:56:29 Magnet Name: 2Q4W-31 Project: PEP II Injection Line Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 179.9497 +- 1.260583E-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 5.789 0.008 148.13 0.06 1.130 0.001 2 512.412 0.065 44.44 0.00 100.000 0.000 3 0.270 0.029 51.26 1.34 0.053 0.006 4 0.505 0.042 17.73 1.17 0.099 0.008 5 0.218 0.093 24.43 1.62 0.042 0.018 6 0.525 0.049 -14.66 0.55 0.102 0.010 7 0.881 0.119 -20.30 2.55 0.172 0.023 8 0.184 0.073 -1.51 14.01 0.036 0.014 9 0.158 0.022 -8.53 1.33 0.031 0.004 10 1.010 0.011 -9.68 0.05 0.197 0.002 11 0.028 0.010 -1.92 4.83 0.006 0.002 12 0.012 0.007 0.95 2.98 0.002 0.001 13 0.026 0.003 -4.03 0.90 0.005 0.001 14 0.198 0.007 -7.15 0.04 0.039 0.001 15 0.010 0.004 -2.66 8.46 0.002 0.001 16 0.012 0.009 -4.41 6.29 0.002 0.002 The magnetic center is at X = -113.3 +- 0.2 microns Y = 182.3 +- 0.3 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 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)