SLAC Magnetic Measurements Date: 01-30-1995 Time: 09:30:52 Magnet Name: 2Q4-15 Project: PEP II Injection Line Test Stand: Rotating Coil Stand 2 Measurement Coil: DC100 Operator: Wendy Sibbring Run Number: 1 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: 10:07:19 Magnet Name: 2Q4-15 Project: PEP II Injection Line Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 23.99762 +- 5.610491E-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 0.825 0.000 -72.50 0.09 1.201 0.000 2 68.689 0.017 -41.79 0.01 100.000 0.000 3 0.163 0.007 -8.42 0.42 0.238 0.010 4 0.052 0.003 8.89 1.84 0.075 0.005 5 0.038 0.011 3.91 4.63 0.055 0.016 6 0.232 0.031 17.55 1.51 0.337 0.045 7 0.018 0.008 -17.31 4.59 0.025 0.012 8 0.075 0.026 7.62 10.09 0.109 0.038 9 0.056 0.001 -16.35 0.49 0.082 0.001 10 0.109 0.002 12.49 0.23 0.159 0.003 11 0.010 0.003 -12.44 0.94 0.014 0.004 12 0.007 0.002 6.95 1.20 0.010 0.003 13 0.004 0.001 -0.45 12.06 0.006 0.001 14 0.016 0.000 9.35 0.37 0.023 0.000 15 0.001 0.000 -5.37 5.54 0.002 0.001 16 0.003 0.000 -2.94 0.43 0.004 0.000 The magnetic center is at X = -217.5 +- 0.2 microns Y = 68.6 +- 0.4 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: 10:21:22 Magnet Name: 2Q4-15 Project: PEP II Injection Line Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 29.9981 +- 7.080992E-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 0.991 0.002 -74.92 0.09 1.155 0.003 2 85.787 0.027 -41.79 0.01 100.000 0.000 3 0.212 0.002 -8.85 0.56 0.247 0.002 4 0.062 0.009 8.71 1.30 0.072 0.011 5 0.038 0.005 5.81 2.85 0.045 0.006 6 0.311 0.034 17.31 0.86 0.363 0.040 7 0.022 0.006 3.34 14.12 0.025 0.007 8 0.081 0.036 10.73 3.73 0.095 0.042 9 0.077 0.008 -17.00 1.58 0.090 0.009 10 0.137 0.003 12.69 0.06 0.160 0.004 11 0.013 0.003 -13.53 0.66 0.015 0.003 12 0.010 0.002 6.33 1.35 0.012 0.002 13 0.006 0.002 6.62 11.60 0.007 0.002 14 0.018 0.000 9.01 0.19 0.021 0.000 15 0.002 0.001 5.38 9.43 0.002 0.001 16 0.004 0.001 -3.88 1.02 0.005 0.001 The magnetic center is at X = -211.9 +- 0.5 microns Y = 57.1 +- 0.4 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: 10:35:22 Magnet Name: 2Q4-15 Project: PEP II Injection Line Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 35.99719 +- 6.442774E-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 1.150 0.002 -77.19 0.12 1.118 0.002 2 102.890 0.035 -41.79 0.01 100.000 0.000 3 0.249 0.009 -8.70 0.56 0.242 0.009 4 0.070 0.010 6.05 0.83 0.068 0.010 5 0.053 0.004 3.09 2.37 0.051 0.004 6 0.336 0.034 17.15 1.27 0.327 0.033 7 0.022 0.017 8.76 7.99 0.021 0.016 8 0.078 0.022 -0.08 13.54 0.076 0.021 9 0.084 0.004 -15.16 0.86 0.081 0.004 10 0.164 0.003 12.96 0.07 0.159 0.003 11 0.012 0.008 -5.71 9.06 0.012 0.007 12 0.010 0.001 7.16 0.24 0.010 0.001 13 0.005 0.002 5.89 11.28 0.005 0.002 14 0.024 0.001 9.18 0.19 0.023 0.001 15 0.003 0.001 -8.40 3.10 0.003 0.001 16 0.002 0.001 -3.05 1.83 0.002 0.001 The magnetic center is at X = -207.1 +- 0.5 microns Y = 47.1 +- 0.4 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)