SLAC Magnetic Measurements Date: 07-18-1996 Time: 12:16:07 Magnet Name: 2Q4W-09 Project: PEP II Injection Line Test Stand: 1 Measurement Coil: DC100 Operator: J. BRATMAN Run Number: 1 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: 07-18-1996 Time: 12:55:44 Magnet Name: 2Q4W-09 Project: PEP II Injection Line Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 49.99258 +- 1.348699E-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 0.833 0.004 -91.81 0.17 0.580 0.003 2 143.618 0.045 -45.76 0.02 100.000 0.000 3 0.122 0.007 24.83 4.47 0.085 0.005 4 0.077 0.010 -40.61 2.11 0.054 0.007 5 0.074 0.046 -3.78 30.22 0.052 0.032 6 0.154 0.052 14.74 1.32 0.108 0.036 7 0.126 0.059 5.63 8.17 0.088 0.041 8 0.084 0.050 0.97 13.48 0.058 0.035 9 0.021 0.014 7.45 7.15 0.015 0.010 10 0.284 0.010 8.25 0.23 0.198 0.007 11 0.013 0.003 0.95 12.32 0.009 0.002 12 0.007 0.003 -4.76 9.81 0.005 0.002 13 0.006 0.003 5.70 2.93 0.004 0.002 14 0.058 0.000 5.80 0.20 0.040 0.000 15 0.004 0.002 -5.11 5.04 0.003 0.001 16 0.007 0.003 4.03 6.66 0.005 0.002 The magnetic center is at X = -110.2 +- 0.5 microns Y = -3.5 +- 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 ^ | S N --> x N S Date: 07-18-1996 Time: 13:27:42 Magnet Name: 2Q4W-09 Project: PEP II Injection Line Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 109.9675 +- 1.32145E-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 1.736 0.003 -91.77 0.14 0.550 0.001 2 315.520 0.016 -45.74 0.01 100.000 0.000 3 0.289 0.032 27.71 4.31 0.092 0.010 4 0.185 0.031 -37.84 3.62 0.059 0.010 5 0.151 0.084 2.09 25.40 0.048 0.027 6 0.358 0.059 13.93 1.26 0.114 0.019 7 0.358 0.122 9.39 5.97 0.113 0.039 8 0.189 0.050 7.31 12.46 0.060 0.016 9 0.054 0.019 6.03 3.66 0.017 0.006 10 0.635 0.012 8.36 0.25 0.201 0.004 11 0.023 0.009 5.72 8.31 0.007 0.003 12 0.015 0.007 2.84 10.25 0.005 0.002 13 0.018 0.008 4.60 0.21 0.006 0.003 14 0.131 0.003 5.57 0.08 0.042 0.001 15 0.006 0.004 -5.19 4.01 0.002 0.001 16 0.014 0.011 1.10 3.81 0.004 0.003 The magnetic center is at X = -104.5 +- 0.2 microns Y = -3.2 +- 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 ^ | S N --> x N S Date: 07-18-1996 Time: 13:59:40 Magnet Name: 2Q4W-09 Project: PEP II Injection Line Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 179.9565 +- 3.675595E-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 2.794 0.014 -93.80 0.12 0.545 0.003 2 512.378 0.205 -45.77 0.01 100.000 0.000 3 0.329 0.063 24.91 6.05 0.064 0.012 4 0.300 0.071 1.84 42.48 0.059 0.014 5 0.259 0.078 10.44 27.11 0.051 0.015 6 0.660 0.198 17.50 2.15 0.129 0.039 7 0.597 0.228 5.92 11.97 0.116 0.044 8 0.181 0.080 5.32 10.02 0.035 0.016 9 0.106 0.029 2.78 2.03 0.021 0.006 10 0.999 0.029 8.19 0.05 0.195 0.006 11 0.033 0.014 -2.55 10.40 0.006 0.003 12 0.025 0.011 -1.82 9.64 0.005 0.002 13 0.020 0.002 4.83 1.49 0.004 0.000 14 0.200 0.003 5.56 0.11 0.039 0.001 15 0.012 0.005 1.34 3.73 0.002 0.001 16 0.021 0.008 2.03 6.08 0.004 0.002 The magnetic center is at X = -103.4 +- 0.5 microns Y = -6.9 +- 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 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)