SLAC Magnetic Measurements Date: 01-30-1995 Time: 11:32:59 Magnet Name: 2Q4-13 Project: PEP II Injection Line Test Stand: Rotating Coil Stand 2 Measurement Coil: DC100 Operator: Wendy Sibbring Run Number: 3 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: 12:09:23 Magnet Name: 2Q4-13 Project: PEP II Injection Line Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 23.99767 +- 9.072445E-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 0.316 0.001 -153.70 0.04 0.460 0.001 2 68.687 0.016 -41.77 0.00 100.000 0.000 3 0.202 0.011 -3.85 0.51 0.293 0.016 4 0.040 0.008 -23.99 4.17 0.058 0.012 5 0.042 0.007 1.82 7.63 0.061 0.010 6 0.272 0.003 20.12 1.30 0.396 0.005 7 0.103 0.026 -20.20 2.83 0.150 0.038 8 0.069 0.026 12.87 4.18 0.101 0.037 9 0.085 0.019 -5.08 2.42 0.124 0.027 10 0.087 0.008 12.40 0.62 0.127 0.011 11 0.014 0.002 -0.92 15.16 0.020 0.003 12 0.009 0.001 -1.71 2.03 0.013 0.002 13 0.004 0.001 -3.83 3.22 0.006 0.002 14 0.019 0.001 8.84 0.14 0.028 0.002 15 0.002 0.002 -7.56 3.69 0.003 0.003 16 0.003 0.002 4.29 0.96 0.004 0.003 The magnetic center is at X = -38.7 +- 0.1 microns Y = -78.3 +- 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: 01-30-1995 Time: 12:23:29 Magnet Name: 2Q4-13 Project: PEP II Injection Line Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 29.99739 +- 7.327174E-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 0.427 0.003 -158.97 0.13 0.497 0.004 2 85.783 0.026 -41.76 0.01 100.000 0.000 3 0.251 0.001 -4.19 0.45 0.292 0.002 4 0.050 0.009 -19.89 1.71 0.058 0.010 5 0.041 0.019 -0.25 2.93 0.047 0.022 6 0.327 0.020 19.11 0.65 0.381 0.024 7 0.102 0.015 -18.69 1.34 0.119 0.017 8 0.073 0.035 13.81 2.29 0.085 0.040 9 0.107 0.010 -5.29 1.30 0.124 0.012 10 0.116 0.003 12.62 0.30 0.135 0.004 11 0.019 0.001 0.43 15.73 0.022 0.002 12 0.010 0.001 -0.15 1.40 0.011 0.002 13 0.003 0.001 -4.45 10.06 0.004 0.001 14 0.022 0.001 8.43 0.11 0.026 0.001 15 0.003 0.001 -9.86 1.34 0.003 0.001 16 0.004 0.002 7.35 0.66 0.005 0.002 The magnetic center is at X = -33.9 +- 0.3 microns Y = -88.2 +- 0.6 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: 12:37:31 Magnet Name: 2Q4-13 Project: PEP II Injection Line Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 35.99665 +- 3.643984E-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 0.538 0.003 -160.91 0.15 0.523 0.003 2 102.846 0.029 -41.76 0.01 100.000 0.000 3 0.287 0.013 -4.90 0.70 0.279 0.013 4 0.073 0.008 -17.84 2.27 0.071 0.008 5 0.046 0.031 13.41 11.19 0.044 0.030 6 0.383 0.039 19.46 1.11 0.372 0.038 7 0.097 0.028 -20.03 3.29 0.094 0.027 8 0.111 0.039 14.49 5.85 0.108 0.038 9 0.130 0.035 -5.00 2.12 0.126 0.034 10 0.135 0.015 12.28 0.48 0.131 0.014 11 0.019 0.009 14.52 1.00 0.019 0.008 12 0.011 0.005 -1.26 1.95 0.011 0.005 13 0.005 0.004 -7.43 5.14 0.005 0.004 14 0.025 0.001 8.24 0.92 0.025 0.001 15 0.004 0.002 -6.56 6.24 0.004 0.002 16 0.005 0.002 1.59 6.50 0.005 0.002 The magnetic center is at X = -32.5 +- 0.3 microns Y = -93.9 +- 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)