SLAC Magnetic Measurements Date: 07-08-1996 Time: 11:11:18 Magnet Name: 2Q4W-37 Project: PEP II Injection Line Test Stand: 1 Measurement Coil: DC100 Operator: J. BRATMAN Run Number: 4 Comment: STANDARD MEASUREMENT (115 AMPS) Standardization Currents (A): 115.0 2.0 115.0 2.0 115.0 2.0 115.0 2.0 115.0 2.0 115.0 2.0 Test Currents (A): 10.0 20.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0 80.0 85.0 100.0 115.0 85.0 55.0 20.0 HARMONICS MEASUREMENTS Date: 07-08-1996 Time: 11:55:15 Magnet Name: 2Q4W-37 Project: PEP II Injection Line Run Number: 4 FIELD HARMONICS Magnet Current, Imag = 34.99654 +- 1.868812E-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 1.221 0.004 -109.63 0.06 1.220 0.004 2 100.111 0.019 44.46 0.02 100.000 0.000 3 0.499 0.022 58.17 0.80 0.499 0.022 4 0.189 0.012 23.06 0.51 0.189 0.012 5 0.073 0.017 25.56 3.44 0.073 0.017 6 0.124 0.009 -15.43 1.90 0.124 0.009 7 0.101 0.032 -17.46 5.25 0.101 0.032 8 0.035 0.010 1.90 9.93 0.035 0.010 9 0.022 0.005 12.50 2.27 0.022 0.005 10 0.200 0.003 -9.49 0.06 0.200 0.003 11 0.004 0.002 3.84 3.60 0.004 0.002 12 0.005 0.001 4.66 1.06 0.005 0.001 13 0.006 0.001 5.14 0.76 0.006 0.001 14 0.039 0.001 -7.10 0.13 0.039 0.001 15 0.004 0.001 -0.71 0.98 0.004 0.001 16 0.002 0.001 -5.58 6.99 0.002 0.001 The magnetic center is at X = 218.3 +- 0.7 microns Y = 77.9 +- 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: 07-08-1996 Time: 12:34:34 Magnet Name: 2Q4W-37 Project: PEP II Injection Line Run Number: 4 FIELD HARMONICS Magnet Current, Imag = 74.97907 +- 7.629395E-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 2.335 0.003 -101.67 0.15 1.089 0.001 2 214.282 0.096 44.44 0.01 100.000 0.000 3 1.092 0.040 57.17 0.55 0.510 0.018 4 0.416 0.021 23.36 1.38 0.194 0.010 5 0.151 0.040 24.62 2.06 0.070 0.019 6 0.253 0.041 -14.61 0.90 0.118 0.019 7 0.188 0.104 -10.52 16.99 0.088 0.048 8 0.060 0.015 -5.08 5.53 0.028 0.007 9 0.042 0.014 12.36 1.32 0.019 0.007 10 0.429 0.005 -9.55 0.06 0.200 0.002 11 0.012 0.002 -1.36 4.36 0.006 0.001 12 0.011 0.003 1.32 1.83 0.005 0.002 13 0.011 0.002 6.07 0.72 0.005 0.001 14 0.085 0.002 -7.22 0.18 0.040 0.001 15 0.004 0.003 2.73 4.51 0.002 0.001 16 0.015 0.002 -4.33 8.86 0.007 0.001 The magnetic center is at X = 202.7 +- 0.3 microns Y = 41.9 +- 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 ^ | N S --> x S N Date: 07-08-1996 Time: 12:56:21 Magnet Name: 2Q4W-37 Project: PEP II Injection Line Run Number: 4 FIELD HARMONICS Magnet Current, Imag = 114.9675 +- 2.437827E-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 3.468 0.010 -98.28 0.15 1.057 0.003 2 327.990 0.215 44.50 0.01 100.000 0.000 3 1.743 0.062 57.40 0.72 0.532 0.019 4 0.668 0.033 22.64 0.89 0.204 0.010 5 0.228 0.025 26.78 2.66 0.069 0.008 6 0.455 0.085 -15.56 0.92 0.139 0.026 7 0.320 0.103 -17.94 3.38 0.098 0.032 8 0.138 0.094 9.66 10.41 0.042 0.029 9 0.073 0.030 12.26 2.23 0.022 0.009 10 0.646 0.004 -9.46 0.05 0.197 0.001 11 0.016 0.005 -1.34 8.91 0.005 0.002 12 0.013 0.007 5.43 1.71 0.004 0.002 13 0.018 0.003 5.78 0.61 0.005 0.001 14 0.128 0.002 -7.01 0.08 0.039 0.001 15 0.011 0.006 -0.32 1.29 0.003 0.002 16 0.009 0.005 -3.74 4.50 0.003 0.002 The magnetic center is at X = 198.8 +- 0.6 microns Y = 28.9 +- 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 ^ | 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)