SLAC Magnetic Measurements Date: 07-22-1996 Time: 09:40:45 Magnet Name: 2Q4W-13 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: 07-22-1996 Time: 10:16:39 Magnet Name: 2Q4W-13 Project: PEP II Injection Line Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 49.9921 +- 1.32145E-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 0.834 0.003 -78.27 0.10 0.580 0.002 2 143.856 0.011 44.22 0.01 100.000 0.000 3 0.225 0.013 58.91 0.66 0.157 0.009 4 0.209 0.005 18.87 0.60 0.145 0.003 5 0.067 0.029 13.32 1.73 0.047 0.020 6 0.179 0.029 -13.85 1.42 0.125 0.020 7 0.125 0.056 0.01 22.07 0.087 0.039 8 0.145 0.048 -6.60 14.70 0.101 0.033 9 0.037 0.017 14.29 3.11 0.026 0.012 10 0.278 0.003 -9.72 0.17 0.194 0.002 11 0.009 0.002 -1.75 7.10 0.006 0.001 12 0.007 0.004 3.59 10.54 0.005 0.003 13 0.007 0.003 6.73 2.67 0.005 0.002 14 0.059 0.002 -7.19 0.13 0.041 0.001 15 0.003 0.003 4.26 7.17 0.002 0.002 16 0.004 0.002 -3.62 8.23 0.003 0.001 The magnetic center is at X = 107.8 +- 0.4 microns Y = -22.4 +- 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 ^ | N S --> x S N Date: 07-22-1996 Time: 10:42:09 Magnet Name: 2Q4W-13 Project: PEP II Injection Line Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 109.9706 +- 3.902008E-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 1.859 0.003 -68.76 0.20 0.589 0.001 2 315.724 0.039 44.18 0.00 100.000 0.000 3 0.619 0.006 56.15 1.04 0.196 0.002 4 0.430 0.006 20.03 0.50 0.136 0.002 5 0.196 0.045 7.62 2.51 0.062 0.014 6 0.483 0.181 -16.32 2.31 0.153 0.057 7 0.203 0.103 -4.31 11.57 0.064 0.033 8 0.342 0.101 -5.67 10.19 0.108 0.032 9 0.091 0.037 13.01 3.66 0.029 0.012 10 0.624 0.013 -9.72 0.12 0.198 0.004 11 0.016 0.003 -0.12 9.02 0.005 0.001 12 0.012 0.005 9.94 2.90 0.004 0.001 13 0.018 0.009 7.13 1.84 0.006 0.003 14 0.129 0.005 -7.55 0.22 0.041 0.001 15 0.009 0.003 -0.81 4.35 0.003 0.001 16 0.019 0.009 -2.59 3.97 0.006 0.003 The magnetic center is at X = 104.3 +- 0.2 microns Y = -40.5 +- 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 ^ | N S --> x S N Date: 07-22-1996 Time: 11:08:33 Magnet Name: 2Q4W-13 Project: PEP II Injection Line Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 179.9545 +- 5.438854E-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 3.155 0.005 -63.72 0.24 0.615 0.001 2 513.380 0.064 44.26 0.00 100.000 0.000 3 1.045 0.003 57.72 0.21 0.203 0.001 4 0.748 0.034 19.64 0.77 0.146 0.007 5 0.372 0.046 10.60 1.93 0.073 0.009 6 0.455 0.201 -18.07 4.66 0.089 0.039 7 0.320 0.137 13.46 7.30 0.062 0.027 8 0.566 0.091 -15.02 4.84 0.110 0.018 9 0.211 0.017 13.28 2.35 0.041 0.003 10 1.037 0.005 -9.64 0.12 0.202 0.001 11 0.032 0.004 4.91 3.85 0.006 0.001 12 0.013 0.005 1.47 9.04 0.003 0.001 13 0.020 0.010 1.45 8.23 0.004 0.002 14 0.204 0.011 -7.33 0.05 0.040 0.002 15 0.010 0.007 -1.63 2.50 0.002 0.001 16 0.024 0.009 -2.12 6.04 0.005 0.002 The magnetic center is at X = 104.7 +- 0.3 microns Y = -51.7 +- 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 ^ | 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)