SLAC Magnetic Measurements Date: 04-23-1997 Time: 15:03:26 Project: PEP2INJ Magnet Type: QUAD Magnet Name (Serial #): 2Q4W-04 Bar Code Number: QMR4-9430 Test Stand: 1 Measurement System: DC100 Operator: zw Run Number: 4 Comment: use 300 A trans, standardized on prev run Standardization Currents 1 cycles, 0 to 180 to 0 A Test Currents 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: 04-23-1997 Time: 15:18:57 Magnet Name: 2Q4W-04 Run Number: 4 FIELD HARMONICS Magnet Current, Imag = 49.88981 +- 3.785979E-05 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00006 0.00000 46.53 0.49 0.3953 0.0020 2 0.01417 0.00000 -50.31 0.00 100.0000 0.0074 3 0.00003 0.00000 4.57 0.14 0.2438 0.0009 4 0.00003 0.00000 -26.03 0.29 0.2005 0.0058 5 0.00000 0.00000 -23.67 2.23 0.0156 0.0018 6 0.00002 0.00000 8.89 0.34 0.1543 0.0018 7 0.00001 0.00000 21.22 1.02 0.0366 0.0087 8 0.00000 0.00000 4.56 4.42 0.0095 0.0043 9 0.00000 0.00000 -4.56 1.94 0.0332 0.0041 10 0.00003 0.00000 3.50 0.05 0.1943 0.0013 11 0.00000 0.00000 -14.95 0.61 0.0098 0.0015 12 0.00000 0.00000 1.62 9.03 0.0025 0.0007 13 0.00000 0.00000 10.94 0.59 0.0052 0.0013 14 0.00001 0.00000 1.18 0.03 0.0386 0.0002 15 0.00000 0.00000 8.39 2.62 0.0017 0.0008 16 0.00000 0.00000 -3.18 1.79 0.0046 0.0030 The magnetic center is at X = 54.5 +- 0.5 microns Y = 51.7 +- 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 lead end of the magnet: y ^ | S N --> x N S Date: 04-23-1997 Time: 15:37:52 Magnet Name: 2Q4W-04 Run Number: 4 FIELD HARMONICS Magnet Current, Imag = 109.9005 +- 3.013852E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00015 0.00000 45.96 0.39 0.4813 0.0020 2 0.03118 0.00000 -50.32 0.00 100.0000 0.0142 3 0.00008 0.00000 3.86 0.12 0.2472 0.0037 4 0.00006 0.00000 -26.28 0.27 0.2009 0.0054 5 0.00000 0.00000 -18.83 0.52 0.0132 0.0030 6 0.00005 0.00000 9.29 0.19 0.1469 0.0021 7 0.00001 0.00000 22.99 1.71 0.0175 0.0051 8 0.00001 0.00000 12.91 1.36 0.0190 0.0038 9 0.00001 0.00000 -0.13 1.30 0.0339 0.0061 10 0.00006 0.00000 3.59 0.10 0.1907 0.0007 11 0.00000 0.00000 -13.51 0.28 0.0068 0.0010 12 0.00000 0.00000 -9.01 0.46 0.0037 0.0005 13 0.00000 0.00000 10.74 0.38 0.0048 0.0008 14 0.00001 0.00000 1.14 0.06 0.0394 0.0005 15 0.00000 0.00000 4.72 8.87 0.0011 0.0006 16 0.00000 0.00000 -5.15 0.17 0.0057 0.0006 The magnetic center is at X = 65.7 +- 0.5 microns Y = 63.6 +- 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 lead end of the magnet: y ^ | S N --> x N S Date: 04-23-1997 Time: 15:57:02 Magnet Name: 2Q4W-04 Run Number: 4 FIELD HARMONICS Magnet Current, Imag = 179.8946 +- 2.473383E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00025 0.00000 44.19 0.26 0.5014 0.0016 2 0.05076 0.00000 -50.32 0.00 100.0000 0.0107 3 0.00012 0.00000 3.30 0.28 0.2437 0.0019 4 0.00010 0.00000 -26.14 0.48 0.1960 0.0022 5 0.00000 0.00000 -17.02 1.82 0.0096 0.0018 6 0.00008 0.00000 9.57 0.17 0.1478 0.0037 7 0.00001 0.00000 14.17 3.56 0.0111 0.0022 8 0.00001 0.00000 14.95 1.59 0.0216 0.0025 9 0.00002 0.00000 4.40 1.23 0.0313 0.0051 10 0.00010 0.00000 3.49 0.07 0.1908 0.0019 11 0.00000 0.00000 -3.89 11.69 0.0019 0.0005 12 0.00000 0.00000 5.90 11.79 0.0030 0.0004 13 0.00000 0.00000 10.78 0.70 0.0040 0.0003 14 0.00002 0.00000 1.22 0.04 0.0375 0.0006 15 0.00000 0.00000 4.68 8.75 0.0015 0.0004 16 0.00000 0.00000 0.59 1.39 0.0012 0.0003 The magnetic center is at X = 66.4 +- 0.4 microns Y = 68.3 +- 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 lead end of the magnet: y ^ | S N --> x N S SUMMARY OF THE CALCULATIONS AND CONVENTIONS USED Calculation Of GL: V2 = Nturns * velocity * B2 * L = Nturns * Rcoil * ang_freq * GL * Rcoil = Nturns * Rcoil^2 * ang_freq * GL GL = V2 / (Nturns * Rcoil^2 * ang_freq) For a double coil (for coil bowing correction), GL = ( (1 / Nturns * Rcoil^2)1 + (1 / Nturns * Rcoil^2)2 ) * (V2 / ang_freq) Let CoilConst = ( (1 / Nturns * Rcoil^2)1 + (1 / Nturns * Rcoil^2)2 ) GL = CoilConst * V2 / ang_freq Calculation Of The Harmonics: Magnitude, harmonic n: Vn = Nturns * velocity * Bn * L = Nturns * Rcoil * ang_freq * (BLn) BLn = Vn / (Nturns * Rcoil * ang_freq) Rn = BLn / BL2 = Vn / V2 Phase, harmonic n: At the coil radius, the radial field as a function of angle is, BLn(th) = BLn * cos(n*(th - THspole)) The coil voltage Vn(th) = Nturns * velocity * BLn(th) Vn(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) So, Nturns * Rcoil * ang_freq * BLn = Vn -n * THspole = PhiVn Or, BLn = Vn / (Nturns * Rcoil * ang_freq) THspole = -PhiVn / n Calculation Of The Magnetic Center: In the quadrupole's frame, Bx' = G * y', By' = G * x'. In the coil's frame (unprimed frame) the magnetic center is at (x0, y0). In the coil's frame, Bx = G * (y - y0), By = G * (x - x0). This gives the magnetic center in terms of the measured dipole field. x0 = - By / G, y0 = - Bx / G In terms of the measured integrated strengths, Xcenter = - (1/GL) * BL1 * sin(THspole1) Ycenter = - (1/GL) * BL1 * cos(THspole1)