SLAC Magnetic Measurements Date: 07-17-1997 Time: 10:52:31 Project: PEP2INJ Magnet Type: QUAD Magnet Name (Serial #): 2Q4W-11 Bar Code Number: QM31 9380 Test Stand: 1 Measurement System: DC100 Operator: tss Run Number: 5 Comment: magnet poles were clamped tighter. Standardization Currents 3 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: 07-17-1997 Time: 11:13:48 Magnet Name: 2Q4W-11 Run Number: 5 FIELD HARMONICS Magnet Current, Imag = 50.03725 +- 1.788031E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00003 0.00000 113.86 0.98 0.2370 0.0028 2 0.01428 0.00000 -47.85 0.02 100.0000 0.0400 3 0.00003 0.00000 -9.54 1.15 0.2295 0.0183 4 0.00001 0.00000 -18.07 1.43 0.0816 0.0099 5 0.00001 0.00000 -9.99 3.41 0.0509 0.0149 6 0.00002 0.00001 13.61 1.59 0.1344 0.0395 7 0.00001 0.00000 0.78 14.83 0.0612 0.0148 8 0.00001 0.00001 -10.51 11.46 0.0734 0.0355 9 0.00001 0.00000 -8.02 6.45 0.0428 0.0246 10 0.00003 0.00000 6.30 0.49 0.1932 0.0063 11 0.00000 0.00000 7.47 10.61 0.0064 0.0035 12 0.00000 0.00000 4.47 10.68 0.0091 0.0039 13 0.00000 0.00000 -11.27 1.86 0.0077 0.0025 14 0.00001 0.00000 3.30 0.24 0.0375 0.0028 15 0.00000 0.00000 0.86 4.73 0.0035 0.0015 16 0.00000 0.00000 2.31 5.31 0.0041 0.0037 The magnetic center is at X = 41.2 +- 0.6 microns Y = -18.2 +- 0.7 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: 07-17-1997 Time: 11:32:40 Magnet Name: 2Q4W-11 Run Number: 5 FIELD HARMONICS Magnet Current, Imag = 110.0984 +- 3.114765E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00008 0.00000 96.64 0.56 0.2562 0.0032 2 0.03139 0.00001 -47.89 0.02 100.0000 0.0579 3 0.00007 0.00000 -9.45 1.54 0.2168 0.0123 4 0.00003 0.00000 -18.38 2.04 0.0822 0.0067 5 0.00002 0.00001 -11.64 2.26 0.0519 0.0238 6 0.00004 0.00002 14.23 1.86 0.1413 0.0591 7 0.00002 0.00000 -5.00 12.92 0.0646 0.0157 8 0.00003 0.00001 11.59 8.92 0.0868 0.0197 9 0.00002 0.00000 -7.10 1.55 0.0541 0.0112 10 0.00007 0.00000 6.10 0.34 0.2103 0.0088 11 0.00000 0.00000 4.85 12.32 0.0119 0.0056 12 0.00000 0.00000 -0.02 1.47 0.0132 0.0016 13 0.00000 0.00000 10.09 2.38 0.0084 0.0005 14 0.00001 0.00000 3.66 0.30 0.0401 0.0034 15 0.00000 0.00000 2.47 8.11 0.0028 0.0020 16 0.00000 0.00000 -5.50 4.82 0.0048 0.0025 The magnetic center is at X = 48.3 +- 0.6 microns Y = -5.6 +- 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 non-lead end of the magnet: y ^ | S N --> x N S Date: 07-17-1997 Time: 11:51:47 Magnet Name: 2Q4W-11 Run Number: 5 FIELD HARMONICS Magnet Current, Imag = 180.1984 +- 1.287154E-03 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00014 0.00000 90.82 0.29 0.2676 0.0021 2 0.05114 0.00003 -47.90 0.01 100.0000 0.0946 3 0.00010 0.00001 -9.33 1.69 0.2043 0.0124 4 0.00004 0.00000 -19.27 2.26 0.0806 0.0062 5 0.00002 0.00001 -9.73 4.11 0.0457 0.0272 6 0.00007 0.00003 13.23 0.97 0.1464 0.0559 7 0.00003 0.00001 -6.66 13.48 0.0584 0.0272 8 0.00003 0.00001 1.85 12.68 0.0651 0.0106 9 0.00002 0.00000 -10.57 3.91 0.0367 0.0080 10 0.00010 0.00001 5.88 0.33 0.2020 0.0106 11 0.00001 0.00000 12.45 1.93 0.0183 0.0025 12 0.00000 0.00000 -4.79 1.98 0.0096 0.0016 13 0.00000 0.00000 8.29 0.90 0.0064 0.0006 14 0.00002 0.00000 3.46 0.24 0.0359 0.0026 15 0.00000 0.00000 6.20 3.24 0.0034 0.0010 16 0.00000 0.00000 3.82 8.60 0.0068 0.0035 The magnetic center is at X = 50.8 +- 0.4 microns Y = -0.7 +- 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 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)