SLAC Magnetic Measurements Date: 07-16-1997 Time: 16:15:27 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: 3 Comment: measuring magnet after modifications for intallation into beam line. 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: 07-16-1997 Time: 16:36:41 Magnet Name: 2Q4W-11 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 50.04091 +- 2.991194E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00004 0.00000 161.99 0.71 0.2589 0.0057 2 0.01413 0.00000 -52.58 0.02 100.0000 0.0467 3 0.00003 0.00000 -28.38 1.84 0.1785 0.0174 4 0.00007 0.00000 -28.83 0.30 0.4752 0.0058 5 0.00001 0.00000 -13.57 2.99 0.0635 0.0184 6 0.00002 0.00001 7.11 2.28 0.1399 0.0357 7 0.00001 0.00000 7.20 11.84 0.0652 0.0154 8 0.00001 0.00001 -1.99 15.59 0.0860 0.0418 9 0.00001 0.00000 -13.83 4.84 0.0487 0.0097 10 0.00003 0.00000 1.23 0.35 0.2015 0.0063 11 0.00000 0.00000 6.43 3.14 0.0125 0.0058 12 0.00000 0.00000 0.16 13.70 0.0135 0.0066 13 0.00000 0.00000 -1.27 7.59 0.0057 0.0015 14 0.00001 0.00000 -0.86 0.18 0.0355 0.0035 15 0.00000 0.00000 4.34 3.23 0.0045 0.0007 16 0.00000 0.00000 2.65 3.02 0.0052 0.0023 The magnetic center is at X = 15.2 +- 0.7 microns Y = -46.8 +- 1.0 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: 07-16-1997 Time: 16:55:36 Magnet Name: 2Q4W-11 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 110.1048 +- 2.617172E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00005 0.00000 139.47 1.04 0.1695 0.0054 2 0.03112 0.00002 -52.61 0.02 100.0000 0.0798 3 0.00005 0.00000 -28.82 1.13 0.1724 0.0142 4 0.00015 0.00000 -28.88 0.34 0.4764 0.0034 5 0.00003 0.00000 -13.03 4.33 0.0818 0.0116 6 0.00005 0.00001 9.27 2.86 0.1608 0.0250 7 0.00002 0.00000 6.69 13.43 0.0608 0.0084 8 0.00003 0.00001 1.93 12.38 0.0918 0.0401 9 0.00002 0.00001 -12.55 2.87 0.0485 0.0244 10 0.00006 0.00000 1.80 0.09 0.1863 0.0087 11 0.00000 0.00000 2.98 7.31 0.0071 0.0048 12 0.00000 0.00000 10.04 2.06 0.0092 0.0030 13 0.00000 0.00000 -9.00 2.28 0.0075 0.0020 14 0.00001 0.00000 -1.34 0.41 0.0356 0.0022 15 0.00000 0.00000 -0.13 5.91 0.0048 0.0008 16 0.00000 0.00000 -2.44 2.44 0.0044 0.0017 The magnetic center is at X = 20.9 +- 0.8 microns Y = -24.5 +- 0.9 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: 07-16-1997 Time: 17:14:46 Magnet Name: 2Q4W-11 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 169.8847 +- 3.260172E-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 106.52 0.65 0.2942 0.0023 2 0.05071 0.00004 -52.55 0.01 100.0000 0.1188 3 0.00006 0.00000 -25.63 1.71 0.1276 0.0026 4 0.00023 0.00001 -28.84 0.15 0.4563 0.0120 5 0.00004 0.00001 -12.85 4.75 0.0757 0.0191 6 0.00007 0.00002 8.22 2.55 0.1475 0.0387 7 0.00004 0.00000 9.73 12.11 0.0758 0.0072 8 0.00004 0.00002 4.26 13.72 0.0816 0.0424 9 0.00002 0.00001 -3.33 13.54 0.0490 0.0129 10 0.00010 0.00000 1.73 0.08 0.2035 0.0061 11 0.00001 0.00000 4.95 1.88 0.0110 0.0046 12 0.00000 0.00000 -3.65 5.08 0.0064 0.0019 13 0.00000 0.00000 -1.28 5.23 0.0024 0.0007 14 0.00002 0.00000 -0.75 0.23 0.0356 0.0016 15 0.00000 0.00000 5.31 3.38 0.0037 0.0007 16 0.00000 0.00000 1.84 3.05 0.0043 0.0016 The magnetic center is at X = 53.6 +- 0.5 microns Y = -15.9 +- 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 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)