SLAC Magnetic Measurements Date: 07-17-1997 Time: 09:15:03 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: 4 Comment: measuring magnet after modifications for installation into beam line. Repeat of run 3 do to current. 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: 09:36:20 Magnet Name: 2Q4W-11 Run Number: 4 FIELD HARMONICS Magnet Current, Imag = 50.04578 +- 4.812154E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00002 0.00000 142.78 1.10 0.1536 0.0028 2 0.01415 0.00001 -47.92 0.01 100.0000 0.1354 3 0.00003 0.00000 -25.20 1.04 0.2131 0.0114 4 0.00007 0.00000 -23.57 0.12 0.4796 0.0095 5 0.00001 0.00000 -7.09 3.37 0.0691 0.0177 6 0.00002 0.00000 13.39 2.48 0.1636 0.0292 7 0.00001 0.00000 -6.59 13.19 0.0481 0.0136 8 0.00001 0.00000 5.16 12.65 0.0668 0.0077 9 0.00001 0.00000 -10.56 1.37 0.0409 0.0153 10 0.00003 0.00000 6.23 0.07 0.1893 0.0112 11 0.00000 0.00000 7.51 3.42 0.0129 0.0035 12 0.00000 0.00000 -11.11 1.32 0.0151 0.0027 13 0.00000 0.00000 -3.31 9.95 0.0061 0.0026 14 0.00001 0.00000 3.44 0.28 0.0357 0.0028 15 0.00000 0.00000 -8.33 1.96 0.0048 0.0017 16 0.00000 0.00000 0.62 2.45 0.0069 0.0025 The magnetic center is at X = 17.6 +- 0.6 microns Y = -23.2 +- 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: 09:55:12 Magnet Name: 2Q4W-11 Run Number: 4 FIELD HARMONICS Magnet Current, Imag = 110.1056 +- 4.279607E-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 101.83 1.57 0.1314 0.0010 2 0.03109 0.00002 -47.85 0.01 100.0000 0.1071 3 0.00006 0.00000 -25.16 1.35 0.2022 0.0075 4 0.00015 0.00000 -23.66 0.19 0.4771 0.0078 5 0.00002 0.00000 -10.03 4.36 0.0747 0.0065 6 0.00005 0.00001 14.21 1.68 0.1525 0.0453 7 0.00002 0.00000 9.23 10.69 0.0609 0.0114 8 0.00002 0.00001 1.56 12.27 0.0699 0.0284 9 0.00001 0.00001 -2.14 7.98 0.0415 0.0295 10 0.00006 0.00000 6.22 0.22 0.2022 0.0051 11 0.00000 0.00000 5.86 2.43 0.0071 0.0038 12 0.00000 0.00000 -5.82 1.85 0.0072 0.0011 13 0.00000 0.00000 -7.76 1.45 0.0058 0.0007 14 0.00001 0.00000 3.50 0.16 0.0378 0.0010 15 0.00000 0.00000 -5.04 6.44 0.0027 0.0010 16 0.00000 0.00000 -1.37 5.07 0.0032 0.0010 The magnetic center is at X = 24.4 +- 0.2 microns Y = -5.1 +- 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: 10:14:19 Magnet Name: 2Q4W-11 Run Number: 4 FIELD HARMONICS Magnet Current, Imag = 180.2041 +- 8.765507E-05 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 91.67 0.54 0.2991 0.0006 2 0.05074 0.00004 -47.91 0.01 100.0000 0.1184 3 0.00007 0.00000 -24.18 1.98 0.1296 0.0077 4 0.00024 0.00001 -23.96 0.28 0.4657 0.0101 5 0.00004 0.00001 -8.61 1.92 0.0700 0.0239 6 0.00008 0.00002 13.58 2.24 0.1624 0.0471 7 0.00003 0.00000 -4.80 14.23 0.0551 0.0079 8 0.00004 0.00000 8.23 11.97 0.0819 0.0060 9 0.00002 0.00001 -8.52 1.89 0.0406 0.0149 10 0.00010 0.00000 6.01 0.24 0.1997 0.0059 11 0.00001 0.00000 12.30 1.67 0.0132 0.0040 12 0.00001 0.00000 -7.22 1.17 0.0110 0.0025 13 0.00000 0.00000 3.21 10.07 0.0067 0.0020 14 0.00002 0.00000 3.63 0.23 0.0328 0.0014 15 0.00000 0.00000 -4.28 7.59 0.0035 0.0012 16 0.00000 0.00000 2.69 7.05 0.0040 0.0016 The magnetic center is at X = 56.8 +- 0.1 microns Y = -1.7 +- 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 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)