SLAC Magnetic Measurements Date: 08-07-1996 Time: 14:14:12 Project: PEP2INJ Magnet Type: QUAD Magnet Name (Serial #): 2Q10-06 Bar Code Number: QM24 9310 Test Stand: MAGLAB #1 Measurement System: ROTATING COIL Operator: J. BRATMAN Run Number: 3 Comment: BitBus (180 amps) Standardization Currents 6 cycles, 0 to 180 to 0 A Test Currents 10.0 20.0 30.0 40.0 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 Harmonics Measurements Date: 08-07-1996 Time: 15:03:47 Magnet Name: 2Q10-06 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 49.96699 +- 3.838465E-05 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00022 0.00000 70.44 0.16 0.7259 0.0021 2 0.03009 0.00001 44.79 0.01 100.0000 0.0405 3 0.00004 0.00000 40.83 1.64 0.1417 0.0142 4 0.00001 0.00000 -27.34 9.64 0.0185 0.0113 5 0.00001 0.00000 -5.46 22.29 0.0301 0.0131 6 0.00001 0.00001 14.69 2.25 0.0487 0.0238 7 0.00004 0.00001 6.95 17.02 0.1171 0.0452 8 0.00001 0.00001 1.00 2.37 0.0447 0.0399 9 0.00001 0.00001 -15.52 1.46 0.0259 0.0173 10 0.00007 0.00000 -9.25 0.09 0.2245 0.0038 11 0.00000 0.00000 -4.65 5.64 0.0032 0.0030 12 0.00000 0.00000 -0.72 8.80 0.0054 0.0017 13 0.00000 0.00000 -3.72 9.57 0.0041 0.0029 14 0.00001 0.00000 -6.68 0.18 0.0428 0.0021 15 0.00000 0.00000 -1.49 4.35 0.0034 0.0011 16 0.00000 0.00000 0.19 1.84 0.0052 0.0018 The magnetic center is at X = -129.9 +- 0.4 microns Y = -46.2 +- 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: 08-07-1996 Time: 15:37:41 Magnet Name: 2Q10-06 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 110.061 +- 2.131115E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00049 0.00000 67.23 0.13 0.7405 0.0032 2 0.06619 0.00002 44.84 0.01 100.0000 0.0370 3 0.00010 0.00000 45.97 0.58 0.1495 0.0065 4 0.00001 0.00000 9.40 19.35 0.0120 0.0037 5 0.00003 0.00001 -12.50 9.05 0.0451 0.0205 6 0.00005 0.00002 13.27 8.57 0.0828 0.0293 7 0.00006 0.00003 1.29 17.52 0.0914 0.0451 8 0.00007 0.00000 -7.15 13.90 0.1068 0.0051 9 0.00002 0.00001 -4.32 13.63 0.0229 0.0145 10 0.00015 0.00000 -9.20 0.17 0.2231 0.0073 11 0.00000 0.00000 1.36 7.73 0.0075 0.0012 12 0.00000 0.00000 -2.06 7.51 0.0046 0.0015 13 0.00000 0.00000 -9.66 2.87 0.0070 0.0038 14 0.00003 0.00000 -6.50 0.16 0.0420 0.0021 15 0.00000 0.00000 1.93 5.91 0.0039 0.0015 16 0.00000 0.00000 -2.55 7.18 0.0034 0.0020 The magnetic center is at X = -129.7 +- 0.6 microns Y = -54.4 +- 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: 08-07-1996 Time: 16:11:49 Magnet Name: 2Q10-06 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 179.8929 +- 1.395303E-03 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00081 0.00000 66.71 0.14 0.7526 0.0020 2 0.10782 0.00003 44.79 0.00 100.0000 0.0430 3 0.00017 0.00001 43.80 1.24 0.1614 0.0063 4 0.00002 0.00001 -11.60 3.18 0.0176 0.0049 5 0.00004 0.00002 -13.26 7.84 0.0358 0.0171 6 0.00009 0.00004 4.25 16.40 0.0840 0.0358 7 0.00010 0.00005 1.27 16.74 0.0928 0.0452 8 0.00014 0.00002 7.11 12.11 0.1269 0.0163 9 0.00003 0.00002 -12.98 6.40 0.0296 0.0156 10 0.00024 0.00001 -9.21 0.16 0.2185 0.0062 11 0.00001 0.00000 5.56 6.75 0.0071 0.0013 12 0.00000 0.00000 -2.55 10.74 0.0032 0.0014 13 0.00001 0.00000 -6.67 4.69 0.0073 0.0037 14 0.00005 0.00000 -6.59 0.07 0.0424 0.0023 15 0.00000 0.00000 -0.00 6.14 0.0046 0.0020 16 0.00000 0.00000 2.60 4.93 0.0023 0.0010 The magnetic center is at X = -131.3 +- 0.4 microns Y = -56.5 +- 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 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)