SLAC Magnetic Measurements Date: 04-23-1997 Time: 08:45:58 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: 3 Comment: remeasure after machining Standardization Currents 6 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: 09:17:32 Magnet Name: 2Q4W-04 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 50.00435 +- 4.959106E-05 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 2.51 0.18 0.3803 0.0028 2 0.01418 0.00000 -29.42 0.00 100.0000 0.0216 3 0.00003 0.00000 22.06 0.05 0.2262 0.0059 4 0.00003 0.00000 -5.22 0.15 0.2154 0.0046 5 0.00000 0.00000 21.54 1.67 0.0063 0.0021 6 0.00002 0.00000 0.01 29.56 0.1521 0.0053 7 0.00000 0.00000 -21.21 1.20 0.0286 0.0058 8 0.00000 0.00000 -6.42 4.86 0.0149 0.0083 9 0.00000 0.00000 -10.25 2.22 0.0204 0.0071 10 0.00003 0.00000 -11.61 0.05 0.1880 0.0020 11 0.00000 0.00000 0.97 3.11 0.0058 0.0011 12 0.00000 0.00000 4.65 1.98 0.0033 0.0021 13 0.00000 0.00000 1.72 0.69 0.0043 0.0004 14 0.00001 0.00000 -3.62 0.04 0.0376 0.0007 15 0.00000 0.00000 4.37 3.43 0.0012 0.0004 16 0.00000 0.00000 -3.85 1.12 0.0010 0.0002 The magnetic center is at X = 3.2 +- 0.2 microns Y = 72.2 +- 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: 04-23-1997 Time: 09:36:30 Magnet Name: 2Q4W-04 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 110.1791 +- 1.090363E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00013 0.00000 11.12 0.09 0.4085 0.0029 2 0.03116 0.00000 -29.45 0.00 100.0000 0.0157 3 0.00008 0.00000 25.78 0.23 0.2493 0.0047 4 0.00007 0.00000 -5.48 0.34 0.2091 0.0033 5 0.00000 0.00000 3.82 14.64 0.0072 0.0050 6 0.00004 0.00000 29.56 0.12 0.1411 0.0031 7 0.00001 0.00000 -15.40 2.51 0.0241 0.0044 8 0.00001 0.00000 -0.57 0.57 0.0219 0.0090 9 0.00001 0.00000 -5.26 13.56 0.0188 0.0022 10 0.00006 0.00000 -11.80 0.08 0.1915 0.0023 11 0.00000 0.00000 2.49 0.72 0.0055 0.0024 12 0.00000 0.00000 11.02 1.20 0.0033 0.0004 13 0.00000 0.00000 2.45 0.83 0.0033 0.0008 14 0.00001 0.00000 -3.71 0.01 0.0398 0.0005 15 0.00000 0.00000 4.09 9.20 0.0011 0.0002 16 0.00000 0.00000 -5.14 0.29 0.0046 0.0004 The magnetic center is at X = 15.0 +- 0.2 microns Y = 76.1 +- 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: 04-23-1997 Time: 09:55:43 Magnet Name: 2Q4W-04 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 180.3553 +- 4.577637E-05 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00021 0.00000 11.81 0.20 0.4193 0.0028 2 0.05079 0.00001 -29.49 0.00 100.0000 0.0162 3 0.00012 0.00000 21.34 0.17 0.2350 0.0030 4 0.00010 0.00000 -5.53 0.40 0.1929 0.0039 5 0.00000 0.00000 -3.72 23.17 0.0054 0.0029 6 0.00007 0.00000 28.62 0.16 0.1461 0.0085 7 0.00002 0.00000 -16.98 2.32 0.0430 0.0039 8 0.00001 0.00000 3.14 2.44 0.0220 0.0050 9 0.00001 0.00000 -1.03 12.63 0.0149 0.0053 10 0.00010 0.00000 -11.54 0.04 0.1961 0.0007 11 0.00000 0.00000 6.05 1.62 0.0063 0.0017 12 0.00000 0.00000 -0.74 1.00 0.0023 0.0011 13 0.00000 0.00000 3.46 0.30 0.0038 0.0002 14 0.00002 0.00000 -3.47 0.09 0.0375 0.0005 15 0.00000 0.00000 8.16 0.92 0.0018 0.0007 16 0.00000 0.00000 1.58 0.85 0.0026 0.0004 The magnetic center is at X = 16.3 +- 0.3 microns Y = 78.0 +- 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)