SLAC Magnetic Measurements Date: 01-14-1997 Time: 13:23:41 Project: SLC Magnet Type: QUAD Magnet Name (Serial #): 314 Bar Code Number: Test Stand: 1 Measurement System: COIL Operator: tss Run Number: 2 Comment: Screws on with washers Standardization Currents 4 cycles, 2 to 140 to 2 A Test Currents 5.0 25.0 50.0 75.0 100.0 110.0 120.0 125.0 130.0 140.0 140.0 130.0 125.0 120.0 110.0 100.0 75.0 50.0 25.0 5.0 Harmonics Measurements Date: 01-14-1997 Time: 13:54:46 Magnet Name: 314 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 125.2657 +- 1.118038E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00060 0.00000 -59.47 0.11 1.1785 0.0029 2 0.05072 0.00004 45.02 0.02 100.0000 0.1156 3 0.00011 0.00001 54.55 1.28 0.2130 0.0154 4 0.00001 0.00000 -32.65 8.07 0.0162 0.0088 5 0.00004 0.00000 -18.47 1.16 0.0760 0.0073 6 0.00011 0.00001 -22.89 0.48 0.2265 0.0111 7 0.00002 0.00001 -12.42 18.45 0.0450 0.0219 8 0.00004 0.00001 -19.51 1.58 0.0706 0.0104 9 0.00006 0.00001 9.68 0.91 0.1228 0.0171 10 0.00015 0.00000 -8.74 0.05 0.2961 0.0035 11 0.00000 0.00000 7.31 6.80 0.0078 0.0018 12 0.00000 0.00000 -2.21 2.12 0.0071 0.0037 13 0.00000 0.00000 -2.22 9.83 0.0046 0.0020 14 0.00001 0.00000 -7.28 0.25 0.0275 0.0011 15 0.00000 0.00000 -1.08 4.72 0.0047 0.0019 16 0.00000 0.00000 3.32 8.24 0.0042 0.0010 The magnetic center is at X = 192.9 +- 0.5 microns Y = -113.7 +- 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 ^ | N S --> x S N Date: 01-14-1997 Time: 14:01:59 Magnet Name: 314 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 140.2822 +- 1.105604E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00067 0.00000 -58.80 0.16 1.1778 0.0024 2 0.05672 0.00004 45.01 0.02 100.0000 0.1013 3 0.00011 0.00001 53.20 1.13 0.2009 0.0162 4 0.00001 0.00000 -32.62 8.56 0.0141 0.0019 5 0.00004 0.00000 -17.99 1.96 0.0706 0.0026 6 0.00012 0.00001 -21.85 0.85 0.2120 0.0132 7 0.00003 0.00001 9.62 20.31 0.0502 0.0131 8 0.00003 0.00001 -15.45 3.54 0.0538 0.0108 9 0.00004 0.00001 6.39 0.55 0.0626 0.0202 10 0.00017 0.00000 -8.70 0.11 0.3006 0.0009 11 0.00000 0.00000 6.89 7.29 0.0054 0.0027 12 0.00000 0.00000 -3.24 7.94 0.0079 0.0030 13 0.00000 0.00000 -0.15 5.99 0.0052 0.0019 14 0.00001 0.00000 -7.52 0.26 0.0247 0.0003 15 0.00000 0.00000 -0.69 1.58 0.0022 0.0005 16 0.00000 0.00000 7.33 1.41 0.0045 0.0005 The magnetic center is at X = 191.4 +- 0.5 microns Y = -115.9 +- 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 ^ | N S --> x S N Date: 01-14-1997 Time: 14:11:49 Magnet Name: 314 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 125.2661 +- 4.037096E-05 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00060 0.00000 -59.03 0.15 1.1837 0.0027 2 0.05097 0.00005 45.00 0.02 100.0000 0.1346 3 0.00010 0.00001 53.40 1.70 0.1941 0.0127 4 0.00001 0.00000 -21.75 15.63 0.0154 0.0055 5 0.00004 0.00000 -17.75 1.60 0.0753 0.0093 6 0.00010 0.00001 -21.83 0.57 0.1920 0.0152 7 0.00003 0.00000 -23.11 1.24 0.0619 0.0067 8 0.00002 0.00001 -11.94 4.29 0.0462 0.0234 9 0.00005 0.00001 7.76 1.32 0.1016 0.0142 10 0.00016 0.00000 -8.77 0.08 0.3067 0.0043 11 0.00000 0.00000 -12.64 3.49 0.0055 0.0008 12 0.00000 0.00000 11.46 2.09 0.0050 0.0026 13 0.00000 0.00000 -9.07 2.14 0.0087 0.0027 14 0.00001 0.00000 -6.84 0.41 0.0253 0.0013 15 0.00000 0.00000 3.06 7.27 0.0014 0.0006 16 0.00000 0.00000 5.47 1.87 0.0023 0.0008 The magnetic center is at X = 192.8 +- 0.5 microns Y = -115.7 +- 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 ^ | 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 = ( (Nturns * Rcoil^2)1 + (Nturns * Rcoil^2)2 )^-1 * (V2 / ang_freq) Let CoilConst = ( (Nturns * Rcoil^2)1 + (Nturns * Rcoil^2)2 )^-1 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)