SLAC Magnetic Measurements Date: 01-05-1999 Time: 17:50:39 Project: POSITSRC Magnet Type: QUAD Magnet Name (Serial #): Q527 Bar Code Number: Test Stand: 1 Measurement System: DC2 Operator: zw Run Number: 2 Comment: GL vs I, fixed noise problem in run 1 Standardization Currents 6 cycles, 1 to 12 to 1 A Test Currents 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 Harmonics Measurements Date: 01-05-1999 Time: 18:19:48 Magnet Name: Q527 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 7.098072 +- 1.345746E-05 A Harmonics at Rcoil = .008634 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00006 0.00000 89.43 0.13 0.5537 0.0021 2 0.01159 0.00000 -44.31 0.01 100.0000 0.0137 3 0.00002 0.00000 -54.22 2.13 0.1535 0.0091 4 0.00000 0.00000 -4.76 18.10 0.0359 0.0126 5 0.00001 0.00000 -20.57 0.86 0.0536 0.0032 6 0.00002 0.00000 16.10 0.27 0.2046 0.0034 7 0.00000 0.00000 -10.13 1.30 0.0339 0.0034 8 0.00000 0.00000 10.78 2.41 0.0124 0.0019 9 0.00000 0.00000 -15.92 0.82 0.0177 0.0052 10 0.00001 0.00000 -13.94 1.74 0.0502 0.0091 11 0.00001 0.00000 -5.26 1.14 0.0894 0.0196 12 0.00000 0.00000 -6.52 1.74 0.0215 0.0090 13 0.00000 0.00000 12.14 1.12 0.0368 0.0202 14 0.00000 0.00000 -0.96 2.29 0.0216 0.0076 15 0.00000 0.00000 -0.69 0.76 0.0119 0.0044 16 0.00000 0.00000 0.45 7.53 0.0065 0.0026 17 0.00000 0.00000 -2.29 3.01 0.0112 0.0030 18 0.00000 0.00000 4.76 2.29 0.0089 0.0025 19 0.00000 0.00000 -7.82 10.40 0.0088 0.0020 20 0.00000 0.00000 0.66 1.19 0.0085 0.0021 View from the non-lead end of the magnet: y ^ | S N --> x N S The magnetic center is at X = 47.8 +- 0.2 microns Y = 0.5 +- 0.1 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. Date: 01-05-1999 Time: 18:33:47 Magnet Name: Q527 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 12.1502 +- 4.959106E-05 A Harmonics at Rcoil = .008634 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00011 0.00000 91.95 0.68 0.5680 0.0007 2 0.01988 0.00000 -44.34 0.01 100.0000 0.0263 3 0.00001 0.00000 42.47 4.32 0.0444 0.0066 4 0.00001 0.00000 -1.58 16.91 0.0393 0.0111 5 0.00000 0.00000 -17.68 4.61 0.0139 0.0054 6 0.00004 0.00000 16.17 0.28 0.2175 0.0076 7 0.00001 0.00000 -15.11 1.07 0.0495 0.0038 8 0.00000 0.00000 -4.03 3.34 0.0229 0.0024 9 0.00001 0.00000 -6.54 2.11 0.0305 0.0074 10 0.00002 0.00000 14.74 0.57 0.0916 0.0080 11 0.00002 0.00001 -7.35 0.91 0.0806 0.0252 12 0.00002 0.00000 -6.01 0.74 0.1055 0.0102 13 0.00000 0.00000 -5.35 5.47 0.0247 0.0156 14 0.00001 0.00000 -11.55 4.03 0.0257 0.0094 15 0.00000 0.00000 -1.74 2.47 0.0104 0.0041 16 0.00000 0.00000 10.42 2.60 0.0127 0.0050 17 0.00000 0.00000 2.50 7.89 0.0065 0.0039 18 0.00000 0.00000 -8.67 17.57 0.0086 0.0025 19 0.00000 0.00000 -6.48 4.35 0.0077 0.0031 20 0.00000 0.00000 -5.57 11.27 0.0082 0.0031 View from the non-lead end of the magnet: y ^ | S N --> x N S The magnetic center is at X = 49.0 +- 0.1 microns Y = -1.7 +- 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. 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), V2 = [(Nturns * Rcoil^2)1 + (Nturns * Rcoil^2)2] * ang_freq * GL 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)