SLAC Magnetic Measurements Date: 08-02-1996 Time: 09:16:30 Project: PEP2INJ Magnet Type: QUAD Magnet Name (Serial #): 2Q4W-03 Bar Code Number: QM27 9340 Test Stand: MAGLAB #1 Measurement System: ROTATING COIL Operator: J. BRATMAN Run Number: 1 Comment: BitBus (180 amps) 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: 08-02-1996 Time: 09:57:13 Magnet Name: 2Q4W-03 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 49.96592 +- 4.370285E-05 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00008 0.00000 -137.76 0.11 0.5637 0.0014 2 0.01433 0.00000 -45.67 0.00 100.0000 0.0156 3 0.00003 0.00000 1.18 0.12 0.1960 0.0026 4 0.00004 0.00000 -21.75 0.40 0.2712 0.0063 5 0.00001 0.00000 -11.29 1.29 0.0405 0.0046 6 0.00003 0.00000 10.69 0.30 0.1808 0.0039 7 0.00002 0.00000 12.82 0.70 0.1180 0.0107 8 0.00001 0.00000 13.57 1.55 0.0609 0.0037 9 0.00000 0.00000 4.07 0.83 0.0112 0.0034 10 0.00003 0.00000 8.39 0.03 0.2086 0.0021 11 0.00000 0.00000 12.53 1.63 0.0044 0.0010 12 0.00000 0.00000 -12.64 0.55 0.0048 0.0007 13 0.00000 0.00000 1.60 1.23 0.0023 0.0008 14 0.00001 0.00000 5.91 0.06 0.0384 0.0011 15 0.00000 0.00000 -1.51 3.04 0.0013 0.0003 16 0.00000 0.00000 9.08 1.96 0.0024 0.0012 The magnetic center is at X = -72.0 +- 0.2 microns Y = -79.3 +- 0.2 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: 08-02-1996 Time: 10:32:45 Magnet Name: 2Q4W-03 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 110.0583 +- 3.644983E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00016 0.00000 -137.66 0.11 0.5190 0.0011 2 0.03152 0.00000 -45.66 0.00 100.0000 0.0105 3 0.00006 0.00000 2.92 0.25 0.1990 0.0027 4 0.00008 0.00000 -21.67 0.38 0.2572 0.0059 5 0.00001 0.00000 -14.51 1.42 0.0441 0.0041 6 0.00007 0.00000 13.20 0.07 0.2126 0.0022 7 0.00003 0.00000 16.55 0.57 0.0798 0.0060 8 0.00002 0.00000 21.57 0.90 0.0649 0.0055 9 0.00000 0.00000 0.37 1.23 0.0126 0.0019 10 0.00006 0.00000 8.48 0.04 0.2060 0.0005 11 0.00000 0.00000 -15.11 1.08 0.0060 0.0008 12 0.00000 0.00000 -7.32 0.98 0.0055 0.0010 13 0.00000 0.00000 0.57 0.51 0.0045 0.0009 14 0.00001 0.00000 5.78 0.03 0.0412 0.0007 15 0.00000 0.00000 -8.11 1.09 0.0029 0.0010 16 0.00000 0.00000 -0.00 0.79 0.0060 0.0014 The magnetic center is at X = -66.4 +- 0.2 microns Y = -72.9 +- 0.2 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: 08-02-1996 Time: 11:08:32 Magnet Name: 2Q4W-03 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 179.8894 +- 4.346747E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00027 0.00000 -138.30 0.15 0.5234 0.0018 2 0.05123 0.00000 -45.65 0.00 100.0000 0.0135 3 0.00010 0.00000 3.68 0.19 0.1964 0.0024 4 0.00013 0.00000 -21.56 0.32 0.2555 0.0033 5 0.00002 0.00000 -13.44 0.93 0.0412 0.0031 6 0.00011 0.00000 13.31 0.15 0.2190 0.0013 7 0.00004 0.00000 16.18 0.29 0.0732 0.0071 8 0.00003 0.00000 0.10 21.72 0.0667 0.0050 9 0.00001 0.00000 0.03 1.10 0.0144 0.0033 10 0.00011 0.00000 8.46 0.03 0.2053 0.0006 11 0.00000 0.00000 -12.03 1.53 0.0045 0.0015 12 0.00000 0.00000 -6.75 0.81 0.0054 0.0007 13 0.00000 0.00000 2.19 1.03 0.0041 0.0004 14 0.00002 0.00000 5.91 0.14 0.0397 0.0005 15 0.00000 0.00000 -2.88 2.48 0.0016 0.0005 16 0.00000 0.00000 6.46 2.11 0.0041 0.0021 The magnetic center is at X = -66.1 +- 0.3 microns Y = -74.2 +- 0.3 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)