SLAC Magnetic Measurements Date: 07-31-1996 Time: 09:09:58 Project: PEP2INJ Magnet Type: QUAD Magnet Name (Serial #): 2Q4W-11 Bar Code Number: QM31 9380 Test Stand: MAGLAB #1 Measurement System: ROTATING COIL Operator: J. BRATMAN Run Number: 2 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: 07-31-1996 Time: 09:52:22 Magnet Name: 2Q4W-11 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 49.96641 +- 3.737625E-05 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00011 0.00000 24.75 0.10 0.7328 0.0043 2 0.01438 0.00000 -45.63 0.00 100.0000 0.0104 3 0.00001 0.00000 -28.60 1.28 0.0701 0.0063 4 0.00001 0.00000 17.53 0.75 0.0660 0.0063 5 0.00000 0.00000 -10.85 24.63 0.0249 0.0153 6 0.00002 0.00000 19.68 1.90 0.1653 0.0327 7 0.00001 0.00000 -7.22 10.25 0.0490 0.0191 8 0.00001 0.00000 -9.56 6.23 0.0791 0.0108 9 0.00000 0.00000 -1.49 10.48 0.0143 0.0048 10 0.00003 0.00000 8.34 0.02 0.1989 0.0025 11 0.00000 0.00000 -3.06 7.35 0.0055 0.0012 12 0.00000 0.00000 6.43 5.22 0.0042 0.0006 13 0.00000 0.00000 -5.93 9.52 0.0052 0.0013 14 0.00001 0.00000 5.71 0.16 0.0384 0.0014 15 0.00000 0.00000 2.11 8.82 0.0040 0.0008 16 0.00000 0.00000 -0.28 8.93 0.0034 0.0013 The magnetic center is at X = 58.3 +- 0.4 microns Y = 126.4 +- 0.7 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: 07-31-1996 Time: 10:30:11 Magnet Name: 2Q4W-11 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 110.0585 +- 6.475105E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00024 0.00000 25.51 0.06 0.7631 0.0013 2 0.03164 0.00000 -45.55 0.00 100.0000 0.0099 3 0.00004 0.00000 -30.92 0.24 0.1207 0.0009 4 0.00002 0.00000 15.81 2.16 0.0655 0.0047 5 0.00001 0.00000 -28.14 1.07 0.0385 0.0045 6 0.00006 0.00000 13.46 0.31 0.1928 0.0070 7 0.00002 0.00000 10.41 0.62 0.0559 0.0055 8 0.00002 0.00000 20.93 0.60 0.0610 0.0078 9 0.00001 0.00000 -16.64 1.82 0.0208 0.0041 10 0.00007 0.00000 8.48 0.04 0.2097 0.0015 11 0.00000 0.00000 -5.80 12.82 0.0050 0.0025 12 0.00000 0.00000 4.15 1.06 0.0043 0.0008 13 0.00000 0.00000 -6.24 10.85 0.0034 0.0012 14 0.00001 0.00000 5.78 0.09 0.0399 0.0008 15 0.00000 0.00000 -0.68 5.39 0.0021 0.0006 16 0.00000 0.00000 2.09 5.39 0.0058 0.0042 The magnetic center is at X = 62.4 +- 0.2 microns Y = 130.8 +- 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: 07-31-1996 Time: 11:07:57 Magnet Name: 2Q4W-11 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 179.8912 +- 3.891739E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00038 0.00000 25.46 0.03 0.7394 0.0009 2 0.05142 0.00001 -45.54 0.00 100.0000 0.0162 3 0.00006 0.00000 -28.15 0.42 0.1134 0.0016 4 0.00003 0.00000 18.20 1.33 0.0538 0.0062 5 0.00002 0.00000 34.03 1.60 0.0466 0.0065 6 0.00011 0.00001 18.96 0.26 0.2065 0.0114 7 0.00006 0.00000 14.01 0.69 0.1174 0.0016 8 0.00005 0.00000 -11.21 0.82 0.0949 0.0085 9 0.00001 0.00000 14.88 1.73 0.0172 0.0024 10 0.00010 0.00000 8.59 0.05 0.1952 0.0013 11 0.00000 0.00000 9.30 0.49 0.0057 0.0006 12 0.00000 0.00000 3.75 0.59 0.0028 0.0009 13 0.00000 0.00000 -6.38 10.71 0.0048 0.0015 14 0.00002 0.00000 5.92 0.02 0.0398 0.0007 15 0.00000 0.00000 -1.96 9.65 0.0026 0.0018 16 0.00000 0.00000 -3.61 8.42 0.0052 0.0027 The magnetic center is at X = 60.4 +- 0.1 microns Y = 126.8 +- 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 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)