SLAC Magnetic Measurements Date: 07-30-1996 Time: 13:52:59 Project: PEP2INJ Magnet Type: QUAD Magnet Name (Serial #): 2Q4W-08 Bar Code Number: QMR2-9410 Test Stand: MAGLAB #1 Measurement System: ROTATING COIL Operator: pdr 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: 07-30-1996 Time: 14:26:17 Magnet Name: 2Q4W-08 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 49.96612 +- 2.405075E-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 -40.08 0.06 0.5427 0.0020 2 0.01432 0.00000 44.25 0.00 100.0000 0.0115 3 0.00005 0.00000 53.32 0.16 0.3414 0.0036 4 0.00000 0.00000 -11.36 1.35 0.0305 0.0043 5 0.00001 0.00000 -33.27 0.97 0.0958 0.0035 6 0.00003 0.00000 -13.04 0.25 0.1922 0.0035 7 0.00002 0.00000 -18.82 0.15 0.1199 0.0033 8 0.00001 0.00000 4.36 0.08 0.0530 0.0044 9 0.00000 0.00000 -15.27 1.49 0.0163 0.0035 10 0.00003 0.00000 -9.74 0.03 0.1964 0.0005 11 0.00000 0.00000 -1.56 1.12 0.0066 0.0009 12 0.00000 0.00000 -6.36 11.44 0.0022 0.0006 13 0.00000 0.00000 6.33 11.58 0.0046 0.0004 14 0.00001 0.00000 -7.00 0.08 0.0397 0.0015 15 0.00000 0.00000 -1.13 3.43 0.0030 0.0016 16 0.00000 0.00000 2.85 5.86 0.0032 0.0021 The magnetic center is at X = 66.4 +- 0.3 microns Y = -78.9 +- 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 ^ | N S --> x S N Date: 07-30-1996 Time: 14:49:31 Magnet Name: 2Q4W-08 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 110.0592 +- 2.131115E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00019 0.00000 -33.59 0.10 0.6105 0.0023 2 0.03149 0.00000 44.25 0.00 100.0000 0.0008 3 0.00011 0.00000 53.61 0.07 0.3424 0.0047 4 0.00001 0.00000 -11.12 2.20 0.0323 0.0053 5 0.00003 0.00000 -33.39 0.61 0.0996 0.0033 6 0.00006 0.00000 -13.16 0.35 0.1915 0.0002 7 0.00004 0.00000 -18.66 0.43 0.1187 0.0073 8 0.00001 0.00000 4.64 0.88 0.0452 0.0031 9 0.00000 0.00000 -16.43 2.03 0.0146 0.0044 10 0.00006 0.00000 -9.80 0.02 0.1934 0.0013 11 0.00000 0.00000 -0.64 0.76 0.0077 0.0010 12 0.00000 0.00000 0.04 6.14 0.0017 0.0007 13 0.00000 0.00000 0.04 12.88 0.0041 0.0005 14 0.00001 0.00000 -7.13 0.02 0.0401 0.0007 15 0.00000 0.00000 -3.75 6.63 0.0028 0.0012 16 0.00000 0.00000 -3.38 3.06 0.0042 0.0020 The magnetic center is at X = 64.2 +- 0.3 microns Y = -96.6 +- 0.4 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: 07-30-1996 Time: 15:13:19 Magnet Name: 2Q4W-08 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 179.8921 +- 3.282414E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00033 0.00000 -31.34 0.05 0.6436 0.0015 2 0.05118 0.00001 44.25 0.00 100.0000 0.0302 3 0.00018 0.00000 53.49 0.12 0.3439 0.0025 4 0.00002 0.00000 -11.93 2.44 0.0339 0.0020 5 0.00005 0.00000 -34.03 0.59 0.0977 0.0023 6 0.00010 0.00000 -13.50 0.33 0.1960 0.0029 7 0.00006 0.00000 -18.40 0.10 0.1157 0.0067 8 0.00002 0.00000 2.95 0.42 0.0442 0.0077 9 0.00001 0.00000 -16.03 1.85 0.0125 0.0018 10 0.00010 0.00000 -9.84 0.01 0.1946 0.0015 11 0.00000 0.00000 -0.54 0.62 0.0065 0.0009 12 0.00000 0.00000 -4.83 5.06 0.0014 0.0006 13 0.00000 0.00000 6.10 11.37 0.0053 0.0009 14 0.00002 0.00000 -7.18 0.09 0.0389 0.0003 15 0.00000 0.00000 -1.41 0.56 0.0027 0.0008 16 0.00000 0.00000 -0.25 7.05 0.0029 0.0011 The magnetic center is at X = 63.6 +- 0.2 microns Y = -104.4 +- 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 ^ | 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 = ( (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)