SLAC Magnetic Measurements Date: 11-03-1997 Time: 09:22:18 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): Q1A_10 Measurement System: 5334 Operator: js Run Number: 15 Comment: After installing potting dam. Temperature Measurements Table Top Thermistor, T = 21.3898 deg C Slice Thermistor # 1, T = 21.41965 deg C Slice Thermistor # 2, T = 21.4613 deg C Harmonics Measurements Date: 11-03-1997 Time: 09:30:08 Magnet Name: Q1A_10 Run Number: 15 FIELD HARMONICS Harmonics at Rcoil = .040056 m Main Harmonic N = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.174800E-01 0.474883E-08 179.93 0.00 71.24202 0.00060 2 0.245361E-01 0.206754E-06 -44.81 0.00 100.00000 0.00119 3 0.302587E-05 0.611021E-08 33.51 0.04 0.01233 0.00002 4 0.224518E-05 0.882665E-09 -2.49 0.00 0.00915 0.00000 5 0.692448E-04 0.146974E-08 -0.09 0.00 0.28222 0.00001 6 0.170897E-04 0.607270E-08 14.71 0.00 0.06965 0.00002 7 0.109612E-05 0.176065E-07 -1.69 0.08 0.00447 0.00007 8 0.156182E-05 0.675283E-08 17.50 0.01 0.00637 0.00003 9 0.732617E-06 0.841186E-08 18.84 0.07 0.00299 0.00003 10 0.432163E-06 0.351737E-07 4.59 0.63 0.00176 0.00014 11 0.101358E-06 0.250597E-07 6.61 1.00 0.00041 0.00010 12 0.221920E-06 0.489290E-07 -10.39 0.74 0.00090 0.00020 13 0.149344E-06 0.334565E-08 -3.37 0.17 0.00061 0.00001 14 0.197185E-06 0.508450E-08 4.02 0.12 0.00080 0.00002 15 0.139328E-06 0.353054E-08 3.01 0.67 0.00057 0.00001 16 0.167453E-06 0.789186E-09 -3.01 0.26 0.00068 0.00000 17 0.109789E-06 0.607649E-08 2.68 0.03 0.00045 0.00002 18 0.910034E-06 0.193839E-08 5.13 0.08 0.00371 0.00001 19 0.182540E-05 0.174828E-07 7.48 0.00 0.00744 0.00007 20 0.275784E-06 0.915369E-08 -7.77 0.12 0.00112 0.00004 21 0.607737E-06 0.115606E-07 -6.27 0.02 0.00248 0.00005 22 0.120020E-06 0.109808E-07 -0.73 0.13 0.00049 0.00004 23 0.423196E-06 0.173261E-07 -0.41 0.10 0.00172 0.00007 24 0.230448E-06 0.124603E-07 6.46 0.00 0.00094 0.00005 25 0.466770E-07 0.280236E-09 -1.41 0.12 0.00019 0.00000 26 0.115680E-06 0.768178E-08 2.87 0.25 0.00047 0.00003 27 0.714244E-07 0.927788E-09 4.66 0.55 0.00029 0.00000 28 0.456892E-07 0.153030E-08 -3.09 0.23 0.00019 0.00001 29 0.167522E-07 0.754659E-10 2.05 0.07 0.00007 0.00000 30 0.267582E-07 0.982653E-08 -2.62 0.01 0.00011 0.00004 31 0.255288E-07 0.123927E-08 1.24 0.25 0.00010 0.00001 32 0.152162E-07 0.133900E-08 1.77 0.61 0.00006 0.00001 33 0.182911E-07 0.216735E-08 -0.87 4.17 0.00007 0.00001 34 0.216841E-07 0.668595E-08 -0.14 0.77 0.00009 0.00003 35 0.252620E-07 0.393753E-09 0.20 0.29 0.00010 0.00000 36 0.214812E-07 0.196378E-08 -0.62 0.31 0.00009 0.00001 37 0.227353E-07 0.330656E-08 -2.56 0.64 0.00009 0.00001 38 0.128121E-07 0.480228E-08 -1.63 1.36 0.00005 0.00002 39 0.323714E-07 0.608097E-09 1.34 0.16 0.00013 0.00000 40 0.270860E-07 0.347597E-08 1.31 0.32 0.00011 0.00001 The magnetic center is at X = 33.4 +- 0.1 microns Y = -28536.7 +- 0.2 microns View from the top of the magnet: y ^ | S N --> x N S Temperature Measurements Table Top Thermistor, T = 21.39859 deg C Slice Thermistor # 1, T = 21.42365 deg C Slice Thermistor # 2, T = 21.4671 deg C SUMMARY OF THE CALCULATIONS AND CONVENTIONS USED Field expansion (Bryant, CERN 92-05, p. 55) Br = Sum Bref (r / rref)^n-1 [-an cos(n th) + bn sin(n th)] Bt = Sum Bref (r / rref)^n-1 [ an sin(n th) + bn cos(n th)] For flux calculations, we re-express Bt Bt = - Sum Brefn (r / rref)^n-1 sin[n (th - THspole)] Flux from the origin to a wire bundle of N turns at R Flux = Int_0^R Bt L N dr = - Sum Brefn L N rref (1 / n) (R / rref)^n sin[n (th - THspole)] Fluxn = - Brefn L N rref (1 / n) (R / rref)^n sin[n (th - THspole)] Integrator output The integrated coil voltage VT is sampled and Fourier analyzed The FFT gives VTn and PhiVTn in the formula VTn(i) = VTn cos(n 2pi i / N + PhiVTn), VT(i) = Sum(VTn(i)) VTn(th) = VTn cos(n th + PhiVTn) Equating the flux to the integrator output gives Brefn L N rref (1 / n) (R / rref)^n = VTn BLn|_rref = n VTn / (N rref (R / rref)^n) <<<--- -sin[n (th - THspole)] = cos(n th + PhiVTn) = -sin(n th + PhiVTn - pi / 2) - n THspole = PhiVTn - pi / 2 THspole = - (PhiVTn - pi / 2) / n <<<--- For our planar bucking coil, we have: Nm turns at Rm (main winding) Nd turns at Rd and -Rd (dipole bucking) Nq turns at Rq and -Rq (quadrupole bucking) various return windings at R = 0 The sin[n (th - THspole)] dependence must be included for -R. At -R, sin[n (th + pi - THspole)] = cos(n pi) sin[n (th - THspole)] = (-1)^n sin[n (th - THspole)]. VTn = BLn|_rref rref (1 / n) { Nm (Rm / rref)^n - Nd (Rd / rref)^n + Nd (-Rd / rref)^n - Nq (Rq / rref)^n - Nq (-Rq / rref)^n } Set rref = Rm, take out Nm VTn = BLn|_Rm Rm (1 / n) Nm { 1 + (-1 + (-1)^n) (Nd / Nm) (Rd / Rm)^n + (-1 - (-1)^n) (Nq / Nm) (Rq / Rm)^n } BLn|_Rm = n VTn / (Rm Nm) { 1 + (-1 + (-1)^n) (Nd / Nm) (Rd / Rm)^n + (-1 - (-1)^n) (Nq / Nm) (Rq / Rm)^n }^(-1) Define BFn = { 1 + (-1 + (-1)^n) (Nd / Nm) (Rd / Rm)^n + (-1 - (-1)^n) (Nq / Nm) (Rq / Rm)^n } BLn|_Rm = n VTn / (Rm Nm BFn) THspole = - (PhiVTn - pi / 2) / n Harmonic Strength Ratios: The main field, denoted by capital N, is the field harmonic with the largest strength at the coil radius. The field strength ratio is defined by Rn = BLn / BLN It gives the ratio of each harmonic field strength to the main field strength at the coil radius. 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)