SLAC Magnetic Measurements Date: 04-19-1999 Time: 15:31:14 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): SK1_2 Measurement System: 5334 Operator: mks Run Number: 7 Comment: after 4th tune Temperature Measurements Table Top Thermistor, T = 21.69022 deg C Slice Thermistor # 1, T = 22.59521 deg C Slice Thermistor # 2, T = 22.31885 deg C Harmonics Measurements Date: 04-19-1999 Time: 15:36:12 Magnet Name: SK1_2 Run Number: 7 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 0.109856E-03 0.398148E-05 -71.49 5.45 0.46113 0.01671 2 0.238232E-01 0.115745E-04 44.82 0.01 100.00000 0.06871 3 0.181074E-04 0.114360E-07 -29.58 0.01 0.07601 0.00006 4 0.492233E-04 0.337423E-08 -13.89 0.00 0.20662 0.00010 5 0.457239E-04 0.115488E-07 -22.76 0.00 0.19193 0.00011 6 0.336473E-04 0.116415E-08 -16.28 0.00 0.14124 0.00007 7 0.341679E-04 0.109922E-07 -10.52 0.00 0.14342 0.00008 8 0.180894E-05 0.483544E-08 9.18 0.02 0.00759 0.00002 9 0.491862E-05 0.211776E-08 -11.39 0.02 0.02065 0.00001 10 0.607823E-05 0.601176E-09 -2.83 0.00 0.02551 0.00001 11 0.793941E-05 0.985665E-08 11.86 0.00 0.03333 0.00004 12 0.530485E-05 0.166619E-08 -10.95 0.00 0.02227 0.00001 13 0.354856E-05 0.943169E-08 -6.65 0.04 0.01490 0.00004 14 0.489263E-05 0.351247E-08 -12.53 0.00 0.02054 0.00002 15 0.428647E-06 0.526927E-08 -10.29 0.09 0.00180 0.00002 16 0.120051E-05 0.178329E-08 5.04 0.00 0.00504 0.00001 17 0.117505E-05 0.144547E-08 0.21 0.01 0.00493 0.00001 18 0.203338E-05 0.443524E-11 -7.24 0.01 0.00854 0.00000 19 0.281078E-05 0.220280E-08 -3.58 0.00 0.01180 0.00001 20 0.963820E-06 0.742659E-09 -1.37 0.02 0.00405 0.00000 21 0.929400E-06 0.345955E-08 2.27 0.00 0.00390 0.00001 22 0.767988E-06 0.686742E-08 6.50 0.01 0.00322 0.00003 23 0.361482E-06 0.446114E-08 1.64 0.01 0.00152 0.00002 24 0.287036E-06 0.216555E-08 -5.66 0.07 0.00120 0.00001 25 0.120538E-06 0.511082E-08 6.04 0.04 0.00051 0.00002 26 0.104725E-06 0.330558E-08 -2.55 0.03 0.00044 0.00001 27 0.800223E-07 0.488442E-08 4.25 0.05 0.00034 0.00002 28 0.247792E-07 0.794534E-09 -4.41 0.22 0.00010 0.00000 29 0.474540E-07 0.144201E-08 0.44 0.03 0.00020 0.00001 30 0.155334E-07 0.182540E-08 0.33 0.27 0.00007 0.00001 31 0.149083E-07 0.267867E-08 -1.63 1.18 0.00006 0.00001 32 0.146067E-07 0.276902E-09 2.68 0.23 0.00006 0.00000 33 0.195374E-07 0.157581E-08 3.44 0.14 0.00008 0.00001 34 0.494204E-07 0.924705E-08 2.58 0.35 0.00021 0.00004 35 0.135294E-07 0.277547E-09 -2.47 0.00 0.00006 0.00000 36 0.204842E-07 0.209436E-08 -0.78 0.80 0.00009 0.00001 37 0.180153E-07 0.298472E-08 1.13 1.32 0.00008 0.00001 38 0.195088E-07 0.626437E-08 -1.15 0.80 0.00008 0.00003 39 0.104878E-07 0.111333E-08 -1.03 0.58 0.00004 0.00000 40 0.174160E-07 0.686725E-08 1.32 1.75 0.00007 0.00003 The magnetic center is at X = 175.2 +- 8.4 microns Y = -58.6 +- 16.8 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 21.72778 deg C Slice Thermistor # 1, T = 22.4426 deg C Slice Thermistor # 2, T = 22.2886 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)