SLAC Magnetic Measurements Date: 11-09-1997 Time: 15:08:20 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): Q1B_02 Measurement System: 7055 Operator: js Run Number: 7 Comment: 2nd tune. Temperature Measurements Table Top Thermistor, T = 21.32953 deg C Slice Thermistor # 1, T = 21.35529 deg C Slice Thermistor # 2, T = 21.45859 deg C Harmonics Measurements Date: 11-09-1997 Time: 15:15:38 Magnet Name: Q1B_02 Run Number: 7 FIELD HARMONICS Harmonics at Rcoil = .0635 m Main Harmonic N = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.154858E-03 0.835273E-06 140.70 0.31 0.45531 0.00246 2 0.340119E-01 0.547618E-06 44.80 0.00 100.00000 0.00228 3 0.286160E-05 0.680643E-08 11.65 0.01 0.00841 0.00002 4 0.507051E-05 0.384262E-09 2.30 0.02 0.01491 0.00000 5 0.714498E-05 0.691921E-08 -33.97 0.00 0.02101 0.00002 6 0.101406E-04 0.176715E-08 7.95 0.00 0.02981 0.00001 7 0.136319E-04 0.460614E-08 -0.33 0.00 0.04008 0.00001 8 0.839131E-05 0.680757E-09 -15.66 0.00 0.02467 0.00000 9 0.682238E-05 0.132809E-08 -2.40 0.00 0.02006 0.00000 10 0.121331E-04 0.496675E-08 -13.32 0.00 0.03567 0.00001 11 0.670998E-05 0.321779E-08 13.35 0.00 0.01973 0.00001 12 0.559125E-05 0.109139E-09 7.45 0.00 0.01644 0.00000 13 0.580931E-05 0.504997E-09 7.08 0.00 0.01708 0.00000 14 0.920579E-05 0.212276E-08 2.60 0.00 0.02707 0.00001 15 0.630102E-05 0.600426E-08 -0.26 0.00 0.01853 0.00002 16 0.354967E-05 0.927571E-09 -2.82 0.00 0.01044 0.00000 17 0.478951E-05 0.571163E-09 -5.28 0.00 0.01408 0.00000 18 0.877672E-05 0.721775E-08 4.90 0.00 0.02580 0.00002 19 0.291713E-04 0.675846E-08 -0.96 0.00 0.08577 0.00002 20 0.668304E-05 0.220189E-08 -3.63 0.01 0.01965 0.00001 21 0.254956E-04 0.114687E-08 4.24 0.00 0.07496 0.00000 22 0.223835E-04 0.769069E-08 6.34 0.00 0.06581 0.00002 23 0.195301E-04 0.279397E-08 7.42 0.00 0.05742 0.00001 24 0.853186E-05 0.125328E-08 1.38 0.00 0.02508 0.00000 25 0.852482E-05 0.119489E-07 -2.19 0.00 0.02506 0.00004 26 0.208840E-04 0.161363E-07 -2.35 0.00 0.06140 0.00005 27 0.242438E-05 0.776538E-08 -0.89 0.00 0.00713 0.00002 28 0.571041E-05 0.203136E-08 -4.53 0.00 0.01679 0.00001 29 0.306401E-05 0.221689E-08 5.24 0.01 0.00901 0.00001 30 0.161358E-04 0.157906E-07 3.25 0.00 0.04744 0.00005 31 0.124300E-05 0.280815E-07 3.24 0.00 0.00365 0.00008 32 0.600984E-06 0.132058E-07 3.88 0.05 0.00177 0.00004 33 0.948368E-06 0.571845E-10 -0.05 0.04 0.00279 0.00000 34 0.561697E-05 0.297405E-08 2.01 0.00 0.01651 0.00001 35 0.805006E-06 0.345869E-08 -1.97 0.01 0.00237 0.00001 36 0.811190E-06 0.345165E-08 1.83 0.02 0.00239 0.00001 37 0.674366E-06 0.232291E-09 3.54 0.02 0.00198 0.00000 38 0.799266E-06 0.445129E-08 -3.32 0.01 0.00235 0.00001 39 0.203639E-06 0.939291E-08 -0.43 0.04 0.00060 0.00003 40 0.853704E-06 0.950538E-08 -2.42 0.00 0.00251 0.00003 The magnetic center is at X = -183.1 +- 1.6 microns Y = 223.7 +- 1.6 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 21.25363 deg C Slice Thermistor # 1, T = 21.29645 deg C Slice Thermistor # 2, T = 21.38019 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)