SLAC Magnetic Measurements Date: 11-09-1997 Time: 15:41:51 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): Q1B_02 Measurement System: 7055 Operator: js Run Number: 8 Comment: After replacing bolt in block 28. Temperature Measurements Table Top Thermistor, T = 21.18015 deg C Slice Thermistor # 1, T = 21.22455 deg C Slice Thermistor # 2, T = 21.22464 deg C Harmonics Measurements Date: 11-09-1997 Time: 15:47:49 Magnet Name: Q1B_02 Run Number: 8 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 0.183104E-03 0.892804E-06 147.58 0.23 0.53842 0.00263 2 0.340079E-01 0.493604E-06 44.77 0.00 100.00000 0.00205 3 0.633443E-05 0.202288E-06 -7.15 0.73 0.01863 0.00059 4 0.608336E-05 0.305190E-06 -14.61 0.26 0.01789 0.00090 5 0.114193E-04 0.254344E-06 -34.32 0.06 0.03358 0.00075 6 0.102818E-04 0.184838E-06 12.39 0.17 0.03023 0.00054 7 0.139864E-04 0.157776E-06 2.21 0.11 0.04113 0.00046 8 0.678879E-05 0.219874E-06 -13.21 0.11 0.01996 0.00065 9 0.993080E-05 0.226128E-06 -3.03 0.05 0.02920 0.00066 10 0.164299E-04 0.999817E-07 -12.49 0.08 0.04831 0.00029 11 0.953655E-05 0.166718E-06 14.51 0.10 0.02804 0.00049 12 0.885305E-05 0.149942E-06 9.74 0.10 0.02603 0.00044 13 0.104018E-04 0.238639E-06 6.84 0.02 0.03059 0.00070 14 0.132456E-04 0.294858E-08 3.00 0.08 0.03895 0.00001 15 0.114003E-04 0.249709E-06 -0.29 0.01 0.03352 0.00073 16 0.728797E-05 0.461769E-07 -3.33 0.12 0.02143 0.00014 17 0.810440E-05 0.212105E-06 -5.53 0.05 0.02383 0.00062 18 0.739583E-05 0.227252E-06 6.06 0.03 0.02175 0.00067 19 0.261686E-04 0.205232E-06 -0.99 0.02 0.07695 0.00060 20 0.429573E-05 0.999985E-07 -4.31 0.14 0.01263 0.00029 21 0.269561E-04 0.930313E-07 4.17 0.02 0.07926 0.00027 22 0.216967E-04 0.467380E-07 6.15 0.03 0.06380 0.00014 23 0.181233E-04 0.320124E-07 7.44 0.03 0.05329 0.00009 24 0.853098E-05 0.231371E-07 1.14 0.07 0.02509 0.00007 25 0.914610E-05 0.206718E-06 -2.26 0.04 0.02689 0.00061 26 0.205372E-04 0.601376E-07 -2.44 0.03 0.06039 0.00018 27 0.238477E-05 0.113752E-06 -0.78 0.20 0.00701 0.00033 28 0.589100E-05 0.208384E-06 -4.62 0.05 0.01732 0.00061 29 0.359368E-05 0.224421E-06 5.17 0.06 0.01057 0.00066 30 0.158752E-04 0.144999E-06 3.19 0.03 0.04668 0.00043 31 0.142585E-05 0.912936E-07 3.66 0.28 0.00419 0.00027 32 0.925711E-06 0.186705E-06 3.16 0.31 0.00272 0.00055 33 0.954242E-06 0.133323E-06 -0.51 0.45 0.00281 0.00039 34 0.585524E-05 0.199978E-06 2.06 0.05 0.01722 0.00059 35 0.109474E-05 0.239427E-06 -1.62 0.14 0.00322 0.00070 36 0.676125E-06 0.731241E-07 2.29 0.70 0.00199 0.00022 37 0.936691E-06 0.119273E-06 3.31 0.39 0.00275 0.00035 38 0.938738E-06 0.269631E-06 -3.31 0.09 0.00276 0.00079 39 0.354442E-06 0.265877E-06 -0.15 0.35 0.00104 0.00078 40 0.974376E-06 0.204582E-06 -2.35 0.24 0.00287 0.00060 The magnetic center is at X = -183.3 +- 1.5 microns Y = 288.6 +- 1.6 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 21.17499 deg C Slice Thermistor # 1, T = 21.18939 deg C Slice Thermistor # 2, T = 21.16074 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)