SLAC Magnetic Measurements Date: 10-31-1997 Time: 09:22:33 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): Q1A_10 Measurement System: 5334 Operator: js Run Number: 3 Comment: Post assembly. Temperature Measurements Table Top Thermistor, T = 21.17645 deg C Slice Thermistor # 1, T = 21.30307 deg C Slice Thermistor # 2, T = 21.31897 deg C Harmonics Measurements Date: 10-31-1997 Time: 09:28:19 Magnet Name: Q1A_10 Run Number: 3 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 0.173573E-01 0.124797E-06 -179.61 0.00 70.77449 0.00150 2 0.245248E-01 0.488945E-06 -45.08 0.00 100.00000 0.00282 3 0.329549E-03 0.155938E-06 -48.70 0.01 1.34374 0.00064 4 0.124063E-03 0.128151E-06 23.89 0.04 0.50587 0.00052 5 0.109074E-03 0.249616E-06 -23.09 0.01 0.44475 0.00102 6 0.104306E-03 0.113538E-06 -27.03 0.02 0.42531 0.00046 7 0.164001E-04 0.151372E-06 -7.26 0.10 0.06687 0.00062 8 0.519074E-04 0.814834E-07 -1.89 0.03 0.21165 0.00033 9 0.276414E-04 0.257548E-06 12.48 0.01 0.11271 0.00105 10 0.212254E-04 0.219314E-06 12.90 0.04 0.08655 0.00089 11 0.986661E-05 0.250614E-06 3.72 0.02 0.04023 0.00102 12 0.185040E-04 0.142755E-06 2.29 0.06 0.07545 0.00058 13 0.746095E-05 0.255306E-06 10.01 0.02 0.03042 0.00104 14 0.588434E-05 0.148792E-06 -3.00 0.14 0.02399 0.00061 15 0.265039E-05 0.248184E-06 5.40 0.12 0.01081 0.00101 16 0.732298E-06 0.241829E-06 -1.93 0.43 0.00299 0.00099 17 0.411601E-06 0.239824E-06 -3.12 4.29 0.00168 0.00098 18 0.150148E-05 0.267429E-06 2.35 0.03 0.00612 0.00109 19 0.140815E-05 0.791720E-07 3.26 4.17 0.00574 0.00032 20 0.420426E-06 0.252292E-06 5.33 0.46 0.00171 0.00103 21 0.671271E-06 0.284228E-07 -4.89 1.26 0.00274 0.00012 22 0.620285E-06 0.446448E-07 -0.21 1.21 0.00253 0.00018 23 0.392558E-06 0.206088E-06 -1.09 2.12 0.00160 0.00084 24 0.327292E-06 0.248121E-06 -4.63 1.56 0.00133 0.00101 25 0.305794E-06 0.238696E-06 -1.20 0.87 0.00125 0.00097 26 0.340849E-06 0.280038E-06 1.05 0.64 0.00139 0.00114 27 0.315378E-06 0.258141E-06 -0.68 2.26 0.00129 0.00105 28 0.298105E-06 0.266189E-06 -2.48 0.17 0.00122 0.00109 29 0.309503E-06 0.263227E-06 0.88 1.24 0.00126 0.00107 30 0.310115E-06 0.272710E-06 -3.52 0.28 0.00126 0.00111 31 0.293350E-06 0.262857E-06 3.56 0.25 0.00120 0.00107 32 0.288723E-06 0.252231E-06 -0.65 0.34 0.00118 0.00103 33 0.302566E-06 0.273179E-06 -0.16 0.36 0.00123 0.00111 34 0.310010E-06 0.287106E-06 0.40 2.98 0.00126 0.00117 35 0.312921E-06 0.278656E-06 -2.00 0.30 0.00128 0.00114 36 0.313569E-06 0.274962E-06 0.14 1.87 0.00128 0.00112 37 0.329318E-06 0.294214E-06 -0.15 0.46 0.00134 0.00120 38 0.329389E-06 0.292194E-06 0.76 0.23 0.00134 0.00119 39 0.344784E-06 0.274198E-06 0.35 2.00 0.00141 0.00112 40 0.332670E-06 0.255811E-06 0.34 2.93 0.00136 0.00104 The magnetic center is at X = -194.4 +- 0.1 microns Y = -28348.8 +- 0.6 microns View from the top of the magnet: y ^ | S N --> x N S Temperature Measurements Table Top Thermistor, T = 21.14182 deg C Slice Thermistor # 1, T = 21.24338 deg C Slice Thermistor # 2, T = 21.25549 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)