SLAC Magnetic Measurements Date: 01-25-1998 Time: 13:31:37 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): Q1B_06 Measurement System: 7055 Operator: js Run Number: 13 Comment: After installing potting dam. Temperature Measurements Table Top Thermistor, T = 20.88394 deg C Slice Thermistor # 1, T = 20.92575 deg C Slice Thermistor # 2, T = 20.95013 deg C Harmonics Measurements Date: 01-25-1998 Time: 13:37:40 Magnet Name: Q1B_06 Run Number: 13 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 0.214096E-03 0.231666E-07 122.48 0.03 0.62624 0.00007 2 0.341877E-01 0.232838E-06 45.05 0.00 100.00000 0.00096 3 0.445344E-05 0.789153E-07 -35.77 0.34 0.01303 0.00023 4 0.307870E-05 0.101153E-06 5.09 0.35 0.00901 0.00030 5 0.645734E-05 0.794944E-07 -24.43 0.08 0.01889 0.00023 6 0.712331E-04 0.855689E-07 -15.40 0.01 0.20836 0.00025 7 0.625956E-06 0.956259E-07 -10.98 0.24 0.00183 0.00028 8 0.771765E-05 0.834902E-07 16.11 0.02 0.02257 0.00024 9 0.563169E-05 0.893272E-07 -1.89 0.04 0.01647 0.00026 10 0.428091E-05 0.640991E-07 -8.84 8.91 0.01252 0.00019 11 0.465410E-05 0.502484E-07 3.09 0.09 0.01361 0.00015 12 0.293594E-05 0.908274E-07 -2.57 0.05 0.00859 0.00027 13 0.857757E-06 0.851134E-07 -0.22 0.02 0.00251 0.00025 14 0.225691E-05 0.533493E-07 5.80 0.15 0.00660 0.00016 15 0.186212E-05 0.153950E-07 10.51 0.19 0.00545 0.00005 16 0.758836E-06 0.560072E-07 9.79 0.44 0.00222 0.00016 17 0.109659E-05 0.907682E-07 -2.50 0.15 0.00321 0.00027 18 0.382670E-04 0.239561E-08 5.02 0.01 0.11193 0.00001 19 0.263668E-04 0.742921E-07 -8.80 0.01 0.07712 0.00022 20 0.635225E-04 0.376167E-08 0.00 0.00 0.18580 0.00001 21 0.435602E-05 0.100903E-06 -1.05 0.02 0.01274 0.00030 22 0.144039E-04 0.882715E-07 -1.72 0.01 0.04213 0.00026 23 0.142354E-04 0.852283E-07 0.09 0.01 0.04164 0.00025 24 0.106990E-04 0.898331E-07 -2.86 0.01 0.03129 0.00026 25 0.625972E-05 0.105503E-06 5.13 0.00 0.01831 0.00031 26 0.405126E-05 0.430359E-07 -2.79 0.04 0.01185 0.00013 27 0.817633E-05 0.413261E-07 5.14 0.02 0.02392 0.00012 28 0.431136E-05 0.824130E-07 2.54 0.01 0.01261 0.00024 29 0.370106E-05 0.111653E-06 -2.69 0.01 0.01083 0.00033 30 0.106895E-04 0.322907E-07 2.68 0.02 0.03127 0.00009 31 0.197466E-05 0.119406E-06 -0.54 0.02 0.00578 0.00035 32 0.121985E-05 0.206305E-07 -1.49 0.10 0.00357 0.00006 33 0.160878E-05 0.875325E-07 3.13 0.05 0.00471 0.00026 34 0.793321E-05 0.878445E-07 2.65 0.01 0.02320 0.00026 35 0.474578E-06 0.492163E-07 1.36 0.35 0.00139 0.00014 36 0.114312E-05 0.514117E-07 2.50 0.11 0.00334 0.00015 37 0.922195E-06 0.363789E-07 0.03 0.17 0.00270 0.00011 38 0.123801E-05 0.942860E-07 -2.11 0.05 0.00362 0.00028 39 0.566319E-06 0.906746E-07 -2.02 0.19 0.00166 0.00027 40 0.826861E-06 0.613416E-07 -2.56 0.19 0.00242 0.00018 The magnetic center is at X = -335.5 +- 0.1 microns Y = 213.5 +- 0.2 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 20.88245 deg C Slice Thermistor # 1, T = 20.86838 deg C Slice Thermistor # 2, T = 20.88977 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)