SLAC Magnetic Measurements Date: 01-04-1998 Time: 07:53:55 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): Q1A_23 Measurement System: 5334 Operator: js Run Number: 1 Comment: Post-assembly map. Temperature Measurements Table Top Thermistor, T = 20.9725 deg C Slice Thermistor # 1, T = 21.10651 deg C Slice Thermistor # 2, T = 21.08258 deg C Harmonics Measurements Date: 01-04-1998 Time: 07:59:21 Magnet Name: Q1A_23 Run Number: 1 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 0.173292E-01 0.161121E-06 179.69 0.00 70.53934 0.00132 2 0.245667E-01 0.397676E-06 -45.47 0.00 100.00000 0.00229 3 0.361133E-03 0.464555E-06 51.28 0.01 1.47001 0.00189 4 0.205656E-03 0.397602E-06 -12.02 0.03 0.83713 0.00162 5 0.151018E-03 0.385000E-06 -34.46 0.01 0.61473 0.00157 6 0.906236E-04 0.482753E-06 -14.63 0.01 0.36889 0.00197 7 0.300490E-04 0.398784E-06 21.11 0.04 0.12232 0.00162 8 0.548360E-04 0.387583E-06 2.13 0.03 0.22321 0.00158 9 0.355113E-04 0.185402E-06 11.15 0.08 0.14455 0.00075 10 0.121109E-04 0.415940E-06 8.01 0.01 0.04930 0.00169 11 0.235801E-04 0.360234E-06 14.06 0.06 0.09598 0.00147 12 0.175726E-04 0.379772E-06 1.25 0.07 0.07153 0.00155 13 0.129673E-04 0.233016E-06 -7.13 0.12 0.05278 0.00095 14 0.810917E-05 0.358741E-06 -10.61 0.12 0.03301 0.00146 15 0.548554E-05 0.100073E-06 0.95 0.30 0.02233 0.00041 16 0.340084E-05 0.270450E-06 -9.84 0.36 0.01384 0.00110 17 0.170405E-05 0.419441E-06 2.82 0.29 0.00694 0.00171 18 0.113584E-05 0.291231E-06 7.48 0.88 0.00462 0.00119 19 0.702963E-06 0.368632E-06 -4.48 3.58 0.00286 0.00150 20 0.177226E-05 0.437638E-06 7.74 0.03 0.00721 0.00178 21 0.716810E-06 0.141695E-06 -1.43 2.22 0.00292 0.00058 22 0.636824E-06 0.291549E-06 3.50 2.86 0.00259 0.00119 23 0.677915E-06 0.222123E-06 1.64 1.37 0.00276 0.00090 24 0.539307E-06 0.414592E-06 -2.32 0.05 0.00220 0.00169 25 0.533714E-06 0.421907E-06 2.23 0.04 0.00217 0.00172 26 0.602393E-06 0.441688E-06 1.70 0.19 0.00245 0.00180 27 0.547485E-06 0.409780E-06 -0.49 1.88 0.00223 0.00167 28 0.546784E-06 0.447481E-06 0.65 4.84 0.00223 0.00182 29 0.505038E-06 0.476790E-06 -1.31 2.93 0.00206 0.00194 30 0.513275E-06 0.482527E-06 -3.78 1.22 0.00209 0.00196 31 0.519138E-06 0.469300E-06 1.02 1.53 0.00211 0.00191 32 0.520521E-06 0.482087E-06 -1.81 0.87 0.00212 0.00196 33 0.517447E-06 0.440145E-06 -1.20 0.67 0.00211 0.00179 34 0.510597E-06 0.485954E-06 -0.23 1.31 0.00208 0.00198 35 0.512121E-06 0.470503E-06 1.76 1.15 0.00208 0.00192 36 0.529382E-06 0.474168E-06 0.24 0.89 0.00215 0.00193 37 0.515576E-06 0.483425E-06 2.17 2.43 0.00210 0.00197 38 0.534709E-06 0.468194E-06 0.18 1.99 0.00218 0.00191 39 0.570830E-06 0.455742E-06 -0.50 0.85 0.00232 0.00186 40 0.569255E-06 0.468989E-06 -0.57 1.15 0.00232 0.00191 The magnetic center is at X = 155.1 +- 0.0 microns Y = -28254.8 +- 0.5 microns View from the top of the magnet: y ^ | S N --> x N S Temperature Measurements Table Top Thermistor, T = 20.96548 deg C Slice Thermistor # 1, T = 21.09079 deg C Slice Thermistor # 2, T = 21.07504 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)