SLAC Magnetic Measurements Date: 04-19-1999 Time: 15:50:25 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): SK1_2 Measurement System: 5334 Operator: mks Run Number: 8 Comment: after 5th tune Temperature Measurements Table Top Thermistor, T = 21.85498 deg C Slice Thermistor # 1, T = 22.61743 deg C Slice Thermistor # 2, T = 22.42618 deg C Harmonics Measurements Date: 04-19-1999 Time: 15:55:55 Magnet Name: SK1_2 Run Number: 8 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 0.110132E-03 0.602704E-06 -82.70 0.17 0.46241 0.00253 2 0.238171E-01 0.815839E-06 44.82 0.00 100.00000 0.00484 3 0.297457E-04 0.282398E-08 -2.51 0.01 0.12489 0.00001 4 0.285780E-04 0.231294E-07 -27.82 0.00 0.11999 0.00010 5 0.587278E-04 0.271230E-07 -19.38 0.00 0.24658 0.00011 6 0.361358E-04 0.845832E-09 -12.28 0.00 0.15172 0.00001 7 0.148595E-04 0.541922E-08 -17.11 0.01 0.06239 0.00002 8 0.152442E-04 0.150740E-07 -10.58 0.00 0.06401 0.00006 9 0.686653E-05 0.686191E-08 -3.77 0.01 0.02883 0.00003 10 0.767164E-05 0.550563E-08 7.29 0.00 0.03221 0.00002 11 0.864612E-05 0.448790E-08 -14.13 0.01 0.03630 0.00002 12 0.168755E-05 0.567957E-08 -7.39 0.03 0.00709 0.00002 13 0.677611E-06 0.162285E-07 -6.87 0.04 0.00285 0.00007 14 0.809159E-05 0.262617E-08 -11.26 0.01 0.03397 0.00001 15 0.190415E-05 0.248934E-08 0.05 0.00 0.00799 0.00001 16 0.207480E-05 0.625096E-08 5.65 0.01 0.00871 0.00003 17 0.469316E-06 0.113513E-08 -7.09 0.08 0.00197 0.00000 18 0.177321E-05 0.544890E-08 -5.00 0.01 0.00745 0.00002 19 0.229447E-05 0.833620E-08 -3.81 0.01 0.00963 0.00004 20 0.792232E-06 0.238234E-08 -2.24 0.04 0.00333 0.00001 21 0.110012E-05 0.892555E-09 1.31 0.03 0.00462 0.00000 22 0.947810E-06 0.174223E-07 6.28 0.00 0.00398 0.00007 23 0.268279E-06 0.135827E-07 2.02 0.02 0.00113 0.00006 24 0.273346E-06 0.856230E-08 -4.80 0.03 0.00115 0.00004 25 0.209872E-06 0.139367E-08 5.46 0.06 0.00088 0.00001 26 0.152964E-06 0.412608E-08 -2.94 0.13 0.00064 0.00002 27 0.478459E-07 0.494009E-08 2.92 0.96 0.00020 0.00002 28 0.112107E-07 0.250293E-08 0.79 1.01 0.00005 0.00001 29 0.381992E-07 0.132742E-07 0.39 0.18 0.00016 0.00006 30 0.127065E-07 0.497330E-09 -0.02 0.33 0.00005 0.00000 31 0.215172E-07 0.430605E-08 -4.94 0.37 0.00009 0.00002 32 0.143480E-07 0.310268E-08 1.72 1.73 0.00006 0.00001 33 0.116354E-07 0.130868E-08 -3.24 1.48 0.00005 0.00001 34 0.502353E-07 0.438532E-08 2.58 0.05 0.00021 0.00002 35 0.173200E-07 0.154181E-08 0.38 3.22 0.00007 0.00001 36 0.108498E-07 0.163568E-08 0.73 0.10 0.00005 0.00001 37 0.112510E-07 0.148463E-08 1.70 1.15 0.00005 0.00001 38 0.138957E-07 0.169606E-08 -0.89 0.60 0.00006 0.00001 39 0.168304E-07 0.554167E-08 0.91 0.50 0.00007 0.00002 40 0.219691E-07 0.417505E-08 -0.72 0.14 0.00009 0.00002 The magnetic center is at X = 183.7 +- 1.0 microns Y = -23.5 +- 0.6 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 21.89331 deg C Slice Thermistor # 1, T = 22.47501 deg C Slice Thermistor # 2, T = 22.39423 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)