SLAC Magnetic Measurements Date: 01-26-1998 Time: 08:29:23 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): Q1A_28 Measurement System: 5334 Operator: js Run Number: 01 Comment: Post build map. Temperature Measurements Table Top Thermistor, T = 21.31958 deg C Slice Thermistor # 1, T = 21.48425 deg C Slice Thermistor # 2, T = 21.42719 deg C Harmonics Measurements Date: 01-26-1998 Time: 08:34:47 Magnet Name: Q1A_28 Run Number: 01 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 0.175042E-01 0.122007E-06 -179.86 0.00 71.92169 0.00245 2 0.243378E-01 0.811182E-06 -45.19 0.00 100.00000 0.00471 3 0.283569E-03 0.209839E-07 -51.11 0.01 1.16514 0.00009 4 0.186826E-03 0.204309E-06 -41.74 0.01 0.76764 0.00084 5 0.251777E-03 0.106127E-06 31.07 0.01 1.03451 0.00044 6 0.902269E-04 0.147411E-07 -5.15 0.02 0.37073 0.00006 7 0.532517E-04 0.178188E-06 13.17 0.01 0.21880 0.00073 8 0.109220E-04 0.125175E-06 1.20 0.07 0.04488 0.00051 9 0.319933E-04 0.166532E-06 1.80 0.01 0.13146 0.00068 10 0.172912E-04 0.142449E-06 8.57 0.04 0.07105 0.00059 11 0.109841E-04 0.943746E-07 3.09 0.06 0.04513 0.00039 12 0.145743E-04 0.134890E-06 -6.12 0.02 0.05988 0.00055 13 0.588641E-05 0.174575E-06 -0.76 0.01 0.02419 0.00072 14 0.737020E-06 0.101867E-06 -2.41 0.83 0.00303 0.00042 15 0.150458E-05 0.146345E-06 -8.90 0.15 0.00618 0.00060 16 0.124495E-05 0.162413E-06 -5.30 0.25 0.00512 0.00067 17 0.133925E-05 0.185304E-06 -1.41 0.03 0.00550 0.00076 18 0.581659E-06 0.169032E-06 4.43 4.81 0.00239 0.00069 19 0.595717E-06 0.721195E-07 -1.64 0.76 0.00245 0.00030 20 0.380544E-06 0.171704E-06 -3.08 0.25 0.00156 0.00071 21 0.451590E-06 0.149949E-06 4.20 0.40 0.00186 0.00062 22 0.344426E-06 0.110411E-06 -4.11 1.07 0.00142 0.00045 23 0.234758E-06 0.154152E-06 1.12 2.50 0.00096 0.00063 24 0.234224E-06 0.176652E-06 3.02 0.33 0.00096 0.00073 25 0.245341E-06 0.151459E-06 3.96 2.36 0.00101 0.00062 26 0.241583E-06 0.188797E-06 4.50 0.12 0.00099 0.00078 27 0.250733E-06 0.175132E-06 0.54 0.34 0.00103 0.00072 28 0.208563E-06 0.176791E-06 -1.43 0.90 0.00086 0.00073 29 0.196283E-06 0.166692E-06 -2.62 2.11 0.00081 0.00068 30 0.201832E-06 0.179222E-06 -3.00 0.60 0.00083 0.00074 31 0.207393E-06 0.188026E-06 -0.41 4.65 0.00085 0.00077 32 0.200683E-06 0.185705E-06 1.35 1.73 0.00082 0.00076 33 0.210140E-06 0.179028E-06 -1.03 2.35 0.00086 0.00074 34 0.200733E-06 0.188367E-06 -0.45 0.34 0.00082 0.00077 35 0.210266E-06 0.190508E-06 -1.21 1.02 0.00086 0.00078 36 0.198280E-06 0.187603E-06 -1.97 0.70 0.00081 0.00077 37 0.221215E-06 0.203264E-06 -0.81 3.45 0.00091 0.00084 38 0.238329E-06 0.191752E-06 -1.73 0.21 0.00098 0.00079 39 0.262700E-06 0.179119E-06 0.94 2.01 0.00108 0.00074 40 0.231113E-06 0.175544E-06 1.93 1.07 0.00095 0.00072 The magnetic center is at X = -69.2 +- 0.2 microns Y = -28808.9 +- 1.0 microns View from the top of the magnet: y ^ | S N --> x N S Temperature Measurements Table Top Thermistor, T = 21.28195 deg C Slice Thermistor # 1, T = 21.40472 deg C Slice Thermistor # 2, T = 21.39011 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)