SLAC Magnetic Measurements Date: 04-27-1999 Time: 16:10:03 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): SK1_2 Measurement System: 5334 Operator: mks Run Number: 24 Comment: redo first tuneing step Temperature Measurements Table Top Thermistor, T = 18.80847 deg C Slice Thermistor # 1, T = 19.0798 deg C Slice Thermistor # 2, T = 19.1853 deg C Harmonics Measurements Date: 04-27-1999 Time: 16:15:01 Magnet Name: SK1_2 Run Number: 24 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 0.126817E-03 0.156240E-05 91.77 0.01 0.27501 0.00339 2 0.461134E-01 0.827014E-06 -45.37 0.00 100.00000 0.00254 3 0.192718E-03 0.203727E-08 1.82 0.00 0.41792 0.00001 4 0.131491E-03 0.531873E-08 -42.73 0.00 0.28515 0.00001 5 0.110110E-03 0.137152E-07 -28.17 0.00 0.23878 0.00003 6 0.113225E-03 0.979708E-08 -14.79 0.00 0.24554 0.00002 7 0.176631E-04 0.629370E-08 4.10 0.00 0.03830 0.00001 8 0.313577E-05 0.157271E-07 17.17 0.02 0.00680 0.00003 9 0.100095E-04 0.700356E-08 1.63 0.01 0.02171 0.00002 10 0.232762E-04 0.265727E-07 -15.21 0.00 0.05048 0.00006 11 0.499891E-05 0.153170E-07 -3.23 0.02 0.01084 0.00003 12 0.462321E-05 0.336695E-07 8.00 0.03 0.01003 0.00007 13 0.486682E-05 0.280515E-07 10.32 0.00 0.01055 0.00006 14 0.580573E-05 0.386183E-07 4.18 0.01 0.01259 0.00008 15 0.184715E-05 0.309967E-09 3.37 0.00 0.00401 0.00000 16 0.181797E-05 0.999665E-08 4.76 0.06 0.00394 0.00002 17 0.112475E-05 0.204226E-07 -7.66 0.07 0.00244 0.00004 18 0.276023E-05 0.165915E-07 3.56 0.01 0.00599 0.00004 19 0.298488E-05 0.403393E-07 -5.13 0.03 0.00647 0.00009 20 0.163900E-05 0.996732E-08 -0.04 0.02 0.00355 0.00002 21 0.146526E-05 0.577523E-08 4.72 0.04 0.00318 0.00001 22 0.390945E-06 0.814109E-08 -7.28 0.08 0.00085 0.00002 23 0.137356E-06 0.256499E-07 0.67 0.61 0.00030 0.00006 24 0.151104E-06 0.155699E-07 3.44 3.37 0.00033 0.00003 25 0.704526E-07 0.898712E-09 0.59 0.48 0.00015 0.00000 26 0.148574E-06 0.351882E-09 2.33 0.15 0.00032 0.00000 27 0.951862E-07 0.302904E-08 1.30 0.08 0.00021 0.00001 28 0.506883E-07 0.300647E-08 2.82 0.14 0.00011 0.00001 29 0.369113E-07 0.691344E-08 -0.14 2.87 0.00008 0.00001 30 0.301844E-07 0.135037E-08 -2.55 1.73 0.00007 0.00000 31 0.945216E-07 0.279729E-08 -2.07 0.21 0.00020 0.00001 32 0.616961E-07 0.647752E-08 -4.34 0.02 0.00013 0.00001 33 0.723379E-07 0.121611E-07 0.44 0.12 0.00016 0.00003 34 0.758494E-07 0.299440E-08 -1.99 2.27 0.00016 0.00001 35 0.651608E-07 0.285770E-07 3.05 0.22 0.00014 0.00006 36 0.764087E-07 0.110731E-08 1.56 0.61 0.00017 0.00000 37 0.789567E-07 0.115105E-08 1.52 0.57 0.00017 0.00000 38 0.116277E-06 0.197921E-07 0.52 0.32 0.00025 0.00004 39 0.828444E-07 0.100725E-07 0.31 0.57 0.00018 0.00002 40 0.900455E-07 0.908385E-08 -0.93 0.20 0.00020 0.00002 The magnetic center is at X = 110.1 +- 1.4 microns Y = -3.4 +- 0.0 microns View from the top of the magnet: y ^ | S N --> x N S Temperature Measurements Table Top Thermistor, T = 18.82532 deg C Slice Thermistor # 1, T = 19.08234 deg C Slice Thermistor # 2, T = 19.18863 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)