SLAC Magnetic Measurements Date: 04-04-1998 Time: 11:35:51 Project: PEP2INT Magnet Type: Q1TRIM Magnet Name (Serial #): QD1L_D2T Measurement System: 5795 Operator: zw Run Number: 1 Comment: Iquad=0, Id1=0, Id2 = 50.1 A, outer dipole trim winding Temperature Measurements Table Top Thermistor, T = 41.15842 deg C Slice Thermistor # 1, T = -230.5264 deg C Slice Thermistor # 2, T = -230.5264 deg C Harmonics Measurements Date: 04-04-1998 Time: 12:07:15 Magnet Name: QD1L_D2T Run Number: 1 FIELD HARMONICS Harmonics at Rcoil = .045206 m Main Harmonic N = 1 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.538781E-02 0.971281E-07 -2.09 0.00 100.00000 0.00255 2 0.874536E-04 0.125812E-07 -44.23 0.01 1.62318 0.00024 3 0.459944E-04 0.752140E-08 -0.72 0.00 0.85368 0.00014 4 0.492134E-05 0.831024E-08 25.99 0.02 0.09134 0.00015 5 0.457019E-05 0.738076E-08 34.57 0.01 0.08482 0.00014 6 0.190807E-07 0.288468E-08 6.79 2.05 0.00035 0.00005 7 0.320997E-07 0.568138E-08 25.69 0.88 0.00060 0.00011 8 0.173955E-07 0.569284E-08 17.24 2.31 0.00032 0.00011 9 0.223010E-07 0.285056E-08 15.16 3.67 0.00041 0.00005 10 0.121550E-07 0.135136E-08 0.38 4.26 0.00023 0.00003 11 0.132512E-07 0.409626E-08 -8.12 1.88 0.00025 0.00008 12 0.169251E-07 0.675223E-08 -6.63 4.63 0.00031 0.00013 13 0.288320E-07 0.555890E-08 13.26 1.79 0.00054 0.00010 14 0.157938E-07 0.758872E-08 -4.06 4.20 0.00029 0.00014 15 0.101455E-07 0.441138E-08 -6.79 7.19 0.00019 0.00008 16 0.871467E-08 0.357992E-08 -6.89 2.28 0.00016 0.00007 17 0.143587E-07 0.181247E-08 -7.48 1.76 0.00027 0.00003 18 0.152837E-07 0.773890E-08 -5.39 4.32 0.00028 0.00014 19 0.166091E-07 0.446786E-08 4.38 4.48 0.00031 0.00008 20 0.176351E-07 0.293811E-08 4.33 2.32 0.00033 0.00005 21 0.131263E-07 0.997678E-09 0.81 5.87 0.00024 0.00002 22 0.124297E-07 0.422368E-08 -0.41 3.19 0.00023 0.00008 23 0.140470E-07 0.438906E-08 -1.09 2.30 0.00026 0.00008 24 0.161984E-07 0.675730E-09 5.08 0.81 0.00030 0.00001 25 0.131663E-07 0.381496E-08 4.66 1.70 0.00024 0.00007 26 0.177522E-07 0.600582E-08 -6.22 13.85 0.00033 0.00011 27 0.174494E-07 0.679322E-08 -1.08 1.91 0.00032 0.00013 28 0.123514E-07 0.453826E-08 -3.70 0.92 0.00023 0.00008 29 0.156578E-07 0.421144E-08 4.13 3.23 0.00029 0.00008 30 0.138931E-07 0.448096E-08 -1.41 2.67 0.00026 0.00008 31 0.149105E-07 0.456343E-08 0.65 1.08 0.00028 0.00008 32 0.161263E-07 0.408446E-08 -2.67 1.87 0.00030 0.00008 33 0.150813E-07 0.583845E-08 -2.22 10.91 0.00028 0.00011 34 0.101552E-07 0.138922E-08 -3.66 1.16 0.00019 0.00003 35 0.151542E-07 0.436712E-08 2.99 1.25 0.00028 0.00008 36 0.131776E-07 0.351862E-08 3.38 1.41 0.00024 0.00007 37 0.151544E-07 0.528237E-08 1.19 1.40 0.00028 0.00010 38 0.106984E-07 0.272763E-08 -1.55 2.66 0.00020 0.00005 39 0.132587E-07 0.382143E-08 -1.77 3.40 0.00025 0.00007 40 0.115500E-07 0.285251E-08 -4.38 2.51 0.00021 0.00005 The magnetic center is at X = %-101506.4 +- 47.2 microns Y = %2783184.8 +- 403.5 microns View from the top of the magnet: y ^ | S N --> x N S Temperature Measurements Table Top Thermistor, T = 41.17014 deg C Slice Thermistor # 1, T = -230.5264 deg C Slice Thermistor # 2, T = -230.5264 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)