SLAC Magnetic Measurements Date: 04-30-1998 Time: 15:01:19 Project: PEP2INT Magnet Type: QUAD Magnet Name (Serial #): Q1L Measurement System: 2895 Operator: zw Run Number: 28 Comment: qc1in = +10 deg, qc1out = +10deg, Iqtrim = +250 Amps Temperature Measurements Table Top Thermistor, T = 22.92706 deg C Magnet Thermistor # 1, T = 23.89142 deg C Magnet Thermistor # 2, T = 24.04526 deg C Harmonics Measurements Date: 04-30-1998 Time: 15:28:28 Magnet Name: Q1L Run Number: 28 FIELD HARMONICS Harmonics at Rcoil = .045002 m Main Harmonic N = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.272848E+00 0.418564E-05 -90.90 0.00 45.99268 0.00093 2 0.593243E+00 0.788777E-05 -45.05 0.00 100.00000 0.00188 3 0.166867E-03 0.209783E-06 -36.95 0.02 0.02813 0.00004 4 0.152478E-03 0.722846E-07 14.66 0.01 0.02570 0.00001 5 0.218868E-03 0.166579E-06 -18.98 0.01 0.03689 0.00003 6 0.612523E-04 0.177894E-06 9.33 0.01 0.01032 0.00003 7 0.215661E-04 0.105431E-06 -18.45 0.02 0.00364 0.00002 8 0.163734E-04 0.184257E-06 16.00 0.07 0.00276 0.00003 9 0.365410E-04 0.942931E-07 -10.57 0.01 0.00616 0.00002 10 0.130914E-04 0.183620E-06 -0.51 0.12 0.00221 0.00003 11 0.470453E-05 0.191478E-06 0.34 0.23 0.00079 0.00003 12 0.624580E-05 0.593765E-07 -0.20 0.17 0.00105 0.00001 13 0.894527E-05 0.640431E-07 -13.36 0.06 0.00151 0.00001 14 0.116760E-04 0.156228E-06 -7.02 0.04 0.00197 0.00003 15 0.824719E-05 0.340957E-07 -5.21 0.05 0.00139 0.00001 16 0.321040E-05 0.145136E-06 -2.24 0.05 0.00054 0.00002 17 0.887665E-05 0.143009E-06 -7.68 0.06 0.00150 0.00002 18 0.551758E-04 0.269347E-06 3.46 0.01 0.00930 0.00005 19 0.123617E-04 0.117935E-06 -7.91 0.07 0.00208 0.00002 20 0.472977E-04 0.188997E-06 5.76 0.01 0.00797 0.00003 21 0.136224E-04 0.458883E-06 4.68 0.06 0.00230 0.00008 22 0.267227E-04 0.238604E-06 7.85 0.10 0.00450 0.00004 23 0.203322E-04 0.334697E-06 -4.05 0.03 0.00343 0.00006 24 0.859313E-05 0.802629E-06 -2.88 0.18 0.00145 0.00014 25 0.689635E-05 0.217927E-06 -4.55 0.15 0.00116 0.00004 26 0.262692E-04 0.530562E-06 2.51 0.03 0.00443 0.00009 27 0.992298E-05 0.205347E-06 2.65 0.07 0.00167 0.00003 28 0.270829E-05 0.293451E-06 3.97 0.46 0.00046 0.00005 29 0.322793E-05 0.678112E-06 2.73 0.17 0.00054 0.00011 30 0.154456E-04 0.492151E-06 -4.03 0.05 0.00260 0.00008 31 0.269092E-05 0.418966E-06 -1.32 0.19 0.00045 0.00007 32 0.259189E-05 0.261665E-06 -0.94 0.17 0.00044 0.00004 33 0.275122E-05 0.169719E-06 -2.33 0.21 0.00046 0.00003 34 0.506412E-05 0.261008E-06 -3.49 0.15 0.00085 0.00004 35 0.200749E-05 0.194607E-06 -3.78 0.21 0.00034 0.00003 36 0.173338E-05 0.273310E-06 2.34 0.37 0.00029 0.00005 37 0.210907E-05 0.214532E-06 2.75 4.08 0.00036 0.00004 38 0.228308E-05 0.199261E-06 2.47 0.29 0.00038 0.00003 39 0.112161E-05 0.135685E-06 1.55 0.04 0.00019 0.00002 40 0.253564E-05 0.115050E-06 -3.61 0.11 0.00043 0.00002 The magnetic center is at X = -20695.1 +- 0.4 microns Y = -326.4 +- 0.5 microns View from the top of the magnet: y ^ | S N --> x N S Temperature Measurements Table Top Thermistor, T = 22.97815 deg C Magnet Thermistor # 1, T = 24.03815 deg C Magnet Thermistor # 2, T = 24.10663 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)