SLAC Magnetic Measurements Date: 05-08-1998 Time: 13:28:55 Project: PEP2INT Magnet Type: QUAD Magnet Name (Serial #): Q1R Measurement System: 2895 Operator: mks Run Number: 10 Comment: q1Cin +80 deg. q1Cout +100 deg. Temperature Measurements Table Top Thermistor, T = 21.18289 deg C Magnet Thermistor # 1, T = 21.28503 deg C Magnet Thermistor # 2, T = 20.98895 deg C Harmonics Measurements Date: 05-08-1998 Time: 13:56:38 Magnet Name: Q1R Run Number: 10 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 0.278452E+00 0.145154E-04 88.88 0.01 46.17673 0.00242 2 0.603015E+00 0.367379E-05 44.61 0.00 100.00000 0.00086 3 0.292725E-04 0.121458E-06 -49.81 0.07 0.00485 0.00002 4 0.150111E-03 0.205116E-06 -16.97 0.01 0.02489 0.00003 5 0.597186E-04 0.122150E-06 -8.58 0.01 0.00990 0.00002 6 0.114032E-03 0.115299E-06 12.52 0.01 0.01891 0.00002 7 0.122792E-04 0.131206E-06 -9.68 0.02 0.00204 0.00002 8 0.148372E-04 0.105371E-06 -10.19 0.04 0.00246 0.00002 9 0.185160E-04 0.120895E-06 -4.00 0.03 0.00307 0.00002 10 0.629822E-05 0.110954E-06 -1.37 0.06 0.00104 0.00002 11 0.214139E-04 0.932829E-07 1.52 0.02 0.00355 0.00002 12 0.110990E-04 0.355339E-07 -1.41 0.05 0.00184 0.00001 13 0.944601E-05 0.171733E-06 -0.15 0.03 0.00157 0.00003 14 0.122287E-04 0.308811E-07 3.01 0.01 0.00203 0.00001 15 0.635304E-05 0.118560E-06 -0.74 0.06 0.00105 0.00002 16 0.537657E-05 0.769467E-07 10.20 0.01 0.00089 0.00001 17 0.511004E-05 0.112784E-06 -7.80 0.11 0.00085 0.00002 18 0.424473E-04 0.591706E-07 -4.64 0.01 0.00704 0.00001 19 0.652162E-04 0.175436E-06 -2.24 0.00 0.01082 0.00003 20 0.350109E-04 0.205207E-06 -1.27 0.01 0.00581 0.00003 21 0.272719E-04 0.613106E-07 2.27 0.02 0.00452 0.00001 22 0.541282E-04 0.252564E-06 5.90 0.01 0.00898 0.00004 23 0.177700E-04 0.197061E-06 5.12 0.02 0.00295 0.00003 24 0.110328E-04 0.427361E-06 6.25 0.06 0.00183 0.00007 25 0.778699E-05 0.167954E-06 -3.90 0.05 0.00129 0.00003 26 0.357991E-04 0.271746E-06 -3.92 0.02 0.00594 0.00005 27 0.120672E-04 0.176243E-06 -3.03 0.04 0.00200 0.00003 28 0.350317E-05 0.191517E-06 -4.70 0.23 0.00058 0.00003 29 0.334969E-05 0.203242E-06 1.04 0.11 0.00056 0.00003 30 0.187925E-04 0.187165E-06 2.54 0.02 0.00312 0.00003 31 0.273068E-05 0.136541E-06 2.08 0.19 0.00045 0.00002 32 0.176539E-05 0.322561E-06 0.68 0.30 0.00029 0.00005 33 0.884013E-06 0.204650E-06 1.94 0.84 0.00015 0.00003 34 0.247597E-05 0.245920E-06 1.83 0.18 0.00041 0.00004 35 0.752126E-06 0.130571E-06 2.12 0.77 0.00012 0.00002 36 0.696682E-06 0.173319E-06 -3.86 0.14 0.00012 0.00003 37 0.416653E-06 0.707523E-07 -3.46 0.63 0.00007 0.00001 38 0.457069E-06 0.938026E-07 -3.82 0.50 0.00008 0.00002 39 0.359881E-06 0.945899E-07 -4.57 1.22 0.00006 0.00002 40 0.526633E-06 0.733374E-07 4.41 2.55 0.00009 0.00001 The magnetic center is at X = -20776.5 +- 1.1 microns Y = -406.2 +- 2.3 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 21.26019 deg C Magnet Thermistor # 1, T = 21.35989 deg C Magnet Thermistor # 2, T = 21.05646 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)