SLAC Magnetic Measurements Date: 04-23-1998 Time: 09:28:18 Project: PEP2INT Magnet Type: QUAD Magnet Name (Serial #): Q1L Measurement System: 2895 Operator: zw Run Number: 7 Comment: q1cin = 20 deg, q1cout = 0 deg Temperature Measurements Table Top Thermistor, T = 21.45868 deg C Magnet Thermistor # 1, T = 21.8096 deg C Magnet Thermistor # 2, T = 21.81183 deg C Harmonics Measurements Date: 04-23-1998 Time: 09:56:11 Magnet Name: Q1L Run Number: 7 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 0.273121E+00 0.187255E-04 -91.04 0.01 45.55579 0.00335 2 0.599530E+00 0.158038E-04 -45.08 0.00 100.00000 0.00373 3 0.143932E-03 0.632981E-07 -37.14 0.04 0.02401 0.00001 4 0.954743E-04 0.194372E-06 10.06 0.01 0.01592 0.00003 5 0.198056E-03 0.174537E-06 -19.07 0.01 0.03304 0.00003 6 0.985240E-04 0.174795E-06 -13.65 0.02 0.01643 0.00003 7 0.220809E-04 0.273391E-06 -17.07 0.05 0.00368 0.00005 8 0.145822E-04 0.329658E-06 15.41 0.09 0.00243 0.00005 9 0.373493E-04 0.283639E-06 -10.50 0.02 0.00623 0.00005 10 0.132627E-04 0.328059E-06 -1.64 0.11 0.00221 0.00005 11 0.460712E-05 0.220288E-06 -0.60 0.21 0.00077 0.00004 12 0.676178E-05 0.455225E-06 -0.47 0.18 0.00113 0.00008 13 0.983146E-05 0.191583E-06 -12.79 0.12 0.00164 0.00003 14 0.125375E-04 0.958669E-07 -7.17 0.11 0.00209 0.00002 15 0.698793E-05 0.368682E-06 -5.24 0.08 0.00117 0.00006 16 0.366762E-05 0.174253E-06 -1.35 0.18 0.00061 0.00003 17 0.638949E-05 0.185954E-06 -6.84 0.13 0.00107 0.00003 18 0.563774E-04 0.231354E-06 3.46 0.01 0.00940 0.00004 19 0.114351E-04 0.176796E-06 -7.67 0.03 0.00191 0.00003 20 0.477374E-04 0.293598E-06 5.80 0.01 0.00796 0.00005 21 0.135392E-04 0.479857E-06 4.90 0.04 0.00226 0.00008 22 0.276903E-04 0.374651E-06 8.13 0.05 0.00462 0.00006 23 0.215403E-04 0.430513E-06 -4.09 0.08 0.00359 0.00007 24 0.731236E-05 0.498986E-06 -3.58 0.06 0.00122 0.00008 25 0.391309E-05 0.135124E-06 -4.78 0.23 0.00065 0.00002 26 0.278170E-04 0.219210E-06 2.54 0.03 0.00464 0.00004 27 0.107208E-04 0.352454E-06 2.29 0.02 0.00179 0.00006 28 0.146274E-05 0.220040E-06 -5.90 0.65 0.00024 0.00004 29 0.313360E-05 0.880831E-07 3.85 0.09 0.00052 0.00001 30 0.156069E-04 0.467054E-06 -4.04 0.01 0.00260 0.00008 31 0.274649E-05 0.308165E-06 5.19 0.16 0.00046 0.00005 32 0.157898E-05 0.132499E-06 0.33 0.62 0.00026 0.00002 33 0.240046E-05 0.163222E-06 -2.98 0.46 0.00040 0.00003 34 0.489953E-05 0.387769E-06 -3.98 0.07 0.00082 0.00006 35 0.155468E-05 0.401880E-06 -3.27 0.25 0.00026 0.00007 36 0.236137E-05 0.232513E-06 0.60 0.27 0.00039 0.00004 37 0.338678E-05 0.446029E-06 -2.19 0.23 0.00056 0.00007 38 0.142622E-05 0.292876E-06 -1.97 0.79 0.00024 0.00005 39 0.236901E-05 0.296444E-06 2.68 0.09 0.00040 0.00005 40 0.253820E-05 0.275628E-06 -4.14 0.35 0.00042 0.00005 The magnetic center is at X = -20497.7 +- 1.5 microns Y = -371.3 +- 2.1 microns View from the top of the magnet: y ^ | S N --> x N S Temperature Measurements Table Top Thermistor, T = 21.22269 deg C Magnet Thermistor # 1, T = 21.64661 deg C Magnet Thermistor # 2, T = 21.47916 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)