SLAC Magnetic Measurements Date: 04-25-1998 Time: 09:50:16 Project: PEP2INT Magnet Type: QUAD Magnet Name (Serial #): Q1L Measurement System: 2895 Operator: zw Run Number: 20 Comment: q1cin = +60 deg, q1cout = -60 deg Temperature Measurements Table Top Thermistor, T = 21.42215 deg C Magnet Thermistor # 1, T = 22.59671 deg C Magnet Thermistor # 2, T = 22.5195 deg C Harmonics Measurements Date: 04-25-1998 Time: 10:17:27 Magnet Name: Q1L Run Number: 20 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 0.273437E+00 0.527804E-05 -91.08 0.00 50.96356 0.00130 2 0.536535E+00 0.893021E-05 -46.28 0.00 100.00000 0.00235 3 0.135531E-03 0.201292E-06 -36.79 0.03 0.02526 0.00004 4 0.101057E-03 0.773211E-07 9.54 0.03 0.01884 0.00001 5 0.206059E-03 0.269308E-06 -19.19 0.01 0.03841 0.00005 6 0.807297E-04 0.310740E-06 -15.95 0.01 0.01505 0.00006 7 0.224255E-04 0.360028E-06 -17.27 0.03 0.00418 0.00007 8 0.141027E-04 0.200751E-06 15.50 0.11 0.00263 0.00004 9 0.365141E-04 0.250189E-06 -10.39 0.03 0.00681 0.00005 10 0.129181E-04 0.181808E-06 -1.67 0.16 0.00241 0.00003 11 0.430078E-05 0.237763E-06 -0.25 0.30 0.00080 0.00004 12 0.554144E-05 0.275417E-06 -0.87 0.21 0.00103 0.00005 13 0.101383E-04 0.174475E-06 -12.63 0.11 0.00189 0.00003 14 0.120480E-04 0.232241E-06 -7.34 0.07 0.00225 0.00004 15 0.715846E-05 0.490634E-06 -5.47 0.04 0.00133 0.00009 16 0.260842E-05 0.532162E-07 -0.19 0.28 0.00049 0.00001 17 0.793434E-05 0.144533E-06 -7.48 0.11 0.00148 0.00003 18 0.559468E-04 0.357611E-06 3.44 0.01 0.01043 0.00007 19 0.115398E-04 0.154015E-06 -7.54 0.05 0.00215 0.00003 20 0.462751E-04 0.256566E-06 5.73 0.01 0.00862 0.00005 21 0.133054E-04 0.189155E-06 4.67 0.10 0.00248 0.00004 22 0.275199E-04 0.379632E-06 7.94 0.04 0.00513 0.00007 23 0.201394E-04 0.484083E-06 -4.18 0.06 0.00375 0.00009 24 0.567963E-05 0.268738E-06 -3.37 0.16 0.00106 0.00005 25 0.580046E-05 0.607167E-06 -4.95 0.09 0.00108 0.00011 26 0.272756E-04 0.294819E-06 2.60 0.01 0.00508 0.00005 27 0.111172E-04 0.181930E-06 2.37 0.06 0.00207 0.00003 28 0.145204E-05 0.488699E-06 -5.98 0.20 0.00027 0.00009 29 0.331267E-05 0.184940E-06 3.59 0.07 0.00062 0.00003 30 0.165791E-04 0.187742E-06 -3.95 0.05 0.00309 0.00003 31 0.225490E-05 0.106896E-06 -5.10 0.72 0.00042 0.00002 32 0.251536E-05 0.261367E-06 -0.31 0.25 0.00047 0.00005 33 0.265759E-05 0.249879E-06 -3.25 0.28 0.00050 0.00005 34 0.387198E-05 0.351538E-06 -3.68 0.11 0.00072 0.00007 35 0.157400E-05 0.198288E-06 -3.04 0.68 0.00029 0.00004 36 0.140630E-05 0.124962E-06 0.87 1.03 0.00026 0.00002 37 0.179323E-05 0.257807E-06 3.05 1.23 0.00033 0.00005 38 0.143029E-05 0.783139E-07 0.13 0.84 0.00027 0.00001 39 0.219149E-05 0.206511E-06 3.49 1.82 0.00041 0.00004 40 0.201997E-05 0.434149E-06 -3.56 0.03 0.00038 0.00008 The magnetic center is at X = -22930.5 +- 0.6 microns Y = -433.3 +- 0.6 microns View from the top of the magnet: y ^ | S N --> x N S Temperature Measurements Table Top Thermistor, T = 21.64014 deg C Magnet Thermistor # 1, T = 22.64905 deg C Magnet Thermistor # 2, T = 22.63791 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)