SLAC Magnetic Measurements Date: 04-25-1998 Time: 17:05:17 Project: PEP2INT Magnet Type: QUAD Magnet Name (Serial #): Q1L Measurement System: 2895 Operator: zw Run Number: 23 Comment: q1cin = 0 deg, q1cout = 0 deg Temperature Measurements Table Top Thermistor, T = 25.24451 deg C Magnet Thermistor # 1, T = 24.43689 deg C Magnet Thermistor # 2, T = 24.78366 deg C Harmonics Measurements Date: 04-25-1998 Time: 17:33:10 Magnet Name: Q1L Run Number: 23 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 0.272511E+00 0.110067E-03 -90.92 0.01 44.92358 0.01968 2 0.606610E+00 0.102777E-03 -45.82 0.00 100.00000 0.02396 3 0.133857E-03 0.112339E-06 -38.04 0.03 0.02207 0.00002 4 0.100417E-03 0.810413E-07 10.16 0.02 0.01655 0.00001 5 0.218599E-03 0.256546E-06 -19.17 0.01 0.03604 0.00004 6 0.125041E-03 0.151901E-06 -14.98 0.01 0.02061 0.00003 7 0.212675E-04 0.112020E-06 -17.58 0.03 0.00351 0.00002 8 0.143305E-04 0.138628E-06 15.36 0.09 0.00236 0.00002 9 0.376053E-04 0.155545E-06 -10.36 0.03 0.00620 0.00003 10 0.140699E-04 0.100995E-06 -1.58 0.13 0.00232 0.00002 11 0.415578E-05 0.826998E-07 0.01 0.35 0.00069 0.00001 12 0.554284E-05 0.356299E-06 -0.24 0.19 0.00091 0.00006 13 0.103061E-04 0.108270E-06 -13.41 0.14 0.00170 0.00002 14 0.115712E-04 0.419186E-06 -7.19 0.13 0.00191 0.00007 15 0.834397E-05 0.144508E-06 -5.34 0.14 0.00138 0.00002 16 0.377261E-05 0.436540E-06 -1.22 0.63 0.00062 0.00007 17 0.805091E-05 0.288032E-06 -7.37 0.15 0.00133 0.00005 18 0.561029E-04 0.232658E-06 3.40 0.02 0.00925 0.00004 19 0.118440E-04 0.290971E-06 -7.62 0.03 0.00195 0.00005 20 0.461851E-04 0.636535E-06 5.85 0.01 0.00761 0.00010 21 0.132434E-04 0.755686E-06 5.06 0.10 0.00218 0.00012 22 0.282528E-04 0.644963E-06 8.01 0.05 0.00466 0.00011 23 0.204011E-04 0.314808E-06 -4.14 0.02 0.00336 0.00005 24 0.658975E-05 0.484873E-06 -3.08 0.28 0.00109 0.00008 25 0.403695E-05 0.536751E-06 -5.05 0.23 0.00067 0.00009 26 0.269195E-04 0.476023E-06 2.59 0.01 0.00444 0.00008 27 0.107399E-04 0.239951E-06 2.61 0.07 0.00177 0.00004 28 0.145017E-05 0.397443E-06 4.83 1.00 0.00024 0.00007 29 0.295378E-05 0.533093E-06 2.22 0.15 0.00049 0.00009 30 0.157750E-04 0.125621E-06 -3.88 0.06 0.00260 0.00002 31 0.217260E-05 0.433096E-06 -4.56 1.32 0.00036 0.00007 32 0.204443E-05 0.553522E-06 -0.16 0.35 0.00034 0.00009 33 0.128951E-05 0.386594E-06 -1.26 0.64 0.00021 0.00006 34 0.432110E-05 0.498044E-07 -3.50 0.10 0.00071 0.00001 35 0.213029E-05 0.517396E-06 -3.11 0.84 0.00035 0.00009 36 0.115810E-05 0.183493E-06 -0.95 0.54 0.00019 0.00003 37 0.130029E-05 0.333410E-06 -1.14 1.37 0.00021 0.00005 38 0.183734E-05 0.155134E-06 1.84 0.25 0.00030 0.00003 39 0.147738E-05 0.327872E-06 0.13 1.01 0.00024 0.00005 40 0.213926E-05 0.353176E-06 -4.20 0.43 0.00035 0.00006 The magnetic center is at X = -20213.9 +- 8.9 microns Y = -324.2 +- 5.0 microns View from the top of the magnet: y ^ | S N --> x N S Temperature Measurements Table Top Thermistor, T = 25.41452 deg C Magnet Thermistor # 1, T = 24.56229 deg C Magnet Thermistor # 2, T = 24.89172 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)