SLAC Magnetic Measurements Date: 04-25-1998 Time: 09:10:39 Project: PEP2INT Magnet Type: QUAD Magnet Name (Serial #): Q1L Measurement System: 2895 Operator: zw Run Number: 19 Comment: q1cin = +40 deg, q1cout = -40 deg Temperature Measurements Table Top Thermistor, T = 21.14087 deg C Magnet Thermistor # 1, T = 22.59979 deg C Magnet Thermistor # 2, T = 22.38696 deg C Harmonics Measurements Date: 04-25-1998 Time: 09:37:47 Magnet Name: Q1L Run Number: 19 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 0.273036E+00 0.186377E-03 -91.09 0.05 48.09061 0.04059 2 0.567753E+00 0.281790E-03 -46.06 0.00 100.00000 0.07019 3 0.135701E-03 0.449916E-07 -36.62 0.01 0.02390 0.00001 4 0.101762E-03 0.129662E-06 9.52 0.01 0.01792 0.00002 5 0.205035E-03 0.957607E-07 -19.12 0.00 0.03611 0.00002 6 0.879593E-04 0.125689E-06 -15.35 0.01 0.01549 0.00002 7 0.212222E-04 0.784650E-07 -17.43 0.03 0.00374 0.00001 8 0.149189E-04 0.880513E-07 15.46 0.04 0.00263 0.00002 9 0.369996E-04 0.970924E-07 -10.44 0.02 0.00652 0.00002 10 0.133720E-04 0.774477E-07 -1.30 0.03 0.00236 0.00001 11 0.448200E-05 0.241991E-06 -0.84 0.15 0.00079 0.00004 12 0.600157E-05 0.239672E-06 -0.43 0.16 0.00106 0.00004 13 0.100969E-04 0.160637E-06 -12.76 0.05 0.00178 0.00003 14 0.116807E-04 0.221128E-06 -7.10 0.02 0.00206 0.00004 15 0.703079E-05 0.914681E-07 -5.50 0.08 0.00124 0.00002 16 0.314510E-05 0.546639E-07 -0.17 0.12 0.00055 0.00001 17 0.804692E-05 0.144799E-06 -7.55 0.01 0.00142 0.00003 18 0.558094E-04 0.262121E-06 3.43 0.00 0.00983 0.00005 19 0.108208E-04 0.307123E-06 -7.53 0.05 0.00191 0.00005 20 0.455792E-04 0.487310E-07 5.74 0.01 0.00803 0.00001 21 0.132474E-04 0.207428E-06 4.67 0.06 0.00233 0.00004 22 0.274409E-04 0.299260E-06 8.06 0.05 0.00483 0.00005 23 0.207324E-04 0.434517E-06 -4.19 0.07 0.00365 0.00008 24 0.633396E-05 0.334681E-06 -3.85 0.08 0.00112 0.00006 25 0.525044E-05 0.133335E-06 -4.90 0.11 0.00092 0.00002 26 0.270230E-04 0.325487E-06 2.62 0.03 0.00476 0.00006 27 0.110889E-04 0.387577E-06 2.47 0.03 0.00195 0.00007 28 0.166780E-05 0.136694E-06 4.67 5.52 0.00029 0.00002 29 0.325237E-05 0.789212E-07 2.97 0.23 0.00057 0.00001 30 0.154695E-04 0.943653E-07 -4.01 0.02 0.00272 0.00002 31 0.209544E-05 0.165198E-06 -3.79 0.24 0.00037 0.00003 32 0.193916E-05 0.356199E-06 -0.82 0.38 0.00034 0.00006 33 0.232805E-05 0.352202E-06 -2.98 1.13 0.00041 0.00006 34 0.367301E-05 0.489051E-06 -3.84 0.04 0.00065 0.00009 35 0.100954E-05 0.387833E-06 -3.54 1.69 0.00018 0.00007 36 0.187310E-05 0.917593E-07 3.34 0.17 0.00033 0.00002 37 0.204281E-05 0.346548E-06 2.14 0.47 0.00036 0.00006 38 0.148608E-05 0.310929E-06 -0.58 0.26 0.00026 0.00005 39 0.189907E-05 0.323431E-06 -2.56 0.39 0.00033 0.00006 40 0.161577E-05 0.174523E-06 -3.64 0.15 0.00028 0.00003 The magnetic center is at X = -21637.8 +- 18.3 microns Y = -410.7 +- 19.0 microns View from the top of the magnet: y ^ | S N --> x N S Temperature Measurements Table Top Thermistor, T = 21.32275 deg C Magnet Thermistor # 1, T = 22.59894 deg C Magnet Thermistor # 2, T = 22.47769 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)