SLAC Magnetic Measurements Date: 04-02-1998 Time: 16:45:33 Project: PEP2INT Magnet Type: Q1TRIM Magnet Name (Serial #): QD1L_QTR Measurement System: 5795 Operator: zw Run Number: 2 Comment: removed harmonics S/N check, harmonics too small Temperature Measurements Table Top Thermistor, T = 41.1853 deg C Slice Thermistor # 1, T = -230.5264 deg C Slice Thermistor # 2, T = -230.5264 deg C Harmonics Measurements Date: 04-02-1998 Time: 16:53:34 Magnet Name: QD1L_QTR Run Number: 2 FIELD HARMONICS Harmonics at Rcoil = .045206 m Main Harmonic N = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.598060E-03 0.298023E-06 97.71 0.03 7.05049 0.00352 2 0.848253E-02 0.260770E-06 43.96 0.00 100.00000 0.00435 3 0.581532E-05 0.946056E-08 -40.75 0.02 0.06856 0.00011 4 0.181660E-05 0.162743E-08 -23.01 0.05 0.02142 0.00002 5 0.266012E-05 0.475166E-08 -11.74 0.01 0.03136 0.00006 6 0.388649E-05 0.370028E-08 -16.43 0.02 0.04582 0.00004 7 0.564892E-07 0.150480E-08 -10.23 0.40 0.00067 0.00002 8 0.149174E-07 0.361026E-09 -6.58 3.88 0.00018 0.00000 9 0.530478E-07 0.734624E-08 -7.58 0.02 0.00063 0.00009 10 0.617057E-07 0.597407E-08 -10.35 0.58 0.00073 0.00007 11 0.153909E-07 0.151962E-08 14.59 2.18 0.00018 0.00002 12 0.125926E-07 0.196896E-08 2.04 2.21 0.00015 0.00002 13 0.956832E-08 0.230078E-08 -2.29 13.06 0.00011 0.00003 14 0.118152E-07 0.249423E-08 -1.91 5.76 0.00014 0.00003 15 0.885057E-08 0.294595E-08 7.72 1.84 0.00010 0.00003 16 0.188734E-07 0.363925E-08 6.59 3.82 0.00022 0.00004 17 0.112635E-07 0.122796E-08 3.39 3.86 0.00013 0.00001 18 0.146342E-07 0.528957E-08 -2.70 1.23 0.00017 0.00006 19 0.139529E-07 0.184843E-08 -3.76 2.06 0.00016 0.00002 20 0.127744E-07 0.318789E-08 -4.79 0.35 0.00015 0.00004 21 0.219110E-07 0.149205E-08 -7.32 4.43 0.00026 0.00002 22 0.199999E-07 0.299824E-08 2.28 0.51 0.00024 0.00004 23 0.764954E-08 0.248090E-08 -5.59 0.22 0.00009 0.00003 24 0.889879E-08 0.574879E-08 6.51 0.10 0.00010 0.00007 25 0.139070E-07 0.780227E-09 -1.26 9.80 0.00016 0.00001 26 0.121554E-07 0.130905E-08 6.64 3.54 0.00014 0.00002 27 0.117417E-07 0.324113E-08 1.98 3.60 0.00014 0.00004 28 0.941726E-08 0.308259E-08 -0.93 7.45 0.00011 0.00004 29 0.180133E-07 0.973422E-08 -3.81 2.89 0.00021 0.00011 30 0.143813E-07 0.966032E-09 -5.10 0.49 0.00017 0.00001 31 0.166880E-07 0.548715E-08 -3.78 2.13 0.00020 0.00006 32 0.159660E-07 0.780409E-08 -4.64 0.03 0.00019 0.00009 33 0.114246E-07 0.176921E-08 -1.09 1.57 0.00013 0.00002 34 0.914503E-08 0.237671E-08 -0.70 1.59 0.00011 0.00003 35 0.223156E-07 0.729419E-08 -0.79 1.61 0.00026 0.00009 36 0.174786E-07 0.431780E-08 -4.14 2.59 0.00021 0.00005 37 0.143629E-07 0.634296E-09 -4.01 1.25 0.00017 0.00001 38 0.117547E-07 0.415799E-08 -1.12 1.58 0.00014 0.00005 39 0.125246E-07 0.933394E-08 -2.64 0.72 0.00015 0.00011 40 0.141094E-07 0.337531E-09 -0.98 0.31 0.00017 0.00000 The magnetic center is at X = -3158.4 +- 1.6 microns Y = 427.5 +- 1.6 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 41.2012 deg C Slice Thermistor # 1, T = -230.5264 deg C Slice Thermistor # 2, T = -230.5264 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)