SLAC Magnetic Measurements Date: 01-06-1998 Time: 07:20:28 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): Q1B_06 Measurement System: 7055 Operator: js Run Number: 1 Comment: post-assembly map. Temperature Measurements Table Top Thermistor, T = 21.06122 deg C Slice Thermistor # 1, T = 21.33356 deg C Slice Thermistor # 2, T = 21.16541 deg C Harmonics Measurements Date: 01-06-1998 Time: 07:26:10 Magnet Name: Q1B_06 Run Number: 1 FIELD HARMONICS Harmonics at Rcoil = .0635 m Main Harmonic N = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.278067E-03 0.529632E-06 136.40 0.07 0.81450 0.00155 2 0.341396E-01 0.819564E-06 44.87 0.00 100.00000 0.00339 3 0.520402E-04 0.120690E-07 -21.19 0.01 0.15243 0.00004 4 0.131490E-03 0.422006E-09 -31.78 0.00 0.38515 0.00001 5 0.795417E-04 0.257387E-07 -28.11 0.00 0.23299 0.00008 6 0.149214E-03 0.950240E-08 15.47 0.00 0.43707 0.00003 7 0.181748E-03 0.167493E-07 -20.99 0.00 0.53237 0.00005 8 0.128581E-03 0.285800E-07 8.16 0.00 0.37663 0.00008 9 0.870238E-04 0.343680E-07 -0.88 0.00 0.25491 0.00010 10 0.625778E-04 0.225991E-07 -17.25 0.00 0.18330 0.00007 11 0.573229E-04 0.103828E-07 -2.79 0.00 0.16791 0.00003 12 0.105704E-03 0.185828E-07 -11.14 0.00 0.30962 0.00005 13 0.503922E-04 0.130349E-07 12.60 0.00 0.14761 0.00004 14 0.776322E-04 0.417276E-08 -10.63 0.00 0.22740 0.00001 15 0.296528E-04 0.152631E-07 7.86 0.00 0.08686 0.00004 16 0.669804E-04 0.153486E-07 0.33 0.00 0.19620 0.00005 17 0.286289E-04 0.102282E-07 1.43 0.00 0.08386 0.00003 18 0.488606E-04 0.697037E-08 3.51 0.00 0.14312 0.00002 19 0.875822E-05 0.207128E-07 -3.99 0.00 0.02565 0.00006 20 0.322236E-04 0.115870E-08 8.90 0.00 0.09439 0.00000 21 0.108737E-04 0.874161E-08 1.70 0.00 0.03185 0.00003 22 0.128119E-04 0.186537E-08 -2.83 0.00 0.03753 0.00001 23 0.386249E-05 0.180376E-08 5.31 0.00 0.01131 0.00001 24 0.801449E-05 0.795353E-09 0.25 0.00 0.02348 0.00000 25 0.615562E-06 0.439903E-08 -3.71 0.03 0.00180 0.00001 26 0.385302E-05 0.688874E-08 5.72 0.01 0.01129 0.00002 27 0.318119E-05 0.135436E-07 2.51 0.01 0.00932 0.00004 28 0.907281E-06 0.227391E-08 -3.76 0.01 0.00266 0.00001 29 0.523019E-06 0.149501E-07 -2.83 0.01 0.00153 0.00004 30 0.486754E-05 0.131645E-07 1.87 0.01 0.01426 0.00004 31 0.598449E-06 0.877688E-08 -1.12 0.05 0.00175 0.00003 32 0.866115E-06 0.144579E-07 -1.07 0.04 0.00254 0.00004 33 0.129543E-05 0.235339E-07 3.34 0.00 0.00379 0.00007 34 0.647551E-05 0.210337E-07 2.53 0.00 0.01897 0.00006 35 0.124346E-06 0.233236E-07 0.67 0.26 0.00036 0.00007 36 0.613446E-06 0.572129E-08 4.76 0.00 0.00180 0.00002 37 0.211690E-06 0.205656E-07 -2.43 2.34 0.00062 0.00006 38 0.477039E-06 0.229405E-07 1.78 0.04 0.00140 0.00007 39 0.105700E-05 0.120484E-07 -3.40 0.04 0.00310 0.00004 40 0.510278E-06 0.178474E-08 1.19 0.05 0.00149 0.00001 The magnetic center is at X = -356.7 +- 0.8 microns Y = 374.5 +- 0.9 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 21.0564 deg C Slice Thermistor # 1, T = 21.26331 deg C Slice Thermistor # 2, T = 21.13687 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)