SLAC Magnetic Measurements Date: 04-20-1999 Time: 16:18:30 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): SK1_2 Measurement System: 5334 Operator: mks Run Number: 19 Comment: 13th tuning step. Temperature Measurements Table Top Thermistor, T = 21.28775 deg C Slice Thermistor # 1, T = 21.57321 deg C Slice Thermistor # 2, T = 21.53381 deg C Harmonics Measurements Date: 04-20-1999 Time: 16:23:29 Magnet Name: SK1_2 Run Number: 19 FIELD HARMONICS Harmonics at Rcoil = .040056 m Main Harmonic N = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.130007E-03 0.968539E-06 -87.80 0.31 0.55631 0.00414 2 0.233695E-01 0.739470E-06 44.82 0.00 100.00000 0.00447 3 0.456930E-05 0.752789E-08 12.83 0.00 0.01955 0.00003 4 0.104659E-04 0.323780E-08 42.74 0.00 0.04478 0.00001 5 0.661651E-05 0.289424E-08 6.17 0.00 0.02831 0.00001 6 0.380429E-05 0.485329E-08 -3.45 0.01 0.01628 0.00002 7 0.784892E-06 0.260513E-09 -8.35 0.03 0.00336 0.00000 8 0.448378E-05 0.422256E-08 21.10 0.00 0.01919 0.00002 9 0.466498E-05 0.526302E-08 17.25 0.03 0.01996 0.00002 10 0.247495E-06 0.311846E-08 -9.61 0.10 0.00106 0.00001 11 0.180111E-05 0.457311E-08 -10.96 0.07 0.00771 0.00002 12 0.182487E-05 0.154357E-07 -11.47 0.02 0.00781 0.00007 13 0.158495E-05 0.340146E-07 -9.75 0.02 0.00678 0.00015 14 0.100554E-05 0.102744E-07 2.04 0.03 0.00430 0.00004 15 0.860693E-06 0.316030E-08 4.13 0.02 0.00368 0.00001 16 0.177620E-06 0.121150E-07 -1.27 0.04 0.00076 0.00005 17 0.128709E-06 0.278515E-08 4.21 0.27 0.00055 0.00001 18 0.135777E-05 0.545157E-08 -5.71 0.01 0.00581 0.00002 19 0.233735E-05 0.862633E-08 -4.26 0.00 0.01000 0.00004 20 0.690201E-06 0.124667E-07 -0.47 0.01 0.00295 0.00005 21 0.836823E-06 0.447017E-09 1.84 0.01 0.00358 0.00000 22 0.398735E-06 0.186176E-08 5.42 0.04 0.00171 0.00001 23 0.320365E-06 0.815533E-09 1.44 0.07 0.00137 0.00000 24 0.280924E-06 0.643495E-08 -5.05 0.03 0.00120 0.00003 25 0.112908E-06 0.117441E-08 5.41 0.13 0.00048 0.00001 26 0.138448E-06 0.426938E-08 -2.92 0.13 0.00059 0.00002 27 0.672472E-07 0.957471E-09 4.18 0.13 0.00029 0.00000 28 0.270364E-07 0.450321E-09 -3.66 0.24 0.00012 0.00000 29 0.228880E-07 0.208795E-08 -1.37 0.57 0.00010 0.00001 30 0.287757E-07 0.854582E-09 3.90 0.16 0.00012 0.00000 31 0.147064E-07 0.151969E-08 -4.82 0.40 0.00006 0.00001 32 0.168816E-07 0.342756E-08 2.87 0.32 0.00007 0.00001 33 0.117180E-07 0.246100E-08 0.95 0.29 0.00005 0.00001 34 0.333993E-07 0.718824E-08 2.95 0.42 0.00014 0.00003 35 0.214722E-07 0.221838E-08 1.61 0.20 0.00009 0.00001 36 0.133748E-07 0.106582E-09 -0.32 1.55 0.00006 0.00000 37 0.141077E-07 0.720958E-09 1.02 2.70 0.00006 0.00000 38 0.164677E-07 0.566213E-08 -2.22 0.05 0.00007 0.00002 39 0.144462E-07 0.339171E-08 0.04 2.40 0.00006 0.00001 40 0.169324E-07 0.787155E-09 0.01 1.50 0.00007 0.00000 The magnetic center is at X = 222.7 +- 1.7 microns Y = -8.6 +- 1.2 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 21.30484 deg C Slice Thermistor # 1, T = 21.57983 deg C Slice Thermistor # 2, T = 21.54086 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)