SLAC Magnetic Measurements Date: 11-23-1997 Time: 16:20:19 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): Q1B_02 Measurement System: 7055 Operator: mks Run Number: 15 Comment: Before bolting to Q1B_01. Temperature Measurements Table Top Thermistor, T = 21.05289 deg C Slice Thermistor # 1, T = 21.22415 deg C Slice Thermistor # 2, T = 21.2872 deg C Harmonics Measurements Date: 11-23-1997 Time: 16:26:14 Magnet Name: Q1B_02 Run Number: 15 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 0.263541E-03 0.956061E-07 90.24 0.01 0.77441 0.00028 2 0.340310E-01 0.540488E-07 45.16 0.00 100.00000 0.00022 3 0.364390E-05 0.334239E-08 -30.22 0.01 0.01071 0.00001 4 0.216446E-05 0.225282E-08 30.94 0.04 0.00636 0.00001 5 0.194841E-05 0.240470E-08 21.37 0.00 0.00573 0.00001 6 0.373398E-05 0.310035E-08 -19.58 0.01 0.01097 0.00001 7 0.207108E-05 0.285356E-10 21.88 0.00 0.00609 0.00000 8 0.192023E-05 0.153136E-09 -16.04 0.00 0.00564 0.00000 9 0.345731E-05 0.129182E-08 -7.60 0.00 0.01016 0.00000 10 0.116970E-05 0.116955E-08 -8.01 0.00 0.00344 0.00000 11 0.339580E-05 0.338332E-09 15.69 0.00 0.00998 0.00000 12 0.104194E-05 0.118928E-08 8.57 0.00 0.00306 0.00000 13 0.228417E-05 0.216369E-08 9.32 0.00 0.00671 0.00001 14 0.257515E-05 0.534442E-09 6.35 0.00 0.00757 0.00000 15 0.131595E-05 0.538307E-09 -3.56 0.01 0.00387 0.00000 16 0.127627E-05 0.246280E-08 -6.77 0.01 0.00375 0.00001 17 0.128632E-05 0.610123E-08 9.79 0.00 0.00378 0.00002 18 0.435243E-05 0.133241E-08 1.39 0.00 0.01279 0.00000 19 0.266292E-04 0.110413E-08 -2.97 0.00 0.07825 0.00000 20 0.919309E-05 0.139153E-09 3.19 0.00 0.02701 0.00000 21 0.312192E-04 0.756700E-09 0.20 0.00 0.09174 0.00000 22 0.270199E-04 0.401088E-09 2.37 0.00 0.07940 0.00000 23 0.169832E-04 0.298314E-08 4.36 0.00 0.04991 0.00001 24 0.720022E-05 0.864020E-10 -1.64 0.00 0.02116 0.00000 25 0.923869E-05 0.890168E-08 -0.00 0.00 0.02715 0.00003 26 0.219318E-04 0.789896E-08 -4.52 0.00 0.06445 0.00002 27 0.534788E-06 0.114159E-08 -4.20 0.01 0.00157 0.00000 28 0.565487E-05 0.445016E-08 4.47 0.00 0.01662 0.00001 29 0.232131E-05 0.772081E-08 1.79 0.01 0.00682 0.00002 30 0.148917E-04 0.456430E-08 2.73 0.00 0.04376 0.00001 31 0.143197E-05 0.557566E-08 -2.88 2.89 0.00421 0.00002 32 0.701399E-06 0.880021E-09 -4.88 0.00 0.00206 0.00000 33 0.267105E-05 0.127450E-07 3.41 0.00 0.00785 0.00004 34 0.503785E-05 0.539103E-08 3.14 0.00 0.01480 0.00002 35 0.113507E-05 0.890122E-08 -1.06 0.01 0.00334 0.00003 36 0.106296E-05 0.917885E-08 -1.43 0.02 0.00312 0.00003 37 0.104220E-05 0.919550E-08 -1.30 0.01 0.00306 0.00003 38 0.712630E-06 0.180052E-09 -1.42 0.01 0.00209 0.00000 39 0.592647E-06 0.305820E-08 2.46 0.04 0.00174 0.00001 40 0.827827E-06 0.867146E-08 2.53 0.00 0.00243 0.00003 The magnetic center is at X = -491.7 +- 0.2 microns Y = 2.1 +- 0.1 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 21.00064 deg C Slice Thermistor # 1, T = 21.17914 deg C Slice Thermistor # 2, T = 21.23859 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)