SLAC Magnetic Measurements Date: 04-04-1998 Time: 10:38:50 Project: PEP2INT Magnet Type: Q1TRIM Magnet Name (Serial #): QD1L_D1T Measurement System: 5795 Operator: zw Run Number: 1 Comment: Iquad = 0, Id1 = 50.1 A, Id2 = 0, inner dipole trim winding Temperature Measurements Table Top Thermistor, T = 41.11002 deg C Slice Thermistor # 1, T = -230.5264 deg C Slice Thermistor # 2, T = -230.5264 deg C Harmonics Measurements Date: 04-04-1998 Time: 11:07:10 Magnet Name: QD1L_D1T Run Number: 1 FIELD HARMONICS Harmonics at Rcoil = .045206 m Main Harmonic N = 1 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.591070E-02 0.384320E-06 -91.30 0.00 100.00000 0.00920 2 0.450203E-05 0.433377E-06 21.37 0.39 0.07617 0.00733 3 0.510426E-04 0.922414E-08 29.03 0.00 0.86356 0.00017 4 0.215387E-05 0.942708E-08 18.97 0.05 0.03644 0.00016 5 0.555960E-05 0.676747E-08 17.01 0.01 0.09406 0.00011 6 0.552355E-07 0.107973E-07 -21.48 0.80 0.00093 0.00018 7 0.779991E-07 0.481940E-08 -13.02 0.63 0.00132 0.00008 8 0.149327E-07 0.401664E-08 -0.40 11.05 0.00025 0.00007 9 0.186902E-07 0.515209E-08 7.10 1.93 0.00032 0.00009 10 0.982913E-08 0.218020E-08 15.37 4.98 0.00017 0.00004 11 0.115702E-07 0.445663E-08 -9.69 14.15 0.00020 0.00008 12 0.124330E-07 0.465867E-08 -2.84 4.47 0.00021 0.00008 13 0.137020E-07 0.450459E-08 5.36 4.02 0.00023 0.00008 14 0.139081E-07 0.186285E-08 11.12 3.57 0.00024 0.00003 15 0.131214E-07 0.283977E-08 5.51 3.29 0.00022 0.00005 16 0.113491E-07 0.365772E-08 -7.10 2.37 0.00019 0.00006 17 0.178439E-07 0.486124E-08 8.69 2.32 0.00030 0.00008 18 0.125121E-07 0.364790E-08 3.90 5.02 0.00021 0.00006 19 0.109685E-07 0.748672E-08 2.94 2.09 0.00019 0.00013 20 0.132949E-07 0.441206E-08 6.72 8.23 0.00022 0.00007 21 0.130497E-07 0.190543E-08 -4.02 8.43 0.00022 0.00003 22 0.127845E-07 0.173973E-08 -4.62 1.30 0.00022 0.00003 23 0.128241E-07 0.336207E-08 0.93 2.39 0.00022 0.00006 24 0.901686E-08 0.299948E-08 -4.78 10.06 0.00015 0.00005 25 0.183782E-07 0.293012E-08 2.31 2.60 0.00031 0.00005 26 0.131758E-07 0.469747E-08 -3.22 2.59 0.00022 0.00008 27 0.145875E-07 0.242494E-08 5.65 2.60 0.00025 0.00004 28 0.171832E-07 0.137880E-08 6.17 1.56 0.00029 0.00002 29 0.163587E-07 0.443217E-08 -2.61 3.76 0.00028 0.00007 30 0.142250E-07 0.387851E-08 0.61 3.14 0.00024 0.00007 31 0.147576E-07 0.518264E-08 -4.09 5.43 0.00025 0.00009 32 0.135184E-07 0.477007E-08 -4.22 1.31 0.00023 0.00008 33 0.178696E-07 0.513230E-08 -2.89 1.33 0.00030 0.00009 34 0.172038E-07 0.604189E-08 -3.58 2.67 0.00029 0.00010 35 0.210160E-07 0.192578E-08 1.86 1.31 0.00036 0.00003 36 0.124338E-07 0.465656E-08 1.11 2.37 0.00021 0.00008 37 0.165749E-07 0.861061E-08 -0.31 1.49 0.00028 0.00015 38 0.137662E-07 0.368949E-08 3.00 1.13 0.00023 0.00006 39 0.134590E-07 0.527399E-08 4.11 4.53 0.00023 0.00009 40 0.917113E-08 0.224142E-08 2.09 3.82 0.00016 0.00004 The magnetic center is at X = %59335628.0 +- %5711800.0 microns Y = %1346046.0 +- 129618.4 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 41.13168 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)