SLAC Magnetic Measurements Date: 05-08-1998 Time: 16:27:54 Project: PEP2INT Magnet Type: QUAD Magnet Name (Serial #): Q1R Measurement System: 2895 Operator: se Run Number: 15 Comment: q1cin=100, q1cout=120 Temperature Measurements Table Top Thermistor, T = 21.67606 deg C Magnet Thermistor # 1, T = 21.77341 deg C Magnet Thermistor # 2, T = 21.47519 deg C Harmonics Measurements Date: 05-08-1998 Time: 16:55:36 Magnet Name: Q1R Run Number: 15 FIELD HARMONICS Harmonics at Rcoil = .045002 m Main Harmonic N = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.278485E+00 0.873086E-06 88.88 0.00 47.22130 0.00030 2 0.589744E+00 0.321216E-05 45.91 0.00 100.00000 0.00077 3 0.260912E-04 0.511044E-07 -49.58 0.03 0.00442 0.00001 4 0.150928E-03 0.911505E-07 -16.86 0.00 0.02559 0.00002 5 0.564005E-04 0.907647E-07 -8.45 0.01 0.00956 0.00002 6 0.898411E-04 0.992681E-07 14.02 0.02 0.01523 0.00002 7 0.136685E-04 0.167669E-06 -10.48 0.05 0.00232 0.00003 8 0.150785E-04 0.113589E-06 -9.88 0.06 0.00256 0.00002 9 0.188966E-04 0.503824E-07 -3.74 0.03 0.00320 0.00001 10 0.607191E-05 0.132614E-06 -1.91 0.11 0.00103 0.00002 11 0.214875E-04 0.126910E-06 1.55 0.01 0.00364 0.00002 12 0.113159E-04 0.171993E-06 -1.39 0.01 0.00192 0.00003 13 0.942857E-05 0.723875E-07 -0.19 0.03 0.00160 0.00001 14 0.123324E-04 0.695301E-07 3.00 0.02 0.00209 0.00001 15 0.631962E-05 0.570491E-07 -0.72 0.09 0.00107 0.00001 16 0.542983E-05 0.581427E-07 10.20 0.06 0.00092 0.00001 17 0.495034E-05 0.699691E-07 -7.73 0.08 0.00084 0.00001 18 0.420488E-04 0.262275E-07 -4.63 0.01 0.00713 0.00000 19 0.651619E-04 0.182532E-06 -2.23 0.00 0.01105 0.00003 20 0.346605E-04 0.166276E-06 -1.24 0.01 0.00588 0.00003 21 0.268779E-04 0.286086E-06 2.29 0.01 0.00456 0.00005 22 0.540343E-04 0.243744E-06 5.89 0.01 0.00916 0.00004 23 0.176982E-04 0.450887E-06 5.10 0.04 0.00300 0.00008 24 0.109653E-04 0.838955E-06 6.11 0.08 0.00186 0.00014 25 0.784481E-05 0.360275E-06 -3.89 0.07 0.00133 0.00006 26 0.351220E-04 0.338007E-06 -3.91 0.03 0.00596 0.00006 27 0.120752E-04 0.340519E-06 -3.10 0.03 0.00205 0.00006 28 0.307741E-05 0.685362E-06 -4.71 0.11 0.00052 0.00012 29 0.324176E-05 0.163601E-06 1.23 0.08 0.00055 0.00003 30 0.187889E-04 0.906870E-07 2.54 0.02 0.00319 0.00002 31 0.285102E-05 0.300306E-06 1.93 0.12 0.00048 0.00005 32 0.199573E-05 0.299761E-06 0.72 0.16 0.00034 0.00005 33 0.138087E-05 0.373305E-06 1.44 0.39 0.00023 0.00006 34 0.250863E-05 0.315237E-06 1.60 0.12 0.00043 0.00005 35 0.120888E-05 0.127493E-06 1.50 0.10 0.00020 0.00002 36 0.639121E-06 0.133191E-06 -3.84 0.16 0.00011 0.00002 37 0.281316E-06 0.992511E-07 -4.64 1.55 0.00005 0.00002 38 0.427665E-06 0.103418E-06 -4.12 0.22 0.00007 0.00002 39 0.240855E-06 0.683389E-07 -4.34 0.99 0.00004 0.00001 40 0.366630E-06 0.136482E-06 4.32 1.85 0.00006 0.00002 The magnetic center is at X = -21246.4 +- 0.1 microns Y = -416.3 +- 0.3 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 21.70044 deg C Magnet Thermistor # 1, T = 21.78656 deg C Magnet Thermistor # 2, T = 21.52695 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)