SLAC Magnetic Measurements Date: 05-11-1998 Time: 17:23:03 Project: PEP2INT Magnet Type: QUAD Magnet Name (Serial #): Q1R Measurement System: 2895 Operator: zw Run Number: 30 Comment: Iqtrim = +250 A, QCs set for max strength Temperature Measurements Table Top Thermistor, T = 21.38211 deg C Magnet Thermistor # 1, T = 21.04016 deg C Magnet Thermistor # 2, T = 21.13531 deg C Harmonics Measurements Date: 05-11-1998 Time: 17:50:48 Magnet Name: Q1R Run Number: 30 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 0.278414E+00 0.375713E-05 88.83 0.00 46.57065 0.00081 2 0.597831E+00 0.661940E-05 44.39 0.00 100.00000 0.00157 3 0.341692E-04 0.953762E-07 59.47 0.03 0.00572 0.00002 4 0.212590E-03 0.170575E-06 -19.04 0.01 0.03556 0.00003 5 0.590905E-04 0.152311E-06 -9.20 0.01 0.00988 0.00003 6 0.467103E-04 0.104787E-06 -11.37 0.03 0.00781 0.00002 7 0.156704E-04 0.102706E-06 -10.94 0.03 0.00262 0.00002 8 0.155981E-04 0.352116E-07 -9.96 0.07 0.00261 0.00001 9 0.198366E-04 0.295864E-07 -4.41 0.01 0.00332 0.00000 10 0.732488E-05 0.276267E-06 -4.45 0.09 0.00123 0.00005 11 0.213824E-04 0.906894E-07 1.49 0.01 0.00358 0.00002 12 0.112869E-04 0.202420E-06 -1.54 0.11 0.00189 0.00003 13 0.952037E-05 0.696279E-07 -0.41 0.06 0.00159 0.00001 14 0.121524E-04 0.152960E-06 2.99 0.05 0.00203 0.00003 15 0.623245E-05 0.205881E-06 -0.75 0.04 0.00104 0.00003 16 0.537416E-05 0.207674E-06 10.24 0.03 0.00090 0.00003 17 0.521547E-05 0.771892E-07 -8.24 0.11 0.00087 0.00001 18 0.422953E-04 0.630107E-07 -4.71 0.01 0.00707 0.00001 19 0.653726E-04 0.900436E-07 -2.25 0.00 0.01093 0.00002 20 0.352786E-04 0.131414E-06 -1.28 0.01 0.00590 0.00002 21 0.278968E-04 0.102575E-06 2.22 0.01 0.00467 0.00002 22 0.539897E-04 0.173822E-06 5.88 0.00 0.00903 0.00003 23 0.178908E-04 0.395594E-06 5.03 0.07 0.00299 0.00007 24 0.114596E-04 0.273361E-06 6.22 0.04 0.00192 0.00005 25 0.770611E-05 0.448782E-06 -4.07 0.05 0.00129 0.00008 26 0.354311E-04 0.703101E-07 -4.00 0.04 0.00593 0.00001 27 0.128094E-04 0.175534E-06 -3.15 0.10 0.00214 0.00003 28 0.377346E-05 0.217487E-06 -5.18 0.26 0.00063 0.00004 29 0.309962E-05 0.284878E-06 0.83 0.11 0.00052 0.00005 30 0.189709E-04 0.187463E-06 2.52 0.03 0.00317 0.00003 31 0.259452E-05 0.182746E-06 2.10 0.17 0.00043 0.00003 32 0.188020E-05 0.353913E-06 0.74 0.28 0.00031 0.00006 33 0.839987E-06 0.436375E-06 1.55 0.27 0.00014 0.00007 34 0.255926E-05 0.258284E-06 1.78 0.11 0.00043 0.00004 35 0.953031E-06 0.982862E-07 2.17 0.30 0.00016 0.00002 36 0.744473E-06 0.806364E-07 -4.31 0.17 0.00012 0.00001 37 0.360556E-06 0.924318E-07 -2.86 0.56 0.00006 0.00002 38 0.471773E-06 0.578215E-07 -4.13 0.12 0.00008 0.00001 39 0.325176E-06 0.647012E-07 3.62 0.70 0.00005 0.00001 40 0.381491E-06 0.617751E-07 4.30 1.35 0.00006 0.00001 The magnetic center is at X = -20953.3 +- 0.4 microns Y = -429.5 +- 0.8 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 21.5224 deg C Magnet Thermistor # 1, T = 21.10092 deg C Magnet Thermistor # 2, T = 21.20471 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)