SLAC Magnetic Measurements Date: 11-09-1997 Time: 17:26:10 Project: PEP2INT Magnet Type: PMSLICES Magnet Name (Serial #): Q1B_02 Measurement System: 7055 Operator: mks Run Number: 10 Comment: 4th tuning step. Temperature Measurements Table Top Thermistor, T = 21.19693 deg C Slice Thermistor # 1, T = 21.30591 deg C Slice Thermistor # 2, T = 21.40295 deg C Harmonics Measurements Date: 11-09-1997 Time: 17:32:09 Magnet Name: Q1B_02 Run Number: 10 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 0.210987E-03 0.810726E-05 153.43 2.33 0.62072 0.02385 2 0.339908E-01 0.942871E-05 44.79 0.01 100.00000 0.03923 3 0.106191E-05 0.360086E-08 -39.42 0.06 0.00312 0.00001 4 0.125567E-05 0.427349E-09 2.65 0.02 0.00369 0.00000 5 0.326012E-05 0.124726E-08 20.09 0.00 0.00959 0.00000 6 0.208956E-05 0.482271E-08 24.77 0.00 0.00615 0.00001 7 0.138066E-05 0.296541E-08 1.24 0.02 0.00406 0.00001 8 0.429214E-05 0.305863E-08 -13.70 0.01 0.01263 0.00001 9 0.155436E-05 0.412746E-08 18.63 0.00 0.00457 0.00001 10 0.379758E-05 0.407874E-08 -10.43 0.01 0.01117 0.00001 11 0.331243E-05 0.261355E-08 12.80 0.00 0.00975 0.00001 12 0.378899E-05 0.914724E-09 4.92 0.00 0.01115 0.00000 13 0.289338E-05 0.285809E-08 0.09 0.00 0.00851 0.00001 14 0.477597E-05 0.183331E-08 6.53 0.00 0.01405 0.00001 15 0.210194E-05 0.302168E-08 -2.70 0.01 0.00618 0.00001 16 0.152634E-05 0.267647E-08 -6.44 0.00 0.00449 0.00001 17 0.199659E-05 0.169257E-08 -6.73 0.00 0.00587 0.00001 18 0.662725E-05 0.394084E-08 4.66 0.00 0.01950 0.00001 19 0.271027E-04 0.441106E-09 -1.65 0.00 0.07974 0.00002 20 0.706252E-05 0.564887E-08 -6.08 0.00 0.02078 0.00002 21 0.275461E-04 0.236560E-08 4.55 0.00 0.08104 0.00002 22 0.242445E-04 0.266664E-08 6.30 0.00 0.07133 0.00002 23 0.179380E-04 0.169894E-08 7.14 0.00 0.05277 0.00002 24 0.940980E-05 0.172122E-08 1.13 0.00 0.02768 0.00001 25 0.924078E-05 0.399586E-08 -2.05 0.00 0.02719 0.00001 26 0.213025E-04 0.367618E-08 -2.41 0.00 0.06267 0.00002 27 0.210066E-05 0.634373E-09 -1.38 0.01 0.00618 0.00000 28 0.576030E-05 0.448790E-08 -4.66 0.00 0.01695 0.00001 29 0.386385E-05 0.424279E-08 5.36 0.00 0.01137 0.00001 30 0.160054E-04 0.137179E-07 3.24 0.00 0.04709 0.00004 31 0.120867E-05 0.801833E-09 3.35 0.01 0.00356 0.00000 32 0.746444E-06 0.165568E-08 3.46 0.00 0.00220 0.00000 33 0.649024E-06 0.530355E-08 -0.08 0.05 0.00191 0.00002 34 0.570466E-05 0.464024E-08 2.02 0.00 0.01678 0.00001 35 0.728000E-06 0.396113E-08 -1.69 0.01 0.00214 0.00001 36 0.616388E-06 0.224946E-08 1.63 0.01 0.00181 0.00001 37 0.685767E-06 0.186589E-08 3.50 0.01 0.00202 0.00001 38 0.808054E-06 0.787537E-08 -3.28 0.02 0.00238 0.00002 39 0.195567E-06 0.487693E-08 -4.24 0.04 0.00058 0.00001 40 0.762295E-06 0.468896E-08 -2.73 0.00 0.00224 0.00001 The magnetic center is at X = -176.3 +- 15.9 microns Y = 352.5 +- 15.3 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 21.14395 deg C Slice Thermistor # 1, T = 21.19653 deg C Slice Thermistor # 2, T = 21.20212 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)