SLAC Magnetic Measurements Date: 05-08-1998 Time: 20:43:32 Project: PEP2INT Magnet Type: QUAD Magnet Name (Serial #): Q1R Measurement System: 2895 Operator: se Run Number: 20 Comment: q1cin=120, q1cout=60, repeat short run for comparison Temperature Measurements Table Top Thermistor, T = 21.68695 deg C Magnet Thermistor # 1, T = 21.72723 deg C Magnet Thermistor # 2, T = 21.72595 deg C Harmonics Measurements Date: 05-08-1998 Time: 20:50:53 Magnet Name: Q1R Run Number: 20 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 0.278347E+00 0.324845E-05 88.95 0.00 47.83416 0.00056 2 0.581900E+00 0.596046E-07 44.48 0.00 100.00000 0.00001 3 0.288738E-04 0.460059E-07 -51.75 0.08 0.00496 0.00001 4 0.148537E-03 0.166372E-06 -16.64 0.00 0.02553 0.00003 5 0.571690E-04 0.547261E-07 -7.93 0.01 0.00982 0.00001 6 0.892701E-04 0.126503E-06 12.90 0.01 0.01534 0.00002 7 0.134328E-04 0.875616E-07 -9.31 0.01 0.00231 0.00002 8 0.150220E-04 0.170849E-08 -10.16 0.03 0.00258 0.00000 9 0.184929E-04 0.378313E-07 -3.89 0.01 0.00318 0.00001 10 0.609329E-05 0.759326E-07 -1.62 0.05 0.00105 0.00001 11 0.211721E-04 0.425971E-07 1.52 0.03 0.00364 0.00001 12 0.112784E-04 0.133758E-06 -1.45 0.05 0.00194 0.00002 13 0.920216E-05 0.456284E-07 -0.15 0.03 0.00158 0.00001 14 0.120627E-04 0.411724E-07 3.00 0.02 0.00207 0.00001 15 0.623018E-05 0.123373E-08 -0.71 0.04 0.00107 0.00000 16 0.535548E-05 0.842574E-07 10.18 0.03 0.00092 0.00001 17 0.464971E-05 0.186821E-06 -7.87 0.03 0.00080 0.00003 18 0.417279E-04 0.704968E-07 -4.64 0.00 0.00717 0.00001 19 0.648146E-04 0.462460E-07 -2.22 0.00 0.01114 0.00001 20 0.345104E-04 0.375985E-08 -1.25 0.03 0.00593 0.00000 21 0.268832E-04 0.706332E-07 2.26 0.01 0.00462 0.00001 22 0.542962E-04 0.861910E-07 5.89 0.00 0.00933 0.00001 23 0.177380E-04 0.194028E-06 5.06 0.03 0.00305 0.00003 24 0.112181E-04 0.412038E-06 6.10 0.08 0.00193 0.00007 25 0.736595E-05 0.134987E-06 -3.92 0.04 0.00127 0.00002 26 0.353418E-04 0.465625E-07 -3.94 0.02 0.00607 0.00001 27 0.119517E-04 0.264457E-06 -3.12 0.11 0.00205 0.00005 28 0.361823E-05 0.636456E-06 -4.96 0.22 0.00062 0.00011 29 0.327114E-05 0.221695E-06 1.12 0.15 0.00056 0.00004 30 0.188604E-04 0.459640E-07 2.54 0.00 0.00324 0.00001 31 0.269939E-05 0.795021E-07 2.24 0.29 0.00046 0.00001 32 0.183066E-05 0.100523E-06 0.73 0.10 0.00031 0.00002 33 0.831201E-06 0.545960E-06 -1.29 10.91 0.00014 0.00009 34 0.254491E-05 0.153070E-06 1.83 0.19 0.00044 0.00003 35 0.102706E-05 0.281272E-06 1.85 0.24 0.00018 0.00005 36 0.811139E-06 0.121124E-06 -4.05 0.27 0.00014 0.00002 37 0.470155E-06 0.555736E-07 -2.21 0.09 0.00008 0.00001 38 0.504955E-06 0.480771E-07 -3.93 0.11 0.00009 0.00001 39 0.308138E-06 0.992689E-07 4.39 1.08 0.00005 0.00002 40 0.361238E-06 0.909281E-07 2.83 0.32 0.00006 0.00002 The magnetic center is at X = -21522.7 +- 0.3 microns Y = -396.1 +- 0.1 microns View from the top of the magnet: y ^ | N S --> x S N Temperature Measurements Table Top Thermistor, T = 21.69574 deg C Magnet Thermistor # 1, T = 21.73288 deg C Magnet Thermistor # 2, T = 21.72311 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)