SLAC Magnetic Measurements Date: 07-02-1998 Time: 10:06:17 Project: PEP2LER Magnet Type: SEXT Magnet Name (Serial #): 153 Measurement System: 2895 Operator: zw Run Number: 1 Comment: 200 A run Standardization Currents 3 cycles, 0 to 200 to 0 A Test Currents 25.0 50.0 75.0 100.0 125.0 150.0 175.0 200.0 Harmonics Measurements Date: 07-02-1998 Time: 10:55:53 Magnet Name: 153 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.1719 +- 2.717719E-03 A Harmonics at Rcoil = .045002 m Main Harmonic N = 3 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.490219E-04 0.706916E-05 114.36 2.52 0.23779 0.03429 2 0.431550E-03 0.296683E-05 85.92 0.42 2.09335 0.01441 3 0.206152E-01 0.671227E-05 -30.65 0.00 100.00000 0.04605 4 0.815372E-04 0.755928E-06 -14.54 3.35 0.39552 0.00367 5 0.310965E-04 0.457831E-05 13.84 1.31 0.15084 0.02221 6 0.111220E-04 0.764236E-05 -12.67 2.49 0.05395 0.03707 7 0.891936E-05 0.423088E-05 14.72 5.63 0.04327 0.02052 8 0.114727E-04 0.470861E-05 -2.79 2.04 0.05565 0.02284 9 0.708126E-04 0.145972E-05 9.75 0.70 0.34350 0.00708 10 0.664976E-05 0.631509E-05 -4.46 36.00 0.03226 0.03063 11 0.589483E-05 0.724894E-05 -15.60 4.28 0.02859 0.03516 12 0.528813E-05 0.775721E-05 7.97 7.82 0.02565 0.03763 13 0.635167E-05 0.829869E-05 -7.19 3.44 0.03081 0.04026 14 0.670741E-05 0.747155E-05 -1.34 0.38 0.03254 0.03624 15 0.169523E-04 0.402818E-05 4.58 1.20 0.08223 0.01954 16 0.596556E-05 0.739731E-05 -0.78 2.25 0.02894 0.03588 17 0.574404E-05 0.801662E-05 -6.46 8.89 0.02786 0.03889 18 0.616531E-05 0.758951E-05 9.77 3.02 0.02991 0.03682 19 0.633000E-05 0.801088E-05 -5.78 3.43 0.03071 0.03886 20 0.641461E-05 0.825757E-05 -8.25 6.91 0.03112 0.04006 21 0.596347E-05 0.717428E-05 -3.32 6.40 0.02893 0.03480 22 0.740246E-05 0.721682E-05 2.91 16.36 0.03591 0.03501 23 0.758929E-05 0.755590E-05 -0.83 3.23 0.03681 0.03665 24 0.803913E-05 0.697879E-05 5.13 3.20 0.03900 0.03385 25 0.709963E-05 0.786970E-05 1.96 4.18 0.03444 0.03817 26 0.782172E-05 0.675568E-05 -5.19 4.46 0.03794 0.03277 27 0.776839E-05 0.765207E-05 5.56 9.40 0.03768 0.03712 28 0.671163E-05 0.794282E-05 2.75 1.02 0.03256 0.03853 29 0.699681E-05 0.738266E-05 4.90 1.92 0.03394 0.03581 30 0.734960E-05 0.760977E-05 3.54 2.30 0.03565 0.03691 31 0.684413E-05 0.807895E-05 -4.88 11.61 0.03320 0.03919 32 0.665060E-05 0.776058E-05 2.07 3.28 0.03226 0.03764 33 0.627618E-05 0.836766E-05 -1.71 6.75 0.03044 0.04059 34 0.635441E-05 0.795866E-05 -1.64 2.44 0.03082 0.03861 35 0.651037E-05 0.822167E-05 -2.92 1.01 0.03158 0.03988 36 0.651158E-05 0.859079E-05 -1.15 1.34 0.03159 0.04167 37 0.668940E-05 0.791868E-05 -4.56 8.01 0.03245 0.03841 38 0.700817E-05 0.773994E-05 -4.10 9.47 0.03400 0.03754 39 0.735828E-05 0.857938E-05 -2.28 2.29 0.03569 0.04162 40 0.100414E-04 0.925565E-05 0.80 1.57 0.04871 0.04490 Date: 07-02-1998 Time: 11:32:43 Magnet Name: 153 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3861 +- 1.449539E-02 A Harmonics at Rcoil = .045002 m Main Harmonic N = 3 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.121328E-03 0.509211E-06 94.32 0.09 0.29592 0.00124 2 0.828947E-03 0.268595E-05 85.88 0.02 2.02177 0.00655 3 0.410010E-01 0.425595E-05 -30.61 0.00 100.00000 0.01468 4 0.163533E-03 0.989544E-06 -18.15 0.06 0.39885 0.00241 5 0.583677E-04 0.684463E-06 15.23 0.16 0.14236 0.00167 6 0.158533E-04 0.137328E-05 -18.11 2.01 0.03867 0.00335 7 0.145570E-04 0.210680E-05 13.35 1.61 0.03550 0.00514 8 0.184020E-04 0.155509E-05 -1.20 0.26 0.04488 0.00379 9 0.141667E-03 0.135447E-05 9.51 0.07 0.34552 0.00330 10 0.581630E-05 0.498058E-06 -8.59 1.92 0.01419 0.00121 11 0.422372E-05 0.783574E-06 15.87 3.69 0.01030 0.00191 12 0.316860E-05 0.121310E-05 9.10 12.22 0.00773 0.00296 13 0.451967E-05 0.135886E-05 -12.94 1.39 0.01102 0.00331 14 0.448207E-05 0.122712E-05 -1.94 0.89 0.01093 0.00299 15 0.290726E-04 0.138942E-05 5.60 0.09 0.07091 0.00339 16 0.205122E-05 0.303405E-06 -0.11 1.60 0.00500 0.00074 17 0.244803E-05 0.670895E-06 -8.89 7.91 0.00597 0.00164 18 0.276151E-05 0.610646E-06 -8.62 2.40 0.00674 0.00149 19 0.223491E-05 0.375529E-06 -6.23 3.10 0.00545 0.00092 20 0.359944E-05 0.123746E-05 -4.74 4.21 0.00878 0.00302 21 0.324517E-05 0.162571E-05 -5.56 3.45 0.00791 0.00397 22 0.454583E-05 0.996269E-06 -2.76 1.18 0.01109 0.00243 23 0.324659E-05 0.126892E-05 3.23 3.58 0.00792 0.00309 24 0.681719E-05 0.212671E-05 -1.29 3.09 0.01663 0.00519 25 0.574457E-05 0.129042E-05 4.42 3.04 0.01401 0.00315 26 0.696849E-05 0.737726E-06 -0.47 0.51 0.01700 0.00180 27 0.604803E-05 0.274318E-05 1.81 4.29 0.01475 0.00669 28 0.404883E-05 0.107742E-05 -2.84 3.73 0.00987 0.00263 29 0.511379E-05 0.212367E-05 5.56 1.69 0.01247 0.00518 30 0.335709E-05 0.120537E-05 -1.77 1.62 0.00819 0.00294 31 0.244397E-05 0.729927E-06 -1.10 1.64 0.00596 0.00178 32 0.294182E-05 0.446790E-06 1.60 2.12 0.00717 0.00109 33 0.316394E-05 0.817303E-06 -3.43 0.50 0.00772 0.00199 34 0.328207E-05 0.426167E-06 3.28 2.72 0.00800 0.00104 35 0.233884E-05 0.104750E-05 -0.17 3.09 0.00570 0.00255 36 0.340698E-05 0.851142E-06 3.72 1.80 0.00831 0.00208 37 0.351605E-05 0.127221E-05 -3.85 1.73 0.00858 0.00310 38 0.538883E-05 0.642423E-06 4.15 2.25 0.01314 0.00157 39 0.657440E-05 0.179232E-05 0.19 1.81 0.01603 0.00437 40 0.100714E-04 0.197758E-05 0.54 1.71 0.02456 0.00482 SUMMARY OF THE CALCULATIONS AND CONVENTIONS USED Calculation Of SL: V3 = Nturns * velocity * B3 * L = Nturns * Rcoil * ang_freq * 1/2 * SL * Rcoil^2 = Nturns * Rcoil^3 * ang_freq * 1/2 * SL SL = 2 * V3 / (Nturns * Rcoil^3 * ang_freq) For a double coil (for coil bowing correction), SL = ( (1 / Nturns * Rcoil^3)1 + (1 / Nturns * Rcoil^3)2 ) * (2 * V3 / ang_freq) Let CoilConst = ( (1 / Nturns * Rcoil^3)1 + (1 / Nturns * Rcoil^3)2 ) SL = CoilConst * 2 * V3 / ang_freq Calculation Of The Harmonics: Magnitude, harmonic n: Vn = Nturns * velocity * Bn * L = Nturns * Rcoil * ang_freq * (BLn) BLn = Vn / (Nturns * Rcoil * ang_freq) Rn = BLn / BL3 = Vn / V3 Phase, harmonic n: At the coil radius, the radial field as a function of angle is, BLn(th) = BLn * cos(n*(th - THspole)) The coil voltage Vn(th) = Nturns * velocity * BLn(th) Vn(th) = Nturns * Rcoil * ang_freq * BLn * cos(n*(th - THspole)) The FFT gives Vn and PhiVn in the formula Vn(i) = Vn * cos(n*2pi*i/N + PhiVn) So, Nturns * Rcoil * ang_freq * BLn = Vn -n * THspole = PhiVn Or, BLn = Vn / (Nturns * Rcoil * ang_freq) THspole = -PhiVn / n Calculation Of The Sextupole Center: In the sextupole's frame, Bx' = S * x' * y' By' = 1/2 * S * (x'^2 - y'^2). In the coil's frame (unprimed frame) the magnetic center is at (x0, y0). In the coil's frame, Bx = S * (x - x0) * (y - y0) By = 1/2 * S * [(x - x0)^2 - (y - y0)^2]. The magnetic center can be found in terms of the measured quadrupole field. Compare Br and Btheta on the x-axis to Bxquad = -S * (x0 * y + y0 * x) Byquad = -S * (x0 * x - y0 * y). Evaluate at x = Rcoil, y = 0 and compare to Br(theta = 0) = Bx, Btheta(theta = 0) = By. In terms of the measured integrated strengths, this gives Xcenter = x0 = - (1/(SL * Rcoil)) * BL2 * sin(2 * THspole2) Ycenter = y0 = - (1/(SL * Rcoil)) * BL2 * cos(2 * THspole2)