Los Alamos National Laboratory Poisson Superfish Program Automesh written by James H. Billen and Lloyd M. Young The original Poisson Superfish codes were developed by Ron F. Holsinger in collaboration with Klaus Halbach. These programs are provided as a service to the accelerator community by the Los Alamos Accelerator Code Group (LAACG). (c) Copyright 1985-2005, by the Regents of the University of California. This software was produced under U. S. Government contract W-7405-ENG-36 by Los Alamos National Laboratory, which is operated by the University of California for the U. S. Department of Energy. Neither the Government nor the University makes any warranty, express or implied, or assumes any liability or responsibility for its use, or represents that use of this software would not infringe privately owned rights. Unpublished - rights reserved under Copyright Laws of the United States. Program Automesh 7.17 released 1-13-2006 Program file: C:\LANL\AUTOFISH.EXE Problem file: C:\LANL\Examples\RADIOF~1\PILLBO~1\PILLBOX-FNAL-205.AF 12-14-2007 17:20:38 SF.INI file: C:\LANL\SF.INI 11-12-2007 14:55:22 Problem description: 201 MHz MUCOOL cavity with rounded pillbox profile In this problem, Kmax < Lmax Coordinates and lengths have dimensions of centimeters. Region data: IREG = 1 MAT = 1 CUR = 0.0 DEN = 0.0 ITRI = 0 [equal weight triangles] IBOUND = 1 [Neumann boundary] IPDIAG = 0 [no extra Automesh diagnostics] DX = 0.2 XMIN = 0.0 XMAX = 21 DY = 0.1732051 [=DX*sin(60)] YMIN = 0.0 YMAX = 56.85 DX1 = 0.2 KMAX = 106 DY1 = 0.1733232 LMAX = 329 ITOT = 35748 Memory used for the solution file: 1.287 M Memory used for Automesh setup data: 466.048 K Region 1 boundary points from the PO namelist: Point NT X0 Y0 X Y R THETA A B 1 1 21.00 0.000 2 1 0.000 0.000 3 1 0.000 56.85 4 1 18.54 56.85 5 1 21.00 56.85 6 1 21.00 0.000 Number of user-supplied fixed points = 6 Fixed points added at line regions = 0 Fixed points added on overlapping regions = 0 Total number of fixed points = 6 Logical path finding for region 1 (includes extra boundary points at intersections of line regions plus points from other user-supplied segments) Point NT X Y R A B Fwd Bkw 2 1 0.000 0.000 106 106 3 1 0.000 56.85 329 329 4 1 18.54 56.85 93 93 5 1 21.00 56.85 14 14 6 1 21.00 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28.4249990 106 164 21.0000000 28.2516758 106 163 21.0000000 28.0783527 106 162 21.0000000 27.9050295 106 161 21.0000000 27.7317063 106 160 21.0000000 27.5583832 106 159 21.0000000 27.3850600 106 158 21.0000000 27.2117368 106 157 21.0000000 27.0384137 106 156 21.0000000 26.8650905 106 155 21.0000000 26.6917674 106 154 21.0000000 26.5184442 106 153 21.0000000 26.3451210 106 152 21.0000000 26.1717979 106 151 21.0000000 25.9984747 106 150 21.0000000 25.8251515 106 149 21.0000000 25.6518284 106 148 21.0000000 25.4785052 106 147 21.0000000 25.3051820 106 146 21.0000000 25.1318589 106 145 21.0000000 24.9585357 106 144 21.0000000 24.7852125 106 143 21.0000000 24.6118894 106 142 21.0000000 24.4385662 106 141 21.0000000 24.2652430 106 140 21.0000000 24.0919199 106 139 21.0000000 23.9185967 106 138 21.0000000 23.7452736 106 137 21.0000000 23.5719504 106 136 21.0000000 23.3986272 106 135 21.0000000 23.2253041 106 134 21.0000000 23.0519809 106 133 21.0000000 22.8786577 106 132 21.0000000 22.7053346 106 131 21.0000000 22.5320114 106 130 21.0000000 22.3586882 106 129 21.0000000 22.1853651 106 128 21.0000000 22.0120419 106 127 21.0000000 21.8387187 106 126 21.0000000 21.6653956 106 125 21.0000000 21.4920724 106 124 21.0000000 21.3187492 106 123 21.0000000 21.1454261 106 122 21.0000000 20.9721029 106 121 21.0000000 20.7987798 106 120 21.0000000 20.6254566 106 119 21.0000000 20.4521334 106 118 21.0000000 20.2788103 106 117 21.0000000 20.1054871 106 116 21.0000000 19.9321639 106 115 21.0000000 19.7588408 106 114 21.0000000 19.5855176 106 113 21.0000000 19.4121944 106 112 21.0000000 19.2388713 106 111 21.0000000 19.0655481 106 110 21.0000000 18.8922249 106 109 21.0000000 18.7189018 106 108 21.0000000 18.5455786 106 107 21.0000000 18.3722555 106 106 21.0000000 18.1989323 106 105 21.0000000 18.0256091 106 104 21.0000000 17.8522860 106 103 21.0000000 17.6789628 106 102 21.0000000 17.5056396 106 101 21.0000000 17.3323165 106 100 21.0000000 17.1589933 106 99 21.0000000 16.9856701 106 98 21.0000000 16.8123470 106 97 21.0000000 16.6390238 106 96 21.0000000 16.4657006 106 95 21.0000000 16.2923775 106 94 21.0000000 16.1190543 106 93 21.0000000 15.9457311 106 92 21.0000000 15.7724080 106 91 21.0000000 15.5990848 106 90 21.0000000 15.4257617 106 89 21.0000000 15.2524385 106 88 21.0000000 15.0791153 106 87 21.0000000 14.9057922 106 86 21.0000000 14.7324690 106 85 21.0000000 14.5591458 106 84 21.0000000 14.3858227 106 83 21.0000000 14.2124995 106 82 21.0000000 14.0391763 106 81 21.0000000 13.8658532 106 80 21.0000000 13.6925300 106 79 21.0000000 13.5192068 106 78 21.0000000 13.3458837 106 77 21.0000000 13.1725605 106 76 21.0000000 12.9992373 106 75 21.0000000 12.8259142 106 74 21.0000000 12.6525910 106 73 21.0000000 12.4792679 106 72 21.0000000 12.3059447 106 71 21.0000000 12.1326215 106 70 21.0000000 11.9592984 106 69 21.0000000 11.7859752 106 68 21.0000000 11.6126520 106 67 21.0000000 11.4393289 106 66 21.0000000 11.2660057 106 65 21.0000000 11.0926825 106 64 21.0000000 10.9193594 106 63 21.0000000 10.7460362 106 62 21.0000000 10.5727130 106 61 21.0000000 10.3993899 106 60 21.0000000 10.2260667 106 59 21.0000000 10.0527435 106 58 21.0000000 9.87942038 106 57 21.0000000 9.70609722 106 56 21.0000000 9.53277405 106 55 21.0000000 9.35945089 106 54 21.0000000 9.18612773 106 53 21.0000000 9.01280456 106 52 21.0000000 8.83948140 106 51 21.0000000 8.66615823 106 50 21.0000000 8.49283507 106 49 21.0000000 8.31951190 106 48 21.0000000 8.14618874 106 47 21.0000000 7.97286557 106 46 21.0000000 7.79954241 106 45 21.0000000 7.62621924 106 44 21.0000000 7.45289608 106 43 21.0000000 7.27957291 106 42 21.0000000 7.10624975 106 41 21.0000000 6.93292659 106 40 21.0000000 6.75960342 106 39 21.0000000 6.58628026 106 38 21.0000000 6.41295709 106 37 21.0000000 6.23963393 106 36 21.0000000 6.06631076 106 35 21.0000000 5.89298760 106 34 21.0000000 5.71966443 106 33 21.0000000 5.54634127 106 32 21.0000000 5.37301810 106 31 21.0000000 5.19969494 106 30 21.0000000 5.02637177 106 29 21.0000000 4.85304861 106 28 21.0000000 4.67972545 106 27 21.0000000 4.50640228 106 26 21.0000000 4.33307912 106 25 21.0000000 4.15975595 106 24 21.0000000 3.98643279 106 23 21.0000000 3.81310962 106 22 21.0000000 3.63978646 106 21 21.0000000 3.46646329 106 20 21.0000000 3.29314013 106 19 21.0000000 3.11981696 106 18 21.0000000 2.94649380 106 17 21.0000000 2.77317063 106 16 21.0000000 2.59984747 106 15 21.0000000 2.42652430 106 14 21.0000000 2.25320114 106 13 21.0000000 2.07987798 106 12 21.0000000 1.90655481 106 11 21.0000000 1.73323165 106 10 21.0000000 1.55990848 106 9 21.0000000 1.38658532 106 8 21.0000000 1.21326215 106 7 21.0000000 1.03993899 106 6 21.0000000 0.866615823 106 5 21.0000000 0.693292659 106 4 21.0000000 0.519969494 106 3 21.0000000 0.346646329 106 2 21.0000000 0.173323165 106 1 21.0000000 0.00000000 Region 1 done, 6 fixed points, 867 total boundary points. Logical boundary segment end points for region 1: Segment Starting Point Ending Point K L K L 1 106 1 1 1 2 1 1 1 329 3 1 329 93 329 4 93 329 106 329 5 106 329 106 1 Drive point at X =00.0, K = 1, Y = 55, L = 318. Region 2 mesh points K L X Y 1 318 0.00000000 55.0000000 Processing boundary data... Memory used for additional setup arrays: 920.560 K Region 1 Material = 1 Region boundary indicator = 1 Equal-weight triangles Region 1 is closed. Region 2 Material = 1 Region boundary indicator = -1 Driving field = 1 Equal-weight triangles Region 2 contains a single point. Logical boundary segment end points for all regions: Segment Starting Point Ending Point Index K L Index K L 1 1 106 1 106 1 1 2 106 1 1 434 1 329 3 434 1 329 526 93 329 4 526 93 329 539 106 329 5 539 106 329 867 106 1 Relaxation parameters, 34008 unknown points. Optimizing mesh by successive over relaxation... -------X coordinate-------- -------Y coordinate-------- Cycle Residual ETA RHO Residual ETA RHO 1 6.986E-03 1.0000 1.6000 4.566E-05 1.0000 1.6000 2 9.598E-03 0.6821 1.6000 6.288E-05 0.6870 1.6000 3 6.561E-03 0.6837 1.6000 4.333E-05 0.6891 1.6000 4 4.480E-03 0.6829 1.6000 2.991E-05 0.6903 1.6000 5 3.064E-03 0.6839 1.6000 2.067E-05 0.6912 1.6000 6 2.093E-03 0.6830 1.6000 1.432E-05 0.6928 1.6000 7 1.433E-03 0.6845 1.6000 9.943E-06 0.6943 1.6000 8 9.788E-04 0.6833 1.6000 6.929E-06 0.6968 1.6000 9 6.715E-04 0.6861 1.6000 4.851E-06 0.7001 1.6000 10 4.598E-04 0.6847 1.6000 3.419E-06 0.7048 1.6000 11 3.174E-04 0.6903 1.6000 2.434E-06 0.7120 1.6000 12 2.190E-04 0.6901 1.6000 1.758E-06 0.7220 1.6000 13 1.540E-04 0.7030 1.6000 1.295E-06 0.7367 1.6000 14 1.092E-04 0.7090 1.6000 9.793E-07 0.7563 1.6000 15 8.067E-05 0.7390 1.6000 7.653E-07 0.7814 1.6000 16 6.139E-05 0.7610 1.6000 6.199E-07 0.8100 1.6000 17 4.993E-05 0.8133 1.6000 5.202E-07 0.8392 1.6000 18 4.225E-05 0.8463 1.6000 4.504E-07 0.8659 1.6000 19 3.782E-05 0.8951 1.6000 3.999E-07 0.8878 1.6000 20 3.461E-05 0.9152 1.6000 3.618E-07 0.9048 1.6000 21 3.256E-05 0.9407 1.6000 3.319E-07 0.9172 1.6000 22 3.084E-05 0.9473 1.6000 3.074E-07 0.9263 1.6000 23 2.954E-05 0.9579 1.6000 2.868E-07 0.9329 1.6000 24 2.835E-05 0.9598 1.6000 2.690E-07 0.9379 1.6000 25 2.735E-05 0.9646 1.6000 2.533E-07 0.9417 1.6000 26 6.431E-05 2.3517 1.8306 4.271E-07 1.6860 1.7890 27 6.090E-05 0.9470 1.8306 3.979E-07 0.9316 1.7890 28 5.761E-05 0.9460 1.8306 3.711E-07 0.9328 1.7890 29 5.461E-05 0.9481 1.8306 3.466E-07 0.9340 1.7890 30 5.180E-05 0.9486 1.8306 3.242E-07 0.9353 1.7890 31 4.927E-05 0.9510 1.8306 3.036E-07 0.9366 1.7890 32 4.689E-05 0.9519 1.8306 2.848E-07 0.9378 1.7890 33 4.474E-05 0.9542 1.8306 2.674E-07 0.9391 1.7890 34 4.274E-05 0.9552 1.8306 2.514E-07 0.9403 1.7890 35 4.091E-05 0.9573 1.8306 2.367E-07 0.9415 1.7890 36 3.921E-05 0.9583 1.8306 2.232E-07 0.9427 1.7890 37 3.765E-05 0.9602 1.8306 2.106E-07 0.9438 1.7890 38 3.619E-05 0.9612 1.8306 1.990E-07 0.9450 1.7890 39 3.484E-05 0.9629 1.8306 1.883E-07 0.9461 1.7890 40 3.358E-05 0.9638 1.8306 1.784E-07 0.9472 1.7890 41 3.241E-05 0.9652 1.8306 1.691E-07 0.9482 1.7890 42 3.131E-05 0.9661 1.8306 1.605E-07 0.9492 1.7890 43 3.029E-05 0.9673 1.8306 1.526E-07 0.9502 1.7890 44 2.932E-05 0.9681 1.8306 1.451E-07 0.9512 1.7890 45 2.842E-05 0.9692 1.8306 1.382E-07 0.9522 1.7890 46 2.756E-05 0.9699 1.8306 1.317E-07 0.9531 1.7890 47 2.676E-05 0.9708 1.8306 1.256E-07 0.9540 1.7890 48 2.599E-05 0.9715 1.8306 1.199E-07 0.9548 1.7890 49 2.527E-05 0.9722 1.8306 1.146E-07 0.9557 1.7890 50 2.458E-05 0.9728 1.8306 1.096E-07 0.9565 1.7890 51 4.240E-05 1.7249 1.9083 1.547E-07 1.4108 1.8721 52 4.092E-05 0.9651 1.9083 1.473E-07 0.9521 1.8721 53 3.948E-05 0.9647 1.9083 1.403E-07 0.9525 1.8721 54 3.807E-05 0.9645 1.9083 1.337E-07 0.9530 1.8721 55 3.672E-05 0.9645 1.9083 1.275E-07 0.9535 1.8721 56 3.542E-05 0.9645 1.9083 1.216E-07 0.9540 1.8721 57 3.417E-05 0.9647 1.9083 1.161E-07 0.9545 1.8721 58 3.296E-05 0.9648 1.9083 1.109E-07 0.9550 1.8721 59 3.181E-05 0.9650 1.9083 1.059E-07 0.9555 1.8721 60 3.070E-05 0.9651 1.9083 1.013E-07 0.9560 1.8721 61 2.964E-05 0.9654 1.9083 9.688E-08 0.9566 1.8721 62 2.861E-05 0.9655 1.9083 9.272E-08 0.9571 1.8721 63 2.763E-05 0.9657 1.9083 8.879E-08 0.9576 1.8721 64 2.669E-05 0.9659 1.9083 8.506E-08 0.9581 1.8721 65 2.578E-05 0.9661 1.9083 8.154E-08 0.9586 1.8721 66 2.491E-05 0.9662 1.9083 7.820E-08 0.9590 1.8721 67 2.408E-05 0.9664 1.9083 7.503E-08 0.9595 1.8721 68 2.327E-05 0.9666 1.9083 7.203E-08 0.9600 1.8721 69 2.250E-05 0.9667 1.9083 6.919E-08 0.9605 1.8721 70 2.175E-05 0.9668 1.9083 6.649E-08 0.9610 1.8721 71 2.103E-05 0.9670 1.9083 6.392E-08 0.9614 1.8721 72 2.034E-05 0.9671 1.9083 6.149E-08 0.9619 1.8721 73 1.967E-05 0.9672 1.9083 5.917E-08 0.9624 1.8721 74 1.903E-05 0.9673 1.9083 5.697E-08 0.9628 1.8721 75 1.841E-05 0.9675 1.9083 5.488E-08 0.9633 1.8721 76 2.262E-05 1.2286 1.9310 6.798E-08 1.2388 1.9113 77 2.180E-05 0.9637 1.9310 6.543E-08 0.9624 1.9113 78 2.100E-05 0.9634 1.9310 6.298E-08 0.9626 1.9113 79 2.023E-05 0.9632 1.9310 6.065E-08 0.9629 1.9113 80 1.948E-05 0.9630 1.9310 5.842E-08 0.9632 1.9113 81 1.876E-05 0.9629 1.9310 5.629E-08 0.9635 1.9113 82 1.806E-05 0.9627 1.9310 5.425E-08 0.9638 1.9113 83 1.738E-05 0.9626 1.9310 5.230E-08 0.9641 1.9113 84 1.673E-05 0.9625 1.9310 5.044E-08 0.9644 1.9113 85 1.610E-05 0.9624 1.9310 4.866E-08 0.9647 1.9113 86 1.549E-05 0.9623 1.9310 4.695E-08 0.9650 1.9113 87 1.491E-05 0.9622 1.9310 4.532E-08 0.9652 1.9113 88 1.434E-05 0.9621 1.9310 4.376E-08 0.9655 1.9113 89 1.380E-05 0.9620 1.9310 4.226E-08 0.9658 1.9113 90 1.327E-05 0.9619 1.9310 4.083E-08 0.9661 1.9113 91 1.277E-05 0.9618 1.9310 3.945E-08 0.9663 1.9113 92 1.228E-05 0.9617 1.9310 3.814E-08 0.9666 1.9113 93 1.181E-05 0.9616 1.9310 3.687E-08 0.9669 1.9113 94 1.135E-05 0.9616 1.9310 3.566E-08 0.9671 1.9113 95 1.091E-05 0.9615 1.9310 3.450E-08 0.9674 1.9113 96 1.049E-05 0.9614 1.9310 3.338E-08 0.9677 1.9113 97 1.009E-05 0.9613 1.9310 3.231E-08 0.9679 1.9113 98 9.697E-06 0.9613 1.9310 3.128E-08 0.9682 1.9113 Iteration converged. Generation completed. Problem description: 201 MHz MUCOOL cavity with rounded pillbox profile In this problem, Kmax < Lmax Problem file: C:\LANL\Examples\RADIOF~1\PILLBO~1\PILLBOX-FNAL-205.AF 12-14-2007 17:20:38 Problem file length: 892 bytes Originating program: Autofish Problem type: Unknown RF Cavity Problem constants and variables. Letter A in the code column indicates a value supplied in the Automesh input file. Variable Code Value Description ALPHAT 3.930000000E-03 Temperature coefficient of resistance ASCALE 3767.30313 Scaling factor for H at drive point BETA 0.0 Particle velocity BETA1 0.100000000 Starting BETA in transit-time table BETA2 0.950000000 Ending BETA in transit-time table CCLDELK 1.00000000 Increment for coupling for table in SFO CCLMAXK 6.00000000 Highest coupling for table in SFO CCLMINK 1.00000000 Lowest coupling for table in SFO CLENGTH 0.0 Cavity length for normalization in SFO CLIGHT 2.997924580E+10 Exact speed of light in cm/sec CONV 1.00000000 Length conversion (number of units per cm) DBETA 5.000000000E-02 BETA increment in transit-time table DELFR 0.0 Frequency step size for a resonance search DIAGDLL 0 If 1, DLL writes diagnostics to DiagDLL.txt DPHI 180.000000 Phase length of the problem geometry DSLOPE 1.00000000 Slope of D(k^2) function DSTOLER 2.000000000E-02 Tolerance required on D(k^2) DX1 0.200000000 First X mesh interval (at XMIN) DXMIN 0.200000000 Minimum X mesh interval (found by Automesh) DYMIN 0.173323165 Minimum Y mesh interval (found by Automesh) ENORM 1000000.00 Field normalization for NORM=4 option EPS0 8.854187818E-12 Permittivity of free space EPSIK 1.000000000E-04 Frequency convergence parameter EPSO 1.000000000E-05 Convergence parameter in mesh optimization EZERO 1000000.00 E0 for normalization in SFO when NORM=0 EZEROT 1000000.00 E0*T for normalization in SFO when NORM=1 FMU0 1.256637061E-06 Permeability of free space FREQ A 200.000000 RF cavity resonant frequency FREQD 0.0 Design frequency for a cavity (MHz) HPHI 5000.00000 Normalization magnetic field for NORM=2 IBETA 0 If >0, SFO writes transit-time vs BETA ICCC 1 1 for real arrays, 2 for complex arrays ICCP 1 If 1, compute material power loss ICORNER1 0 First corner segment for computing average H ICORNER2 0 Last corner segment for computing average H ICYLIN 1 0 for X,Y problems, 1 for Z,R problems IMAX 108 KMAX+2 INFODATA 0 Number of tuning-code parameters IOBSEG -1 First segment of the CCL outer boundary IPIVOT 1 Pivoting in matrix inversion routines IRESID 0 If 1, calculate potential residuals IRMAX 25 Used in optimization of RHOXY IRTYPE 0 Surface resistance option indicator ISLOT 0 If 1, SFO computes coupling-slot power loss ITFILE 0 If 1, SFO writes transit-time plot file ITOT 35748 (KMAX+2)*(LMAX+2) KDRI 1 K coordinate of the drive point KMAX 106 Number of horizontal logical mesh points KMETHOD 0 Wavenumber computation method (1= use beta) KPROB A 1 Problem type indicator (Superfish) LAST35 0 Code for last program to update T35 file LCYCLE 98 Iteration number in mesh optimization LDRI 318 L coordinate of the drive point LINT 1 Logical-mesh coordinate for Ez integration LMAX 329 Number of vertical logical mesh points MAXCY -1 Maximum number of cycles (-1: use default) MAXPPR 868 Maximum points per region NAIR 34767 Number of air points NBND 106 Number of Dirichlet boundary points NBSLF 1 Left-side boundary condition NBSLO 0 Lower boundary condition NBSRT 1 Right-side boundary condition NBSUP 1 Upper boundary condition NDRI 34346 Drive point index = IRLAX(NPINP) NEGAT 0 Zero-area triangle indicator NFE 0 Number of iron points NHSTEM 1 Number of half stems NINTER 0 Number of interface points NMATR 0 Number of material records in T35 file NORM 0 Normalization method in SFO NPBOUND 867 Total number of boundary points in the mesh NPINP 34874 Total points in problem NPONTS 34008 Number of unknown relaxation points NREG 2 Number of regions NRMSEG 1 Normalization segment number for NORM=2 NSEG 5 Number of boundary segments NSPL 1 Number of special-potential points NSTEP 0 Number of steps for a resonance search OMEGAM 1.000000000E-03 Used in optimization of RHOXY PI 3.14159265 The number pi to machine precision PLCELL 360.000000 Phase length per cell for multicell problems RESIDR 1.000000000E-08 Residual resistance of a superconductor RFMU 1.00000000 Permeability for rf surface resistance RHO 1.724100000E-06 Material resistivity (Ohm-m) RHOR 1.724100000E-06 Reference resistivity (Ohm-cm) at TEMPR RHOXY 1.60000000 Over-relaxation factor in mesh optimization RMASS -2.00000000 Rest mass energy of particle in SFO RS 0.0 RF surface resistance (Ohms) RSTEM 1.00000000 Stem radius in cm SLOSS 3.000000000E-02 Coupling-slot power factor per % coupling TC 9.20000000 Critical temperature of a superconductor TEMPC 20.0000000 Normal conductor operating temperature TEMPK 2.00000000 Operating temperature of a superconductor TEMPR 20.0000000 Reference temperature for IRTYPE=3 TRIAVG 1.733231646E-02 Average area of all triangles TRIMAX 2.284919964E-02 Area of the largest positive-area triangle TRIMIN 7.400625351E-03 Area of the smallest positive-area triangle VOLUME 213221.049 Cavity volume (cylindrical symmetry only) XDRI A 0.0 X coordinate of the drive point XMAXG 21.0000000 Upper X bound of the problem geometry XMING 0.0 Lower X bound of the problem geometry XNORM1 0.0 Starting X for NORM=4 integration path XNORM2 0.0 Ending X for NORM=4 integration path XYAREA 1193.84996 Total cross sectional area YDRI A 55.0000000 Y coordinate of the drive point YMAXG 56.8499980 Upper Y bound of the problem geometry YMING 0.0 Lower Y bound of the problem geometry YNORM1 0.0 Starting Y for NORM=4 integration path YNORM2 0.0 Ending Y for NORM=4 integration path ZCTR 0.0 Reference Z in transit-time integrals