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8} Combinatorial Geometry


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The Combinatorial Geometry (CG) used by FLUKA is a modification of the package developed at ORNL for the neutron and gamma-ray transport program MORSE [Emm75] which was based on the original combinatorial geometry by MAGI (Mathematical Applications Group, Inc.) [Gub67,Lic79]. The default input format is fixed, and different from that adopted elsewhere in the FLUKA code. The input sequence must be completely contained between a GEOBEGIN and a GEOEND card (see the corresponding description in 7}). Two concepts are fundamental in CG: bodies and regions. Originally, MORSE bodies were defined as convex solid bodies (finite portions of space completely delimited by surfaces of first or second degree, i.e. planes or quadrics). In FLUKA, the definition has been extended to include infinite cylinders (circular and elliptical) and planes (half-spaces). Use of such "infinite bodies" is encouraged since it makes input preparation and modification much easier and less error-prone. They also provide a more accurate and faster tracking. Regions are defined as combinations of bodies obtained by boolean operations: Union, Subtraction and Intersection. Each region is not necessarily simply connected (it can be made of two or more non contiguous parts), but must be of homogeneous material composition. Because the ray tracing routines cannot track across the outermost boundary, all the regions must be contained within a surrounding "blackhole" (an infinitely absorbing material, in MORSE jargon "external void", designated by the FLUKA material number 1), so that all escaping particles are absorbed. It is suggested to make the external blackhole region rather big, so as not to interfere with possible future modifications of the problem layout. The external blackhole must be completely surrounded by the boundary of a closed body, and therefore cannot be defined by means of half-spaces or infinite cylinders only. Inside such outermost boundary, EACH POINT OF SPACE MUST BELONG TO ONE AND ONLY ONE REGION. Note that in MORSE the concept of "region" refers to a portion of space of homogeneous statistical importance or weight setting, which may extend over one or several "zones" (homogeneous in material composition). Since the two MORSE concepts of region and zone coincide in FLUKA (there is a one-to-one correspondence), the term "region" will be used here to define "a portion of space of uniform material composition, obtained by boolean operations on one or more subregions", while "zone" will indicate one of such subregions, obtained by boolean operations on one or more geometrical bodies. Repetition of sets of regions according to symmetry transformations is possible in FLUKA through the card LATTICE and through a user-written routine. This allows, for instance, to model in detail only a single cell of a calorimeter and to replicate it in the entire volume. Combinatorial Geometry input ---------------------------- CG input must respect the following sequential order: GEOBEGIN card (in FLUKA standard format, or in free format if requested by a previous FREE command) Geometry title (in special format, or in free geometry format if requested by an initial GLOBAL command) Body data (in special or free geometry format) END card (in special or free geometry format) Region data (in special or free geometry format) END card (in special or free geometry format) LATTICE cards (optional, in FLUKA standard format, or in free format if requested by a previous FREE command) Region volumes (optional, see Geometry title card) GEOEND card (in FLUKA standard format, or in free format if requested by a previous FREE command)

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