--------------------------------- Even though, for setting-up purposes, it is conceivable that no estimator be requested in a preliminary run, in most cases FLUKA is used to predict the expectation value of one or more quantities, as determined by the radiation field and by the material geometry described by the user: for such a task several different estimators are available. The quantities which are most commonly scored are dose and fluence, but others are available. Dose equivalent is generally calculated from differential fluence using conversion coefficients. The simplest estimator available to the user is a historical vestige, survived from the "ancient" FLUKA (pre-1988) where the only possible output quantities were energy deposition and star density in regions. It is invoked by option SCORE, requesting evaluation of one to four different quantities. These can be different forms of energy density (proportional to dose), or of star density (approximately proportional to fluence of selected high-energy hadrons). For this estimator, the detectors are pre-determined: the selected quantities are reported for each region of the geometry. The corresponding results, printed in the main output immediately after the last history has been completed, are presented in 6 columns as follows: region region region first second third fourth number name volume quantity quantity quantity quantity 1 ...... ...... ........ ........ ........ ........ 2 ...... ...... ........ ........ ........ ........ etc. on a line for each geometry region. The region volumes (in cm3) have the value 1.0, or values optionally supplied by the user at the end of the geometry description. All other columns are normalised per region volume and per primary particle. The input could be as follows:SCORE 208.0 210.0 The same, in a name-based input: SCORE ENERGY BEAMPART Other estimators are more flexible: the corresponding detectors can be requested practically in any number, can be written as unformatted or text files, and in most cases can provide differential distributions with respect to one or more variables. On the other hand, their output is presented in a very compact array form and must generally be post-processed by the user. For this purpose several utility programs are available: but output in text format can even be exported to a spreadsheet for post-processing. USRBDX is the command required to define a detector for the boundary-crossing estimator. It calculates fluence or current, mono- or bi-directional, differential in energy and angle on any boundary between two selected regions. The area normalisation needed to obtain a current in particles per cm2 is performed using an area value input by the user: if none is given, the area is assumed to be = 1 cm2 and the option amounts simply to counting the total number of particles crossing the boundary. Similarly if fluence is scored, but in this case each particle is weighted with the secant of the angle between the particle trajectory and the normal to the boundary surface at the crossing point. This is one of the estimators proposed for our example. We will request two boundary crossing detectors, one to estimate fluence and one for current, of particles crossing the boundary which separates the upstream and the downstream half of the target. The following group of cards can be inserted: USRBDX 99.0 209.0 -47.0 3.0 4.0 400. piFluenUD USRBDX +50.0 +50.0 0.0 10.0 & USRBDX -1.0 209.0 -47.0 3.0 4.0 400. piCurrUD USRBDX +50.00 +50.0 0.0 10.0 & The same, in a name-based input: USRBDX 99.0 PIONS+- -47.0 UpstrBe DwnstrBe 400. piFluenUD USRBDX +50.0 +50.0 0.0 10.0 & USRBDX -1.0 PIONS+- -47.0 UpstrBe DwnstrBe 400. piCurrUD USRBDX +50.00 +50.0 0.0 10.0 & According to the instructions reported in the description of the USRBDX command, it can be seen that the combined fluence of pi+ and pi- is requested only when particles exit region "3" ("UpstrBe", the upstream half of the target) to enter into region "4" ("DwnstrBe", the downstream half). There is no interest in the reverse, therefore "one-way scoring" is selected. The scoring of the first detector will be inverse cosine-weighted, in order to define correctly the fluence. Results will be written unformatted on unit 47 for both quantities (so there will be two "Detectors" on the same output unit, but this is not mandatory). The energy distribution is going to be binned in 50 logarithmic intervals, from 0.001 GeV (the default minimum) up to 50 GeV. The angular distribution will be binned into 10 linear solid angle intervals from 0. to 2pi (having chosen the one-way estimator). The results will be normalised dividing by the area of the boundary (separation surface between the two regions, in this case the transverse section of the target), and will provide a double- differential fluence or current averaged over that surface in cm-2 GeV-1 sr-1. Other fluence scoring options, based respectively on a track-length and on a collision estimator, are USRTRACK and USRCOLL which request the estimation of volume-averaged fluence (differential in energy) for any type of particle or family of particles in any selected region. The volume normalisation needed to obtain the fluence as track-length density or collision density is performed using a volume value input by the user: if none is given, the volume is assumed to be = 1 cm3 and the result will be respectively the total track-length in that region, or the total number of collisions (weighted with the mean free path at each collision point). Note that if additional normalisation factors are desired (e.g. beam power) this can be achieved by giving in input the "volume" or "area" value multiplied or divided by those factors. Options USRTRACK, USRCOLL and USRBDX can also calculate energy fluence, if the "particle" type is set = 208 (energy, name ENERGY) or 211 (electron and photon energy, name EM-ENRGY). In our example, we are requesting two track-length detectors, to get the average fluence in the upstream half and in the downstream half of the target, respectively. USRTRACK -1.0 209.0 -48.0 3.0 1000.0 20. piFluenU USRTRACK 50.0 0.001 & USRTRACK -1.0 209.0 -49.0 4.0 1000.0 20. piFluenD USRTRACK 50.0 0.001 & The volume input is 20 x 20 x 2.5 = 1000 cm3. We are requesting an energy spectrum in 20 logarithmic intervals between 0.001 and 50 GeV. In this case, we ask that the corresponding output be printed, unformatted, on two different files. In a name-based input, the above example could be: USRTRACK -1.0 PIONS+- -48.0 UpstrBe 1000.0 20. piFluenU USRTRACK 50.0 0.001 & USRTRACK -1.0 PIONS+- -49.0 DwnstrBe 1000.0 20. piFluenD USRTRACK 50.0 0.001 & Option USRBIN provides detailed space distributions of energy deposition, star density or integrated fluence (not energy fluence, unless by writing a special user routine). Using some suitable graphics package, USRBIN output can be presented in the form of colour maps. Programs for this purpose are available in the $FLUPRO/flutil directory (pawlevbin.f and various kumac files), and on the FLUKA website www.fluka.org. USRBIN results are normalised to bin volumes calculated automatically by the program (except in the case of region binning and special 3-variable binning which are only seldom used). The binning structure does not need to coincide with any geometry region. In our example we propose to ask for two Cartesian space distributions, one of charged pion fluence and one of total energy deposited. The first will extend over a volume larger than the target, because fluence can be calculated even in vacuum. Energy deposition, on the other hand, will be limited to the target volume. USRBIN 10.0 209.0 -50.0 50.0 50.0 50. piFluBin USRBIN -50.0 -50.0 -10.0 100.0 100.0 60.0 & USRBIN 10.0 208.0 -51.0 10.0 10.0 5. Edeposit USRBIN -10.0 -10.0 0.0 20.0 20.0 5.0 & Also in this case, the request is for output on two separate files. Or, using names: USRBIN 10.0 PIONS+- -50.0 50.0 50.0 50. piFluBin USRBIN -50.0 -50.0 -10.0 100.0 100.0 60.0 & USRBIN 10.0 ENERGY -51.0 10.0 10.0 5. Edeposit USRBIN -10.0 -10.0 0.0 20.0 20.0 5.0 & Angular yields around a fixed direction of particles exiting a given surface can be calculated using option USRYIELD. The results are double-differential distributions with respect to a pair of variables, one of which is generally energy-like (kinetic energy, momentum, etc.) and the other one angle-like (polar angle, rapidity, Feynman-x, etc.) Distributions in LET (Linear Energy Transfer) can also be requested by this option. An arbitrary normalisation factor can be input. Another commonly used scoring option is RESNUCLEi, which calculates residual nuclei production in a given region. A normalisation factor (usually the region volume) can be input. A detailed summary of the requested detectors is printed on standard output. The same information is printed in the same format in estimator ASCII output files, and is available in coded form in unformatted estimator files.
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