FLUKA treats an arbitrary three-dimensional configuration of materials in geometric regions bounded by first- and second-degree surfaces.
The official FLUKA site: FLUKA Online Manual
Derived from the Combinatorial Geometry package, it has been entirely rewritten. A completely new, fast tracking strategy has been developed, with special attention to charged particle transport, especially in magnetic fields. New bodies have been introduced, resulting in increased rounding accuracy and speed. Input preparation has been made much easier by the possibility to use names instead of numbers, free format and nested parentheses. The distance to nearest boundary is taken into account for improved performance.
Two models are used also in hadron-nucleus interactions. Both modules are followed by equilibrium processes: evaporation, fission, Fermi break-up, gamma deexcitation. The PEANUT model is set to become the default at all energies: please read the release notes for further details about this possibility. Hadron elastic scattering is described by means of parameterised nucleon-nucleon cross sections, tabulated nucleon-nucleus cross sections and tabulated phase shift data for pion-proton and phase-shift analysis for kaon-proton scattering.
Detailed kinematics of elastic scattering is performed on hydrogen nuclei and transport of proton recoils. Pre-compiled libraries for these event generators are included in the distributed packages: the source code is not yet included, pending finalization of proper licensing. Transport of charged particles is based on an original treatment of multiple Coulomb scattering and of ionisation fluctuations which allows the code to handle accurately some challenging problems such as electron backscattering and energy deposition in thin layers even in the few keV energy range.
Energy loss of charged particles is based on the Bethe-Bloch theory, with optional delta-ray production and transport with account for spin effects and ionisation fluctuations.
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Shell and other low-energy corrections are derived from Ziegler, the density effect is according to Sternheimer. For all charged particles hadrons and muons as well as electrons and positrons a special transport algorithm, based on Moliere's theory of multiple Coulomb scattering improved by Bethe, accounts for correlations between lateral and longitudinal displacement and the deflection angle, between projected angles, and between projected step length and total deflection. The algorithm includes an accurate treatment of boundaries and curved trajectories in magnetic fields, an automatic control of the step, a path length correction, spin-relativistic effects at the level of the second Born approximation, nuclear size effects scattering suppression on option, and a correction for cross section variation with energy over the step.
Bremsstrahlung and electron pair production at high energy by heavy charged particles are treated as a continuous energy loss and deposition or as discrete processes depending on user choice. Muon photonuclear interactions are simulated with or without transport of the produced secondaries. Differences between positrons and electrons are taken into account concerning both stopping power and bremsstrahlung.
The bremsstrahlung differential cross sections of Seltzer and Berger have been extended to include the finite value at "tip" energy, and the angular distribution of bremsstrahlung photons is sampled accurately. The Landau-Pomeranchuk-Migdal suppression effect and the Ter-Mikaelyan polarisation effect in the soft part of the bremsstrahlung spectrum are also implemented. Positron annihilation is simulated both in flight and at rest. Delta-ray production by positrons and electrons is described via Bhabha and Moller scattering. The lowest transport limit for electrons is 1 keV.
Although in high-Z materials the Moliere multiple scattering model becomes unreliable below keV, a single-scattering option is available which allows obtaining satisfactory results in any material also in this low energy range. Photon interactions include pair production with actual angular distribution of electrons and positrons, Compton effect with account for atomic bonds through use of inelastic Hartree-Fock form factors, photoelectric effect with actual photoelectron angular distribution, detailed interaction on six K and L single sub-shells, optional emission of fluorescence photons and an approximate treatment of Auger electrons, and Rayleigh effect.
Photon polarisation can be taken into account for Compton, Rayleigh and photoelectric effects. Photomuon production is described according to Tsai. For neutrons with energy lower than 20 MeV, FLUKA uses its own neutron cross section libraries P5 Legendre angular expansion, or 72 neutron energy groups , containing more than different materials, selected for their interest in physics, dosimetry and accelerator engineering and derived from the most recently evaluated data.
Gamma-ray generation and different temperatures are available. Doppler broadening is applied for temperatures above 0 K. The neutron transport is based on standard multigroup transport with photon and fission neutron generation, detailed kinematics of elastic scattering on hydrogen nuclei, transport of proton recoils and protons from N n,p C reaction.
Capture photons are generated according to the multigroup treatment, but transported with the more accurate electromagnetic package of FLUKA which performs continuous transport in energy and allows for secondary electron generation. The 2. For nuclei other than hydrogen, kerma factors are used to calculate energy deposition including from low-energy fission.
Pointwise cross section transport is available for a few nuclei and reactions. Electron, muon, and tau anti neutrinos are produced and tracked on option, without interactions, but neutrino interactions are implemented, independently from tracking. Generation and transport are available on user's request of Cherenkov and scintillation radiation. Transport of light of given wavelength in materials can be simulated with user-defined optical properties.
FLUKA has extended scoring capabilities, requiring in most cases no user-written code. The step size is independent of bin size. Energy deposition can be weighted by a quenching factor Birks law. Scoring can be done in a time window. It is possible to simulate coincidences and anti-coincidences. Fluence and current can be scored as a function of energy and angle, via boundary-crossing, collision and track-length estimators coincident with regions or region boundaries.
Track-length fluence can be scored in a binning structure Cartesian or cylindrical independent of geometry. Particle yield from a target is available or differential cross section with respect to several different kinematic variables. Other scoring possibilities include residual nuclei, fission density, momentum transfer density, neutron balance, unweighted energy deposition. All quantities from radioactive decay of residual nuclei can be scored according to user-defined irradiation and cooling time profiles decay radiation transport is provided on request. FLUKA can be used in analogue mode or with a variety of variance reduction options.
These include: Leading particle biasing for electrons and photons: region dependent, below user-defined energy threshold and for selected physical effects; Russian Roulette and splitting at boundary crossing based on region relative importance; region-dependent multiplicity tuning in high energy nuclear interactions; region-dependent biased down-scattering and non-analogue absorption of low-energy neutrons; biased decay length for increased daughter production, biased inelastic nuclear interaction length; biased interaction lengths for electron and photon electromagnetic interactions; biased angular distribution of decay secondary particles; region-dependent weight window in three energy ranges and energy group dependent for low energy neutrons.
Neutrons in the FLUKA low energy libraries are available for about materials or isotopes, temperature, and self-shielding combinations. All other particle interactions and transport are based on models and are not restricted by any material tabulation. Electron, positron and photon interactions and transport are possible between 1 keV and 10 PeV. Runtimes vary greatly depending on computer speed, problem layout, and beam energy.
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Data files: Bremsstrahlung cross sections, Coherent atomic form factors, Fluorescence emission data, Photon cross sections, Low-energy neutron cross sections groups , Nuclide masses, abundances and other data, Hadron elastic cross sections, Pion cross sections, Fission nuclide yields and neutron multiplicities, Silicon Damage tabulations.
Muraro, P. As a consequence, we learn that several fundamental quantities are related in ways not known in classical physics. All of these relationships are verified by experiment and have fundamental consequences. The altered definition of energy contains some of the most fundamental and spectacular new insights into nature found in recent history. The first postulate of relativity states that the laws of physics are the same in all inertial frames.
Einstein showed that the law of conservation of energy is valid relativistically, if we define energy to include a relativistic factor. There are many aspects of the total energy E that we will discuss—among them are how kinetic and potential energies are included in E , and how E is related to relativistic momentum.
But first, note that at rest, total energy is not zero.
For example, if energy is stored in the object, its rest mass increases. This also implies that mass can be destroyed to release energy. The implications of these first two equations regarding relativistic energy are so broad that they were not completely recognized for some years after Einstein published them in , nor was the experimental proof that they are correct widely recognized at first.
Einstein, it should be noted, did understand and describe the meanings and implications of his theory. One gram is a small mass—less than half the mass of a penny. We can multiply this mass, in SI units, by the speed of light squared to find the equivalent rest energy. Convert units. This is an enormous amount of energy for a 1.
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We do not notice this energy, because it is generally not available. Rest energy is large because the speed of light c is a large number and c 2 is a very large number, so that mc 2 is huge for any macroscopic mass. The 9.
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If a way can be found to convert rest mass energy into some other form and all forms of energy can be converted into one another , then huge amounts of energy can be obtained from the destruction of mass. Today, the practical applications of the conversion of mass into another form of energy , such as in nuclear weapons and nuclear power plants, are well known.