-------------- Variance reduction techniques, a speciality of modern FLUKA, have been progressively introduced along the years. Transport biasing under user control is a common feature of low-energy codes, but in the high energy field biasing has generally been restricted to built-in weighted sampling in event generators, not tunable by the user. In addition, Monte Carlo codes are in general either weighted or analogue, but not both. In the modern FLUKA, the user can decide in which mode to run the code, and has the possibility to adjust the degree of biasing by region, particle and energy. Many different biasing options have been made available. Multiplicity reduction in high-energy hadron-nucleus interactions was the first one to be introduced by Fasso` (in 1987), to manage the huge number of secondaries produced by the 20 TeV proton beams of SSC. Ferrari made possible for the user to tune it on a region dependent basis. In 1990 Ferrari added also geometry splitting and Russian Roulette for all particles based on user-defined region importances and several biasing options for low-energy neutrons, inspired by MORSE, but adapted to the FLUKA structure. Region, energy and particle dependent weight windows were introduced by Fasso` and Ferrari in 1992. In this case the implementation was different from that of MORSE (two biasing levels instead of three), and the technique was not applied only to neutrons but to all FLUKA particles. Decay length biasing was also introduced by Ferrari (useful for instance to improve statistics of muons or other decay products, or to amplify the effect of rare short-lived particles surviving at some distance from the production point). Inelastic length biasing, similar to the previous option and also implemented by Ferrari, makes possible to modify the interaction length of some hadrons (and of photons) in one or all materials. It can be used to force a larger frequency of interactions in a low-density medium, and it is essential in all shielding calculations for electron accelerators. Two biasing techniques were implemented by Fasso` and Ferrari, which are applicable only to low-energy neutrons. Neutron Non Analogue Absorption (or survival biasing) was derived from MORSE where it was systematically applied and out of user control. In FLUKA it was generalised to give full freedom to the user to fix the ratio between scattering and absorption probability in selected regions and within a chosen energy range. While it is mandatory in some problems in order to keep neutron slowing down under control, it is also possible to switch it off completely to get an analogue simulation. Neutron Biased Downscattering, also for low-energy neutrons, gives the possibility to accelerate or slow down the moderating process in selected regions. It is an option not easily managed by the average user, since it requires a good familiarity with neutronics. Leading particle biasing, which existed already in EGS4, was deeply modified in 1994 by Fasso` and Ferrari, by tuning it by region, particle, interaction type and energy. A special treatment was made for positrons, to account for the penetrating power of annihilation photons. In 1997, in the framework of his work for ICARUS and CNGS, Ferrari implemented biasing of the direction of decay neutrinos.
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