18.18} Biasing

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 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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