7.18.1} Simple biasing options

 The easiest biasing command is fittingly called BIASING. It provides two
 different kinds of variance reduction: Multiplicity Reduction and Importance
 Biasing, which is based on the two complementary techniques Geometry Splitting
 and Russian Roulette (RR).

 Splitting and Russian Roulette are two classical variance reduction techniques,
 which are described in most textbooks on Monte Carlo [Car75, Lux91].
 A detailed description of how they are implemented in FLUKA is available in a
 Note to option BIASING. Importance biasing consists in assigning an importance
 value to each geometry region. The number of particles moving from a region to
 another will increase (by splitting) or decrease (via RR) according to the
 ratio of importances, and the particle statistical weight will be modified
 inversely so that the total weight will remain unchanged. In this way, the user
 can strive to keep the particle population constant, making up for attenuation,
 or to make it decrease in regions far from the detectors where there is a lower
 probability to contribute to the score.  In FLUKA, importance biasing can be
 done separately for hadrons/muons, electrons/positrons/photons and low-energy
 neutrons.

 Multiplicity Reduction is a simple technique which was introduced for the first
 time in FLUKA (now it has been adopted also by other programs), in order to
 decrease the computer time needed to simulate a very high energy hadron
 cascade.  At energies of several hundred GeV and more, the number of
 secondaries produced in a hadron-nucleus interaction is very large and the
 total number can increase geometrically in the following interactions,
 requiring an unacceptably long computer time. Since many secondaries are
 particles of the same kind and with a similar angular and energy distribution,
 the user can decide to follow only a region-dependent fraction of them.

 A biasing option performing a similar multiplicity reduction on electromagnetic
 showers is EMF-BIAS. In this case the technique is known as Leading Particle
 Biasing and consists in sampling only one of the two secondary particles which
 are present in the final state of most electromagnetic interactions. The
 secondary of higher energy is sampled with higher probability.  The EMF-BIAS
 option can be tuned per region below user-defined energy thresholds and is used
 very often in shielding calculations for high-energy electron accelerators. The
 same command can be used also to bias the electron and photon mean free path
 for various types of interaction, for instance to enhance the probability of
 interaction in a thin or low-density target.

 In a similar way, option LAM-BIAS can be used to increase the probability of
 hadronic interactions, and in particular photohadron reactions.  These are the
 dominant reactions for high-energy electron accelerator induced activity and
 shielding design, but because their cross section is small compared to that of
 electromagnetic effects, analogue sampling would be very inefficient. The same
 command can help to get a higher probability of hadron interaction in a thin
 target. It can also be used to bias a particle decay length (for instance, to
 enhance muon or neutrino production) and the emission angle of the decay
 secondaries in a direction indicated by the user.

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