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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