biases the multiplicity of secondaries (only for hadron or muon/photon
photonuclear interactions) on a region by region basis.
Sets importance sampling (Russian Roulette/splitting) at boundary crossing
by region and by particle.
See also EMF-BIAS, LOW-BIAS, LAM-BIAS, WW-FACTOr, WW-PROFIle, WW-THRESh
The meaning of WHAT(1)...WHAT(6) and SDUM is different depending on the
sign of WHAT(1):
If WHAT(1) >= 0.0 :
WHAT(1) specifies the particles to be biased:
= 0.0 : all particles
= 1.0 : hadrons and muons
= 2.0 : electrons, positrons and photons
= 3.0 : low energy neutrons
WHAT(2) = RR (or splitting) factor by which the average number of
secondaries produced in a collision should be reduced (or
increased). Meaningful only for hadron or muon/photon
photonuclear interactions.
This value can be overridden in the user routine UBSSET by
assigning a value to variable RRHADR, see 13})
Default = 1.0
WHAT(3) = region importance (allowed values range from 0.0001 to 10000.)
This value can be overridden in the user routine UBSSET by
assigning a value to one or more of the variables IMPHAD, IMPLOW
and IMPEMF (depending on the value of WHAT(1))
Default = 1.0
WHAT(4) = lower bound of the region indices with importance equal to
WHAT(3) and/or with multiplicity biasing factor equal to WHAT(2).
("From region WHAT(4)...")
Default = 2.0
WHAT(5) = upper bound of the region indices with importance equal to
WHAT(3) and/or with multiplicity biasing factor equal to WHAT(2).
("...to region WHAT(5)...")
Default = WHAT(4)WHAT(6) = step length in assigning indices.
("...in steps of WHAT(6)").
Default = 1.0
SDUM = PRINT : importance biasing counters are printed (useful to tune
importances and weight windows)
= NOPRINT: counters are not printed (cancels any previous PRINT
request)
= USER: importance biasing according to the user defined
routine USIMBS
= NOUSER: reset to default (cancels any previous USER request)
= RRPRONLY: multiplicity biasing for primary particles only
= blank: ignored
Default: NOPRINT, NOUSER, multiplicity biasing for all
generations (if requested)
If WHAT(1) < 0.0 :
WHAT(1) : flag indicating that all region importances shall be modified by
a particle-dependent factor, based on a modifying parameter as
explained in the Note 3 below
WHAT(2) >= 0.0 : modifying parameter M (see Note 3). See also WARNING
below.
< 0.0 : M is reset to the default value 1.0 (i.e. no
modification)
WHAT(3) = lower bound of the particle numbers to which the indicated
modifying parameter applies
("From particle WHAT(3)...")
Default: = 1.0
WHAT(4) = upper bound of the particle numbers to which the indicated
modifying parameter applies
("...to particle WHAT(4)...")
Default: = WHAT(3) if WHAT(3) > 0, all particles otherwise
WHAT(5) = step length in assigning particle numbers
("...in steps of WHAT(5)").
Default: 1.0.
WHAT(6) = not used
SDUM = PRIMARY : importance biasing is applied also to primary
particles (cancels any previous NOPRIMARy request)
NOPRIMARy : importance biasing is applied only to secondaries
Default = PRIMARY
WARNING:
Even if a BIASING card is issued only to set PRIMARY/NOPRIMARy, remember
that a value of 0. is meaningful for WHAT(2). Leaving blank WHAT(2) to
WHAT(5)has the effect of turning off all importance biasing for all
particles!
Default (option BIASING not given): no multiplicity or RR/splitting biasing
Notes:
1) WHAT(2), with WHAT(1) >= 0, governs the application of Russian
Roulette (or splitting) at hadronic collisions, in order to achieve
a reduction (resp. an increase) of the multiplicity of secondaries.
The same secondary is loaded onto the particle stack for further
transport 0, 1 or any number of times depending on a random choice,
such that ON AVERAGE the requested multiplicity reduction (or
increase) is achieved. The weight of the stacked particles is
automatically adjusted in order to account for the bias thus
introduced.
If Russian Roulette has been requested, the reduction will not
affect the leading particle, which will always be retained, with
unmodified weight. Also, no RR is performed when the number of
secondaries is less than 3. On the contrary, there are no such
limitations for splitting (multiplicity increase).
There is some analogy with leading particle biasing as performed for
electrons and photons with option EMF-BIAS, and for hadrons in codes
like CASIM [Van75].
WHAT(3), with WHAT(1) >= 0, governs RR/splitting at boundary
crossing. The number of particles of the selected type crossing a
given boundary is reduced/increased on average by a factor equal to
the ratio of the importances on either side of the boundary. What is
relevant are the relative importances of adjacent regions, not their
absolute values. As a guideline, in shielding and, in general,
strong attenuation problems, the importance of a region should be
about inversely proportional to the corresponding attenuation factor
(absorption plus distance attenuation). This would exactly
compensate the dilution of particle density leading to a particle
population approximately uniform in space. In some cases, however,
when the user is interested in improving statistics only in a
limited portion of space, a uniform population density is not
desirable, but it is convenient to set importances so as to increase
particle densities in a particular direction.
2) Different importances can be given to the same region for different
particles, using the particle-dependent modifying factor M which can
be defined setting WHAT(1) < 0.
The modifying parameter M (WHAT(2), with WHAT(1) > 0) works as
follows:
At a boundary crossing, let us call I1 the importance of the
upstream region, and I2 that of the downstream region.
- If I2 < I1, Russian Roulette will be played.
Without any modifying factor, the chance of particle survival
is I2/I1.
For 0. <= M <= 1., the survival chance is modified to:
1. - M * (1. - I2/I1)
It can be seen that a value M = 0. resets the chance of survival
to 1., namely inhibits Russian Roulette biasing.
A value M = 1. leaves the survival chance unmodified, while any
value between 0. and 1. INCREASES the probability of survival
with respect to the basic setting.
For M >= 1., the survival chance is modified to:
I2/(M * I1)
So, a value larger than 1. DECREASES the probability of survival
with respect to the basic setting.
- If I2 > I1, there will be splitting. Without any modifying
factor, the number of particles is increased on average by a
factor I2/I1.
With the modifying factor, the number of particles is increased
instead by:
1. + M * (I2/I1 - 1.)
It can be seen that a value M = 0. resets the splitting factor
to 1., namely inhibits splitting.
A value M = 1. leaves the number of particles unmodified; a
value between 0.0 and 1.0 DECREASES the amount of splitting with
respect to the basic setting; a value > 1 INCREASES the amount
of splitting.
Hint: One of the most common uses of the modifying factor is to play
Russian Roulette/splitting only for some selected particles: one
does that by inhibiting biasing for all other particles, i.e.
setting = 0. the modifying factor M (WHAT(2), with WHAT(1) < 0).
3) In the most general case, increasing a region's importance leads
to an increased particle "traffic" through that region and
consequently to a better scoring statistics in regions "beyond".
However, it should be avoided to have relatively large
importances in scoring regions compared with those in adjacent
ones to avoid correlated tallies. If that happens, the scoring
statistics might look only apparently good. It must be avoided
also to have too different importances in adjacent zones: the
best biasing has to be done gently, without forcing and in a way
as continuous as possible.
4) All these biasing techniques are intended to improve statistics
in some parts of phase space AT THE EXPENSES OF THE OTHER PARTS.
Biased runs in particular can neither accelerate convergence in
all regions, nor reproduce natural fluctuations and
correlations. Do not bias unless you know what you are doing!
5) Advice: When choosing the multiplicity reduction option of
BIASING, or any other biasing option which can introduce weight
fluctuations in a given region, it is suggested to set also a
weight window (cards WW-FACTOR and WW-THRESh) in order to avoid
too large fluctuations in weight. The window must be consistent
with the other weight-modifying options, i.e. it must be
approximately centred on the average value of the weight
expected in the region in question. If necessary, set SDUM =
PRINT to get such information.
In case no window has been set, the code still keeps weights
under control (but only those of low-energy neutrons) by
imposing a maximum deviation from a central value. This
reference level is usually equal to the inverse of the neutron
importance in the region in question. However, since for
technical reasons in FLUKA allowed importance values range only
from 0.0001 to 10000., the user can multiply all the importances
by a factor, ONLY FOR THE PURPOSE OF CALCULATING THE REFERENCE
WEIGHT LEVEL, by means of option WW-PROFIle.
If the only biasing is via region importances set by WHAT(3),
only limited fluctuations arise (all particles of a given kind
have about the same weight in the same region), and no window is
needed.
Example:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+...
BIASING 2.0 0.0 10.0 7.0 11.0 2.0
BIASING 2.0 0.0 15.0 8.0 9.0 0.0
BIASING -1.0 0.0 3.0 4.0 0.0 0.0
BIASING 1.0 0.7 0.4 3.0 8.0 0.0 PRINT
* In this example, the first two BIASING cards set an importance = 10
* for electrons, positrons and photons in regions 7, 9 and 11; and
* an importance = 15 in regions 8 and 9 for the same particles.
* However, the following card requires a modifying factor = 0.0
* (no splitting or Russian Roulette) for electrons and positrons.
* The net result is that biasing at boundary crossing with the above
* region importances is played only for photons.
* The fourth card sets a reduction factor = 0.7 for the multiplicity
* of hadronic events in regions 3, 4, 5, 6, 7 and 8; the importance
* of these same regions is set = 0.4; and it is required that biasing
* counters be printed.
