FLUKA: BIASING
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BIASING
biases the multiplicity of secondaries (only for hadron, heavy ion, or
muon/photon nuclear 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)
= i0 + 1000 * i1
i0 = 0: specifies the particles to be biased:
= 0.0 : all particles
= 1.0 : hadrons, heavy ions and muons
= 2.0 : electrons, positrons and photons
= 3.0 : low energy neutrons
i1 = generation above which RR (or splitting) is played,
meaningful only if SDUM
= RR-GENER. Please note that
this parameter is global and not region dependent
Default
: all, particles, all generations
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, heavy ion, or muon/photon
nuclear 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 100000.)
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)
).
If SDUM
= USER, setting WHAT(3)
= 1. for a region will suppress
all calls to routine USIMBS during tracking inside that region.
Default
= 1.0
WHAT(4)
= lower bound (or corresponding name) 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 (or corresponding name) 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: resets to default (cancels any previous USER request)
= RRPRONLY: multiplicity biasing for primary particles only.
Please note that this setting is global and it is not
region dependent. It is mutually exclusive with
RR-GENER
= RR-GENER: multiplicity biasing only for particle of generation
higher than the value set with WHAT(1)
. Please note
that this setting is global and it is not region
dependent. It is mutually exclusive with RRPRONLY
= 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 (or corresponding name) of the particle numbers to
which the indicated modifying parameter applies
("From particle WHAT(3)
...")
Default
: = 1.0
WHAT(4)
= upper bound (or corresponding name) 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)
= (kinetic) energy threshold below which RR/splitting at
interactions is played, only for sdum = RRTHRESH, ignored
otherwise. Please note that it is not particle dependent
Default
: infinite
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
= RRTHRESH: signals that WHAT(6)
must be interpreted as the
maximum energy for RR/splitting at interactions
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].
2) 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.
3) 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).
4) 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.
5) 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!
6) 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 100000., 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.
7) Importance biasing cannot be made by user routine USIMBS and by
setting region importances at the same time.
Example, for a number-based input:
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
The following is the same example, in a name-based input:
BIASING 2.0 0.0 10.0 Seventh Eleventh 2.0
BIASING 2.0 0.0 15.0 Eighth Ninth 0.0
BIASING -1.0 0.0 ELECTRON POSITRON 0.0 0.0
BIASING 1.0 0.7 0.4 Third Eighth 0.0 PRINT
* Start_Devel_seq
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