LAM–BIAS¶

Summary

Used to bias the decay length of unstable particles, the inelastic nuclear interaction length of hadrons, photons, electrons and muons and the direction of decay secondaries

See also EMF–BIAS

The meaning of WHAT(1)…WHAT(6) depends on the value of SDUM.
SDUM = DCDRBIAS and SDUM = DCY–DIRE are used to activate and define decay direction biasing.
SDUM = GDECAY selects decay length biasing and inelastic nuclear interaction biasing.
If SDUM = blank, decay life biasing and inelastic nuclear interaction biasing are selected.
Other LAM–BIAS cards with SDUM = DECPRI, DECALL, INEPRI, INEALL allow to restrict biasing to primary particles or to extend it also to further generations.
For SDUM = DCY–DIRE:

The decay secondary product direction is biased in a direction indicated by the user by means of a unit vector of components U, V, W (see Notes 4 and 5):

WHAT(1) =: U (x-direction cosine) of the preferred direction to be used in decay direction biasing
Default: = 0.0
WHAT(2) =: V (y-direction cosine) of the preferred direction to be used in decay direction biasing
Default: = 0.0
WHAT(3) =: W (z-direction cosine) of the preferred direction to be used in decay direction biasing
Default: = 1.0
WHAT(4) > 0.0:: \(\lambda\) for decay direction biasing. The degree of biasing decreases with increasing lambda (see Note 5)
= 0.0:: a user provided routine (UDCDRL) will be called at each decay event, to provide both direction and lambda for decay direction biasing
< 0.0:: resets to default ( \(\lambda\) = 0.25)
Default: = 0.25
WHAT(5),: WHAT(6): not used

For SDUM = DCDRBIAS:

WHAT(1) > 0.0:: decay direction biasing is activated (see Notes 4 and 5):
= 0.0:: ignored
< 0.0:: decay direction biasing is switched off
WHAT(2),: WHAT(3): not used
WHAT(4) =: lower bound of the particle id-numbers (or corresponding name) for which decay direction biasing is to be applied

(“From particle ``WHAT(4)``…”)
Default: = 1.0
WHAT(5) =: upper bound of the particle id-numbers (or corresponding name) for which decay direction biasing is to be applied

(“…to particle ``WHAT(5)``…”)
Default: = WHAT(4) if WHAT(4) > 0.0, 64.0 otherwise
WHAT(6) =: step length in assigning numbers

(“…in steps of ``WHAT(6)`` ”)
Default: = 1.0

For all other SDUMs:

WHAT(1) :: biasing parameter for decay length or life, applying only to unstable particles (with particle numbers ≥ 8). Its meaning differs depending on the value of SDUM, as described below.

For ``SDUM = GDECAY``:

WHAT(1) < 0.0:
the mean decay length (in cm) of the particle in the laboratory frame is set = |WHAT(1)| if smaller than the physical decay length (otherwise it is left unchanged). At the decay point sampled according to the biased probability, Russian Roulette (i.e. random choice) decides whether the particle actually will survive or not after creation of the decay products. The latter are created in any case and their weight is adjusted taking into account the ratio between biased and physical survival probability.

WHAT(1) > 0.0:
the mean decay length (in cm) of the particle in the laboratory frame is set = WHAT(1) if smaller than the physical decay length (otherwise it is left unchanged). Let \(P_u\) = unbiased probability and \(P_b\) = biased probability: at the decay point sampled according to \(P_b\), the particle always survives with a reduced weight \(W (1 - P_u/P_b)\), where \(W\) is the current weight of the particle before the decay. Its daughters are given a weight \(W \cdot P_u/P_b\) (as in case WHAT(1) < 0.0).

WHAT(1) = 0.0:
ignored

For ``SDUM`` = blank:

-1.0 < WHAT(1) < 0.0:
the mean life of the particle in its rest frame is reduced by a factor = |WHAT(1)|. At the decay point sampled according to the biased probability, Russian Roulette (i.e. random choice) decides whether the particle actually will survive or not after creation of the decay products. The latter are created in any case and their weight adjusted taking into account the ratio between biased and physical survival probability.

0.0 < WHAT(1) < 1.0:
the mean life of the particle in the rest frame is reduced by a factor = WHAT(1). At the decay point sampled according to the biased probability, the particle always survives with a reduced weight. Its daughters are given the same weight.

|WHAT(1)| > 1.0:
a possible previously given biasing parameter is reset to the default value (no biasing)

WHAT(1) = 0.0:
ignored

WHAT(2) :

biasing factor for hadronic inelastic interactions

-1.0 < WHAT(2) < 0.0:: the hadronic inelastic interaction length of the particle is reduced by a multiplying factor |WHAT(2)|. At the interaction point sampled according to the biased probability, Russian Roulette (i.e. random choice) decides whether the particle actually will survive or not after creation of the secondaries. The latter are created in any case and their weight is adjusted taking into account the ratio between biased and physical survival probability.
0.0 < WHAT(2) < 1.0:: the hadronic inelastic interaction length of the particle is reduced by a multiplying factor WHAT(2). At the interaction point sampled according to the biased probability, the particle always survives with a reduced weight. The secondaries are created in any case and their weight adjusted taking into account the ratio between biased and physical survival probability.
WHAT(2) = 0.0:: ignored
|WHAT(2)| ≥ 1.0:: a possible previously set biasing factor is reset to the default value of 1.0 (no biasing).

WHAT(3) > 2.0:

number or name of the material to which the inelastic biasing factor has to be applied.

< 0.0:

resets to the default a previously assigned value

= 0.0:

ignored if a value has been previously assigned to a specific material; otherwise: all materials (default)

0.0 <``WHAT(3)``≤ 2.0: all materials.

WHAT(4) =

lower bound of the particle id-numbers (or corresponding name) for which decay or inelastic interaction biasing is to be applied

(“From particle ``WHAT(4)``…”)

Default

= 1.0

WHAT(5) =

upper bound of the particle id-numbers (or corresponding name) for which decay or inelastic interaction biasing is to be applied

(“…to particle ``WHAT(5)``…”)

Default

= WHAT(4) if WHAT(4) > 0.0, 64.0 otherwise

WHAT(6) =

step length in assigning numbers

(“…in steps of ``WHAT(6)`` ”)

Default

= 1.0

For SDUM = DECPRI, DECALL, INEPRI, INEALL:

SDUM

= DECPRI: decay biasing, as requested by another LAM–BIAS card with SDUM = GDECAY

or blank, must be applied only to primary particles.

=

DECALL: decay biasing, as requested by another LAM–BIAS card with SDUM = GDECAY

or blank, must be applied to all generations (default).

=

INEPRI: inelastic hadronic interaction biasing, as requested by another LAM–BIAS card

with SDUM = blank, must be applied only to primary particles.

=

INEALL: inelastic hadronic interaction biasing, as requested by another LAM–BIAS card

with SDUM = blank, must be applied to all generations (default)

Default

(option LAM–BIAS not given): no decay length, decay direction, or inelastic interaction biasing

Notes

Option LAM–BIAS can be used for three different kinds of biasing:
1. biasing of the particle decay length (or life),
2. biasing of the direction of the decay secondaries, and
3. biasing of the inelastic hadronic interaction length.
Depending on the SDUM value, two different kinds of biasing are applied to the particle decay length (or life). In both cases, the particle is transported to a distance sampled from an imposed (biased) exponential distribution: If WHAT(1) is positive, decay products are created, but the particle survives with its weight and the weight of its daughters is adjusted according to the ratio between the biased and the physical survival probability at the sampled distance. If WHAT(1) is negative, decay is performed and the weight of the daughters is set according to the biasing, but the survival of the primary particle is decided by Russian Roulette according to the biasing. Again, the weights are adjusted taking the bias into account.
The laboratory decay length corresponding to the selected mean decay life is obtained by multiplication by \(\beta\gamma c\)
Decay direction biasing is activated by a LAM–BIAS card with SDUM = DCDRBIAS. The direction of decay secondaries is sampled preferentially close to the direction specified by the user by means of a second LAM–BIAS card with SDUM = DCY–DIRE.
The biasing function for the decay direction is of the form \({e}^{{ -\frac{ 1 - cos(\theta)}{\lambda}}}\) where \(\theta\) is the polar angle between the sampled direction and the preferential direction (transformed to the centre of mass reference system). The degree of biasing is largest for small positive values of \(\lambda\) (producing direction biasing strongly peaked along the direction of interest) and decreases with increasing \(\lambda\). Values of \(\lambda\) ≥ 1.0 result essentially in no biasing.
Biasing of hadronic inelastic interaction length can be done either in one single material (indicated by WHAT(3)) or in all materials (default). No other possibility is foreseen for the moment.
When choosing the Russian Roulette alternative, it is suggested to set also a weight window (options WW–FACTOR and WW–THRESh,) in order to avoid too large weight fluctuations.
Reduction factors excessively small can result in an abnormal increase of the number of secondaries to be loaded on the stack, especially at high primary energies. In such cases, FLUKA issues a message that the secondary could not be loaded because of a lack of space. The weight adjustment is modified accordingly (therefore the results are not affected) but if the number of messages exceeds a certain limit, the run is terminated.
Biasing of the hadronic inelastic interaction length can be applied also to photons, electrons and positrons (provided option PHOTONUC is also requested with the relevant parameters) and muons (provided option MUPHOTON is also requested); actually, it is often a good idea to do this in order to increase the probability of photonuclear interaction.
For photons, a typical reduction factor of the hadronic inelastic interaction length is the order of 0.01 to 0.05 for a shower initiated by 1 GeV photons or electrons, and of 0.1 to 0.5 for one at 10 TeV. For electrons and positrons, a typical reduction factor is about \(5*\times 10^{-4}\)

Examples (number based):

*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+...
LAM-BIAS      -3.E+3        1.        1.       13.       16.        0.GDECAY
*  The mean decay length of pions and kaons (particles 13, 14, 15 and 16)
*  is set equal to 30 m. Survival of the decaying particle is decided by
*  Russian Roulette.
LAM-BIAS         0.0      0.02       11.        7.        0.        0.INEPRI
*  The interaction length for nuclear inelastic interactions of primary
*  photons (particle 7) is reduced by a factor 50 in material 11.
*  (Note that such a large reduction factor is often necessary for photons,
*  but generally is not recommended for hadrons). The photon survives after
*  the nuclear interaction with a reduced weight.

The same examples, name based:

*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+...
LAM-BIAS      -3.E+3        1.        1.     PION+     KAON-        0.GDECAY
*
LAM-BIAS         0.0      0.02       11.    PHOTON        0.        0.INEPRI