Used to bias the decay length of unstable particles, the inelastic
nuclear interaction length of hadrons, photons and muons and the
direction of decay secondaries
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; and 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 below):
WHAT(1) = U (x-direction cosine) of decay direction biasing
Default: 0.0
WHAT(2) = V (y-direction cosine) of decay direction biasing
Default: 0.0)
WHAT(3) = W (z-direction cosine) of 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 below).
= 0.0: a user provided routine (UDCDRL, see 13}) is 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) = not used
WHAT(6) = not used
for SDUM = DCDRBIAS:
WHAT(1) > 0.0: decay direction biasing is activated
= 0.0: ignored
< 0.0: decay direction biasing is switched off
WHAT(2) = not used
WHAT(3) = not used
WHAT(4) = lower bound of the particle numbers for which decay
direction biasing is to be applied
("From particle WHAT(4)...").
Default = 1.0.
WHAT(5) = upper bound of the particle numbers for which decay
direction biasing is to be applied
("...to particle WHAT(5)...").
Default = WHAT(4) if WHAT(4) > 0, 64 otherwise.
WHAT(6) = step length in assigning numbers. ("...in steps of
WHAT(6)").
Default = 1.0.
for all other SDUM's:
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 explained in the
following.
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 adjusted taking into account the ratio
between biased and physical survival probability.
> 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 P_u/P_b (as in
case WHAT(1) < 0.0).
= 0.0 : ignored
for SDUM = blank:
-1 < WHAT(1) < 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 < WHAT(1) < +1. : 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 : a possible previously given biasing parameter
is reset to the default value (no biasing)
WHAT(1) = 0 : ignored
WHAT(2) : biasing factor for hadronic inelastic interactions
-1 < WHAT(2) < 0. : the hadronic inelastic interaction length of the
particle is reduced by a 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 products. The latter are created in
any case and their weight adjusted taking into
account the ratio between biased and physical
survival probability.
0. < WHAT(2) < 1. : the hadronic inelastic interaction length of the
particle is reduced by a 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.
= 0.0 : ignored
|WHAT(2)| >= 1.0 : a possible previously set biasing factor is
reset to the default value of 1 (no biasing).
WHAT(3) : If > 2.0 : number 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 numbers 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 numbers for which decay
or inelastic interaction biasing is to be applied
("...to particle WHAT(5)...").
Default = WHAT(4) if WHAT(4) > 0, 46 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 or inelastic
interaction or decay direction biasing
Note: 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
exp{-[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.
Note that biasing of the hadronic inelastic interaction length can be
applied also to photons (provided option PHOTONUC is also
requested) and muons (provided option MU-PHOTON is also requested);
actually, it is often a good idea to do this in
order to increase the probability of photon nuclear interaction.
When choosing the Russian Roulette alternative, it is
suggested to set also a weight window (cards WW-FACTOR and
WW-THRESh) in order to avoid too large weight fluctuations.
Reduction factors excessively large 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.
For photons, a typical reduction factor of the hadronic inelastic
interaction length is the order of 0.01-0.05 for a shower initiated
by 1 GeV photons or electrons, and of 0.1-0.5 for one at 10 TeV.
Examples:
*...+....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 is not recommended for hadrons). The photon survives after the
* nuclear interaction with a reduced weight.
