LOW–BIAS¶

Summary

Requests non-analogue absorption and/or an energy cutoff during low-energy neutron transport on a region by region basis

See also PART–THR, LOW–DOWN, LOW–NEUT

WHAT(1) > 0.0:: group cutoff (neutrons in energy groups with number ≥ WHAT(1) are not transported).

This value can be overridden in user routine UBSSET by assigning a value to variable IGCUTO
Default: = 0.0 (no cutoff)
WHAT(2) > 0.0:: group limit for non-analogue absorption (neutrons in energy groups ≥ WHAT(2) undergo non-analogue absorption).

Non-analogue absorption is applied to the NMGP-WHAT(2)+1 groups with energies equal or lower than those of group WHAT(2) if WHAT(2) is not > NMGP, otherwise it isn’t applied to any group (NMGP is the number of neutron groups in the cross section library used: it is = 260 in the standard FLUKA neutron library).

This value can be overridden in user routine UBSSET by assigning a value to variable IGNONA.
Default: : if option DEFAULTS is used with SDUM = CALORIMEtry, ICARUS, NEUTRONS or PRECISIOn, the default is = NMGP+1 (usually 261), meaning that non-analogue absorption is not applied at all.

If DEFAULTS is missing, or is present with any other SDUM value, the default is the number of the first thermal group (usually 230).
WHAT(3) > 0.0:: non-analogue survival probability. Must be ≤ 1.0

This value can be overridden in user routine UBSSET by assigning a value to variable PNONAN.
Default: : if option DEFAULTS is used with SDUM = EET/TRANsmut, HADROTHErapy, NEW–DEFAults or SHIELDINg, the default is 0.95.

If DEFAULTS is missing, or is present with any other SDUM value, the default is 0.85.
WHAT(4) =: lower bound of the region indices (or corresponding name) in which the indicated neutron cutoff and/or survival parameters apply

(“From region ``WHAT(4)``…”)
Default: = 2.0
WHAT(5) =: upper bound of the region indices (or corresponding name) in which the indicated neutron cutoff and/or survival parameters apply

(“…to region ``WHAT(5)``…”)
Default: = WHAT(4)
WHAT(6) =: step length in assigning indices.

(“…in steps of ``WHAT(6)`` ”)
Default: = 1.0
SDUM: : not used
Default: (option LOW–BIAS not given): the physical survival probability is used for all groups except thermal ones, which are assigned a probability of 0.85. However, if option DEFAULTS has been chosen with SDUM = EET/TRANsmut, HADROTHErapy, NEW–DEFAults or SHIELDINg, this default value is changed to 0.95.

If SDUM = CALORIMEtry, ICARUS, NEUTRONS or PRECISIOn, the default is equal to the physical survival probability for all groups, including thermal.

See also Table 7.1 at.

Notes

The groups are numbered in decreasing energy order (see Low-energy neutrons in FLUKA for a detailed description). Setting a group cutoff larger than the last group number (e.g. 261 when using a 260-group cross section set) results in all neutrons been transported, i.e. no cutoff is applied.
Similarly, if WHAT(2) is set larger than the last group number, non-analogue neutron absorption isn’t applied to any group (this is recommended for calorimetry studies and all cases where fluctuations and correlations are important).
The survival probability is defined as \(1 { - \frac{ \Sigma_{abs}}{ \Sigma_T}}\) where \(\Sigma_{abs}\) is the inverse of the absorption mean free path and \(\Sigma_T\) the inverse of the mean free path for absorption plus scattering (total macroscopic cross section). The LOW–BIAS option allows the user to control neutron transport by imposing an artificial survival probability and corrects the particle weight taking into account the ratio between physical and biased survival probability.
In some programs (e.g. MORSE) [Emm75] the survival probability is always forced to be = 1.0. In FLUKA, if the LOW–BIAS option is not chosen, the physical survival probability is used for all non-thermal groups, and the default 0.85 is used for the thermal groups. (The reason for this exception is to avoid endless thermal neutron scattering in materials having a low thermal neutron absorption cross section). To get the physical survival probability applied to all groups, as needed for fully analogue calculations, the user must use LOW–BIAS with WHAT(2) larger than the last group number.
In selecting a forced survival probability for the thermal neutron groups, the user should have an idea of the order of magnitude of the actual physical probability. The latter can take very different values: for instance it can range between a few per cent for thermal neutrons in \(^{10}\)B to about 80-90 % in Lead and 99 % in Carbon. Often, small values of survival probability will be chosen for the thermal groups in order to limit the length of histories, but not if thermal neutron effects are of particular interest.
Concerning the other energy groups, if there is interest in low-energy neutron effects, the survival probability for energy groups above thermals in non-hydrogenated materials should be set at least = 0.9, otherwise practically no neutron would survive enough collisions to be slowed down. In hydrogenated materials, a slightly lower value could be acceptable. Setting less than 80 % is likely to lead to erroneous results in most cases.
Use of a survival probability equal or smaller than the physical one is likely to introduce important weight fluctuations among different individual particles depending on the number of collisions undergone. To limit the size of such fluctuations, which could slow down statistical convergence, it is recommended to define a weight window by means of options WW–THRESh, WW–FACTOr and WW-PROFIle.

Example (number based):

*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+...
LOW-BIAS        60.0      47.0      0.95       5.0      19.0       0.0
LOW-BIAS       261.0     230.0      0.82       7.0      15.0       4.0
*  Note that the second LOW-BIAS card overrides the settings of the first one
*  concerning regions 7, 11 and 15. Therefore, we will have an energy cutoff
*  equal to the upper edge of the 60th group (4.493290 MeV in the standard
*  FLUKA neutron library) in regions 5,6,8,9,10,12,13,14,16,17,18 and 19. In
*  these same regions, analogue neutron absorption is requested down to an
*  energy equal to the upper edge of group 47 (6.592384 MeV in the standard
*  library), and biased absorption, with a fixed probability of 95%, at lower
*  energies.
*  In regions 7, 11 and 15, no cutoff is applied (supposing we are using the
*  standard 260-group library), and non-analogue absorption is requested for
*  groups 230 to 260 (the thermal groups in our case), with a probability of
*  82%.

The same example, name based:

*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+...
LOW-BIAS        60.0      47.0      0.95  FifthReg  Nineteen       0.0
LOW-BIAS       261.0     230.0      0.82  RegSeven   Fifteen       4.0