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### Low-Energy Neutron Treatment in FLUKA

### Low-Energy Neutron FLUKA Application

CERN FLUKA User Meeting

M. Brugger, A. Fasso, A. Ferrari, V. Vlachoudis

for the FLUKA-Collaboration

19th April 2007

Overview

- ENEA multigroup cross-sections: 72 groups, ~100 elements/isotopes
- Gamma-ray generation, different temperatures, Doppler broadening, self-shielding
- Transport: standard multigroup transport with photon and fission neutron generation
- Detailed kinematics and recoil transport for elastic and inelastic scattering on hydrogen and for 14N(n,p), 10B(n, a) and 6Li(n,x)
- Correlated capture gamma generation for selected isotopes
- Photons transported with EMF
- Kerma factors are used to calculate energy deposition
- Residual nuclei production

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

General

- In FLUKA, the transport of low-energy neutrons is performed by a multigroup algorithm
- switched on by respective DEFAULTS or LOW-NEUT
- The energy boundary below which multigroup transport takes over depends in principle on the cross section library used
- The library which is presently distributed with the code has an upper energy limit of 19.6 MeV
- There are two neutron energy thresholds to be considered:
- one for high-energy neutrons (set by option PART-THR)
- one for low-energy neutrons (set by option LOW-BIAS)
- The high-energy neutron threshold represents in fact the energy boundary between continuous and discontinuous neutron transport

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Energy groups are numbered from 1 to 72 in decreasing energy order

Option LOW-NEUT specifies the characteristics of the neutron library used (number of neutron and gamma energy groups, maximum energy)

Do not change the high-energy boundary (currently 19.6 MeV)

Rarely needed, because already provided by most DEFAULTS

However, it offers also a few special options:

request of point-wise cross sections

fission neutron multiplicity forced = 1, with adjusted weight

request to print a variable amount of information on cross-sections, kerma factors, etc

LOW-NEUT - IMPORTANTFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

activates low-energy neutron transport

WHAT(1) = number of neutron groups in the cross-section set used.

The ENEA standard neutron library has 72 groups (see 10}).

Default = 72

WHAT(2) = number of gamma groups

No default if WHAT(1) is given, 22 otherwise. (The ENEA

neutron library has 22 gamma groups).

WHAT(3) = maximum energy of the low-energy cross-section neutron library.

For the ENEA neutron library, the maximum energy is 0.0196 GeV.

Note that rounding (for instance 20 MeV instead of 19.6)

is not allowed!

Default = 0.0196 GeV.

WHAT(4) = printing flag: from 0.0 to 3.0 increases the amount of

output about cross-sections, kerma factors, etc.

1.0 : Standard output includes integral cross sections,

kerma factors and probabilities

2.0 : In addition, downscattering matrices and group

neutron-to-gamma transfer probabilities are printed

3.0 : In addition, scattering probabilities and angles are

printed

Default: 0.0 (minimum output)

WHAT(5) = number of neutron groups to be considered thermal ones. (The

ENEA neutron library has one thermal group).

= 0, ignored

< 0: resets to the default = 1.0

Default = 1.0

WHAT(6) = i0 + 10 * i1:

i0 = 1: available pointwise cross sections used (see Note

below) and explicit and correlated 6-Li(n,gamma)7-Li,

10-B(n,t gamma)4-He, 40-Ar(n,gamma)41-Ar,

x-Xe(n,gamma)x+1-Xe and 113-Cd(n,gamma)114-Cd

photon cascade requested

= 0: ignored

=<-1: resets to the default (pointwise cross sections

are not used)

i1 = 1, fission neutron multiplicity forced to 1, with

proper weight

= 0, ignored

=<-1: resets to the default (normal fission multiplicity)

Default = -11., unless option DEFAULTS is present with

SDUM = CALORIMEtry, ICARUS, NEUTRONS or PRECISIOn,

in which case the default is 1.0 (pointwise cross sections

are used when available and fission multiplicity is not

forced)

SDUM: Not used

LOW-NEUT - Parameters- Pointwise Treatment:
- Hydrogen: release version: 10-100ev, development: down to 0
- 6Li: almost all reactions correlated (prob. not the elastic one)
- 10B always done, 14N always done
- 40Ar (not Nat!!!): however special version (file) required

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

When applied to neutrons, the cut-off energy defined by PART-THRes refers to the energy boundary between high-energy and low-energy neutrons, i.e. the upper limit of the first energy group in the multigroup transport scheme.

The actual cut-off for low-energy neutrons must be set by option LOW-BIAS.

If PART-THR is used to set an energy cut-off for high-energy neutrons, and that cut-off is larger than the higher energy boundary of the first group declared explicitly with LOW-NEUT or implicitly via DEFAULTS, the cut-off is forced to coincide with it, i.e., all neutrons (including the low-energy) will be killed below the selected cut-off.

Be careful NOT to set the neutron cut-off LOWER than the higher energy boundary of the first neutron group: the results are unpredictable and there is no check in the program (as the continuous model would be extended to this energy)!

If low-energy neutron transport is not requested (explicitly via LOW-NEUT or implicitly via DEFAULTS), the energy of neutrons below threshold is deposited on the spot.

PART-THR - IMPORTANTFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Used to set:

an energy cut-off (as a group number)

a group limit for non-analogue absorption

a non-analogue survival probability

e.g., cut-off group number = 72 => thermal neutrons are not transported

e.g., cut-off group number = 73 => no cut-off

Default survival probability = 0.95 for thermal neutrons, = physical probability for all other energy groups(but can be modified by DEFAULTS)

WHAT(2) greater/equal than 73 => fully analogue survival

Read the Manual Notes for more “survival” information!

LOW-BIAS - IMPORTANTFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

PART-THR

sets different energy transport cut-offs for hadrons, muons and neutrinos

For WHAT(5) = 0.0 :

WHAT(1) < 0.0 : kinetic energy cut-off (GeV)

> 0.0 : momentum cut-off (GeV/c)

For WHAT(5) >= 1.0 :

WHAT(1) < 0.0 : gamma cut-off (Lorentz factor, = E/mc**2)

> 0.0 : eta cut-off (= beta*gamma = v/c E/mc**2)

Default (WHAT(1) = 0.0): the cut-off is 0 for neutrinos,

and 0.0196 GeV for high-energy neutrons.

For any other hadrons, and for muons:

if option DEFAULTS is missing, or is present with

SDUM = NEW-DEFAults or SHIELDINg, the default cut-off

kinetic energy is 0.01 GeV.

If SDUM = HADROTHErapy, ICARUS or PRECISIOn, the default

cut-off kinetic energy is 0.0001 GeV.

If SDUM = CALORIMEtry, the default cut-off kinetic energy

is = 0.001 * m/m_p GeV (m = particle mass, m_p = proton mass)

In any other case, the default cut-off is 0.050 GeV.

(For low-energy neutrons, the threshold is set by option LOW-BIAS

and for e+e- and photons by EMFCUT, see Notes below).

WHAT(2) = lower bound of the particle id-numbers to which the cut-off

applies ("From particle WHAT(2)...").

Default = 1.0

WHAT(3) = upper bound of the particle id-numbers to which the cut-off

applies ("...to particle WHAT(3)...").

Default = WHAT(2)

WHAT(4) = step length in assigning numbers

("...in steps of WHAT(4)")

Default = 1.0.

WHAT(6) = 1.0 restricts the given cut-off to charged particles only

Default: the cut-off applies to all particles indicated by

WHAT(2-4)

SDUM : not used

LOW-BIAS

requests non-analogue absorption and/or an energy cut-off during low-energy neutron transport on a region by region basis

WHAT(1) > 0.0 : group cut-off (neutrons in energy groups with number

>= WHAT(1) are not transported).

Default = 0.0 (no cut-off)

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 = 72 in the standard FLUKA neutron library)

Default: if option DEFAULTS is used with SDUM = CALORIMEtry,

ICARUS, NEUTRONS or PRECISIOn, the default is = NMGP+1

(usually 73), 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 NMGP (usually 72), i.e. the

number of the last group (usually a thermal group).

WHAT(3) > 0.0 : non-analogue SURVIVAL probability. Must be =< 1.

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 in which the indicated

neutron cut-off and/or survival parameters apply

("From region WHAT(4)...")

Default = 2.0.

WHAT(5) = upper bound of the region indices in which the indicated

neutron cut-off 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.

PART-THR / LOW-BIAS - ParametersFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Widely used in low-energy neutron transport programs (not only Monte-Carlo, but also Discrete Ordinate codes)

Energy range of interest divided in a given number of discrete intervals (“energy groups”)

Elastic and inelastic reactions simulated not as exclusive processes, but by group-to-group transfer probabilities (downscattering matrix)

The scattering transfer probability between different groups represented by a Legendre polynomial expansion truncated at the (N+1)th term:

The Multigroup TechniqueFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Both fully biased and semi-analogue approaches are available

Energy range up to 19.6 MeV divided into 72 energy groups of approximately equal logarithmic width (one thermal)

Angular probabilities for inelastic scattering obtained by a discretization of a P5 Legendre polynomial expansion of the actual scattering distribution which preserves its first 6 moments

The generalized Gaussian quadrature scheme to generate the discrete distribution is rather complicated: details can be found in the MORSE manual (M.B. Emmett, ORNL-4972, “The Morse Monte Carlo Transport Code”, February 1975)

The result, in the case of a P5 expansion, is a set of 6 equations giving 3 discrete polar angles (actually, angle cosines) and 3 corresponding cumulative probabilities

Prepared originally by experts of ENEA using a specialized code (NJOY) and several ad-hoc programs written to adjust the output to the particular structure of this library (FLUKA special FORMAT)

Continuously enriched and updated on the basis of the most recent evaluations (ENDF/B, JEFF, JENDL etc.)

The Multigroup TechniqueFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Format similar to that known as ANISN format, but modified to include Kerma factor data, residual nuclei and partial exclusive cross sections (when available)

Partial cross sections are not used directly by FLUKA, but can be folded over calculated spectra to get reaction rates and induced activities

The first cross-section table for an isotope (isotropic term P0) contains the cumulative transfer probabilities from each group g to any group g’:

= sum over all the g’ (including the “in-scattering” term g’ = g)

The next cross-section table provides the P1 term for the same isotope, the next the P2 multigroup cross sections, etc...

StructureFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

The library contains about 150 different materials(at partly different temperatures), selected for their interest in physics, dosimetry and accelerator engineering

The cross sections of some of the materials are available at two or three different temperatures:

(103@293K, 41@87K, 1@120K, 1@93K, 1@4K)

e.g., important for simulations of calorimeters containing cryogenic liquids or SC devices

if not default to be selected using LOW-MAT

the naming parameters have to be taken from the manual

Doppler broadening at the relevant temperature is taken into account

MaterialsFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Materials in the low-energy neutron cross section file are identified by a name or by 3 numbers

If the user doesn't specify any identifier number, the correspondence with materials defined in input (or pre-defined) is established with the first material in the file having that name

Option LOW-MAT can override that correspondence

If n identifier numbers are provided (n;= 1; 2; 3), the first material satisfying all the n given identifiers will be selected

In most cases, option LOW-MAT is not needed

If a material name different from the used one is used (in the MATERIAL definition) the user is obliged to define the corresponding low-energy neutron cross sections or the run will be stopped

Note that it is possible to have more than one FLUKA material corresponding to the same low-energy neutron material (for instance two irons with different density

LOW-MAT - IMPORTANTFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

sets the correspondence between FLUKA materials and low-energy neutron cross-sections

WHAT(1) = number of the FLUKA material, either taken from the list of standard FLUKA materials (see 5}), or defined via

a MATERIAL option.

No default!

WHAT(2) = first numerical identifier of the corresponding

low-energy neutron material. Not used if = 0.0

WHAT(3) = second numerical identifier of the corresponding low-energy neutron

material. Not used if = 0.0

WHAT(4) = third numerical identifier of the corresponding low-energy neutron

material. Not used if = 0.0

WHAT(5) = compound material if > 0. This applies only to pre-mixed

low-energy neutron compound materials, which could

possibly be available in the future; at the moment

however, none is yet available. (It would be allowed

anyway only if the corresponding FLUKA material is also a

compound).

Default: compound if the FLUKA material is a compound,

otherwise not.

WHAT(6) = atomic or molecular density (in atoms/(10**-24 cm3), or

number of atoms contained in a 1-cm long cylinder with

base 1 barn. To be used ONLY if referring to a pre-mixed

compound data set (see COMPOUND and note to WHAT(5) above)

Note that no such data set has been made available yet.

SDUM = name of the low-energy neutron material.

Default: same name as the FLUKA material.

LOW-MAT - ParametersFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Materials

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Materials

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Materials

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Materials

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Materials

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Materials

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Materials

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Materials

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Energy Weighting

- Averaging inside each energy groupaccording to the weighting function used in the (slightly modified) VITAMIN-J cross section library.
- In order of increasing energy:
- a Maxwellian at the relevant temperature
- a 1/E spectrum in the intermediate energy range
- a fission spectrum
- again a 1/E spectrum

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Hydrogen cross sections (important in neutron slowing-down) available for different types of molecular binding (free, H2O, CH2)

At present, the library contains only single isotopes or elements of natural isotopic composition (but the possibility exists to include in future also pre-mixed materials)

Neutron energy deposition in most materials calculated by means of Kerma factors (including contributions from low-energy fission)

However, recoil protons and protons from 14N(n,p) reaction are produced and transported explicitly (important for dosimetry)

For a few isotopes only, neutron transport can be done also using continuous (pointwise) cross sections

for 1H, 6Li applied as a user option(WHAT(6) of option LOW-NEUT)

above 10 eV in 1H (new development version down to 0!), for all (except elastic) reactions in 6Li, and only for the reaction 10B(n,t)4He in 10B)

For the reaction 14N(n,p)14C pointwise neutron transport is always applied.

Other FeaturesFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

A completely new library is in preparation

with 260 groups (31 of which thermal)

processed at different temperatures and different self-shielding factors in MATXS format.

It is planned to use such a library to collapse smaller libraries for dedicated purposes.

Furthermore, more materials will be added in order to allow for respective point-wise treatment

The New LibraryFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

The FLUKA multigroup scheme is reliable and much faster than any possible approach using continuous cross sections.

However, it is important to remember that there are two (three) rare situations where the group approximation could give crude results

Situations where each neutron is likely to scatter only once

very thin materials

Self-shielding

very pure materials

(additional limitation: only one thermal group !)

Possible ArtefactsFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

An artefact is possible, due to the discrete P5 angular distribution (e.g., mono-directional neutrons scattering in a very thin foil).

In practice the problem vanishes entirely as soon as there is the possibility of two or more scatterings. Indeed, after a collision:

only the polar angle is sampled from a discrete distribution

the azimuthal angle is chosen randomly from a uniform distribution

In addition, the 3 discrete angles are different for each g/g’ combination and for each element or isotope

Thus, usually any memory of the initial direction is very quickly lost after just a few collisions.

Possible Artefacts: Single ScatterFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

In general, gamma generation by low-energy neutrons (but not gamma transport) is treated too in the frame of a multigroup scheme

A downscattering matrix provides the probability, for a neutron in a given energy group, to generate a photon in each of 22 gamma energy groups, covering the range 10 keV to 20 MeV

With the exception of a few important gamma lines, such as the 2.2 MeV transition of Deuterium and the 478 keV photon from 10B(n,g) reaction, the actual energy of the generated photon is sampled randomly in the energy interval corresponding to its gamma group

The gamma generation matrix does not include only capture gammas, but also gammas produced in other inelastic reactions such as (n,n’)

Gamma GenerationFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

For a few elements (e.g., Cd, Xe, Ar), for which evaluated (fully correlated!) gamma production cross sections are not available, a different algorithm, based on published energy level data, has been provided to generate explicitly the full cascade of mono-energetic gammas

In all cases, the generated gammasare transported in the same way as all other photons in FLUKA, using continuous cross sections and an explicit and detailed description of all their interactions with matter, allowing for the generation of electrons, positrons, and even secondary particles from photonuclear reactions

Note that gamma generation data are not available for all the materials of the FLUKA library! For information, consult the manual, Chap. 10!

Gamma GenerationFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

In the multigroup transport scheme, the production of secondary neutrons via (n,xn) reactions is taken into account implicitly by the so-called non-absorption probability

treated by the statistical weight of the neutron (and the downscattering matrix)

The non-absorption probability is a group-dependent factor by which the weight of a neutron is multiplied after exiting a collision

If the only possible reactions are capture and scattering, the non-absorption probability is smaller or equal 1, but at energies above the threshold for (n,2n) reaction it can take values larger than 1

In FLUKA, the neutron probability of non absorption can have the actual physical value, or any value defined by the user on a region basis (LOW-BIAS)

Secondary NeutronsFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Fission neutrons, however, are treated separately and created explicitly using a group-dependent fission probability

They are assumed to be emitted isotropically

Their energy is sampled from the fission spectrum appropriate for the relevant isotope and neutron energy

The fission neutron multiplicity and fission fragment yields from binary and ternary fission are obtained separately from data extracted from European, American and Japanese databases

Fission NeutronsFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Recoil protons and protons from 14N(n,p) reaction are produced and transported explicitly

For these the detailed kinematics of elastic scattering, continuous energy loss with energy straggling, delta ray production, multiple and single scattering, are all taken into account

The same applies to light fragments (a,3H) from neutron capture in 6Li, if point-wise transport has been requested by the user

as mentioned before, everything applies to Hydrogen and Argon (40)

All other charged secondaries produced in low-energy neutron reactions, including fission fragments, are not transported but their energy is deposited at the point of interaction via Kerma factors

Generation of Charged ParticlesFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

For many materials, but not for all, group-dependent information on the residual nuclei produced by low-energy neutron interactions is available in the FLUKA library

This information can be used to score residual nuclei, but it is important that users check its availability before requesting scoring

Residual NucleiFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

With LOW-NEUT, WHAT(4) = 1.0:

for each neutron energy group:

group energy limits

average energies

velocities and momenta corresponding to the group energy limits

energy limits of each gamma group

thermal neutron velocities

for each material used:

availability of residual nuclei information and, for each neutron energy group:

SIGT = total cross section in barn

SIGST = “scattering” cross section in barn (actually it is equal to s(n,n) + 2s (n,2n) + 3s (n,3n) etc…)

PNUP = upscatter probability (can be different from zero only if there are several thermal groups)

PNABS = Probability of Non-ABSorption (= scattering)PNABS = SIGST/SIGT, and can sometimes be> 1 because of (n,xn) reactions

GAMGEN = GAMma GENeration probability = gamma production cross sectiondivided by SIGT and multiplied by the average number of g per (n, g) reaction

NU*FIS = fission neutron production = fission cross section divided by SIGT and multiplied by , the average number of neutrons per fission

EDEP = Kerma contribution in GeV per collision

PNEL, PXN, PFISS, PNGAM = partial cross sections, expressed as probabilities (i.e., ratios to SIGT). In the order: non-elastic, (n,xn), fission, (n,gamma)

The line: (RESIDUAL NUCLEI INFORMATIONS AVAILABLE), if present, indicates the possibility to use option RESNUCLEi with WHAT(1)= 2.0

Available Cross Section InformationFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

With LOW-NEUT, WHAT(4) = 2.0:

all the previous information, plus:

the downscattering matrix (group-to-group transfer probabilities)

Available Cross Section InformationFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

With LOW-NEUT, WHAT(4) = 2.0:

all the previous information, plus:

the downscattering matrix (group-to-group transfer probabilities)

Meaning of the table:

After scattering in material 4 of a neutron in energy group 6, the probability of getting a neutron in the same group is 49.27%; that to get a neutron in the following group (group 7) is 1.48%, in group 8 is 0.06% etc….

This matrix, normalized to 1, gives the relative probability of each neutron group: but the actual probability per collision must be obtained by multiplying by PNABS (the scattering cross section divided by the total cross section and multiplied by the average number of neutrons per non-absorption reaction)

Available Cross Section InformationFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

With LOW-NEUT, WHAT(4) = 2.0 (continued):

neutron-to-gamma group transfer probabilities, for instance:

The meaning is similar to that explained before, except that each number refers to the probability of getting a gamma in the corresponding gamma group

Again, this matrix, normalized to 1, gives the relative probability of each gamma group: but the actual probability per collision must be obtained by multiplying by GAMGEN, the gamma production cross section divided by the total cross section and multiplied by the average number of gammas per (n,g) reaction

Available Cross Section InformationFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

With LOW-NEUT, WHAT(4) = 3.0:

all the previous information, plus:

for each material used and for each neutron energy group:Cumulative scattering probabilities and scattering polar angle cosines, as in the following example:

The above table reports 3 discrete angle cosines (corresponding to a Legendre P5 expansion) for each group-to-group scattering combination, with the respective cumulative probabilities. For instance:6 7 0.4105 0.8383 0.8199 0.1057 1.0000 -0.7588means that neutron scattering from energy group 6 to group 7 has a 0.4105 probability to be at a polar angle of 33deg (0.8383 = cos(33deg)); a probability (0.8199 – 0.4105) = 0.4094 to be at 84deg = arccos(0.1057); and a probability (1.000 – 0.8199) = 0.1801 to be at 139deg = arccos(-0.7588)

A -1.0000 probability indicates an isotropic distribution

Available Cross Section InformationFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

With LOW-NEUT, WHAT(4) = 3.0:

all the previous information, plus:

for each material used and for each neutron energy group:Cumulative scattering probabilities and scattering polar angle cosines, as in the following example:

The above table reports 3 discrete angle cosines (corresponding to a Legendre P5 expansion) for each group-to-group scattering combination, with the respective cumulative probabilities. For instance:6 7 0.4105 0.8383 0.8199 0.1057 1.0000 -0.7588means that neutron scattering from energy group 6 to group 7 has a 0.4105 probability to be at a polar angle of 33deg (0.8383 = cos(33deg)); a probability (0.8199 – 0.4105) = 0.4094 to be at 84deg = arccos(0.1057); and a probability (1.000 – 0.8199) = 0.1801 to be at 139deg = arccos(-0.7588)

A -1.0000 probability indicates an isotropic distribution

Available Cross Section InformationFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Chris Theis:

when FLUKA transports a neutron from one group to another the energy is deposited according to the Kerma value of the original group (independently to what group the transfer is done)

according to the downscattering matrix weighting of these events is done assuring that the average energy deposition will be correct (given the fact that the Kerma values make sense for the given material)

however, as stated before for an event-by-event analysis the results will not be physical

therefore, the question appears why the energy deposition is done only with respect to the original group but not as combination of both the starting and end group – similar to a point-wise treatment, however within the accuracy of the group structure?

Energy DepositionFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Answer:

the Kerma value is defined taking into account the average energy deposition of all possible group transfers

the available ENDF data is not correlated, thus even a group-to-group treatment is not possible

Energy DepositionFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Stefan Roesler: How to ‘kill’ neutrons

How can a user kill all low-energy neutrons when he has for instance selected as DEFAULTS the option NEW-DEF

Answer:

In order to kill all low-energy neutrons below the group transport boundary one should use LOW-BIAS with WHAT(1) set to 1, i.e., selecting the highest energy group as cut-off boundary (inclusive)

In order to select a higher neutron cut-off PART-THR has to be used which will also stop the low-energy neutron group transport

Example:

no neutron transport below 19.6 MeV

LOW-BIAS 1.0 0.0 Reg1 Reg2

no neutron transport below 200.0 MeV

PART-THR -0.5 NEUTRON

Neutron TreatmentFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

CERN FLUKA User Meeting

for the FLUKA-Collaboration

19th April 2007

Cross sections relevant for Nuclear Astrophysics

Measurements of neutron cross sections relevant for Nuclear Waste Transmutation and related Nuclear Technologies

Neutrons as probes for fundamental Nuclear Physics & other applications

n_ToF FacilityFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Geometry

Simplified geometry

Lead Block: Cylinder R=40cm, h=40cm

Water layer: Cylinder R=40cm, h=5cm

Beam

Particle: Protons

Momentum: 24 ± 0.0824 GeV/c

Position: offset by 1.7cm (horizontal)

Direction: towards Z

Options

No EMF

Cutoffs

Pions+/-, Protons 1 MeV

Other 100 keV

Neutrons 72 groups down to thermal

Kill: Pizero, neutrino, anti-neutrino, electrons, photons

1

SPH1

2

3

p+

XYP4

XYP5

XYP3

ZCC2

y

x

z

Lead Spallation Target - SimplifiedBlack Body

Pb

H2O

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

SPH1

2

3

p+

XYP4

XYP5

XYP3

ZCC2

y

x

z

Lead Spallation Target Example [1/2]Special !!!

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Lead Spallation Target Example [2/2]

Electron Positron Neutrino A-v Photon Pizero

pion+, pion-

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Problems

USRBDX scores also the particles exiting transversely from the water layer (region 3) to the black hole.

For the fluence at 200m we are interested only in the forward direction

With the solid angle binning for angles the fluence at 200m changes, since weaverage thehalo+flat part

Solutions

To correct this one can add an extra region 4 made with vacuum in front of region 3

Use solid angle binning in USRBDX

Score each neutron (position, direction, time) and propagate them to 200m. Then use only those falling inside a certain areaFLUKA Settings:Card: USERWEI to enable the call to fluscw.f, orCard: USERDUMP to enable the call to mgdraw.f

Estimation of Fluence & Resolution (~200m)Halo

L=200m

Neutron Fluence

80cm

Flat

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

More Geometry Details

*SimpleGeo (C. Theis)

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Target in the Pit

Earth

Target

Pit filled(concrete)

Beam

Marble

Beam Pipe

*SimpleGeo (C. Theis)

Concrete

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

n_TOF Tunnel Geometry

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

all the final analysis was done with the special version of the EA-MC code coupled with FLUKA etc...

however, as a fast cross check between the various codes the following simulations were made:

FLUKA (all particles and neutrons down to 19.6 MeV) + EAMC (special version)

FLUKA (-”-) + MCNPX

FLUKA as standalone

MCNPX as standalone

n_ToF SimulationsFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

n_ToF - Results

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

all the final analysis was done with the special version of the EA-MC code coupled with FLUKA etc...

however, as a cross check between the various codes the following simulations were made:

FLUKA (all particles and neutrons down to 19.6 MeV) + EAMC (special version)

FLUKA (-”-) + MCNPX

FLUKA as standalone

MCNPX as standalone

the group approach (apart from the 1 thermal group) is a fast alternative providing very good results

n_ToFFLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Neutron Fluence

20% difference between 1 and 1E5 eV ???

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

n-TOF: … Surprise … Surprise

Preparing for Lead target dismount-

Discovery that the water layer is 6 cm thick instead of 5

New FLUKA simulations with

6 cm water (red)

compared with 5 cm (black)

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Gamma Generation: n_TOF Lead Target

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

Example: instrumentation calibration (PTB)

Calibration of three different Bonner spheres (with 3He counters) with monoenergetic neutron beams at PTB (full symbols), compared with simulation (dashed histos and open symbols)

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

CERF: instrumentation calibration (PTB and PSI)

Calibration of the LINUS rem counter with monoenergetic neutron beams at PTB and with quasi-monoenergetic neutron beams at PSI (full symbols), compared with simulation (dashed histos and open symbols)

FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

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