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Low-Energy Neutron Treatment in FLUKA

Low-Energy Neutron Treatment in FLUKA. 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

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Low-Energy Neutron Treatment in FLUKA

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  1. Low-Energy Neutron Treatment in FLUKA CERN FLUKA User Meeting M. Brugger, A. Fasso, A. Ferrari, V. Vlachoudis for the FLUKA-Collaboration 19th April 2007

  2. 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

  3. 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

  4. 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 - IMPORTANT FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  5. 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

  6. 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 - IMPORTANT FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  7. 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 - IMPORTANT FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  8. 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 - Parameters FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  9. 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 Technique FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  10. 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 Technique FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  11. 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... Structure FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  12. 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 Materials FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  13. 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 - IMPORTANT FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  14. 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 - Parameters FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  15. Materials FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  16. Materials FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  17. Materials FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  18. Materials FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  19. Materials FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  20. Materials FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  21. Materials FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  22. Materials FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  23. 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

  24. 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 Features FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  25. 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 Library FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  26. 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 Artefacts FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  27. 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 Scatter FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  28. 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 Generation FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  29. 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 Generation FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  30. 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 Neutrons FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  31. 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 Neutrons FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  32. 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 Particles FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  33. 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 Nuclei FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  34. 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 Information FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  35. With LOW-NEUT, WHAT(4) = 2.0: all the previous information, plus: the downscattering matrix (group-to-group transfer probabilities) Available Cross Section Information FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  36. 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 Information FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  37. 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 Information FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  38. 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 Information FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  39. 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 Information FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  40. Low-Energy Neutron User Question CERN FLUKA User Meeting for the FLUKA-Collaboration 19th April 2007

  41. 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 Deposition FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  42. 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 Deposition FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  43. 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 Treatment FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  44. Low-Energy Neutron FLUKA Application CERN FLUKA User Meeting for the FLUKA-Collaboration 19th April 2007

  45. 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 Facility FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  46. Take a Look from Above nToF FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  47. sample How it looks www.cern.ch/n_TOF

  48. 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 - Simplified Black Body Pb H2O FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

  49. 1 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

  50. Lead Spallation Target Example [2/2] Electron Positron Neutrino A-v Photon Pizero pion+, pion- FLUKA User Meeting - Low-Energy Neutron Treatment in FLUKA

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