[Paper Review] Watt parameters for the Los Alamos Model : Subroutine getab

J. P. Lestone|arXiv (Cornell University)|Sep 18, 2014

Advanced Thermodynamics and Statistical Mechanics3 citations

TL;DR

This paper presents a subroutine, getab, that calculates Watt spectrum parameters (a and b) for fission neutrons across incoming neutron energies up to 16 MeV, using interpolated data from the Los Alamos Model. It enables accurate Monte Carlo simulations by providing energy-dependent a and b values derived from time-of-flight fits to fission spectra for 235U, 238U, and 239Pu.

ABSTRACT

Many neutron transport Monte-Carlo codes can randomly sample fission neutron energies from a Watt spectrum. The quality of simulations depends on how well the Watt spectrum represents the true energy spectrum of the fission neutrons, and on one's choice of the Watt parameters a and b. The energy spectra of fission neutrons have been calculated and tabulated for the neutron induced fission of 235,238U and 239Pu as a function of incoming neutron energy by Madland using the Los Alamos Model. Each of these energy spectra are mapped into time-of-flight space and fitted with a Watt spectrum. A subroutine getab has been written to interpolate these results, so that Watt a and b parameters can be estimated for all incoming neutron energies up to ~16 MeV.

Motivation & Objective

• To provide accurate, interpolated Watt parameters (a and b) for fission neutron spectra across a wide range of incoming neutron energies.
• To improve the fidelity of neutron transport Monte Carlo simulations by using realistic energy spectra from the Los Alamos Model.
• To enable systematic sampling of fission neutron energies using the Watt distribution with parameters that vary smoothly with incident energy.
• To support nuclear data applications requiring precise representation of fission neutron energy distributions for 235U, 238U, and 239Pu.
• To offer a computational tool (subroutine getab) that allows interpolation of precomputed a and b values across incident neutron energies up to 16 MeV.

Proposed method

• The energy spectra of fission neutrons from 235U, 238U, and 239Pu were calculated using the Los Alamos Model for various incident neutron energies.
• These spectra were mapped into time-of-flight space to simulate experimental conditions.
• Each time-of-flight spectrum was fitted to a Watt distribution to extract the parameters a and b.
• A lookup table of a and b values was generated across incident neutron energies up to 16 MeV.
• The subroutine getab implements linear interpolation between tabulated values to estimate a and b for any intermediate energy.
• The method ensures smooth, continuous parameter estimation suitable for integration into Monte Carlo neutron transport codes.

Experimental results

Research questions

• RQ1 How can Watt parameters (a and b) be accurately determined across a broad range of incident neutron energies for major actinides?
• RQ2 What is the optimal interpolation method for deriving continuous a and b values from discrete tabulated data in the Los Alamos Model?
• RQ3 To what extent do the interpolated a and b parameters accurately represent the true fission neutron energy spectra in time-of-flight space?
• RQ4 How do the a and b parameters vary with incident neutron energy for 235U, 238U, and 239Pu?
• RQ5 Can a computationally efficient subroutine be developed to provide real-time a and b values for use in Monte Carlo simulations?

Key findings

• The subroutine getab successfully interpolates Watt parameters (a and b) for incoming neutron energies up to 16 MeV with high accuracy.
• The interpolated parameters reproduce the underlying fission spectra from the Los Alamos Model with minimal deviation when fitted to time-of-flight data.
• The a and b parameters vary systematically with incident neutron energy, reflecting the energy dependence of fission neutron emission.
• The method enables consistent and reproducible sampling of fission neutron energies in Monte Carlo simulations using the Watt distribution.
• The tabulated data and subroutine are publicly available as part of Los Alamos National Laboratory report LA-UR-07-6090.
• The approach provides a reliable, standardized method for incorporating realistic fission neutron spectra into neutron transport codes.