Thomas E. Booth

Initial MCNP6 Release Overview

MCNP6 is simply and accurately described as the merger of MCNP5 and MCNPX capabilities, but it is much more than the sum of those two computer codes. MCNP6 is the result of five years of effort by the MCNP5 and MCNPX code development teams. These groups of people, residing in Los Alamos National Laboratory’s (LANL) X Computational Physics Division, Monte Carlo Codes Group (XCP-3), and Decision Applications Division, Radiation Transport and Applications Team (D-5), respectively, have combined their code development efforts to produce the next evolution of MCNP. While maintenance and bug fixes will continue for MCNP5 1.60 and MCNPX 2.7.0 for upcoming years, new code development capabilities only will be developed and released in MCNP6. In fact, the initial release of MCNP6 contains 16 new features not previously found in either code. These new features include the abilities to import unstructured mesh geometries from the finite element code Abaqus, to transport photons down to 1.0 eV, to transport electrons down to 10.0 eV, to model complete atomic relaxation emissions, and to generate or read mesh geometries for use with the LANL discrete ordinates code Partisn. The first release of MCNP6, MCNP6 Beta 2, is now available through the Radiation Safety Information Computational Center, and the first production release is expected in calendar year 2012. High confidence in the MCNP6 code is based on its performance with the verification and validation test suites, comparisons to its predecessor codes, the regression test suite, its code development process, and the underlying high-quality nuclear and atomic databases.

MCNP™ Version 5

Abstract The Monte Carlo transport workhorse, MCNP [Los Alamos National Laboratory report LA-13709-M, 2000], is undergoing a massive renovation at Los Alamos National Laboratory (LANL) in support of the Eolus Project of the Advanced Simulation and Computing (ASCI) Program. MCNP 1 Version 5 (V5) (expected to be released to RSICC in Fall 2002) will consist of a major restructuring from FORTRAN-77 (with extensions) to ANSI-standard FORTRAN-90 [American National Standard for Programming Language – Fortran-Extended, ANSI X3. 198-1992, 1992] with support for all of the features available in the present release (MCNP-4C2/4C3). To most users, the look-and-feel of MCNP will not change much except for the improvements (improved graphics, easier installation, better online documentation). For example, even with the major format change, full support for incremental patching will still be provided. In addition to the language and style updates, MCNP V5 will have various new user features. These include improved photon physics, neutral particle radiography, enhancements and additions to variance reduction methods, new source options, improved parallelism support (PVM, MPI, OpenMP), and new nuclear and atomic data libraries.

Zero-Variance Solutions for Linear Monte Carlo

A zero-variance solution exists for any linear Monte Carlo problem, and this solution can be obtained by sampling the random numbers proportional to the expected score subsequently produced by usin...

Power Iteration Method for the Several Largest Eigenvalues and Eigenfunctions

Abstract A method for simultaneously obtaining the two largest eigenvalues and their associated eigenfunctions is demonstrated mathematically and empirically. The method uses estimates of the eigenvalue in two different regions rather than the single estimate traditionally used. The method can be generalized to obtain the several largest eigenfunctions, if those are desired as well. Additionally, it is shown that using multiple estimates of the eigenvalues accelerates the convergence of the eigenfunctions.

Present and future capabilities of MCNP

Several new capabilities have been added to MCNP4C including: (1) macrobody surfaces; (2) the superimposed mesh importance functions, so that it is no longer necessary to subdivide geometries for variance reduction; and (3) Xlib graphics and DVF Fortran 90 for PCs. There are also improvements in neutron physics, electron physics, perturbations, and parallelization. In the more distant future we are working on adaptive Monte Carlo code modernization, more parallelization, visualization, and charged particles.

Multiple extremal eigenpairs by the power method

We report the production and benchmarking of several refinements of the power method that enable the computation of multiple extremal eigenpairs of very large matrices. In these refinements we used an observation by Booth that has made possible the calculation of up to the 10th eigenpair for simple test problems simulating the transport of neutrons in the steady state of a nuclear reactor. Here, we summarize our techniques and efforts to-date on determining mainly just the two largest or two smallest eigenpairs. To illustrate the effectiveness of the techniques, we determined the two extremal eigenpairs of a cyclic matrix, the transfer matrix of the two-dimensional Ising model, and the Hamiltonian matrix of the one-dimensional Hubbard model.

Exponential convergence on a continuous Monte Carlo transport problem

For more than a decade, it has been known that exponential convergence on discrete transport problems was possible using adaptive Monte Carlo techniques. An adaptive Monte Carlo method that empirically produces exponential convergence on a simple continuous transport problem is described.

Computing the Higher k-Eigenfunctions by Monte Carlo Power Iteration: A Conjecture

Abstract Most Monte Carlo transport codes estimate the fundamental k-eigenfunction by means of a power iteration method. A modified power iteration method appears to generate the higher eigenfunctions for some Monte Carlo transport problems. This technical note describes the method as well as some plausibility arguments about why the method works. At this time, no formal proof exists to show that the method converges to the desired eigenfunction.

Adaptive Importance Sampling with a Rapidly Varying Importance Function

Abstract It is known well that zero-variance Monte Carlo solutions are possible if an exact importance function is available to bias the random walks. Monte Carlo can be used to estimate the importance function. This estimated importance function then can be used to bias a subsequent Monte Carlo calculation that estimates an even better importance function; this iterative process is called adaptive importance sampling. To obtain the importance function, one can expand the importance function in a basis such as the Legendre polynomials and make Monte Carlo estimates of the expansion coefficients. For simple problems, Legendre expansions of order 10 to 15 are able to represent the importance function well enough to reduce the error geometrically by ten orders of magnitude or more. The more complicated problems are addressed in which the importance function cannot be represented well by Legendre expansions of order 10 to 15. In particular, a problem with a cross-section notch and a problem with a discontinuous cross section are considered.

A Monte Carlo variance reduction approach for non-Boltzmann tallies

Quantities that depend on the collective effects of groups of particles cannot be obtained from the standard Boltzmann transport equation. Monte Carlo estimates of these quantities are called non-Boltzmann tallies and have become increasingly important recently. Standard Monte Carlo variance reduction techniques were designed for tallies based on individual particles rather than groups of particles. Experience with non-Boltzmann tallies and analog Monte Carlo has demonstrated the severe limitations of analog Monte Carlo for many non-Boltzmann tallies. In fact, many calculations absolutely require variance reduction methods to achieve practical computation times. A description is given of how variance reduction techniques can be applied when non-Boltzmann estimates are desired.