Standard Code Description

1. Coding Language and Computing Platforms
   Fortran source code for Linux and Macintosh
2. Description of Purpose
   One of the most well used methods currently employed for reactor analysis is the diffusion approximation. This approximation is typically employed at the whole-core level using homogenized assembly cross sections in a nodal framework as is the case in the DIF3D code developed at Argonne National Laboratory. Perturbation theory methods have been developed for a wide range of applications in reactor analysis many of which are still widely used for reactivity and sensitivity coefficient calculations. The reactivity change (i.e., change in the eigenvalue of the neutron transport equation) due to perturbations introduced in the system can be expressed by a conventional perturbation equation which requires a combination of the unperturbed or perturbed forward flux and the unperturbed or perturbed adjoint flux. The solution to the perturbation equation provides the contribution of a given perturbation to the reactivity change for the entire phase space of the transport equation (space, angle, and energy). The perturbation theory capability is primarily used to produce spatial distributions of the perturbation usable as reactivity coefficients in point kinetics safety analysis or the more simplified asymptotic analysis.
   
   PERSENT was developed at Argonne in 2012 and released in 2013 as a replacement for the Argonne developed VARI3D software. VARI3D was developed in the mid-1980s and was primarily used since to generate reactivity coefficients for safety analysis. The VARI3D software was built around the DIF3D-FD solver which was limited to diffusion theory and triangular-z meshing in hex geometries. The main motivation behind constructing PERSENT was to fix two outstanding problems. The first problem is that for problems with substantial leakage, any reactivity coefficients that resulted in changes to the leakage were known to have errors due to the use of diffusion theory. In the past, two-dimensional transport calculations were used to ​“correct” the 3D diffusion theory perturbation results. The second problem is that most of the sensitivity analysis was being done using 2D R-Z transport calculations with relatively little 3D capabilities available. The sensitivity capability in VARI3D was limited to the 2D R-Z diffusion theory option of DIF3D-FD. For several reactivity coefficients, such as control rods or sample worths, using R-Z was known to introduce considerable errors in the sensitivity analysis work. The PERSENT code resolved these problems by building upon the DIF3D-VARIANT solver capability.
   
   PERSENT presently can generate kinetics parameters and perturbation theory based reactivity coefficients for use in a conventional point kinetics based safety analysis of a reactor. For sensitivity calculations, users can compute eigenvalue, reaction rate, reaction rate ratio, power fraction, reactivity worth, prompt neutron lifetime, and beta effective sensitivities to the microscopic reactions: gamma, alpha, proton, deuteron, tritium, fission, nu, and P0 & P1 scatter cross sections. PERSENT can take these sensitivity coefficients along with those computed in external software and carry out the follow on uncertainty assessment given base uncertainty information on the cross section data.
3. Typical Running Time
   Run time is dictated by the time required for DIF3D-VARIANT to be solved. A single perturbation calculation or sensitivity coefficient calculation requires less than one outer iteration worth of computational time in the DIF3D-VARIANT solver.
4. References
   1. M.A. Smith, et al., ​“VARI3D & PERSENT: Perturbation and Sensitivity Analysis,” ANL/NE-13/8, Argonne National Laboratory, 2013.
   2. C.H. Adams, ​“Specifications for VARI3D – A Multidimensional Reactor Design Sensitivity Code,” FRA-TM-74, Argonne National Laboratory, 1975.
5. Primary Author 
   M.A. Smith, Argonne National Laboratory
6. Materials Available
   The source code and compilation instructions are provided. Precompiled executables for Linux and Macintosh are also included. The source code and executables for all utility programs associated with the Argonne Reactor Code system are also included as is DIF3D. Documentation on DIF3D, PERSENT, and VARI3D is provided along with all of the verification test cases for DIF3D, PERSENT, and VARI3D. Contact nera-​software@​anl.​gov for licensing and distribution information.
7. Sponsor
   U.S. Department of Energy, Office of Nuclear Energy