The TDF System for Thermonuclear Plasma Reaction Rates, Mean Energies and Two-Body Final State Particle Spectra

Abstract

The rate of thermonuclear reactions in hot plasmas as a function of local plasma temperature determines the way in which thermonuclear ignition and burning proceeds in the plasma. The conventional model approach to calculating these rates is to assume that the reacting nuclei in the plasma are in Maxwellian equilibrium at some well-defined plasma temperature, over which the statistical average of the reaction rate quantity {sigma}v is calculated, where {sigma} is the cross-section for the reaction to proceed at the relative velocity v between the reacting particles. This approach is well-understood and is the basis for much nuclear fusion and astrophysical nuclear reaction rate data. The Thermonuclear Data File (TDF) system developed at the Lawrence Livermore National Laboratory (Warshaw 1991), which is the topic of this report, contains data on the Maxwellian-averaged thermonuclear reaction rates for various light nuclear reactions and the correspondingly Maxwellian-averaged energy spectra of the particles in the final state of those reactions as well. This spectral information closely models the output particle and energy distributions in a burning plasma, and therefore leads to more accurate computational treatments of thermonuclear burn, output particle energy deposition and diagnostics, in various contexts. In this report we review and derivemore » the theoretical basis for calculating Maxwellian-averaged thermonuclear reaction rates, mean particle energies, and output particle spectral energy distributions for these reactions in the TDF system. The treatment of the kinematics is non-relativistic. The current version of the TDF system provides exit particle energy spectrum distributions for two-body final state reactions only. In a future report we will discuss and describe how output particle energy spectra for three- and four-body final states can be developed for the TDF system. We also include in this report a description of the algorithmic implementation of the TDF system, which is in two parts: the code which generates the data file itself from the nuclear reaction cross-sections, and the lookup utilities (bundled in a Fortran 77 subroutine library) which are used to retrieve the appropriate thermonuclear data from the file on demand. Unique approaches to generating, retrieving and looking up the data that were developed will be described in some detail. These developments resulted in an unusually compact data file which can be quickly generated, and from which an enormous amount of thermonuclear reaction rate, output particle energy and particle energy spectrum data can be rapidly retrieved. It is this compactness, speed and relative platform independence that distinguishes the LLNL TDF system from others.« less