ORIGEN (software)

ORIGEN
	File:SCALE ORIGEN.png
Developer(s)	Oak Ridge National Laboratory and contributors
Initial release	January 1, 1970; 54 years ago
Engine
Operating system	Linux, Mac OS X, Unix, Windows
Type	Nuclear transmutation
Website	scale.ornl.gov

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ORIGEN (Oak Ridge Isotopics GENeration) is software for simulating nuclear transmutation including decay and activation, developed and maintained by Oak Ridge National Laboratory as part of the SCALE code system.

Description[edit]

ORIGEN solves a set of ordinary differential equations (ODEs) representing the amount of each nuclide at any given time in a system, and can be written as follows:

{\frac {dN_{i}}{dt}}=\left[-\lambda _{i}-\sigma _{i}(t)\phi (t)\right]N_{i}(t)+\sum _{j\neq i}\left[d_{ij}\lambda _{j}+r_{ij}(t)\sigma _{j}(t)\phi (t)\right]N_{j}(t)+F_{i}(t)\;\;N_{i}(0)=N_{i0}\;\;i=1,..,M

where

$M$ is the total number of nuclides,
$N_{i}$ is the number of atoms of nuclide $i$ ,
$\lambda _{i}$ is the decay constant of nuclide $i$ ,
$\sigma _{i}(t)$ is the time-dependent neutron-induced destruction cross section for nuclide $i$ ,
$\phi (t)$ is the time-dependent total neutron flux,
$d_{ij}$ is the fraction of decays of nuclide $j$ which result in creation of nuclide $i$ ,
$r_{ij}(t)$ is the time-dependent fraction of destructions of nuclide $j$ which result in creation of nuclide $i$ , and
$F_{i}(t)$ is the time-dependent source of nuclide $i$ atoms into the system.

Note that $\phi (t)=0$ implies simple decay of all nuclides in the system. This set of equations is similar to rate equations used to model formation of various chemical compounds. The main differences are in the coefficients (decay constants and cross sections) which represent nuclear interactions instead of chemical ones and the large number of nuclides and transitions between them.

For example, a nuclear reactor may have hundreds of fuel zones which all have different cross sections (perhaps due to variations in temperature or neutron energy spectrum) and initial compositions of the fuel. Each zone has hundreds to thousands of nuclides evolving with time, such as the creation of small amounts of hundreds of fission products through fission of actinides. The scale of the simulation requires very fast and accurate solutions to the model equations.

ORIGEN contains two main methods for solving the system of ODEs, both based on the matrix exponential, the legacy MATREX and the newer CRAM.

History[edit]

References[edit]

External links[edit]

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