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Manuscript Title: MFP: a code for calculating equation of state and optical data for noble gases.
Authors: R.R. Peterson, G.A. Moses
Program title: MFP
Catalogue identifier: ABVK_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 20(1980)353
Programming language: Fortran.
Computer: UNIVAC 1110.
Operating system: UNIVAC 1110 EXEC VIII.
RAM: 28K words
Word size: 36
Keywords: Equations of state, Mean free path radiation, Semi-classical, Atomic process, Radiative transfer, Plasma physics.
Classification: 19.1, 21.2.

Nature of problem:
Optical and equation of state data are important to the solution of many problems in high temperature hydrodynamic phenomena. In particular, the propagation of a fireball through a gas is strongly dependent upon radiative transfer and the equation of state of the gas. MFP is a code that computes ionization states and internal energies for gases. It also computes Rosseland and Planck averaged radiation mean free paths. These quantities are computed on a three-dimensional grid of gas density, gas temperature and radiation blackbody temperature. Since transitions between molecular states are not included as radiation absorption mechanisms, data may only be generated for monatomic gases.

Solution method:
The ionization state is of primary importance to the optical behaviour and the internal energy of gases. In MFP the average ionization state is calculated by using the Saha equation. The densities of atoms in the six most common ionization states are determined by assuming that they are spread in a Gaussian about the average ionization state. These populations are subdivided into the lowest 20 excitation states by assuming that ions have hydrogenic energy levels and that the excitation states are in equilibrium at the gas temperature. The internal energy of the gas is taken as the sum of the kinetic energy of ions, the kinetic energy of the ionized electrons, and the ionization energies of these electrons. A cross section for the attenuation of photons at a given energy by an atom in each of the 120 atomic states is calculated in the semi-classical approximation, where photon-ionization, inverse bremsstrahlung, Thomson scattering and atomic line absorption are considered as attenuation mechanisms. The absorption coefficient is the product of the attenuation cross section for each atomic state and the density of atoms in that state, summed over all of the states. Two different methods are used to average over the photon blackbody spectrum to obtain the Planck and Rosseland mean free paths. These quantities are output in machine readable tabulated form on a density, gas temperature, radiation temperature grid. A three-dimensional interpolation program is also included to access this data.

Restrictions:
At present the code MFP cannot generate a data table on a mesh larger than 17 density points by 20 gas temperature points by 20 radiation temperature points. In its present form, MFP should not be used when the temperature is high while the density is low, because the Saha equation becomes inaccurate in this case. These problems may be solved by future revisions of MFP. Care should be taken when chosing the widths of absorption lines as they can cause significant variations in the radiation mean free paths at low radiation temperatures. This shortcoming may be removed in a revision to MFP in which the line widths are explicitly calculated.

Unusual features:
MFP is written in standard FORTRAN except for the use of the NAMELIST facility, through which parameters controlling the operation of the code may be modified. The program is written in a modular form which allows for easy changing of the physical content of the calculation. Included in the published version is a package of utility programs to be used in collecting and managing the large amount of data which can be generated by this code. The program PLOTTER, which provides graphics displays of the results of MFP, is not included in the published version because it may only be used on computers using the Univac graphic package GSP, but it is available from the authors on request.

Running time:
When run on the Univac 1110 at the Madison Academic Computing Center at the University of Wisconsin in Madison, Wisconsin, MFP uses approximately one second of CPU time for each choice of density, gas temperature and radiation temperature.