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Manuscript Title: Numerical solutions of the Boltzmann transport equation.
Authors: S.D. Rockwood, A.E. Greene
Program title: NOMAD
Catalogue identifier: ABVC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 19(1980)377
Programming language: Fortran.
Computer: CDC 7600.
Operating system: LTSS.
RAM: 38K words
Word size: 60
Peripherals: disc.
Keywords: Fluid dynamics, Gas discharge lasers, Electron-energy Distribution, Liquid state physics, Boltzmann transport Equation, Atomic and molecular Transport data.
Classification: 12.

Nature of problem:
The purpose of NOMAD is to calculate the distribution function of electrons accelerated by a dc electric field in a mixture of atomic or molecular gases. This distribution function is then convolved with elastic and inelastic cross sections to provide energy loss rates. The code is most frequently used to provide pumping rates for gas discharge lasers.

Solution method:
NOMAD solves the linear Boltzmann equation in a flux divergent form. It converts the one-dimensional electron energy axis into a discrete energy grid by finite differencing the respective electron energy gain and loss terms. The result is a finite set of coupled, linear differential equations which define the number density of electrons at each energy as a function of time. This matrix of densities is then evolved forward in time using an implicit back-substitution algorthim until a pre- determined convergence criterion defining a steady state is achieved. Once the steady state energy distribution of electron number densities is determined, the elastic and inelastic energy gain and loss terms are used to calculate rates for the gas mixture, heavy particle number density, and electric field strength in question.

The version of NOMAD published here is intended for use in situations where the ionization level is not so high that electron-electron (e-e) collisions will have an important impact on the electron energy distribution. Modifications to handle e-e collisions add significantly to the running time of the program. It should be noted that NOMAD, following the work of Holstein, assumes that the two-term expansion of the Boltzmann equation in terms of spherical harmonics is adequate. It is beyond the scope of this work to discuss the ramifications of this limitation. NOMAD assumes the computer core has been preset to zero.