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Manuscript Title: ATHENE 1: a one-dimensional equilibrium-diffusion code.
Authors: J.P. Christiansen, K.V. Roberts, J.W. Long
Program title: ATHENE 1
Catalogue identifier: ABUT_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 14(1978)423
Programming language: Fortran.
Computer: ICL 4/70.
Operating system: ICL MULTIJOB.
RAM: 72K words
Word size: 32
Keywords: Plasma physics, Thermonuclear fusion, Pinch devices, Reversed field pinches, One-dimensional, Equilibrium, Diffusion, Implicit.
Classification: 19.6.

Subprograms used:
Cat Id Title Reference
ABUF_v1_0 OLYMPUS CPC 7(1974)245
ABUF_v2_0 OLYMPUS FOR IBM 370/165 CPC 9(1975)51
ABUF_v3_0 OLYMPUS FOR CDC 6500 CPC 10(1975)167

Nature of problem:
The purpose of ATHENE 1 is to calculate the evolution of a high-beta toroidal CTR plasma in the cylindrical approximation, taking into account diffusion and other entropy-generating processes in a plasma which evolves through a sequence of magnetohydrodynamic pressure equilibria. The ATHENE 1 model is intended mainly for calculations of plasma-pinch configurations.

Solution method:
The plasma and magnetic field are described by five main variables which are functions of the time t and a single radial space variable r. The solution of the MHD equations in these five variables is split into two stages. In stage 1, which uses a fixed Eulerian mesh, diffusion and other processes change the entropy of the plasma-field configurations. Stage II is a Lagrangian calculation in which the calculation mesh is altered, so that the main variables undergo adiabatic changes until pressure equilibrium is reached. Only stage I of the calculation is described in detail here, stage II having been discussed in C.P.C. 10(1975)264. The four diffusion equations treated in stage I are solved by implicit integration schemes, and exact conservation of energy is ensured.

Version I of ATHENE I provides a simple model for the behaviour of plasma-pinch configurations. A number of physical effects such as ionization and plasma impurities have been omitted, but additional physics can easily be included in the code, e.g. by use of the EXPERT facility. In ATHENE 1 the initial radial profiles of the main variables can be altered as required. So too can the boundary conditions, and the exact conservation of energy provides a useful check against any error arising from modifications to the basic physics of the model. The accuracy of the solutions obtained for the main variables depends on the mesh size as well as on the choice of timestep.

Unusual features:
ATHENE 1 is written in OLYMPUS FORTRAN, i.e. Standard FORTRAN except for the use of the NAMELIST facility. The structure of the code is based on the OLYMPUS system in order to facilitate transfer to other types of computer. Subsets of the physics described in this paper can be excluded if appropriate logical switches are set. It is intended that ATHENE 1 should be used in conjunction with four general-purpose library packages FUNCON (fundamental physical constants), COEFS 1 (plasma-diffusion coefficients), CIRCE (external circuits) and OLYPOP (OLYMPUS output package). Until these are available from the CPC Program Library, a Support File which is included at the end of the ATHENE 1 program deck provides all the essential facilities that are required other than OLYMPUS itself (see Appendix to this paper). Users who already have these packages may simply discard the corresponding modules of the Support File.

Running time:
Execution times depend on the amount of physics included in ATHENE 1 and also on the mesh size. The standard Test 1 described in the paper is carried out on a mesh with 20 cells and requires 150 s for 200 timesteps on the ICL 4/70 at Culham laboratory.