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Manuscript Title: CFRX, a one-and-a-quarter-dimensional transport code for field- reversed configuration studies.
Authors: M.-Y. Hsiao, K.A. Werley, K.M. Ling
Program title: CFRX
Catalogue identifier: ABHZ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 54(1989)329
Programming language: Fortran.
Computer: CRAY-1, CRAY-XMP.
Operating system: CTSS.
RAM: 11K words
Word size: 64
Keywords: Plasma physics, Magnetic confinement, Flux-surface coordinates, Compact torus, Field-reversed Configuration.
Classification: 19.9.

Nature of problem:
A one-and-a-quarter-dimensional transport code which includes radial as well as some two-dimensional effects for field-reversed configurations (FRC's) is described. The set of transport equations is solved as a coupled initial-boundary value problem. The code simulation includes both the closed and open field regions. The axial effects incorporated include global axial force balance, axial losses in the open field region, and flux surface averaging over the closed field region.

Solution method:
For numerical convenience and facilitating the analytical treatment, the governing equations are transformed to a new set of magnetic flux- related independent and dependent variables. The transformed equations are solved numerically by a finite-difference method as a coupled initial-boundary value problem. The equations are split into an "ideal" adiabatic part and a non-adiabatic transport part. The adiabatic equations are solved to obtain the equilibrium magnetic configuration and plasma profiles by using a double Newton iteration to simultaneously converge both the separatix radius and axial length. The time-dependent transport equations are implicitly differenced to ensure numerical stablility, and solved in a block tridiagonal matrix form. A predictor/corrector iteration is then used to converge the equilibrium and transport solutions. This completes one pass through the time-advance loop, which is repeated until some desired simulations time is attained. Finally, the solution is transformed back to physical variables in laboratory coordinates so that the data can be outputted in a useful form.

The plasma description is limited to the regime where the electrons and ions behave as fluids. Additionally, the transport assumption is valid when inertial terms can be neglected in the momentum equations such that the plasma evolves through a series of equilibrium states, and the model used here does not allow for any rotation, namely Upsilon Theta has to be zero.

Running time:
267 sec. on the Cray-1 and 193 sec. on Cray-XMP for the test case.