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Manuscript Title: ZEROD: a computer model for plasma-circuit coupling.
Authors: J.W. Long, J.W. Johnston, A.A. Newton
Program title: ZEROD
Catalogue identifier: ACDG_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 34(1985)231
Programming language: Fortran.
Computer: PRIME 750.
Operating system: PRIMOS.
RAM: 192K words
Word size: 32
Keywords: Plasma physics, Magnetic confinement.
Classification: 19.9.

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 the code is to simulate the time-dependent behaviour of a reversed field pinch plasma which is coupled to an electric circuit. Its main application has been for circuit design, although the code is also useful for investigating reversed field pinch plasma behaviour to an external voltage applied directly to the plasma.

Solution method:
The plasma magnetic field is assumed to evolve through a given series of relaxed states with the state at any time found by calculating the magnetic energy and the toroidal flux. At any instant of time the circuit supplies given additional increments of flux and energy so that the modified magnetic field configuration can be calculated. The differential equations describing the circuit are solved numerically: in the code a simplified representation of the actual circuit is used to reduce the amount of computation, although it would be relatively straightforward to modify the calculation if a more complex representation of the circuit was necessary.

Three possible types of relaxed states have been supplied as user options in the code: the Bessel function model BFM, the modified Bessel function model MBFM and the field free paramagnetic model FFPM. The plasma resistivity may be assumed constant, or a function of time. The latter option uses an empirical formula with variable parameters which may be selected by the user. The formula adopted was chosen to be compatible with experimental results. Provision is given in the code for the user to implement a choice of time-dependent resistivity if necessary. The plasma may be coupled to an external circuit, or user defined time-varying voltages can be applied directly. The published version of the code uses double precision variables since PRIME FORTRAN has only 32 bits available for single precision real variables. On computers with more accurate storage single precision should be adequate.

Unusual features:
The program is written in OLYMPUS FROTRAN i.e. standard FORTRAN except for the use of NAMELIST. The standard test runs are produced by a program compiled using the PRIME FORTRAN 77 compiler.

Running time:
Calculations carried out on HBTXIA employing 1200 time steps with graphical output take approximately 40 secs on the PRIME 700 at Culham Laboratory. Execution times clearly depend on the number of steps necessary, and on the number of circuit modules which supply the plasma energy. The calculation also employs an iteration at each time step, and the required accuracy of the solution will also affect the execution time.