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Manuscript Title: Simulation of the growth of axially symmetric discharges between plane parallel electrodes.
Authors: A.J. Davies, C.J. Evans, P.M. Woodison
Program title: SPARK2D
Catalogue identifier: ABUD_v2_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 14(1978)287
Programming language: Fortran.
Computer: CDC 7600.
Operating system: SCOPE.
RAM: 87K words
Word size: 60
Peripherals: magnetic tape.
Keywords: Plasma physics, Atomic physics, Discharge, Electrical breakdown, Space-charge, Plane-parallel electrode, Positive ion, Negative ion, Electron, Photon, Cathode.
Classification: 19.5.

Nature of problem:
SPARK2 computes the axial and radial development of an axially symmetric electrical discharge between plane parallel electrodes. The processes incorporated are primary ionization, attachment, detachment, secondary cathode emission due to the incidence of photons and positive ions, space-charge distortion of the applied field and the properties of the external electrical circuit. SPARK2 is a two-dimensional extension of SPARK71. It is complementary to and not a replacement for this program.

Solution method:
The charge densities of the electrons and negative ions, and the net charge density, are governed by time-dependent hyperbolic differential equations in two space dimensions. The equations for the electrons and negative ions are integrated along the two characteristic directions in (x,r,t) space, while the equation for the net density is solved by an implicit finite difference scheme. Iteration in the t-direction allows the change in the coefficients of the equations, due to field distortion, to be followed. The electric potential is found by solving Poisson's equation by the fast Fourier transform technique. The x-axis is divided into equal meshes but the mesh points on the r-axis can be chosen arbitrarily.

Restrictions:
As given in the listing, the program will accommodate up to 64 meshes in the x-direction, with 20 meshes in the r-direction for the density calculation and 40 meshes in the r-direction for the potential calculation. These numbers may be increased by changing the DIMENSION and COMMON statements.

Unusual features:
When a certain stage in the discharge development has been reached the non-linearity of the equations becomes so strong that an impossibly high order of accuracy is needed to ensure convergence, and the program will eventually fail due either to instability leading to overflow or to the time step becoming too small for any progress to be made.