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Manuscript Title: Calculation of the form of an equilibrium poloidal magnetic field contained in a polytropic star.
Authors: G.B. Brundrit, M.J. Miketinac
Program title: POLOID
Catalogue identifier: AAAE_v2_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 11(1976)385
Programming language: Fortran.
Computer: UNIVAC 1106.
Operating system: EXEC 8.
RAM: 68K words
Word size: 36
Keywords: Astrophysics, Polytropic star, Equilibrium Configuration, Poloidal magnetic field.
Classification: 1.7.

Nature of problem:
This program is designed to integrate the exact equations, which determine the distribution of the density of a self-gravitating, axisymmetric polytrope of infinite conductivity containing a poloidal magnetic field. In addition other properties of an equilibrium configuration such as mass, volume, radius etc. are calculated. The program can also provide at very small extra cost the rate of change of the density with respect to changes of the polytropic index, n, and of the parameter lambda which characterizes the poloidal magnetic field.

Solution method:
Mathematically, the problem can be formulated as a boundary value problem for three coupled equations, two of which are second order, non- linear, two-dimensional partial differential equations. The solution is obtained numerically by an adaptation of the Stoeckly's finite difference-finite expansion method; in fact, the present program is a major modification of the program TOROID (C.P.C. 7(1974)410).

The numerical scheme developed in the program is valid for all poly- tropes whose polytropic index n is greater than or equal to one. The other parameter of the theory, lambda, is unrestricted, i.e. the program permits the study of stars whose magnetic energy is a "sizeable" percentage of their gravitational energy. Also, the program, with minor modifications, could be used for calculating equilibrium configurations of (a) (uniformly or non-uniformly) rotating polytropes pervaded by poloidal magnetic fields or (b) (rotating) poltropes containing poloidal magnetic fields or a more general type than the one considered above. However, the greatest use of the present program is expected to arise in attempts to construct equilibrium configurations of polytropes containing mixed poloidal toroidal magnetic fields.

Running time:
The time required for the test run is 8 min 28 s on a UNIVAC 1106 computer, of which 5.06 s is taken in compiling.