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Manuscript Title: Geomagnetic field models: scalar and vector potential, induction vector and its gradient tensor computed by a common algorithm.
Authors: G. Kluge
Program title: MAGNES
Catalogue identifier: AAEC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 4(1972)347
Programming language: Fortran.
Computer: IBM 360/65.
Operating system: OS 360.
RAM: 1K words
Word size: 32
Keywords: Geophysics, Space science, Geomagnetic field, Potential theory, Harmonic polynomials, Spherical harmonics, Stokes theorem, Vector potential, Inverse radii.
Classification: 13.

Nature of problem:
The program has been written for handling phenomenological models of the geomagnetic field; it can be adapted to any spherical harmonic expansion of potentials (e.g. gravitational or electrostatic).

Solution method:
The scalar potential is expressed as a harmonic polynomial in terms of Cartesian coordinates with reciprocal radius. Derivatives of any order can be simply calculated in a way similar to Horner's procedure. This results in a unified algorithm for the various fields quantities and also facilitates the generation and use of local approximations to field models.

Running time:
For a field model of degree 8 (i.e. 80 coefficients): 3 ms for the scalar and vector potential, additional 3 ms for the induction vector, further 3 ms for the gradient tensor.