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A simple model of magnetic fields associated with outflow from a source; new orthogonal polynomials

Published online by Cambridge University Press:  02 December 2015

LAWRENCE K. FORBES*
Affiliation:
School of Mathematics and Physics, University of Tasmania, P.O. Box 37, Hobart 7001, Tasmania, Australia email: larry.forbes@utas.edu.au

Abstract

Outflow from a young star might be regarded as approximately equivalent to flow from a point source. If the fluid consists of charged particles, then the magnetic fields produced are governed by Faraday's law. This simple first approximation yields a linear partial differential equation in spherical polar coordinates, and its solution may be represented as the product of a Legendre polynomial with some function of the radial coordinate. This radial function is shown to involve orthogonal polynomials. Their properties are investigated and recurrence formulae for them are derived. Some of the magnetic fields generated by this simple model are illustrated.

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Papers
Copyright
Copyright © Cambridge University Press 2015 

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