Abstract
The purpose of the paper is to furnish two analytic contributions to the Störmer problem (motion of a charged particle in a magnetic dipole field). The fundamental role in these considerations is played by a quantity which depends on the constant velocity of the particle: by treating this quantity or its reciprocal as a small parameter, power series solutions can be obtained for the orbit projection upon a meridian plane valid for both low-energy and high-energy particles.
For high-energy particles, the zero-order approximation is in general an ellipse, but will reduce to a straightline for particular values of the integration constants.
For low-energy particles, the zero-order approximation is given as an infinite series in the variablew=sin2λ, λ being the latitude, and it is shown that this basic orbit is not a magnetic line of force.
Leading terms of the expansions have been given for the first-order approximations in both cases. Higher-order approximations can be obtained recurrently by solving linear, first-order differential equations having the same integrating factor, which depends on the zero-order approximation alone.
The method is suitable for extensive numerical work in conjunction with a computer program of the ‘formac’ class.
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Lanzano, P. Analytic contributions to the Störmer problem. Astrophys Space Sci 2, 319–333 (1968). https://doi.org/10.1007/BF00650909
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DOI: https://doi.org/10.1007/BF00650909