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Abstract <p>This paper presents the results of a longitude reduction of the full three-dimensional (in spatial coordinates) transport equation for galactic cosmic rays. It is shown that, in the simplest case of a quasi-stationary equation, commonly used to describe the intensity of galactic cosmic rays near solar activity minima, where only the coefficient describing particle drift depends on longitude, the resulting axisymmetric equation cannot be reduced to an a priori 2D equation in which the longitudinal component of the particle drift velocity is not considered. The presence of a drift modulation mechanism leads to the fact that, in the 2D reduced equation, the total drift velocity acquires latitude-dependent factor <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(F\)</EquationSource> <!--CosRes2560178Kalinin-m1--> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( - 1 \leqslant F \leqslant 1\)</EquationSource> <!--CosRes2560178Kalinin-m2--> </InlineEquation>, and an additional term appears in the equation, taking into account the contribution of the three-dimensionality of the original equation.</p>

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3D and 2D Transport Equations of Galactic Cosmic Rays in Modern Heliosphere Models. I

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • M. S. Kalinin,
  • M. B. Krainev

摘要

Abstract

This paper presents the results of a longitude reduction of the full three-dimensional (in spatial coordinates) transport equation for galactic cosmic rays. It is shown that, in the simplest case of a quasi-stationary equation, commonly used to describe the intensity of galactic cosmic rays near solar activity minima, where only the coefficient describing particle drift depends on longitude, the resulting axisymmetric equation cannot be reduced to an a priori 2D equation in which the longitudinal component of the particle drift velocity is not considered. The presence of a drift modulation mechanism leads to the fact that, in the 2D reduced equation, the total drift velocity acquires latitude-dependent factor \(F\) , \( - 1 \leqslant F \leqslant 1\) , and an additional term appears in the equation, taking into account the contribution of the three-dimensionality of the original equation.