Empirical model for μ scattering caused by field line curvature in a realistic magnetosphere

<jats:p>The combination of magnetic field line curvature (FLC) and weak magnetic field strength affects charged particle motion in a magnetic field by causing changes of the particle's first adiabatic invariant, μ. In this paper we refer to these changes as FLC induced μ scattering or simply μ scattering. Both large single scatterings and the cumulative effects of many small scatterings (Δμ/μ ≪ 1) influence particle populations in the Earth's magnetosphere. Because FLC‐induced μ scattering is strongly dependent on the magnetic field geometry and strength, realistic magnetospheric models must be employed in order to gain a quantitative understanding of how μ scattering affects the evolution of these populations. This requires a μ‐scattering model that is accurate for many different magnetic field geometries. Though several μ‐scattering models have been developed previously, we demonstrate that their accuracy is limited to the simple field geometries for which they were derived. In realistic magnetic fields, there are regions where these μ‐scattering models depart from Lorentz integration results by a factor of 2 or greater. The source of these discrepancies is attributed to the fact that the only magnetic field information used is the field line curvature <jats:italic>R</jats:italic><jats:sub><jats:italic>C</jats:italic></jats:sub> and magnetic field strength <jats:italic>B</jats:italic> both evaluated at a single point, the magnetic equator. To generalize the analytical representation of μ scattering to a range of magnetic field geometries, we have developed a new μ‐scattering model that uses two additional parameters. These are proportional to the second derivatives of the field line curvature, ∂<jats:sup>2</jats:sup><jats:italic>R</jats:italic><jats:sub><jats:italic>C</jats:italic></jats:sub>/∂<jats:italic>S</jats:italic><jats:sup>2</jats:sup>, and the field intensity, ∂<jats:sup>2</jats:sup><jats:italic>B</jats:italic> /∂<jats:italic>S</jats:italic><jats:sup>2</jats:sup>, where <jats:italic>S</jats:italic> is the distance along the field line and the derivatives are evaluated at the magnetic equator. We have defined an error parameter that measures the fit between the model and Lorentz integration results. Using this parameter, we show that the difference between our model Δμ values and those based on Lorentz integration is, on average, only 4%; this is at least a factor of 5 less than the difference using previous analytical models. Our new model will greatly facilitate quantitative analysis of μ scattering for realistic magnetospheric magnetic field geometries including active as well as quiet conditions.</jats:p>