A model of the near magnetosphere with a dawn‐dusk asymmetry 1. Mathematical structure

<jats:p>A new empirical magnetic field model has been developed, representing the variable configuration of the inner and near magnetosphere for different interplanetary conditions and the ground disturbance levels. This paper describes the mathematical structure of the model, while the results of fitting it to a new set of spacecraft data are presented in a companion paper. The general approach remains the same as in the earlier T96 model, but the mathematical description of all major sources of the magnetospheric field now applies recently developed new methods. In particular, the field deformation technique is extensively used, making it possible to realistically and flexibly represent the fields of the cross‐tail current, the ring current, and the Region 1 and 2 Birkeland currents. The new model ring current includes not only the axisymmetric component but also a partial ring current with field‐aligned closure currents, a feature absent in earlier data‐based models. The field of the cross‐tail current includes two modules whose current densities vary along the Sun‐Earth line with different rates. The cross‐tail current sheet warps in two dimensions in response to the geodipole tilt, its inner edge shifts along the Sun‐Earth line with growing disturbance, and its thickness varies along and across the tail. Birkeland currents of Regions 1 and 2 vary in response to interplanetary conditions, so that at ionospheric altitudes they shift in latitude and change their distribution in local time. The magnetospheric boundary is specified using a most recent empirical model [<jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#jgra16155-bib-0018"><jats:italic>Shue et al.</jats:italic>, 1998</jats:ext-link>]; its size is controlled by the solar wind ram pressure, and its shape also varies in response to changes of the Earth's dipole tilt angle. The model magnetopause ensures a full confinement of the fields of all sources inside the magnetopause, regardless of its shape and size. The model also includes an interplanetary magnetic field–controlled interconnection field, allowing a finite normal <jats:italic>B</jats:italic><jats:sub><jats:italic>n</jats:italic></jats:sub> at the magnetopause and hence open magnetospheric configurations.</jats:p>