Empirical modeling of 3‐D force‐balanced plasma and magnetic field structures during substorm growth phase

<jats:title>Abstract</jats:title><jats:p>Accurate evaluation of the physical processes during the substorm growth phase, including formation of field‐aligned currents (FACs), isotropization by current sheet scattering, instabilities, and ionosphere‐magnetosphere connection, relies on knowing the realistic three‐dimensional (3‐D) magnetic field configuration, which cannot be reliably provided by current available empirical models. We have established a 3‐D substorm growth phase magnetic field model, which is uniquely constructed from empirical plasma sheet pressures under the constraint of force balance. We investigated the evolution of model pressure and magnetic field responding to increasing energy loading and their configurations under different solar wind dynamic pressure (<jats:italic>P</jats:italic><jats:sub>SW</jats:sub>) and sunspot number. Our model reproduces the typical growth phase evolution signatures: plasma pressure increases, magnetic field lines become more stretched, current sheet becomes thinner, and the Region 2 FACs are enhanced. The model magnetic fields agree quantitatively well with observed fields. The magnetic field is substantially more stretched under higher <jats:italic>P</jats:italic><jats:sub>SW</jats:sub>, while the dependence on sunspot number is nonlinear and less substantial. By applying our modeling to a substorm event, we found that (1) the equatorward movement of proton aurora during the growth phase is mainly due to continuous stretching of magnetic field lines, (2) the ballooning instability is more favorable during late growth phase around midnight tail where there is a localized plasma beta peak, and (3) the equatorial mapping of the breakup auroral arc is at <jats:italic>X</jats:italic>~−14 <jats:italic>R<jats:sub>E</jats:sub></jats:italic> near midnight, coinciding with the location of the maximum growth rate for the ballooning instability.</jats:p>