Nonlinear impact of plasma sheet density on the storm‐time ring current

<jats:p>We investigated the nonlinear impact of the plasma sheet density on the total energy of the storm‐time ring current by means of a numerical simulation that self‐consistently solves the kinetic equation of ring current protons and the closure of the electric current between the magnetosphere and ionosphere. Results of the simulation indicate that when the convection electric field is self‐consistently coupled with the ring current, the total energy of the ring current ions trapped by the Earth's magnetic field is roughly proportional to ∼<jats:italic>N</jats:italic><jats:sub><jats:italic>ps</jats:italic></jats:sub><jats:sup>1/2</jats:sup>, where <jats:italic>N</jats:italic><jats:sub><jats:italic>ps</jats:italic></jats:sub> is the plasma sheet density. This nonlinear response results from the strengthened shielding electric field with increasing <jats:italic>N</jats:italic><jats:sub><jats:italic>ps</jats:italic></jats:sub>. The total energy is almost proportional to <jats:italic>N</jats:italic><jats:sub><jats:italic>ps</jats:italic></jats:sub> when using an empirical convection electric field, which is independent of the condition of the simulated ring current. An empirical relationship between <jats:italic>N</jats:italic><jats:sub><jats:italic>ps</jats:italic></jats:sub> and the solar wind density was used to estimate time‐dependent <jats:italic>N</jats:italic><jats:sub><jats:italic>ps</jats:italic></jats:sub>. The result shows that the calculated <jats:italic>Dst</jats:italic>* tends to overshoot the observed one when the non‐self‐consistent electric field is employed. A better agreement was obtained with the self‐consistent electric field. We suggest that the nonlinear response of the ring current to <jats:italic>N</jats:italic><jats:sub><jats:italic>ps</jats:italic></jats:sub> is one of the mechanisms that impedes the growth of the storm‐time ring current. Another mechanism is probably the saturation of the polar cap potential drop for high solar wind electric field.</jats:p>