The formation of thin current sheets is investigated on the basis of an adiabatic ideal MHD model. The primary applications are the substorm growth phase in Earth's magnetotail, prior to the dynamic expansion phase, and evolving structures in the solar corona which may similarly lead into an eruption such as a disappearing filament or a flare. A time-dependent MHD code is used to study the evolution under the influence of an external electric field applied at the boundaries of the system. This electric field may be considered as the consequence of the coupling with the solar wind in Earth's case or as a representation of a converging footpoint motion in a bipolar region on the solar photosphere. Thin current sheets are found to form both in the high-&bgr; and low-&bgr; case (where &bgr; is the ratio of plasma pressure over magnetic pressure). They form in the closed field region even though the external electric field and the footpoint displacement are applied predominantly in the surrounding open field region. Within the limits of numerically stable solutions, the current sheet thickness and the maximum current density remain finite, scaling with a high power of the lobe field increase. Larger amplitudes of the current density and a stronger localization of the current sheet in the radial direction are found when the applied electric field decays more rapidly away from Earth or the solar surface. The value of &ggr;, the polytropic index, has little influence on the evolution and the final current sheet structure. Force-free configurations behave similarly as their equivalent high-&bgr; current sheets. ¿ 1998 American Geophysical Union