Boundary Deformations and Thin Current Sheets in the Magnetosphere

In this work we present sequences of quasi-static evolution of the magnetosphere, starting from a quiet-time equilibrium configuration and applying boundary deformations, under flux, entropy and topology conservation constraints. The initial state and all intermediary states are two-dimensional magnetospheric equilibria, obtained through coupling two models in which the magnetic field is expressed in terms of Euler potentials: an inner/middle magnetosphere numerical solution of the Grad-Shafranov equation with an asymptotic magnetotail model farther away from Earth. We discuss the obtained entropy-conserving evolution, including the possibility of appearance of thin current sheets centered on the equatorial plane. The present work extends previous studies of magnetotail evolution under boundary deformations (arguably caused by solar wind variations) and validates the 'catastrophe scenario,' whereby for certain critical (but finite) boundary deformations equilibrium configurations cease to exist. A singular current sheet of infinite current density characterizes this 'catastrophe point', and this scenario provides a strong argument for the onset of instability, regardless of the dissipation mechanism.