Large-scale energy budget of impulsive magnetic reconnection: Theory and simulation.

We evaluate the large-scale energy budget of magnetic reconnection utilizing an analytical time-dependent impulsive reconnection model and a numerical 2-D MHD simulation. With the generalization to compressible plasma, we can investigate changes in the thermal, kinetic, and magnetic energies. We study these changes in three different regions: (a) the region defined by the outflowing plasma (outflow region, OR), (b) the region of compressed magnetic fields above/below the OR (traveling compression region, TCR), and (c) the region trailing the OR and TCR (wake). For incompressible plasma, we find that the decrease inside the OR is compensated by the increase in kinetic energy. However, for the general compressible case, the decrease in magnetic energy inside the OR is not sufficient to explain the increase in thermal and kinetic energy. Hence, energy from other regions needs to be considered. We find that the decrease in thermal and magnetic energy in the wake, together with the decrease in magnetic energy inside the OR, is sufficient to feed the increase in kinetic and thermal energies in the OR and the increase in magnetic and thermal energies inside the TCR. That way, the energy budget is balanced, but consequently, not all magnetic energy is converted into kinetic and thermal energies of the OR. Instead, a certain fraction gets transfered into the TCR. As an upper limit of the efficiency of reconnection (magnetic energy → kinetic energy) we find ηeff=1/2. A numerical simulation is used to include a finite thickness of the current sheet, which shows the importance of the pressure gradient inside the OR for the conversion of kinetic energy into thermal energy.

Escape of the martian protoatmosphere and initial water inventory.

Latest research in planet formation indicates that Mars formed within a few million years (Myr) and remained as a planetary embryo that never grew to a more massive planet. It can also be expected from dynamical models that most of Mars' building blocks consisted of material that formed in orbital locations just beyond the ice line which could have contained [Formula: see text] of H2O. By using these constraints, we estimate the nebula-captured and catastrophically outgassed volatile contents during the solidification of Mars' magma ocean and apply a hydrodynamic upper atmosphere model for the study of the soft X-ray and extreme ultraviolet (XUV) driven thermal escape of the martian protoatmosphere during the early active epoch of the young Sun. The amount of gas that has been captured from the protoplanetary disk into the planetary atmosphere is calculated by solving the hydrostatic structure equations in the protoplanetary nebula. Depending on nebular properties such as the dust grain depletion factor, planetesimal accretion rates and luminosities, hydrogen envelopes with masses [Formula: see text] to [Formula: see text] could have been captured from the nebula around early Mars. Depending on the before mentioned parameters, due to the planets low gravity and a solar XUV flux that was [Formula: see text] times stronger compared to the present value, our results indicate that early Mars would have lost its nebular captured hydrogen envelope after the nebula gas evaporated, during a fast period of [Formula: see text]. After the solidification of early Mars' magma ocean, catastrophically outgassed volatiles with the amount of [Formula: see text] H2O and [Formula: see text] CO2 could have been lost during [Formula: see text], if the impact related energy flux of large planetesimals and small embryos to the planet's surface lasted long enough, that the steam atmosphere could have been prevented from condensing. If this was not the case, then our results suggest that the timescales for H2O condensation and ocean formation may have been shorter compared to the atmosphere evaporation timescale, so that one can speculate that sporadically periods, where some amount of liquid water may have been present on the planet's surface. However, depending on the amount of the outgassed volatiles, because of impacts and the high XUV-driven atmospheric escape rates, such sporadically wet surface conditions may have also not lasted much longer than [Formula: see text]. After the loss of the captured hydrogen envelope and outgassed volatiles during the first 100 Myr period of the young Sun, a warmer and probably wetter period may have evolved by a combination of volcanic outgassing and impact delivered volatiles [Formula: see text] ago, when the solar XUV flux decreased to values that have been [Formula: see text] times that of today's Sun.

Kink-like mode of a double gradient instability in a compressible plasma current sheet.

A linear MHD instability of the electric current sheet, characterized by a small normal magnetic field component, varying along the sheet, is investigated. The tangential magnetic field component is modeled by a hyperbolic function, describing Harris-like variations of the field across the sheet. For this problem, which is formulated in a 3D domain, the conventional compressible ideal MHD equations are applied. By assuming Fourier harmonics along the electric current, the linearized 3D equations are reduced to 2D ones. A finite difference numerical scheme is applied to examine the time evolution of small initial perturbations of the plasma parameters. This work is an extended numerical study of the so called "double gradient instability", - a possible candidate for the explanation of flapping oscillations in the magnetotail current sheet, which has been analyzed previously in the framework of a simplified analytical approach for an incompressible plasma. The dispersion curve is obtained for the kink-like mode of the instability. It is shown that this curve demonstrates a quantitative agreement with the previous analytical result. The development of the instability is investigated also for various enhanced values of the normal magnetic field component. It is found that the characteristic values of the growth rate of the instability shows a linear dependence on the square root of the parameter, which scales uniformly the normal component of the magnetic field in the current sheet.

Magnetic double-gradient instability and flapping waves in a current sheet.

A new kind of magnetohydrodynamic instability and waves are analyzed for a current sheet in the presence of a small normal magnetic field component varying along the sheet. These waves and instability are related to the existence of two gradients of the tangential (B_{tau}) and normal (B_{n}) magnetic field components along the normal (nabla_{n}B_{tau}) and tangential (nabla_{tau}B_{n}) directions with respect to the current sheet. The current sheet can be stable or unstable if the multiplication of two magnetic gradients is positive or negative. In the stable region, the kinklike wave mode is interpreted as so-called flapping waves observed in Earth's magnetotail current sheet. The kink wave group velocity estimated for the Earth's current sheet is of the order of a few tens of kilometers per second. This is in good agreement with the observations of the flapping motions of the magnetotail current sheet.