Energetics of reconnection: A reply

In this article we address several criticisms of Petschek-type reconnection models which have recently been raised by Heikkila. We discuss features of the time-dependent Petschek-type models in the context of the solar wind-magnetosphere interaction, and point out that such models can incorporate and reproduce observed features at the magnetopause, such as plasma jets and erosion of the current sheet. We argue that some of Heikkila's criticisms can be attributed to weaknesses in the analysis due to incomplete experimental information, rather than to flaws in the concept of reconnection per se; in this category we include the question of which instability leads to the localised breakup of the magnetopause current sheet. Other criticisms are based on an adherence to steady-state models, and cannot be sustained within the extended time-dependent theory. We discuss, for example, how the time-dependent model can provide a consistent picture of how energy from the incoming solar wind is transferred and converted as it enters the magnetosphere.     

Grain Surface Models and Data for Astrochemistry

The cross-disciplinary field of astrochemistry exists to understand the formation, destruction, and survival of molecules in astrophysical environments. Molecules in space are synthesized via a large variety of gas-phase reactions, and reactions on dust-grain surfaces, where the surface acts as a catalyst. A broad consensus has been reached in the astrochemistry community on how to suitably treat gas-phase processes in models, and also on how to present the necessary reaction data in databases; however, no such consensus has yet been reached for grain-surface processes. A team of \({\sim}25\) experts covering observational, laboratory and theoretical (astro)chemistry met in summer of 2014 at the Lorentz Center in Leiden with the aim to provide solutions for this problem and to review the current state-of-the-art of grain surface models, both in terms of technical implementation into models as well as the most up-to-date information available from experiments and chemical computations. This review builds on the results of this workshop and gives an outlook for future directions.     

Analysis of nonstationary heating and cooling of a thermomagnetic engine gadolinium working element

The paper presents the results of calculating nonstatitionary heat exchange between a heattransfer agent (water) and a gadolinium working element of the thermomagnetic engine with the use of ANSYS 13.0 certified software. Recommendations for designing the thermomagnetic engine working elements are given based on the analysis of calculation results.     

Wave resistance defect in a planar flow over periodic reliefs

The dependence of the wave resistance coefficients for planar periodic reliefs on the similarity parameters is investigated. It is proved that the wave resistance coefficients of the infinite reliefs and their finite analogs in the case of the whole wave numbers coincide, whereas in the case of the fractional wave numbers they differ.     

Wave resistance of rough plane channel walls in the supersonic flow

We propose a method that makes it possible to obtain in the framework of linear approximation the exact formulas for the wave resistance of the channel walls with an arbitrary plane pattern in the first and subsequent interference zones. It is shown by a particular example of the sinusoidal pattern that the pressure wave interference may lead to the positive or negative resistance resonance.     

Calculation of tractive nozzle characteristics with altitude compensation

The numerical calculations of flows in conical and contoured nozzles with slots in the supersonic part that operate under overexpansion conditions are presented. The calculations were made with the aid of the authors’ algorithm and program of simulating turbulent two-dimensional (axisymmetric) flows of a viscous heat-conducting gas. The results of computational investigations of tractive slot nozzle characteristics and the amount of combustion product leakage from an annular slot depending on the flight altitude are given. It is shown that the flight altitude at which the gas flow through the annular slot is “chocked” depends on its size and location in the supersonic nozzle part.     

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.     

MHD ANALYSIS OF PETSCHEK-TYPE RECONNECTION IN NON-UNIFORM FIELD AND FLOW GEOMETRIES

Analytical studies of reconnection have, for the most part, been confined to steady and uniform current sheet geometries. In contrast to these implifications, natural phenomena associated with the presence of current sheets indicate highly non-uniform structure and time-varying behaviour. Examples include the violent outbursts of energy on the Sun known as solar flares, and magnetospheric phenomena such as flux transfer events, plasmoids, and auroral activity. Unlike the theoretical models, reconnection therefore occurs in a highly dynamic and structured plasma environment. In this article we review the mathematical tools and techniques which are available to formulate models capable of describing the effects of reconnection in such situations. We confine attention to variants of the reconnection model first discussed by Petschek in the 1960s, in view of its successful application in predicting and interpreting phenomena in the terrestrial magnetosphere. The analysis of Petschek-type reconnection is based on the equations of ideal magnetohydrodynamics (MHD), which describe the large-scale behaviour of the magnetic field and plasma flow outside the diffusion region, which we determine as a localised part of the current sheet in which reconnection is initiated. The approach we adopt here is to transform the MHD equations into a Lagrangian or so-called 'frozen-in' coordinate system. In this coordinate system, the equation of motion transforms into a set of coupled nonlinear equations, in which the presence of inhomogeneous magnetic fields and/or plasma flows gives rise to a term similar to that which appears in the study of the ordinary string equation in a non-homogeneous medium. As demonstrated here, this approach not only clarifies and highlights the effects of such non-uniformities, it also simplifies the solution of the original set of MHD equations. In particular, this is true for those types of problem in which the total pressure can be considered as a known quantity from the outset. To illustrate the method, we solve several 2D problems involving magnetic field and flow non-uniformities: reconnection in a stagnation-point flow geometry with antiparallel magnetic fields; reconnection in a Y-type magnetic field geometry with and without velocity shear across the current sheet; and reconnection in a force-free magnetic field geometry with field lines of the form xy = const. These case examples, chosen for their tractability, each incorporate some aspects of the field and flow geomtries encountered in solar-terrestrial applications, and they provide a starting point for further analytical as well as numerical studies of reconnection.     

Analysis of the effect of various disturbing factors on high-precision forecasts of spacecraft orbits

The necessity of taking many force components disturbing spacecraft (SC) orbits into account is demonstrated for the example of forecasts of GLONASS ephemerides. The disturbances of SCs in high-earth orbits (HEO) and low-earth orbits (LEO) are systematized, and the degree of their effect on SC motion is estimated. Disturbance models are developed that provide essential increases of the accuracy of one-day forecasts of GLONASS and GPS ephemerides. Modeling results are presented that allow, depending on the required accuracy of SC orbit forecasts, the determination of the necessary list of disturbances included in the model.