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.     

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.     

The magnetopause erosion and the magnetosheath magnetic field penetration into the dayside magnetosphere

The earthward displacement of the magnetopause observed during a southward IMF (or the magnetopause erosion) and its dependence on the solar wind plasma and magnetic field parameters is studied by investigating data of about 30 magnetopause crossings by the ISEE 1 and 2 spacecraft. It is shown that the magnetopause erosion may be explained by a depression of the magnetic field intensity in the dayside magnetosphere caused by the penetration of the magnetosheath magnetic field (component perpendicular to the reconnection line) into the magnetosphere. The penetration coefficient (the ratio of the intensity of the penetrated field to the intensity of the magnetosheath magnetic field) is estimated and found to equal approximately 1.     

Shumann resonances and electromagnetic transparence in the atmosphere of Titan

Among the multiple questions that the CASSINI/HUYGENS mission tries to answer is the likelihood of electric discharges in Titan's atmosphere. The instruments “Huygens Atmospheric Structure Instrument” and “Radio and Plasma Wave Science” will probe the electromagnetic emissions during the Huygens descent and Cassini flybys, respectively. Although no lightning was observed during Voyager's encounters with Titan in 1980 and 1981, this does not exclude the existence of lightning phenomena. Recent investigations show that lightning discharges could occur in the lower atmosphere, such as the detection of methane condensation clouds in the troposphere and the theoretical prediction of an electric field that would be sufficient enough to cause lightning. We present a numerical model of Titan's atmosphere with the aim of calculating the resonance frequencies and the atmospheric transparency to electromagnetic waves. The detection and measurement of these resonances, Schumann frequencies, by the Huygens probe, would show the existence of electric activity connected with lightning discharges in the atmosphere. As it happens with the Schumann frequencies of Earth, losses associated with the electric conductivity will make these frequencies to be lower than the theoretically predicted, the fundamental one being located between 11 and 15 Hz. An analytical study shows that the strong losses associated with the high conductivity make it impossible that an electromagnetic wave generated near the surface with a frequency of 10 MHz or lower reaches the outer part of Titan's atmosphere. Therefore the detection of electromagnetic waves coming from Titan's lower atmosphere by the RPWS instrument is very unlikely.