ALBERT

Notes: This paper concentrates on aspects of magnetic field reconnection for a time-varying reconnection rate. There are a number of aspects of time-dependent reconnection that have no analogous behavior with the steady-state case. The localization of such time-varying features is of particular interest due to the fact that modeling is generally based on the steady-state case. In order to get optimal physical and mathematical insight, the most simple model is used: identical plasma and magnetic field behavior (except for the field orientation) on either side of the reconnection layer; furthermore the plasma is assumed to be incompressible. The primary interest is the distribution of different energy modes as a result of reconnection. Following a pulse of reconnection, propagating field reversal regions (FRRs) form. Inside these FRRs, the magnetic field energy is decreased, leading to accelerated plasma jets. As a result of the fast motion of the FRRs, there is an accumulation of magnetic energy external to their leading fronts (analogous to the snow accumulation in front of a moving snow plow), and a corresponding energy rarefaction in their wake regions. © 1998 American Institute of Physics.

Notes: A study of set-up, propagation, and interaction of non-linear and linear magnetohydrodynamic waves driven by magnetic reconnection is presented. The source term of the waves generated by magnetic reconnection is obtained explicitly in terms of the initial background conditions and the local reconnection electric field. The non-linear solution of the problem found earlier, serves as a basis for formulation and extensive investigation of the corresponding linear initial-boundary value problem of compressible magnetohydrodynamics. In plane geometry, the Green's function of the problem is obtained and its properties are discussed. For the numerical evaluation it turns out that a specific choice of the integration contour in the complex plane of phase velocities is much more effective than the convolution with the real Green's function. Many complex effects like intrinsic wave coupling, anisotropic propagation characteristics, generation of surface and side wave modes in a finite beta plasma are retained in this analysis. © 1996 American Institute of Physics.

Notes: Abstract  Nd and Sr isotopic data are presented for the 2449–2441 Ma Olanga and Burakovka layered mafic complexes in the eastern Baltic Shield. These complexes have similar tectonic position, but differ in two aspects: the age of the enclosing crust and the post-crystallization metamorphic history. The Sm–Nd isotopic results for the Kivakka and Lukkulaisvaara intrusions, Olanga Complex, are consistent with the model of closed-system crystallization of a single magma without significant wallrock assimilation. The Rb–Sr systems of minerals were disturbed by late Rb addition during 1.75–1.50 Ga metamorphism. The Nd and Sr isotopic systems in the Burakovka complex show no metamorphic disturbance and indicate mixing of at least four isotopically distinct components. Isotopic variations in the Burakovka Complex can be explained by a 4–20 per cent contamination of a primary komatiitic or picritic magma with a Mesoarchean crust, similar to that exposed in the region. A similar model, applied to the Olanga Complex using a Neoarchean crustal isotopic composition, cannot reproduce the observed isotopic signature. The nearly uniform initial ɛNd values between −1 and −2.3, observed in the Kivakka and Lukkulaisvaara intrusions of the Olanga Complex, as well as in the other 2.50–2.44 Ga layered mafic intrusions throughout the eastern Baltic Shield, are better explained by a mantle plume model with small amounts of crustal contamination and minor involvement of asthenospheric material. This model is also consistent with the geological observations and the temporal distribution of the Paleoproterozoic mafic magmatism in the eastern Baltic Shield. As an alternative, the enriched isotopic characteristics may be explained by melting of a metasomatically modified lithospheric mantle source.

Notes: Abstract A special Lagrangian coordinate system is introduced, in which the magnetic flux tube is the main object of investigation. The flux tube is shown to behave as a nonlinear relativistic string in relation to tangential force. General and particular variational principles are also discussed. With the introduction of a Lagrangian coordinate system the relativistic magnetohydrodynamic equation of motion reduces to a set of nonlinear string equations. From these results it follows that a highly conductive plasma with a ‘frozen-in’ magnetic field can be considered as a gas of nonlinear strings interacting through pressure forces. A method is developed which allows the multi-dimensional nonlinear problems of RMHD (relativistic MHD) with boundary layers to be reduced to a set of two-dimensional problems for flux tubes, i.e., nonlinear strings.

Notes: Abstract 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.

Notes: Abstract 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.