The plasma universe has a cellular structure [Alfvén, 1981]: broad regions where fluid-like plasma theory applies are separated by thin boundaries where fluid theory fails and where a full kinetic description is required. These boundary layers separate plasmas possessing drastically different parameters and are due to sheets of electric currents. Space exploration has shown that such current layers are formed at many places throughout the heliosphere, and by inference throughout the Universe. Investigation of plasma processes within such layers are important as these processes control the mass and energy exchange between adjacent regions. For instance, processes at the Earth's magnetopause control the overall dynamics of the magnetosphere, e.g., phenomena like magnetospheric substorms and aurora. 

Different types of boundary layers may form in space plasmas [Hudson, 1970] A common type is classified as tangential discontinuity (TD). This type of discontinuity describes a structure where the magnetic field and the flow are tangential to the boundary surface. Much of the theoretical work at the Belgian Institute for Space Aeronomy has focussed on such TD layers. In particular, Vlasov equilibrium models of TDs have been developed and analyzed in detail. 

An iterative method to solve the nonlinear Poisson's equation in the case of plasma tangential discontinuities
M. Roth, J. Lemaire and A. Misson
J.  Comput. Phys., 86, 466, 1990 

In order to determine the electric potential in collisionless tangential discontinuities of a magnetized plasma, it is required to solve a non-linear Poisson's equation with sources of charge and current depending on the actual potential solution. This non-linear second-order differential equation is solved by an iterative method. This leads to an ordered sequence of non-linear algebraic equations for each successive approximation of the actual electric potential. It is shown that the method holds for transitions with characteristic thickness (D) as thin as five Debye lengths (Dl). For smaller thicknesses, when D shrinks to 3 Dl or less, the method fails because in that case the iteration procedure does not longer converge. Numerical results are shown for an ion-dominated layer (D 100 - 1000 Dl), as well as for two electron-dominated layers characterized by D 5 Dl and D 2.5 Dl, respectively. In all cases considered in this paper, the relative error on the electric potential obtained as a solution of the quasi-neutrality approximation is of the order of the relative charge density. When the method holds, each successive approximation reduces the relative error on the potential by roughly a factor of 10. For space plasma boundary layers, the quasi-neutrality approximation can be used with much confidence since their thickness is always much larger than the local Debye length.

Vlasov theory of the equilibrium structure of tangential discontinuities in space plasmas
M. Roth, J. De Keyser, and M.M. Kuznetsova
Space Sci. Rev., 76, 251, 1996 

Extensive theoretical work has been performed on the equilibrium structure of tangential discontinuities (TDs) in collisionless plasmas. This paper reviews kinetic models based on steady-state solutions of the Vlasov equation. It is shown that most of the existing models are special cases of a generalized multi-species model. In this generalized model all particle populations --- from both outer regions and from inside the layer --- are described using a unique formalism for the velocity distribution functions. Because of their historical importance, the Harris and Sestero models are reviewed and deduced from the generalized model. The Lee and Kan model is also a special case of the generalized model. The generalized model, however, is also able to describe TDs with velocity shear and large angles of magnetic field rotation. Such a multi-species model with a large number of free parameters and different gradient scales illustrates many observable features of TDs, including their multiscale fine structure. Particular attention is paid to the magnetopause. Observed magnetopause crossings are simulated. The effects of the relative flow velocity and asymmetrical magnetic field profiles on the structure of the magnetopause and on its stability with respect to tearing perturbations are discussed. We also present calculations that demonstrate the potential of the generalized model in explaining the origin of discrete auroral arcs. Numerical simulations of solar wind TDs with heavy ions and a large spectrum of thicknesses are also feasible. This indicates that such a model is of fundamental importance for understanding the detailed structure of solar wind TDs, like those observed by the interplanetary spacecraft ULYSSES. The problems associated with the one-dimensional, time-independent Vlasov approach are discussed and a variational principle is suggested to reduce the arbitrariness resulting from the large number of free parameters. 

Multi-spacecraft validation of a current sheet model
J. De Keyser and M. Roth
In: B. Fleck (ed.), Correlated Phenomena on the Sun, in the Heliosphere and in Geospace, Proceedings of the ESLAB 31 Symposium, ESA SP-415, 75--81, 1997 

We have developed a kinetic equilibrium model that describes current sheet structure in the widely different plasma regimes found in the solar wind and in geospace. In this paper we review the techniques that we have used to validate our model. The generality of the model forced us to consider current sheets in various regimes. The validation process included observations of solar wind current sheets (ULYSSES and WIND) and of the magnetopause (ISEE-1 and -2 and AMPTE/IRM). The availability of a validated model describing current sheets under various circumstances allows us to make general conclusions regarding the existence and the structure of current sheet equilibria. 

Author: J. De Keyser   Curator: J. De Keyser  Johan.DeKeyser@oma.be