The magnetopause is the layer that shields the Earth environment from the solar wind.The magnetopause surface has a rather complex shape; the magnetosheath plasma (shocked solar wind) flows around the magnetopause. The equilibrium magnetopause can be locally a tangential discontinuity (TD)  or a rotational discontinuity (RD). Since we have developed a kinetic model of TDs, our main objective has been a TD description of the magnetopause.

Detection of nonlinear features in plasma and field measurements by Prognoz-8
A.Yu. Sokolov, I. Kh. Khabibrakhmanov, M.M. Kuznetsova, J. Lemaire, M. Roth, J.M. Lesceux ,and F. Verheest 
ESA SP-311, 81, 1990

Investigations of plasma processes by spacecraft have shown the importance and necessity of wave measurements for understanding the interaction between the solar wind and the magnetosphere. Wave measurements carried out by differernt spacecrafts were usually restricted to the frequency range between 5 Hz and the plasma frequency. In order to investigate low frequency plasma waves a diagnostics complex BUD was installed on board of the PROGNOZ-8 satellite, working in the frequency range of 0.01-75 Hz. It was found in the neighbourhood of the magnetopause that there are low frequency, high amplitude disturbances in the electric field (up to 50 mV/m). These were accompanied by similar, correlated or anti-correlated disturbances in the plasma flux, pointing to strong nonlinear effects. 

Effect of the relative flow velocity on the structure and stability of the magnetopause current layer M.M. Kuznetsova, M. Roth, Z. Wang, and M. Ashour-Abdalla 
J. Geophys. Res., 99, 4095, 1994 

The Vlasov kinetic approach is used to study the stability of the magnetopause current layer (MCL) when a sheared flow velocity and a sheared magnetic field both exist simultaneously within it. A modified Harris-Sestero equilibrium where the magnetic field and bulk velocity are changing direction on the same spatial scale is suggested to illustrate the generation of a y component of the magnetic field in the center of the MCL. With this equilibrium it is shown that By (0) can be of the order of Bz (|x|>>0) when the value of the shear flow (U) tends to the ion drift velocity (Ud). The modifications of the initial symmetrical Harris configuration, introduced by the presence of a shear flow, strongly influence the adiabatic interaction of the plasma with the low-frequency tearing-type electromagnetic perturbations as well as the nonadiabatic response of the particles near the center of the MCL. This results in a reduction of the growth rate of the tearing mode.

Kinetic Structure of the Magnetopause: Equilibrium and Percolation
M.M. Kuznetsova, M. Roth and L.M. Zelenyi
in P. Song, B.U. Sonnerup, and M.F. Thomsen, ed(s): Physics of the Magnetopause,
Geophys. Monogr. Ser., vol. 90, AGU, Washington, D.C., 99, 1995

The paper addresses theoretical studies of the magnetopause kinetic fine structure. A considerable amount of effort was made beginning in the early sixties to construct Vlasov equilibrium models of one-dimensional tangential discontinuities which were assumed to provide a reasonable approximation for the structure of the magnetopause current layer (MCL). Simple models of MCLs of finite thickness (with a minimum number of free parameters) can be used to illustrate the effects of asymmetrical boundary conditions on the internal structure of the current layer. One-dimensional current layers are thermodynamical nonequilibrium systems which have an excess of free energy that allows excitation of drift tearing modes which result in destruction of magnetic surfaces. The stochastic percolation model by Galeev et al. (1986), based on the symmetrical charge-neutral Harris equilibrium, is generalized for asymmetrical MCLs. Asymmetry in the B field profile strongly modifies the dependence of the marginal MCL thickness (below which the MCL is subjected to percolation) on the angle of magnetic field rotation . The maximum thickness of MCLs which could be subjected to percolation is achieved when the magnetic field rotation angle is larger than 90°, that is, for southward IMF. Realistic asymmetrical MCLs are likely to be thinner for a northward IMF than for a southward IMF. For northward IMF the MCLs are likely to be thinner for larger values of plasma beta in the magnetosheath.

Thresholds for magnetic percolation through the magnetopause current layer in asymmetrical magnetic fields
M.M. Kuznetsova and M. Roth 
J. Geophys. Res., 100, 155, 1995 

The Vlasov kinetic approach is used to study the stability of magnetic surfaces with respect to spontaneous excitation of collisionless tearing perturbations within magnetopause current layers (MCLs) with asymmetrical magnetc field profiles. For the unperturbed configuration a "tractable" (that is, with a minimum number of free parameters) Vlasov equilibrium model describing a tangential discontinuity is developed. In this model, asymmetrical MCLs are not electrostatically equipotential configurations and their structure is only determined by the angle of the magnetic field rotation (mfr) and the magnetic field asymmetry factor Kb=(B2-B1)/B2, where B1 and B2 are the magnetic field intensities in the adjacent magnetosheath and magnetospheric regions, respectively. The stochastic percolation model by Galeev et al. (1986), based on the symmetrical charge-neutral Harris equilibrium, is generalized for asymmetrical MCLs. Asymmetry in the B field profile strongly modifies the dependence of the marginal MCL thickness (below which the MCL is subjected to percolation) on the polarity of the interplanetary magnetic field (IMF). For a northward IMF (mfr< 90°), the percolation is impossible when Kb >= 0.4, while for moderate values of Kb (0.15 <= Kb < 0.4) only thin MCLs can be percolated. When Kb> 0.3, the maximum thickness of MCLs subjected to percolation is achieved for mfr > 90°, that is, for a southward IMF. Assuming that the magnetopause should, on the average, be close to its stability threshold, realistic asymmetrical MCLs (with Kb > 0.3) should be thinner for a northward IMF than for a southward IMF.

Solar wind interaction with the magnetosphere
M. Roth 
Nouvelles de la Science et des Technologies, 13, 123, 1995

Solar wind interaction with the magnetosphere results in the formation of a current layer called the magnetopause. This paper reviews the kinetic theory of this current layer in the context of a multi-species model describing one-dimensional tangential discontinuities. Qualitative conclusions are drawn about the magnetopause thickness and structure.

Equilibrium conditions for the tangential discontinuity magnetopause
J. De Keyser and M. Roth 
J. Geophys. Res., 102, 9513-9530, 1997

Early satellite observations of the dayside magnetopause have suggested that the magnetic field typically rotates clockwise above the solar-magnetospheric equatorial plane and counterclockwise below it [Sonnerup and Cahill, 1968], in agreement with the theoretical analysis of Su and Sonnerup [1968] for magnetopause crossings of the rotational discontinuity type. The present paper treats the tangential discontinuity case. The influence of magnetosheath magnetic field and plasma flow on the magnetopause equilibrium structure is analyzed by means of a Vlasov model. The nature of the current layer plays a major role; the analysis is carried out for ion-dominated, electron-dominated, and mixed layers. Necessary and sufficient conditions for the existence of an equilibrium magnetopause are derived. It is found that (a) the magnetopause is best modelled as a transition layer of mixed type; (b) at the high magnetic shear dayside magnetopause the magnetic field preferentially rotates clockwise above the equatorial plane and counterclockwise below it, and at the tail flanks it rotates counterclockwise above and clockwise below the equatorial plane; this effect becomes more manifest as the magnetosheath flow is faster and as the difference in proton and electron transition lengths is more pronounced; (c) for low magnetic shear, TD equilibrium is expected to be lost more easily at the dawn side than at the dusk side; (d) the model provides a magnetopause thickness estimate; in particular, the low magnetic shear dawn magnetopause is predicted to be thinner than the dusk magnetopause. 

Correction to ``Equilibrium conditions for the tangential discontinuity magnetopause''
J. De Keyser and M. Roth 
J. Geophys. Res., 102, 19,943, 1997 

In the paper ``Equilibrium conditions for the tangential discontinuity magnetopause'' by J. De Keyser and M. Roth (J. Geophys. Res., 102, 9513-9530, 1997) an error appears in the magnetopause thickness estimate. Therefore the low magnetic shear magnetopause is expected to be thicker at the dawn side than at the dusk side, contrary to what is stated in the abstract and the conclusion of the paper. 

Equilibrium conditions and magnetic field rotation at the tangential discontinuity magnetopause
J. De Keyser and M. Roth 
J. Geophys. Res., 103, 6653-6662, 1998 

De Keyser and Roth recently have developed a kinetic model of the tangential discontinuity magnetopause. This model predicts (1) that not all configurations of magnetic field vectors and magnetosheath velocity allow an equilibrium to exist and (2) that there is a preference for a particular magnetic field rotation sense across the magnetopause due to the different response of ions and electrons to the electric field in the current layer. In the present paper we extend the original model to allow for different magnetospheric and magnetosheath densities and temperatures, and we show that the conclusions remain essentially unchanged. Given the large-scale magnetosheath flow pattern around the magnetosphere, we also compute which regions of the dayside magnetopause may be in tangential discontinuity equilibrium for a given magnetosheath field orientation.

Magnetic field rotation at the dayside magnetopause: AMPTE/IRM observations
J. De Keyser and M. Roth 
J. Geophys. Res., 103, 6663-6674, 1998 

Given the large-scale magnetosheath flow pattern around the magnetosphere, the tangential discontinuity magnetopause model of De Keyser and Roth predicts, for a prescribed magnetic field rotation angle and rotation sense, where equilibrium is possible on the dayside magnetopause surface and where it is not. In this paper we verify these predictions using 5 s time resolution magnetic field and plasma observations of the low-latitude dayside magnetospheric boundary acquired by the Active Magnetospheric Particle Tracer Explorers/Ion Release Module satellite. The model is confirmed by (1) the dominant presence of large positive magnetic field rotations among the dawnside crossings north of the equator, (2) the observation of positive and negative rotations near the stagnation point and at the duskside, and (3) the rare occurrence and questionable tangential discontinuity nature of low magnetic shear dawnside crossings. The absence of tangential discontinuity equilibrium in dawnside low shear crossings is consistent with the observation of increased dawnside low-latitude boundary layer thickness for northward magnetosheath field reported in the literature. 

Electron density at the subsolar magnetopause for high magnetic shear: ISEE 1 and 2 observations
D. Hubert, C. Harvey, M. Roth, and J. De Keyser 
J. Geophys. Res., 103, 6685-6692, 1998 

The ISEE radio wave propagation electron density experiment allowed the determination of the integrated electron density between the ISEE 1 and ISEE 2 satellites at the relatively high rate of 8 or 32 Hz. When the component of the spacecraft separation vector in the direction of the normal to the magnetopause is significantly smaller than the thickness of the current layer, this data set allows the internal structure of the magnetopause to be studied and compared with theoretical predictions. For a particular triple subsolar magnetopause crossing with high magnetic shear, an electron density overshoot is observed in the current layer adjacent to the magnetosheath. The similarity of the three crossings indicates that the internal structure of the magnetopause does not change dramatically during the time interval considered. A superposed epoch analysis of these crossings is consistent with the density profile obtained from kinetic simulations. The general relationship between magnetic field asymmetry, magnetic field rotation angle and electron density overshoot is discussed. It is concluded that a density overshoot could be a typical feature of the subsolar magnetopause with high magnetic shear. This conclusion is supported by two other dayside magnetopause crossings for which high time resolution electron density data are available. 

Plasma Transfer Processes at the magnetopause
D.G. Sibeck, G. Paschmann, R.A. Treumann, S.A. Fuselier, W. Lennartson, M. Lockwood, R. Lundin, K.W. Ogilvie, T.G. Onsager, T.-D. Phan, M. Roth, M. Scholer, N. Sckopke, K. Stasiewicz, and M. Yamauchi
Space Sc. Rev., 88, 207-283, 1999.

This article is the Chapter 5 of the sixth volume of ISSI (International Space Science Institute, Bern) Space Sciences Series. This sixth volume is the outcome of the study project "Source and Loss Processses of Magnetospheric Plasma".

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