Figure 2 - uploaded by Lars G. Westerberg
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The XZ -plane in the MHD simulations showing the Z -component of the magnetic field (in Gauss) as shading and the velocity as arrows.
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![Figure 3. Alfvén Mach number (M A = |U * |/[|B * |/ √ ρ]) along the...](profile/Lars-G-Westerberg/publication/231980554/figure/fig5/AS:668285104308247@1536342993820/Alfven-Mach-number-M-A-U-B-r-along-the-magnetopause-as-a-function-of_Q320.jpg)
We present a coupling between an analytical three-dimensional model covering the plasma flow behaviour through the magnetopause transition layer near a reconnection site, with results from a global MHD simulation describing the plasma flow in the magnetosheath. The structure of the plasma flow near a reconnection site at the dayside terrestrial mag...
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... K and a magnetic field B Z = −5 nT. The shape of the magnetopause is modelled by the equation X = (Y 2 + Z 2 )/(20R E ). We consider the limit of a very small reconnection rate, which means that, in the lowest-order approximation, we assume that the normal components of the velocity and the magnetic field are zero at the magnetopause boundary. In Fig. 2 we present results from the XZ-plane of the MHD simulations showing the Z-component of the magnetic field together with a vector plot of the ...
Citations
... where superscript '0' represents the value at the reconnection site. See Westerberg &Åkerstedt (2006) and Westerberg et al. (2007) for an analysis covering the case of a HT velocity having a gradient in z. In the present work we use data from satellites passing the MP boundary as matching conditions. ...
We present a model where a three-dimensional viscous/resistive analytical model of the large scale plasma flow in the outflow region about a reconnection site at the dayside magnetopause, is coupled with multispacecraft measurements from the Cluster satellite armada. A total of ten magnetopause crossings have been analyzed during the period 10:29–11:05 UT 26 January 2001, where nine are shown to be suitable to be coupled with the analytical model. Five of these nine reconnection events results in a successful coupling. By fitting the analytical expressions of the plasma velocity and magnetic field behavior during the transition of the magnetopause, with data from the Cluster spacecraft we obtain estimates of the location of the X-line together with estimates on the anomalous transport coefficients of kinematic viscosity (ν) and magnetic diffusivity (ηd). We also obtain the development of the magnetopause transition layer away from the X-line. It is shown that the distance from the spacecraft to the X-line varies between 0.01 and 1 Earth radii, while ν + ηd have a value between 4 · 104 km2/s and 4 · 106 km2/s. Furthermore it is shown that the transition layer thickness follows the analytical pattern where it grows proportional to the square root of the distance from the reconnection site. The estimated thickness obtained from each spacecraft is shown to follow the analytical structure well.
... Previous studies have been done covering the large-scale 2D incompressible/compressible flow, a development of the 3D analysis, and a coupling of the 3D analysis with results from MHD simulations. 1,3,4,10 To motivate the inclusion of the Hall terms, we recall that the resistive form of Ohm's law in laboratory space is ...
The influence of the Hall term in the generalized Ohm’s law on the large-scale plasma flow during conditions of ongoing magnetic reconnection at the dayside magnetopause (MP) is investigated. Of special interest is the plasma flow behavior during the transition of the MP transition layer as the Hall effect grows in proportion to the viscous-resistive effects. The governing equations are solved approximately by an ordinary perturbation expansion in orders of large Reynolds and Lundqvist numbers. It is shown that the flow pattern is strongly dependent on the magnitude of the Hall parameter; as it approaches zero, the viscous-resistive solution is obtained, while for an ordering of the same magnitude as the resistivity/viscosity, the Hall effect begins to affect the flow structure severely. For an increasing value on the Hall parameter, oscillations are brought into the system, an effect that is enhanced with the magnitude of the Hall parameter. Furthermore, it is shown that as the Hall effect begins to dominate, the transition layer thickens.
... where superscript '0' represents the value at the reconnection site. See and Westerberg et al. (2007) for an analysis covering the case of a HT velocity having a gradient in z. In the present work we use data from satellites passing the MP boundary as matching conditions. ...
The solar wind interaction with the terrestrial magnetosphere is a source for many spectacular phenomena on or close the Earth's surface. A key question during the last fifty years have been how the solar wind plasma can enter the terrestrial magnetic shield represented by the magnetosphere and its outermost layer called the magnetopause. This have been the seed for many controversies among researchers throughout the years. Today we know that there are several possibilities for the solar wind to break through the magnetic boundary of the Earth. The main plasma transport mechanism at the magnetopause is called magnetic reconnection, where the magnetic energy stored in the solar wind is converted to kinetic energy through a localized break-down of the ideal frozen-in condition of the magnetic field within the plasma. Since its introduction to the space-physical community in the late 1950's, reconnection research have had its primary focus on understanding the onset mechanisms inside the diffusion region where the solar wind magnetic field is reconnected with the magnetospheric magnetic field. In this thesis work we put the context well out of the diffusion region and focuses on the implications of magnetic reconnection onto the surrounding solar wind plasma, rather than on the main mechanisms which initiates the process. We present solutions for the structure of the plasma flow through the magnetopause surface during conditions of ongoing reconnection. This is done through viscous-resistive reconnection models together with models where finite gyro-radius effects are considered. In order to validate the viscous-resistive model we also couple the analytical solutions with in situ measurements made by the Cluster spacecraft fleet. This results in an entirely new way of determining the magnetopause transition layer thickness and the location of the reconnection site from spacecraft data.
In this study the influence of magnetic reconnection onto the magnetosheath flow is investigated by combining a viscous-resistive reconnection model of the flow through the magnetopause, with analytical solutions for the outer magnetosheath flow. The flow structure is shown to change substantially when non-zero uniform plasma velocity and velocity gradient is introduced. Furthermore, the reconnection rate is shown to change for this set of parameter values, which leads to a cut off when the velocity becomes Alf enic. INTRODUCTION Being a key mechanism treating the conversion of magnetic energy into kinetic energy, magnetic reconnection have during the last fifty years been considered to play a vital role in space-, astro-, and stellar physics as well as in laboratory plasma applications. The reconnection process dominates the transport of solar wind plasma into the terrestrial magnetosphere. In recent studies Westerberg Akerstedt (2005, 2006, 2007b,c) have investigated the plasma flow dynamics during the transition of the magnetopause and conditions of ongoing magnetic reconnection. The 3D work have also been combined with in situ data made by the Cluster spacecraft armada (Westerberg et.al., 2008) and with MHD simulations (Westerberg et.al., 2007). All of these studies comprise viscosity and resistivity as non-ideal effects. The 3D analysis (Westerberg Akerstedt, 2006) have also been developed to include finite gyro effects in form of the Hall term in the generalized Ohm's law (Westerberg Akerstedt, 2007a). Petschek (1964) made the first model treating fast reconnection, which could explain processes occurring on the Sun. Previously Sweet (1958a,b); Parker (1957) had presented a ground braking theory in terms of reconnecting magnetic field lines. As their work could not explain the fast reconnection rates occurring on e.g. the Sun's surface, it became a cornerstone model treating slow reconnection. The objective with the present study is to put the 2D viscous-resistive reconnection model (Westerberg Akerstedt, 2005) into the context of the Petschek solution methodology, and thereby also investigating how the reconnection process affect the magne-tosheath flow. A composite solution is built of the inner solution governing the behaviour through the magnetopause boundary, and the solution for the outer magnetosheath flow obtained from the same methodology used by Petschek where the magnetic field and the velocity are expanded along uniform fields.
