Dieter F. Vogl

Anisotropic magnetosheath: Comparison of theory with wind observations near the stagnation streamline

We carry out a first comparison with spacecraft measurements of our recent three-dimensional, one-fluid magnetohydrodynamic (MHD) model for the anisotropic magnetosheath [Erkaev et al., 1999], using data acquired by the Wind spacecraft on an inbound magnetosheath pass on December 24, 1994. The spacecraft trajectory was very close to the stagnation streamline, being displaced by less than 1/2 hour from noon and passing at low southern magnetic latitudes (∼4.5°). All quantities downstream of the bow shock are obtained by solving the Rankine-Hugoniot equations taking the pressure anisotropy into account. In this application of our model we close the MHD equations by a “bounded anisotropy” ansatz using for this purpose the inverse correlation between the proton temperature anisotropy, Ap (≡ Tp⊥/Tp‖− 1), and the proton plasma beta parallel to the magnetic field βp‖ observed on this pass when conditions are steady. In the model the total perpendicular pressure is prescribed and not obtained self-consistently. For all quantities studied we find very good agreement between the predicted and the observed profiles, indicating that the bounded anisotropy method of closing the magnetosheath equations, first suggested by Denton et al. [1994], is valid and reflects the physics of the magnetosheath well. We assess how sensitive our model results are to different parameters in the Ap = α0βp‖−a1 (a1 > 0) relation, taking for a1 the two limiting values (0.4, 0.5) resulting from the two-dimensional hybrid simulations of Gary et al. [1997], and varying a0 in the range 0.6 – 0.8. Input solar wind conditions are as measured on this pass. In general, the model profiles depend more strongly on a0 than on a1. In particular, decreasing a0 narrows the width of the plasma depletion layer (PDL) and widens the mirror stable region. For the lowest value of a0, the mirror stable region extends sunward of the outer edge of the PDL. For the other two values of a0, and regardless of the value of a1, it is contained within the PDL. Finally, we also study phenomenological double-poly tropic laws and find poly tropic indices γ⊥ ≈ 1 and γ‖ ≈ 1.5. These results agree well with those of Hau et al. [1993] inferred from Active Magnetospheric Particle Tracer Explorers/Ion Release Module data on a crossing of the near-subsolar magnetosheath.

Solution for jump conditions at fast shocks in an anisotropic magnetized plasma

We study the magnetic field and plasma parameters downstream of a fast shock as functions of normalized upstream parameters and the rate of pressure anisotropy (defined as the ratio of perpendicular to parallel pressure). We analyse two cases: with the shock (i) perpendicular and (ii) inclined with respect to the magnetic field. The relations on the fast shock in a magnetized anisotropic plasma are solved taking into account the criteria for the mirror instability and firehose instability bounding the pressure anisotropy downstream of the shock. Our analysis shows that the parallel pressure and the parallel temperature as well as the tangential component of the velocity are the parameters that are most sensitive to the rate of pressure anisotropy. The variations of the other parameters, namely density, normal velocity, tangential component of the magnetic field, perpendicular pressure, and perpendicular temperature are much less pronounced, in particular when the perpendicular pressure exceeds the parallel pressure. The variations of all parameters increase substantially for a very low rate of anisotropy, which is bounded by the firehose instability in the case of inclined shocks. Using the criterion for mirror instability as a closure relation for the jump conditions at the fast shock, we obtain the plasma parameters and the magnetic field downstream of the shock as functions of the Alfven Mach number. For each Alfven Mach number, the criterion for mirror instability determines the minimum jumps in such parameters as density, tangential magnetic field component, parallel pressure, and temperature, and determines the maximum values of the velocity components and the perpendicular temperature. Ideal anisotropic magnetohydrodynamics (MHD) has wide applications for space plasma physics. Observations of the field and plasma behaviour in the solar wind as well as in the Earths magnetosheath have highlighted the need for an MHD model where the plasma pressure is treated as a tensor.

The solution of the Rankine–Hugoniot equations for fast shocks in an anisotropic kappa distributed medium

Abstract In this paper, we concentrate on the analysis of the anisotropic Rankine–Hugoniot equations for perpendicular and oblique fast shocks. In particular, as additional information to the anisotropic set of equations, the threshold conditions of the fire-hose and mirror instability are used to bound the range of the pressure anisotropy downstream of the discontinuity. These anisotropic threshold conditions of the plasma instabilities are obtained via a kinetic approach using a generalized Lorentzian distribution function, the so-called kappa distribution function. Depending on up-stream conditions, these instabilities further define stable and unstable regions with regard to the pressure anisotropy downstream of the shock. The calculations are done for different upstream Alfven Mach numbers. We found that low values of the parameter kappa reduce the pressure anisotropy downstream of the shock.

Analysis of mirror modes convected from the bow shock to the magnetopause

Abstract Spacecraft observations confirm the existence of mirror fluctuations in the magnetosheath. The mirror instability occurs in an anisotropic magnetized plasma when the difference between perpendicular and parallel (with respect to the magnetic field) plasma pressure exceeds a threshold depending on the perpendicular plasma beta. The anisotropy of the plasma pressure increases from the shock to the magnetopause as a result of magnetic field line stretching. This gives rise to plasma fluctuations which in turn lead to a relaxation between parallel and perpendicular temperatures. Mirror perturbations do not propagate and are convected with plasma flow along the streamlines. Using an anisotropic steady-state MHD flow model, we calculate the growth of mirror fluctuations from the bow shock to the magnetopause along the subsolar streamline. For the anisotropic MHD model, we use the empirical closure equation suitable for the AMPTE/IRM observations. The amplitudes of mirror fluctuations, which are obtained as a function of distance from the magnetopause, are directly compared with AMPTE/IRM observations on October 24, 1985. With regard to both the amplification of the magnetic field and the plasma density oscillations, as well as the location of maximum amplitudes, model calculations are in good agreement with values obtained from the AMPTE/IRM data.

Dayside magnetopause erosion on geostationary orbit using WIND and GOES data (1996-1999)

During periods of southward interplanetary field and basically constant dynamic pressure, the magnetopause can move earthward due to the so-called phenomenon of magnetopause erosion. In this study, we present several erosion events monitored at geostationary orbit by the GOES spacecrafts underlying WIND measurements in the solar wind. We selected a number of events using 4 years of WIND observations (1996-1999). Specific selection criteria are based on obtaining a progressively decreasing IMF Bz negative, to have various levels of erosion, with and without dynamic pressure changes and of different durations in time. To figure out the erosion effect on geostationary orbit, we have to compare the measured depression in the geostationary magnetic field strength with the magnetic field strength on the well known May 11, 1999, the day the solar wind almost disappeared.

Time-dependent reconnection for anisotropic pressure

An analysis of the reconnection process which extends the famous solution obtained by Petschek for the steady-state case to incorporate the effects of unsteady reconnection in an anisotropic plasma is presented. The case of so-called switch-off shocks, where the Alfven discontinuity and the slow shock degenerate to one discontinuity and the downstream magnetic field vanishes in lowest order, so that the plasma is isotropic in the field reversal region is studied. It is shown that the plasma anisotropy can essentially modify the plasma acceleration, the magnetic field intensity, and the shape of the moving slow shocks. Characteristics of reconnection in several limits, such as the isotropic limit and extreme pressure anisotropy cases corresponding to the fire hose and the mirror instability are analyzed.

The anisotropic jump equations for oblique fast shocks in a kappa distributed medium

Abstract In this paper, we concentrate on the solution of the anisotropic Rankine-Hugoniot equations for inclined fast shocks taking into account a new approach in closing the set of equations. In particular, the threshold conditions of the fire-hose and that of the mirror instability, obtained in a kinetic approach using the so-called kappa distribution function, are used to bound the range of the pressure anisotropy downstream of the discontinuity. We study the variation of the density across the shock for a given Alfven Mach number and upstream pressure anisotropy and find that the parameter kappa is most sensitive to stable plasma conditions, i.e. low values of kappa reduce the pressure anisotropy downstream of the discontinuity.

Analysis of an inclined fast shock including pressure anisotropy

To study magnetosphere-ionosphere interactions, appropriate considerations on the solar wind, the bow shock, the magnetosheath, and the outer ionosphere are of importance. In this study, we concentrate on the analysis of an inclined fast shock including upstream and downstream pressure anisotropy and apply it to conditions at the Earths bow shock. It is the main goal of this work to perform a parameter study of the magnetic field strength and plasma parameters downstream of an inclined fast shock as functions of upstream parameters and downstream pressure anisotropy. For closing the set of equations we use two threshold conditions of plasma instabilities as additional equations to bound the range of the pressure anisotropy, i.e., the criterion of the fire-hose instability and the criterion of the mirror instability. We found that the pressure anisotropy in the solar wind has a small influence on the changes of the relevant physical quantities across the shock wave. We further show that the variations of the plasma and field parameters are strongly influenced by the upstream Alfven Mach number and the angle between the normal vector of the discontinuity and the upstream magnetic field.

Some signatures of magnetic field line reconnection

Reconnection of magnetic field lines is a very important coupling mechanism in space for configurations with considerable skew in the magnetic field. In a magnetospheric context such configurations occur at the dayside magnetopause and in the magnetotail. Thus, reconnection couples phenomena prevailing in the solar wind with ionospheric phenomena. We report on the most important signatures of reconnection. Recent developments of reconnection theory are presented. Reconnection phenomena in the tail are briefly discussed.

Electric potential difference due to MHD slow shocks propagating along the Io flux tube

Many ionospheric and magnetospheric phenomena, e.g., the northern lights, require the existence of accelerated particle populations. One possible explanation for the development of such particles is an electric field directed along magnetic field lines. The main aim of this paper is to investigate the physical mechanisms leading to an electric potential difference along the Jo flux tube with special emphasis on the processes acting in the outer ionosphere of Jupiter. As a starting point, we assume a pressure perturbation at the position of Ιo and follow the evolution of this pressure perturbation from To towards Jupiter. Initially, the pressure pulse produces two slow mode waves propagating along the Ιo flux tube. These slow mode waves are converted into slow shocks traveling towards Jupiter, and are accompanied by a supersonic flow behind the shock front. The crucial point is now that due to the propagation into a more narrow flux tube, the flow velocity behind the shock increases, in particular fast near the surface of Jupiter. Such a strong plasma flow generates an electric potential difference along the magnetic field. We estimate this potential difference using well-known techniques of kinetic theory. It turns out that the strength of the potential drop is directly proportional to the flow energy of ions. Thus, the very heavy ion populations in the Ιo torus plasma provide an appropriate environment in order to generate an electric potential difference of the order of 1 kV. Therefore, the pressure pulse mechanism can contribute to the explanation of aurora and planetary radio emissions together with the generally accepted Alfven wings model.