Jump conditions for pressure anisotropy and comparison with the Earth's bow shock

Abstract. Taking into account the pressure anisotropy in the solar wind, we study the magnetic field and plasma parameters downstream of a fast shock, as functions of upstream parameters and downstream pressure anisotropy. In our theoretical approach, we model two cases: a) the perpendicular shock and b) the oblique shock. We use two threshold conditions of plasma instabilities as additional equations to bound the range of pressure anisotropy. The criterion of the mirror instability is used for pressure anisotropy p \\perp /p\\parrallel > 1. Analogously, the criterion of the fire-hose instability is taken into account for pressure anisotropy p \\perp /p\\parrallel < 1. We found that the variations of the parallel pressure, the parallel temperature, and the tangential component of the velocity are most sensitive to the pressure anisotropy downstream of the shock. Finally, we compare our theory with plasma and magnetic field parameters measured by the WIND spacecraft.

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

Journal of Plasma Physics ◽

10.1017/s002237780000893x ◽

2000 ◽

Vol 64 (5) ◽

pp. 561-578 ◽

Cited By ~ 23

Author(s):

N. V. ERKAEV ◽

D. F. VOGL ◽

H. K. BIERNAT

Keyword(s):

Magnetic Field ◽

Mach Number ◽

Tangential Component ◽

Magnetized Plasma ◽

Normal Velocity ◽

Jump Conditions ◽

Plasma Parameters ◽

Closure Relation ◽

Pressure Anisotropy ◽

The Magnetic Field

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 Alfvén Mach number. For each Alfvén 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 Earth's magnetosheath have highlighted the need for an MHD model where the plasma pressure is treated as a tensor.

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Experimental and numerical investigation of plasma parameters in the magnetosheath

MATEC Web of Conferences ◽

10.1051/matecconf/201814503003 ◽

2018 ◽

Vol 145 ◽

pp. 03003

Author(s):

Polya Dobreva ◽

Monio Kartalev ◽

Olga Nitcheva ◽

Natalia Borodkova ◽

Georgy Zastenker

Keyword(s):

Magnetic Field ◽

Solar Wind ◽

Numerical Investigation ◽

Euler Equations ◽

Ideal Gas ◽

Bow Shock ◽

Plasma Parameters ◽

Wind Spacecraft ◽

The Magnetic Field ◽

Good Agreement

We investigate the behaviour of the plasma parameters in the magnetosheath in a case when Interball-1 satellite stayed in the magnetosheath, crossing the tail magnetopause. In our analysis we apply the numerical magnetosheath-magnetosphere model as a theoretical tool. The bow shock and the magnetopause are self-consistently determined in the process of the solution. The flow in the magnetosheath is governed by the Euler equations of compressible ideal gas. The magnetic field in the magnetosphere is calculated by a variant of the Tsyganenko model, modified to account for an asymmetric magnetopause. Also, the magnetopause currents in Tsyganenko model are replaced by numericaly calulated ones. Measurements from WIND spacecraft are used as a solar wind monitor. The results demonstrate a good agreement between the model-calculated and measured values of the parameters under investigation.

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A case study of the plasma in the magneto-sheath using the numerical magnetosheath-magnetosphere model and THEMIS measure-ments

MATEC Web of Conferences ◽

10.1051/matecconf/201814503004 ◽

2018 ◽

Vol 145 ◽

pp. 03004

Author(s):

Polya Dobreva ◽

Olga Nitcheva ◽

Monio Kartalev

Keyword(s):

Magnetic Field ◽

Field Model ◽

Specific Aspect ◽

Plasma Parameters ◽

Ion Density ◽

Magnetic Field Model ◽

Wind Spacecraft ◽

The Mean ◽

The Magnetic Field

This paper presents a case study of the plasma parameters in the magnetosheath, based on THEMIS measurements. As a theoretical tool we apply the self-consistent magnetosheath-magnetosphere model. A specific aspect of the model is that the positions of the bow shock and the magnetopause are self-consistently determined. In the magnetosheath the distribution of the velocity, density and temperature is calculated, based on the gas-dynamic theory. The magnetosphere module allows for the calculation of the magnetopause currents, confining the magnetic field into an arbitrary non-axisymmetric magnetopause. The variant of the Tsyganenko magnetic field model is applied as an internal magnetic field model. As solar wind monitor we use measurements from the WIND spacecraft. The results show that the model quite well reproduces the values of the ion density and velocity in the magnetosheath. The simlicity of the model allows calulations to be perforemed on a personal computer, which is one of the mean advantages of our model.

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Scattering of field-aligned beam ions upstream of Earth's bow shock

Annales Geophysicae ◽

10.5194/angeo-25-785-2007 ◽

2007 ◽

Vol 25 (3) ◽

pp. 785-799 ◽

Cited By ~ 24

Author(s):

A. Kis ◽

M. Scholer ◽

B. Klecker ◽

H. Kucharek ◽

E. A. Lucek ◽

...

Keyword(s):

Magnetic Field ◽

Solar Wind ◽

Field Measurements ◽

Bow Shock ◽

Ion Distribution ◽

Parallel Side ◽

Earth’S Bow Shock ◽

High Mach ◽

The Magnetic Field

Abstract. Field-aligned beams are known to originate from the quasi-perpendicular side of the Earth's bow shock, while the diffuse ion population consists of accelerated ions at the quasi-parallel side of the bow shock. The two distinct ion populations show typical characteristics in their velocity space distributions. By using particle and magnetic field measurements from one Cluster spacecraft we present a case study when the two ion populations are observed simultaneously in the foreshock region during a high Mach number, high solar wind velocity event. We present the spatial-temporal evolution of the field-aligned beam ion distribution in front of the Earth's bow shock, focusing on the processes in the deep foreshock region, i.e. on the quasi-parallel side. Our analysis demonstrates that the scattering of field-aligned beam (FAB) ions combined with convection by the solar wind results in the presence of lower-energy, toroidal gyrating ions at positions deeper in the foreshock region which are magnetically connected to the quasi-parallel bow shock. The gyrating ions are superposed onto a higher energy diffuse ion population. It is suggested that the toroidal gyrating ion population observed deep in the foreshock region has its origins in the FAB and that its characteristics are correlated with its distance from the FAB, but is independent on distance to the bow shock along the magnetic field.

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The distribution function of diffuse ions and the magnetic field power spectrum upstream of Earth's bow shock

Geophysical Research Letters ◽

10.1029/gl014i007p00681 ◽

1987 ◽

Vol 14 (7) ◽

pp. 681-684 ◽

Cited By ~ 37

Author(s):

E. Möbius ◽

M. Scholer ◽

N. Sckopke ◽

H. Lühr ◽

G. Paschmann ◽

...

Keyword(s):

Magnetic Field ◽

Distribution Function ◽

Power Spectrum ◽

Bow Shock ◽

Earth’S Bow Shock ◽

The Magnetic Field

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Aspects of solar wind interaction with Mars: comparison of fluid and hybrid simulations

Annales Geophysicae ◽

10.5194/angeo-25-145-2007 ◽

2007 ◽

Vol 25 (1) ◽

pp. 145-159

Author(s):

N. V. Erkaev ◽

A. Bößwetter ◽

U. Motschmann ◽

H. K. Biernat

Keyword(s):

Magnetic Field ◽

Solar Wind ◽

Hybrid Model ◽

Field Enhancement ◽

Bow Shock ◽

Solar Wind Interaction ◽

Plasma Parameters ◽

Physical Reason ◽

The Magnetic Field ◽

Hybrid Simulations

Abstract. Mars has no global intrinsic magnetic field, and consequently the solar wind plasma interacts directly with the planetary ionosphere. The main factors of this interaction are: thermalization of plasma after the bow shock, ion pick-up process, and the magnetic barrier effect, which results in the magnetic field enhancement in the vicinity of the obstacle. Results of ideal magnetohydrodynamic and hybrid simulations are compared in the subsolar magnetosheath region. Good agreement between the models is obtained for the magnetic field and plasma parameters just after the shock front, and also for the magnetic field profiles in the magnetosheath. Both models predict similar positions of the proton stoppage boundary, which is known as the ion composition boundary. This comparison allows one to estimate applicability of magnetohydrodynamics for Mars, and also to check the consistency of the hybrid model with Rankine-Hugoniot conditions at the bow shock. An additional effect existing only in the hybrid model is a diffusive penetration of the magnetic field inside the ionosphere. Collisions between ions and neutrals are analyzed as a possible physical reason for the magnetic diffusion seen in the hybrid simulations.

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A model of the magnetosheath magnetic field during magnetic clouds

Annales Geophysicae ◽

10.5194/angeo-32-157-2014 ◽

2014 ◽

Vol 32 (2) ◽

pp. 157-173 ◽

Cited By ~ 8

Author(s):

L. Turc ◽

D. Fontaine ◽

P. Savoini ◽

E. K. J. Kilpua

Keyword(s):

Magnetic Field ◽

Solar Wind ◽

Ecliptic Plane ◽

Bow Shock ◽

Magnetic Clouds ◽

The Sun ◽

Earth’S Bow Shock ◽

D Model ◽

The Magnetic Field ◽

Shock Configuration

Abstract. Magnetic clouds (MCs) are huge interplanetary structures which originate from the Sun and have a paramount importance in driving magnetospheric storms. Before reaching the magnetosphere, MCs interact with the Earth's bow shock. This may alter their structure and therefore modify their expected geoeffectivity. We develop a simple 3-D model of the magnetosheath adapted to MCs conditions. This model is the first to describe the interaction of MCs with the bow shock and their propagation inside the magnetosheath. We find that when the MC encounters the Earth centrally and with its axis perpendicular to the Sun–Earth line, the MC's magnetic structure remains mostly unchanged from the solar wind to the magnetosheath. In this case, the entire dayside magnetosheath is located downstream of a quasi-perpendicular bow shock. When the MC is encountered far from its centre, or when its axis has a large tilt towards the ecliptic plane, the MC's structure downstream of the bow shock differs significantly from that upstream. Moreover, the MC's structure also differs from one region of the magnetosheath to another and these differences vary with time and space as the MC passes by. In these cases, the bow shock configuration is mainly quasi-parallel. Strong magnetic field asymmetries arise in the magnetosheath; the sign of the magnetic field north–south component may change from the solar wind to some parts of the magnetosheath. We stress the importance of the Bx component. We estimate the regions where the magnetosheath and magnetospheric magnetic fields are anti-parallel at the magnetopause (i.e. favourable to reconnection). We find that the location of anti-parallel fields varies with time as the MCs move past Earth's environment, and that they may be situated near the subsolar region even for an initially northward magnetic field upstream of the bow shock. Our results point out the major role played by the bow shock configuration in modifying or keeping the structure of the MCs unchanged. Note that this model is not restricted to MCs, it can be used to describe the magnetosheath magnetic field under an arbitrary slowly varying interplanetary magnetic field.

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What Density of Magnetosheath Sodium Ions Can Provide the Observed Decrease in the Magnetic Field of the “Double Magnetopause” during the First MESSENGER Flyby?

Symmetry ◽

10.3390/sym13071168 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1168

Author(s):

Elena Belenkaya ◽

Ivan Pensionerov

Keyword(s):

Magnetic Field ◽

Analytical Approach ◽

Field Structure ◽

Sodium Ions ◽

Plasma Parameters ◽

Calculation Results ◽

Magnetizing Current ◽

The Magnetic Field ◽

Density Excess

On 14 January 2008, the MESSENGER spacecraft, during its first flyby around Mercury, recorded the magnetic field structure, which was later called the “double magnetopause”. The role of sodium ions penetrating into the Hermean magnetosphere from the magnetosheath in generation of this structure has been discussed since then. The violation of the symmetry of the plasma parameters at the magnetopause is the cause of the magnetizing current generation. Here, we consider whether the change in the density of sodium ions on both sides of the Hermean magnetopause could be the cause of a wide diamagnetic current in the magnetosphere at its dawn-side boundary observed during the first MESSENGER flyby. In the present paper, we propose an analytical approach that made it possible to determine the magnetosheath Na+ density excess providing the best agreement between the calculation results and the observed magnetic field in the double magnetopause.

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Ion motion in the current sheet with sheared magnetic field – Part 1: Quasi-adiabatic theory

Nonlinear Processes in Geophysics ◽

10.5194/npg-20-163-2013 ◽

2013 ◽

Vol 20 (1) ◽

pp. 163-178 ◽

Cited By ~ 18

Author(s):

A. V. Artemyev ◽

A. I. Neishtadt ◽

L. M. Zelenyi

Keyword(s):

Magnetic Field ◽

Current Sheet ◽

Analytical Description ◽

Particle Energy ◽

Tangential Component ◽

Adiabatic Invariant ◽

Ion Motion ◽

Adiabatic Theory ◽

Fast Oscillations ◽

The Magnetic Field

Abstract. We present a theory of trapped ion motion in the magnetotail current sheet with a constant dawn–dusk component of the magnetic field. Particle trajectories are described analytically using the quasi-adiabatic invariant corresponding to averaging of fast oscillations around the tangential component of the magnetic field. We consider particle dynamics in the quasi-adiabatic approximation and demonstrate that the principal role is played by large (so called geometrical) jumps of the quasi-adiabatic invariant. These jumps appear due to the current sheet asymmetry related to the presence of the dawn–dusk magnetic field. The analytical description is compared with results of numerical integration. We show that there are four possible regimes of particle motion. Each regime is characterized by certain ranges of values of the dawn–dusk magnetic field and particle energy. We find the critical value of the dawn–dusk magnetic field, where jumps of the quasi-adiabatic invariant vanish.

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