Transmission of Alfvén waves through the rotational discontinuity at magnetopause

The reflection and refraction of MHD waves through an “open” magnetopause (rotational discontinuity) is studied. It is found that most of the incident wave energy can be transmitted through the open magnetopause. A transverse Alfvén wave (or a compressional magnetosonic wave) from the solar wind incident upon the open magnetopause would generally lead to the generation of both the transverse Alfvén and compressional magnetosonic waves in the magnetosphere. Transmission of Alfvén waves in the coplanar rotational discontinuity is studied in detail. The integral power of the Alfvén-wave transfer is found to be proportional to the open magnetic flux of the magnetosphere and is typically ～ 1% of the power of the total electromagnetic energy transfer through the open magnetopause. The transmitted wave power may contribute significantly to the geomagnetic pulsations observed on the ground, especially in the open-field-line region.     

On one mechanism for the generation of a reverse solar wind shock in the magnetosheath in front of the Earth’s magnetosphere

A possible mechanism for the generation of a reverse fast shock in the magnetosheath in the solar wind flow around the Earth’s magnetosphere is considered. It is shown that such a shock can emerge through the breaking of a nonlinear fast magnetosonic compression wave reflected from the magnetopause toward the bow shock rear. In this case, the magnetopause is represented as a tangential discontinuity with a zero normal magnetic field component at it and the mechanism under consideration is assumed to be secondary with respect to the sudden disturbance of the bow shock-Earth’s magnetosphere system by a nonstationary solar wind shock. A possible confirmation of the process under study by in-situ SC3 experimental observations of the bow shock front motion on the Cluster spacecraft is pointed out.     

Numerical simulation of slow shocks in the solar wind

The evolutionary state of slow forward shock waves is examined with the use of two MHD numerical codes. Our study is intended to be exploratory rather than a detailed parametric one. The first code is one-dimensional (with three components of velocity and magnetic field) which is used to follow a slow shock that propagates into a positive gradient of density versus distance. It is found that the slow shock evolves into an extraneous (intermediate) shock wave. The second code has a spherical, one-dimensional, planar geometry (with two velocity and magnetic field components) which is used to follow a spiral interplanetary magnetic field. It is found that a slow shock type perturbation can generate a forward slow shock; a fast forward shock is generated in the front of the slow shock; a contact discontinuity is formed behind the slow shock, and a compound nonlinear MHD wave is formed behind the contact discontinuity with a fast reverse shock formed further behind. Thus, we demonstrate that the evolution of a slow shock into (solely) a fast shock, as suggested by Whang (1987), is much more complicated.     

Anisotropic propagation of magnetogasdynamic sonic waves in conducting and radiating atmosphere

The propagation of sonic discontinuity in conducting and radiating atmosphere has been discussed under the influence of magnetic field. The velocity of sonic wave and its termination into shock wave has been obtained. We have also obtained the critical time at which sonic wave terminates into shock wave. There is significant effect of magnetic field on sonic velocity and its termination into shock wave.     

Energy interconnection between the plasma cloud ejected from the active region and the shock wave

The relation between the ejected plasma cloud and the shock wave propagating ahead of it is examined for 27 pairs of such events. The flare sprays and the eruptive prominences observed in H line as well as the fast-moving sources of type-IV radio bursts have been considered as such ejected plasma clouds. Propagation of the shock wave in the solar corona has been examined from the observations of type-II radio bursts. Using the Parker model of the propagation of a shock wave, the shock wave velocity has been compared with the plasma cloud velocity. Energy interconnection between these two events has been studied. In the majority of the investigated cases there exists an energetic interconnection between the plasma cloud and the shock wave.     

Non-similarity solutions for cylindrical shock waves in radiative magnetogasdynamics,I

The propagation of radiative-magnetogasdynamic cylindrical shock waves in an exponentially increasing medium is investigated. The shock wave moves with variable velocity and the total energy of the wave is also variable. The transformations in terms of , as given in the text, is necessarily a non-similarity one.     

Solar wind charge exchange during geomagnetic storms

On 2001 March 31 a coronal mass ejection pushed the subsolar magnetopause to the vicinity of geosynchronous orbit at 6.6 R_E. The NASA/GSFC Community Coordinated Modeling Center (CCMC) employed a global magnetohydrodynamic (MHD) model to simulate the solar wind‐magnetosphere interaction during the peak of this geomagnetic storm. Robertson et al. then modeled the expected soft X‐ray emission due to solar wind charge exchange with geocoronal neutrals in the dayside cusp and magnetosheath. The locations of the bow shock, magnetopause and cusps were clearly evident in their simulations. Another geomagnetic storm took place on 2000 July 14 (Bastille Day). We again modeled X‐ray emission due to solar wind charge exchange, but this time as observed from a moving spacecraft. This paper discusses the impact of spacecraft location on observed X‐ray emission and the degree to which the locations of the bow shock and magnetopause can be detected in images (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Development of a real-time algorithm for detection of solar wind discontinuities

A study is presented of an algorithm, based on the statistical analysis of interplanetary magnetic field data, for the real-time detection of discontinuities in the solar wind. The analysis is based on the application of a sliding or searching algorithm together with a minimum variance treatment. A demonstration is given for a Pioneer data set from 29 August, 1966. This particular data set was chosen because it has been extensively studied (in terms of the fast forward MHD shock wave) by previous groups who utilized the three-dimensional Rankine-Hugoniot shock equations after identifying the shock on a subjective basis. Our procedure differs in that it is perfectly objective because of its searching technique. For this particular data set we identify the original shock with excellent agreement with the earlier studies of its normal vector, as well as an additional shock and tangential discontinuity, neither of which had been identified previously.     

Particle trapping at a tangential discontinuity: Multiple incidence

Particle trapping by tangential gradients at the magnetopause is investigated for the case of a tangential discontinuity and taking into account an external magnetosheath magnetic field. Such a field causes a deflection of the reflected particle back to the magnetopause and thus enhances the chances of the particle to be captured by the magnetosphere after having travelled a certain finite distance down the magnetopause. The trapping angle and distances are calculated. Assuming a drifting Maxwellian for the magnetosheath plasma, we estimate that about 5% of that part of the magnetosheath plasma which comes into contact with the magnetopause can enter the dayside magnetopause during the first encounter. After multiple gyrations, about 30% of these particles may be trapped in the magnetosphere.     

The effect of the earth's bow shock and magnetosheath on the interaction of a discontinuity in the solar wind with the magnetosphere

A theoretical model is proposed for the interaction of a plane discontinuity in the solar wind with the magnetosphere. The presence of the bow shock and magnetosheath are taken into account, the calculation being based on the Spreiter et al. (1966) gas-dynamic model for a solar wind Mach Number M = 5. The model proposed predicts the manner in which the shape of the interplanetary discontinuity is distorted in its passage through the magnetosheath; it is found that the point of first impact with the magnetopause makes an angle of 56° with the Sun-Earth line for relatively quiet solar wind conditions.     

Energetic protons associated with a forward-reverse interplanetary shock pair at 1 A.U.

A forward-reverse interplanetary shock was observed on 25 March 1969 by the magnetometer and plasma detector on the HEOS-1 satellite. This relatively rare event was described by Chao et al (1972) who concluded that the shock pair was formed at a distance 0.10–0.13 A.U. upstream of the Earth as a result of the interaction between a fast and a slow solar wind streams. Simultaneous observations of 1 MeV solar proton fluxes were also performed on HEOS-1. A characteristic intensity peak was observed as the forward shock passed by the spacecraft. The evolution of the proton intensity, together with a detailed analysis of anisotropies and pitch angle distributions show a complex dynamic picture of the effect of the forward shock on the ambient proton population. Significant changes in particle fluxes are seen to be correlated with fluctuations in the magnetic field. It is suggested that simple geometrical models of shock-associated acceleration should be expanded to include the effect of magnetic fluctuations on particle fluxes. The interaction region limited by the forward and reverse shocks contained a large variety of magnetic fluctuations. Following the tangential discontinuity separating the fast solar wind stream from the preceding slow stream, a sunward flow was observed in the proton data, followed by a small but significant drop in intensity prior to the reverse shock.     

Outline of a theory of solar wind interaction with the magnetosphere

Some new ideas on the interaction of the solar wind with the magnetosphere are brought forward. The mechanism of reflection of charged particles at the magnetopause is examined. It is shown that in general the reflection is not specular but that a component of momentum of the particle parallel to the magnetopause changes. A critical angle is derived such that particles whose trajectories make an angle less than it with the magnetopause enter the magnetosphere freely, so transferring their forward momentum to it. Spatially or temporally non-uniform entry of charged particles into the magnetosphere causes electric fields parallel to the magnetopause which either allow the free passage of solar wind across it or vacuum reconnection to the interplanetary magnetic field depending on the direction of the latter. These electric fields can be discharged in the ionosphere and so account qualitatively for the dayside agitation of the geomagnetic field observed on the polar caps. The solar wind wind plasma which enters the magnetosphere creates (1) a dawn-dusk electric field across the tail (2) enough force to account for the geomagnetic tail and (3) enough current during disturbed times to account for the auroral electrojets. The entry of solar wind plasma across the magnetosphere and connection of the geomagnetic to interplanetary field can be assisted by wind generated electric field in the ionosphere transferred by the good conductivity along the geomagnetic field to the magnetopause. This may account for some of the observed correlations between phenomena in the lower atmosphere and a component of magnetic disturbance.     

The origin of the global system of field-aligned currents on the dayside of the magnetosphere

There is a component of the current normal to the boundary near the tangential discontinuity (the magnetopause) if the plasma is frozen in the magnetic field. On the assumption that the plasma density obeys the model of Gold's distributionnr ^–4, one finds that if one closes the component of the current in the ionospeere, the global system of field-aligned currents is created which is consistent with the Triad data on the value, direction, and the distribution with the local time.     

Rapid Reconnection and Compressible Plasma Waves

Magnetic reconnection causes the local non-linear decay of an infinitely thin current sheet, i.e., a tangential discontinuity, into large amplitude magnetohydrodynamic waves. This decay process propagates along the initial current sheet and induces linear wave perturbations in the surroundings. The Greens function for the self-consistent linear compressible plane wave problem is constructed and it is shown how to perform the convolution with some source function in form of a local reconnection pulse in an efficient way.     

The dependence of the value of the field-aligned current in the ionosphere on the local time for low velocity of convection

For low velocities of convection, the normal component of the current near the magnetopause is calculated in a case when the magnetopause is a tangential discontinuity. It is shown that for the great pressure of the magnetospheric plasma this component of the current, closing through the ionosphere, create the global system of field-aligned currents which is consistent with the Triad data on the value, the direction and the distribution with the local time.     

WKB approach to the problem of MHD shock propagation through the heliospheric current sheet

The interplanetary shock wave front shape and intensity are calculated numerically by means of the WKB-approach, with nonlinear effects taken into account. The solar flare is modelled as an isotropic point explosion at the solar wind base. The heliospheric current sheet (HCS) is represented by a radially diverging stream with a higher plasma concentration and a lower wind speed. Fast magnetosonic shock wave propagation along the HCS is connected with the effect of regular accumulation of the wave energy in the vicinity of the HCS. In this place the wave intensity is increased, and the corresponding front fragments go ahead to form a shock-wave forerunner as a pimple. The primple, in turn, is located inside a quite a large, but less-contrast, dimple in the wave surface. This dimple approximately coincides with the HCS stream contours. If the flare is outside the HCS boundaries, the picture discussed above is conserved, but asymmetry effects arise. Thus the interplanetary shock is stronger when the Earth's observer and the flare are on the same side of the HCS and is weaker in the opposite case.     

Deep Solar Activity Minimum 2007 – 2009: Solar Wind Properties and Major Effects on the Terrestrial Magnetosphere

We discuss the temporal variations and frequency distributions of solar wind and interplanetary magnetic field parameters during the solar minimum of 2007?–?2009 from measurements returned by the IMPACT and PLASTIC instruments on STEREO-A. We find that the density and total field strength were significantly weaker than in the previous minimum. The Alfvén Mach number was higher than typical. This reflects the weakness of magnetohydrodynamic (MHD) forces, and has a direct effect on the solar wind–magnetosphere interactions. We then discuss two major aspects that this weak solar activity had on the magnetosphere, using data from Wind and ground-based observations: i) the dayside contribution to the cross-polar cap potential (CPCP), and ii) the shapes of the magnetopause and bow shock. For i) we find a low interplanetary electric field of 1.3±0.9 mV?m^?1 and a CPCP of 37.3±20.2 kV. The auroral activity is closely correlated to the prevalent stream–stream interactions. We suggest that the Alfvén wave trains in the fast streams and Kelvin–Helmholtz instability were the predominant agents mediating the transfer of solar wind momentum and energy to the magnetosphere during this three-year period. For ii) we determine 328 magnetopause and 271 bow shock crossings made by Geotail, Cluster 1, and the THEMIS B and C spacecraft during a three-month interval when the daily averages of the magnetic and kinetic energy densities attained their lowest value during the three years under survey. We use the same numerical approach as in Fairfield’s (J. Geophys. Res. 76, 7600, 1971) empirical model and compare our findings with three magnetopause models. The stand-off distance of the subsolar magnetopause and bow shock were 11.8 R _E and 14.35 R _E, respectively. When comparing with Fairfield’s (1971) classic result, we find that the subsolar magnetosheath is thinner by ～1 R _E. This is mainly due to the low dynamic pressure which results in a sunward shift of the magnetopause. The magnetopause is more flared than in Fairfield’s model. By contrast the bow shock is less flared, and the latter is the result of weaker MHD forces.

     

Mass and particle ‘loading’ in plasma-neutral gas interaction

Qualitative considerations of mass and particle loading in plasma-neutral gas interaction are made by the help of a one-dimensional steady model. In the case of particle loading the plasma flow behind a strong shock is accelerated as in the case of mass loading regarded by Biermannet al. (1967) whereas behind a weak shock the flow is decelerated. As an example, one-dimensional time-dependent flows with ionization of the neutral gas by Alfvén's critical velocity effect are calculated. Because of the acceleration of the subsonic flow by loading processes, the existence of a tangential discontinuity in the flow around comets seems questionable.     

MHD shock interactions in coronal structures

We consider the magnetohydrodynamic (MHD) interactions of solar coronal fast shock waves of flare and/or nonflare origin with the boundaries of coronal streamers and coronal holes. Boundaries are treated as MHD tangential discontinuities (TD). Different parameters of the observed corona are used in the investigation. The general case of the oblique interaction is studied.It is shown that a solar fast shock wave must be refracted usually as a fast shock wave inside the coronal streamer. For the special case of the velocity shear across TD, a slow shock wave is generated. On the contrary, the shock wave refracted inside the coronal hole is indeed a slow shock wave.The significance of different effects due to the interaction of fast and slow shock waves on the coronal magnetic field is noticed, especially at the time of a coronal mass ejection (CME). It is also shown, that an oblique fast MHD coronal shock wave may trigger an instability at the boundary of a streamer considered as a TD. It might have a relation with the observed process of abrupt disappearance of the streamer's boundary in the solar corona.On leave from the Academy of Sciences, Central Astronomical Observatory Pulkovo, 196140, St. Petersburg, Russia.