MHD Shock Waves Research Articles

Heliophysics: from observations to models and applications

Study of the physical phenomena and processes on the Sun and in the heliosphere, a natural plasma laboratory, is based on near-earth and space-based observations and building models which help to obtain a general view of how the Sun was made and how it works, while allowing one to address the practical problems of solar activity influencing space weather and its impact on various areas of human activity. In this paper a brief outline is given of the models of trigger mechanisms driving the most powerful manifestations of solar activity — solar flares and mass ejections, the wave mechanism of solar corona heating. Also, analytical solutions are presented for MHD shock waves in solar wind collisionless plasma with heat fluxes.

On the shock induced instabilities in collisionless plasma

Firehose, mirror and ion-acoustic instabilities behind MHD shock waves are discussed for collisionless anisotropic plasma with heat fluxes. For the parallel shock wave it has been demonstrated that initially stable plasma can be destabilized by the shock which leads to turbulence generation in the downstream flow. Upstream parameter domains are determined where such destabilization occurs.

A computational study of the properties of the quasi-perpendicular fast forward shock event during solar maximum

MHD shock waves and discontinuities are often observed in the solar wind. We studied a strong shock wave event on 7 June 2014, during a solar maximum. The properties of forward shock are investigated and all physical parameters of interplanetary shock are analyzed. The upstream parameters, such as Alfven velocity and sound speed are calculated, and the angle ( $${\theta }$$ ) between the upstream magnetic field direction and the shock normal is estimated. To determine the propagation speed of the shock, a full numerical solution of shock adiabatic equation is carried out. The thermal pressure for electrons and ions are calculated and also the pressure ratio and the entropy change across the shock are estimated. The results show that the shock strength is about 3.88 with $${\theta }\approx \text{72 }^{\circ }$$ (a quasi-perpendicular case), and shock propagation velocity is about 678 km/s. The increase in the specific entropy is also evaluated.

Emergence of unstable modes for classical shock waves in isothermal ideal MHD

This note studies classical magnetohydrodynamic shock waves in an inviscid fluidic plasma that is assumed to be a perfect conductor of heat as well as of electricity. For this mathematically prototypical material, it identifies, mainly numerically, two critical manifolds in parameter space, across which slow resp. fast MHD shock waves undergo emergence of a complex conjugate pair of unstable transverse modes. For slow shocks, this emergence occurs in a particularly interesting way already in the parallel case, in which it happens at the spectral value λˆ≡λ∕|ω|=0 and the critical manifold possesses a simple explicit algebraic representation. Results of refined numerical treatment show that within the set of non-parallel slow shocks the unstable mode pair emerges from two generically different spectral values λˆ=±iγ. For fast shocks, the critical manifold does not intersect the parallel regime and the emergence within the set of non-parallel fast shocks again starts from two generically different spectral values.

The magnetic hole as plasma inhomogeneity in the solar wind and related interplanetary medium perturbations

We considered magnetic hole-type plasma structures with a constant total pressure, which are often observed in the flux of the solar wind. The interaction between a linear magnetic hole and the front of the primary or bow shock wave before the Earth’s magnetosphere was studied, and the appearance of a fast shock wave in the magnetosheath and displacement of the bow shock front in the direction of the Earth’s magnetosphere is described. The magnetic hole in the scope of the MHD theory is considered a plasma inhomogeneity bounded by two tangential discontinuities: the front and rear boundaries. Based on the MHD theory of nonlinear interactions of solar wind discontinuity structures with a magnetic hole, the appearance of new automodel and MHD shock waves inside the magnetic hole is shown. The obtained results, which provide evidence of a change in the configuration of the magnetic hole and a displacement of the bow shock front due to the perturbation from the solar wind, are qualitatively verified in many aspects by observations performed earlier by the Cluster and ACE spacecrafts.

Spatially resolved observations of a coronal type II radio burst with multiple lanes

Relative dynamics of the radio sources of the metric type II burst with three emission lanes and coronal mass ejection (CME) occurred in the lower corona (r≲1.5R⊙) during the SOL2011-02-16T14:19 event is studied. The observational data of the Nancay Radioheliograph (NRH) and the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) are used. These observations are also supplemented by the data sets obtained with the STEREO-A and -B, RHESSI, and GOES spacecraft, as well as with the ground-based solar radio spectrometers. It is found that the sources of the radio burst were located ahead of the expanding CME and had a complex spatial structure. The first and the second lanes were both emitted from the “magnetic funnel” — a bundle of open magnetic field lines separated the south and north systems of magnetic loops of the active region. Due to the projection effect and limited angular resolution of the NRH it is not possible to determine, whether the spatial locations of the radio sources of the two first emission lanes differed or not. It is argued that the observations support the hypothesis that the radio sources of the first and second lanes could be emitted respectively ahead of and behind a front of the same weak (the Alfvén Mach number MA≈1.1–1.2), fast mode, quasi-parallel piston MHD shock wave. However, the third lane of the burst was definitely emitted from a different place. Its radio sources were situated ahead of the north-west part of the CME propagated through the north system of magnetic loops. This indicates clearly that different emission lanes of the same type II burst can be a result of propagation of different parts of a single CME through regions with different physical conditions (geometries and plasma densities) in the lower corona.

Can slow solar shock waves heat the corona?

Based on the solution to a generalized Riemann-Kotchine problem, the appearance of dissipative slow shock waves in the plasma of the solar corona, which occur when rotational discontinuities are refracted at a contact discontinuity in the transition region between the chromosphere and corona, is studied. The oblique interaction between a solar rotational discontinuity A and stationary contact discontinuity C in the transition region is considered in the scope of the magnetohydrodynamic model. Here, due to the presence of a large number of nonlinear Alfven waves, there is a real possibility of the appearance of a rotational discontinuity moving to the solar corona in the chromosphere. The appearance of dissipative slow MHD shock waves with an insignificant change in the magnetic field as a result of refraction of nondissipative rotational discontinuities at a contact discontinuity in the transition region is proved. It is supposed that a wave source of plasma heating can exist in upper layers of the corona because of the motion of slow shock waves undergoing the Landau damping. Thus, a new model of heat transfer from the chromosphere to the solar corona is proposed.

Stationary strong magnetohydrodynamic discontinuities and pressure balanced structures in the solar wind stream

Strong disturbances of magnetic clouds in the solar wind stream are considered when solar MHD shock waves from the surrounding plasma collide with these inhomogeneities. The boundaries of the considered plasma inhomogeneities are presented as stationary tangential discontinuities. The collision of solar fast shock waves with the back and front boundaries is studied as a decomposition of an arbitrary discontinuity. It is asserted that secondary waves of rarefaction and reverse shock waves arise depending on the initial conditions. It is pointed out that a change occurs in the configuration of the plasma inhomogeneity under study, which is caused by the incoming perturbation repeatedly observed by spacecrafts.

Deformation and deceleration of coronal wave

Aims. We studied the kinematics and morphology of two coronal waves to better understand the nature and origin of coronal waves. Methods. Using multi-wavelength observations of the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) and the Extreme Ultraviolet Imager (EUVI) on board the twin spacecraft Solar-TErrestrial RElations Observatory (STEREO), we present morphological and dynamic characteristics of consecutive coronal waves on 2011 March 24. We also show the coronal magnetic field based on the potential field source surface model. Results. This event contains several interesting aspects. The first coronal wave initially appeared after a surge-like eruption. Its front was changed and deformed significantly from a convex shape to a line-shaped appearance, and then to a concave configuration during its propagation to the northwest. The initial speeds ranged from 947 km s(-1) to 560 km s(-1). The first wave decelerated significantly after it passed through a filament channel. After the deceleration, the final propagation speeds of the wave were from 430 km s(-1) to 312 km s(-1). The second wave was found to appear after the first wave in the northwest side of the filament channel. Its wave front was more diffused and the speed was around 250 km s(-1), much slower than that of the first wave. Conclusions. The deformation of the first coronal wave was caused by the different speeds along different paths. The sudden deceleration implies that the refraction of the first wave took place at the boundary of the filament channel. The event provides evidence that the first coronal wave may be a coronal MHD shock wave, and the second wave may be the apparent propagation of the brightenings caused by successive stretching of the magnetic field lines.

Modelling the Propagation of a Weak Fast-Mode MHD Shock Wave near a 2D Magnetic Null Point Using Nonlinear Geometrical Acoustics

We present the results of analytical modelling of fast-mode magnetohydrodynamic wave propagation near a 2D magnetic null point. We consider both a linear wave and a weak shock and analyse their behaviour in cold and warm plasmas. We apply the nonlinear geometrical acoustics method based on the Wentzel-Kramers-Brillouin approximation. We calculate the wave amplitude, using the ray approximation and the laws of solitary shock wave damping. We find that a complex caustic is formed around the null point. Plasma heating is distributed in space and occurs at a caustic as well as near the null point due to substantial nonlinear damping of the shock wave. The shock wave passes through the null point even in a cold plasma. The complex shape of the wave front can be explained by the caustic pattern.

Magnetorotational supernovae with different equations of state

AbstractWe present results of the simulation of a magneto-rotational supernova explosion. We show that, due to the differential rotation of the collapsing iron core, the magnetic field increases with time. The magnetic field transfers angular momentum and a MHD shock wave forms. This shock wave produces the supernova explosion. The explosion energy computed in our simulations is 0.5-2.5 ċ 1051erg. We used two different equations of state for the simulations. The results are rather similar.

DISSIPATIVE ENTROPY AND GLOBAL SMOOTH SOLUTIONS IN RADIATION HYDRODYNAMICS AND MAGNETOHYDRODYNAMICS

The equations of ideal radiation magnetohydrodynamics (RMHD) serve as a fundamental mathematical model in many astrophysical applications. It is well known that radiation can have a damping effect on solutions of associated initial-boundary-value problems. In other words, singular solutions like shocks can be prohibited. In this paper, we consider discrete-ordinate approximations of the RMHD-system for general equations of state. If the magnetic fields are absent (i.e. if we consider radiation hydrodynamics), we prove the existence of global-in-time classical solutions for the Cauchy problem in one space dimension under an appropriate smallness condition on the inital data. We also show that counterparts of the compressive shock waves for the full RHD case and counterparts of the slow and fast MHD shock waves for the full RMHD-system can have structures in the presence of radiation if the amplitude is sufficiently small. Moreover, a new entropy function for the RMHD-system is presented.

OUTFLOWS FROM MAGNETOROTATIONAL SUPERNOVAE

We discuss results of 2D simulations of magnetorotational (MR) mechanism of core collapse supernova explosions. Due to the nonuniform collapse, the collapsed core rotates differentially. In the presence of an initial poloidal magnetic field its toroidal component appears and grows with time. Increased magnetic pressure leads to the formation of a compression wave which moves outwards. It transforms into the fast MHD shock wave (supernova shock wave). The shape of the MR supernova explosion qualitatively depends on the configuration of the initial magnetic field. For a dipole-like initial magnetic field, the supernova explosion develops mainly along the rotational axis, forming a mildly collimated jet. A quadrupole-like initial magnetic field leads to the explosion developing mainly along the equatorial plane. The magnetorotational instability was found in our simulations. The supernova explosion energy grows with an increase of the initial core mass and rotational energy of the core, and corresponds to the observational data.

A kinetic description of the dissipative quasi-parallel solar wind termination shock

Context. As a special case of astrophysical MHD shock waves, the solar wind termination shock is typically treated using the MHD jump conditions as they have been determined by Rankine and Hugoniot. A kinetic analysis becomes necessary for both a more detailed view of the governing processes and a deeper understanding of the plasma behaviour. Aims. In the case of a parallel shock, only an electric field can be considered as the main process decelerating the solar wind ions. This field leads to a strong acceleration for the electrons due to the other sign of their charge and the much lower mass of the electrons than of the ions. This situation enforces a two-stream instability, which is considered to be compensated by wave-particle interactions with electrostatic plasma waves. Methods. The kinetic approach leads to an equation in Fokker-Planck form, which can be solved by using It¯ o’s calculus for stochastic differential equations. Results. These two processes (electric field and wave-particle interaction) yield a decelerated subsonic solar wind on the downstream side of the termination shock, showing some new features in the ion distribution function, such as a double-hump structure and a comparatively large number of reflected ions. Within these considerations, we estimate of the spatial size of the shock region.

Cylindrical and Spherical Pistons as Drivers of MHD Shocks

We consider an expanding three-dimensional (3-D) piston as a driver of an MHD shock wave. It is assumed that the source-region surface accelerates over a certain time interval to achieve a particular maximum velocity. Such an expansion creates a large-amplitude wave in the ambient plasma. Owing to the nonlinear evolution of the wavefront, its profile steepens and after a certain time and distance a discontinuity forms, marking the onset of the shock formation. We investigate how the formation time and distance depend on the acceleration phase duration, the maximum expansion velocity (defining also acceleration), the Alfven velocity (defining also Mach number), and the initial size of the piston. The model differs from the 1-D case, since in the 3-D evolution, a decrease of the wave amplitude with distance must be taken into account. We present basic results, focusing on the timing of the shock formation in the low- and high-plasma-beta environment. We find that the shock-formation time and the shock-formation distance are (1) approximately proportional to the acceleration phase duration; (2) shorter for a higher expansion velocity; (3) larger in a higher Alfven speed environment; (4) only weakly dependent on the initial source size; (5) shorter for a stronger acceleration; and (6) shorter for a larger Alfven Mach number of the source surface expansion. To create a shock causing a high-frequency type II burst and the Moreton wave, the source region expansion should, according to our results, achieve a velocity on the order of 1000 km s−1 within a few minutes, in a low Alfven velocity environment.

Driven waves in a two-fluid plasma

We study the physics of wave propagation in a weakly ionised plasma, as it applies to the formation of multifluid, MHD shock waves. We model the plasma as separate charged and neutral fluids which are coupled by ion-neutral friction. At times much less than the ion-neutral drag time, the fluids are decoupled and so evolve independently. At later times, the evolution is determined by the large inertial mismatch between the charged and neutral particles. The neutral flow continues to evolve independently; the charged flow is driven by and slaved to the neutral flow by friction. We calculate this driven flow analytically by considering the special but realistic case where the charged fluid obeys linearized equations of motion. We carry out an extensive analysis of linear, driven, MHD waves. The physics of driven MHD waves is embodied in certain Green functions which describe wave propagation on short time scales, ambipolar diffusion on long time scales, and transitional behavior at intermediate times. By way of illustration, we give an approximate solution for the formation of a multifluid shock during the collision of two identical interstellar clouds. The collision produces forward- and reverse J shocks in the neutral fluid and a transient in the charged fluid. The latter rapidly evolves into a pair of magnetic precursors on the J shocks, wherein the ions undergo force free motion and the magnetic field grows monotonically with time. The flow appears to be self similar at the time when linear analysis ceases to be valid.

On the Structure of MHD Shock Waves in Diffusive-Dispersive Media

We consider the equations of compressible magnetohydrodynamics including the diffusive effects of fluid viscosity, thermal heat conductivity, electrical resistivity, and, in particular, the dispersive influence of the Hall term. The equations describe the dynamics of a plasma as it arises in astrophysical and technical applications. For a model problem we prove an existence result for shock profiles for all values of the Hall parameter. The same question for the complete six-dimensional system seems to be only solvable for small values of the Hall parameter, that is, viewing the Hall effect as a perturbation. To obtain substantial information on the complete system for all ranges of the dissipation parameters we present a careful numerical study. In particular the study confirms a well-known conjecture on the existence and bifurcation of orbits and illustrates the breaking of symmetry due to the Hall term.

Development of Numerical Scheme for MHD Shock Waves with Shape Flexibility and Memory Efficiency using HGA Method

Development of Numerical Scheme for MHD Shock Waves with Shape Flexibility and Memory Efficiency using HGA Method

Numerical Simulation of MHD Shock Wave with an Adapted Mesh Refinement Technique

Numerical Simulation of MHD Shock Wave with an Adapted Mesh Refinement Technique

Two-Dimensional Simulation of the Dynamics of the Collapse of a Rotating Core with Formation of a Neutron Star on an Adaptive Triangular Grid in Lagrangian Coordinates

Results are presented from a two-dimensional numerical simulation of the collapse of a rotating core with formation of a neutron star that has strong differential rotation in its outer regions. A specially developed numerical method is used which is based on a fully conservative implicit operator difference scheme for gravitational gas dynamics problems in lagrangian coordinates on a variable-structure triangular grid. The recoil shock wave generated by the collapse causes ejection of a small amount of material. This cannot explain the explosion of type II supernovae. The strong differential rotation in the presence of even a weak initial magnetic field obtained in these calculations must lead to a rise in the magnetic pressure, formation of an MHD shock wave, and conversion of rotational energy into the energy of radial expansion (magnetorotational supernova explosion).