Evolution of fast and slow shock interactions in the inner heliosphere

We use a one-dimensional, time-dependent adaptive grid MHD code to study the interaction between fast and slow shocks in the solar wind. Our results show that: (1) a forward slow shock (FSS) can be destroyed by a forward fast shock (FFS) that overtakes it from behind; (2) two propagating FSSs can merge into a stronger FSS; (3) a strong FSS can survive by following a strong forward fast shock; and (4) the strength of a FSS is decreased by following an FFS. These simulation results reproduce an important feature of the Helios observations (Richter, 1987) where transient fast shocks were more frequently followed within a few hours by slow shock ype discontinuities rather than by fast reverse shocks.     

Evolution of fast and slow shock interactions in the inner heliosphere

We use a one-dimensional, time-dependent adaptive grid MHD code to study the interaction between fast and slow shocks in the solar wind. Our results show that: (1) a forward slow shock (FSS) can be destroyed by a forward fast shock (FFS) that overtakes it from behind; (2) two propagating FSSs can merge into a stronger FSS; (3) a strong FSS can survive by following a strong forward fast shock; and (4) the strength of a FSS is decreased by following an FFS. These simulation results reproduce an important feature of the Helios observations (Richter, 1987) where transient fast shocks were more frequently followed within a few hours by slow shock ype discontinuities rather than by fast reverse shocks.     

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.     

Interaction of interplanetary MHD shock waves with the magnetopause

The interaction between a shock-wave and the magnetopause is formulated on the basis of one-dimensional magnetohydrodynamics. The magnetopause is assumed to be a tangential discontinuity, and the magnetic field is limited to the case of perpendicularity. Both the forward and reverse shocks' impact on the magnetopause are considered and analyzed separately. The forward shock-magnetopause interaction results in a transmitted shock, a tangential discontinuity, and a simple rarefaction wave. The reverse shock-magnetopause interaction creates a transmitted shock, a tangential discontinuity, and a reflected wave. The propagation of an SSC signal which is related to an interplanetary shock-induced geomagnetic storm's onset-time on Earth is discussed in general terms. It was found in earlier work (Shen and Dryer, 1972) that the propagation velocity of an inter-planetary shock is decreased by about 1015% following its impact with the earth's bow shock; the present study shows that its velocity is then suddenly increased by a factor of two to three after impact with the magnetopause. The fast propagating shock-wave inside the magnetosphere degenerates into a hydromagnetic wave as it advances into an increasing intensity of the distorted dipole geomagnetic field.     

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.     

Nonplanar magnetic reconnection associated with conical slow shocks

We study a nonplanar model of magnetic reconnection associated with conical slow shocks, assuming that the shock surfaces are two identical cones with circular cross sections symmetrical about the ±x-axis. In the inflow region upstream of the shocks, two oppositely directed magnetic fields are separated by a current sheet. The model treats the current sheet as a tangential discontinuity and treats shocks and tangential discontinuity as surfaces of zero thickness. The dynamical structure of the global magnetic field in the continuous regions is studied using compressible, non-resistive MHD equations. In the inflow region, nonplanar magnetic field lines first move toward the current sheet. Near the sheet, the middle sections of the field lines become highly flattened, almost parallel to the sheet. Eventually, then oppositely directed field lines merge across the tangential discontinuity between the two shocks, and the magnetic lines are reconnected at the intersection of the shock and the tangential discontinuity. Reconnected magnetic lines are carried away at high speeds by the MHD flow in the outflow region, downstream of the shocks.     

Weak MHD discontinuities in a radiation-induced flow field

The growth of weak MHD discontinuities have been studied in a radiation induced flow field at very high temperature. Growth and decay properties of weak MHD discontinuities have been discussed under the influences of time-dependent gasdynamic field, the radiation field and the magnetic field with finite electrical conductivity. The effects of thermal radiation and conduction of the global behaviour of weak MHD discontinuities have been studied under a quasi-equilibrium and quasi-isotropic hypothesis of the differential approximation to the radiative heat transfer equation. It is shown that the existence of the time-dependent radiation field gives rise to a radiation induced wave which has a negligibly small effect on the non-relativistic flow properties of the gasdynamic field. It is also shown that the radiation stresses resist the steepening tendency of a compressive weak wave and help in stabilizing it whereas the thermal conduction effects counteracts to destabilize it. It is found that under radiation effects the shock formation is either disallowed or delayed. The two cases of diverging waves and converging waves have been studied separately to answer a particular question as to when a shock discontinuity or a coustic will be formed or disallowed under curvature effects.     

磁通量喷发的大气响应——Ⅲ.太阳附近激波的演化

作为本系列的最后一篇,本文研究日冕大气中的激波演化.结果表明,日冕背景大气和磁场的非均匀性对激波结构和演化起着决定作用。太阳附近形成的慢激波-快磁声波系统,将在向外传播的过程中演变为以中间激波作为必要组成部分的混合激波。该混合激波在沿电流片传播时能继续维持,而在沿单极开放磁场传播时则进一步演变为纯快激波。     

Linear and non-linear MHD wave propagation in steady-state magnetic cylinders

The propagation of linear and non-linear magnetohydrodynamic (MHD) waves in a straight homogeneous cylindrical magnetic flux tube embedded in a homogeneous magnetic environment is investigated. Both the tube and its environment are in steady state. Steady flows break the symmetry of forward (field-aligned) and backward (anti-parallel to magnetic field) propagating MHD wave modes because of the induced Doppler shifts. It is shown that strong enough flows change the sense of propagation of MHD waves. The flow also induces shifts in cut-off values and phase-speeds of the waves. Under photospheric conditions, if the flow is strong enough, the slow surface modes may disappear and the fast body modes may become present. The crossing of modes is also observed due to the presence of flows. The effect of steady-state background has to be considered particularly carefully when evaluating observation signatures of MHD waves for diagnostics in the solar atmosphere.     

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.     

The generation of MHD shock waves during the impulsive phase of the February 27, 1992 flare

In this paper a unique 2.3–4.2 GHz radio spectrum of the flare impulsive phase, showing fast positively drifting bursts superimposed on a slowly negatively drifting burst, is presented. Analyzing this radio spectrum it was found that the flare started somewhere near the transition region, where upward propagating MHD waves were generated during the whole impulsive phase. Moreover, it was found that behind a front of these ascending MHD waves the downward propagating electron beams, which bombarded dense layers of the solar atmosphere, were accelerated. It seems that, simultaneously with the increase of beam bombardment intensity, the intensity of MHD waves was increasing and thus the MHD shock wave generation and the electron beam acceleration and bombardment formed a self-consistently amplifying flare process. At higher coronal heights this process was followed by a type II radio burst, i.e. by the MHD flare shock. To verify this concept, the numerical modeling of the shock-wave generation and propagation in space from a flare site near the transition region up to 3 solar radii was made. Comparing the thermal and magnetic field disturbances, it was found that those of magnetic origin are more relevant in this case. Combining the results of interpretation and numerical simulation, a model of the February 27, 1992 flare is suggested and new aspects of this model are discussed.     

Propagation of solar generated disturbances through the solar wind critical points: One-dimensional analysis

We investigate the proper method for mathematically simulating the formation of an interplanetary disturbance (IPD) in the subsonic, sub-Alfvénic region near the solar surface within the constraints of one-dimensional hydrodynamic and magnetohydrodynamic (MHD) analyses. We then numerically simulate the subsequent propagation of the IPD through the solar wind critical points in the equatorial plane to the outer corona. We show that, if the IPD is initiated outside the critical points, it always contains both a forward and reverse shock (a shock pair). This result contrasts with observations indicating that shock pairs at 1 AU which can be associated with solar events are rare occurrences in the solar wind. On the other hand, IPDs initiated inside the critical points contain only a forward shock at the leading edge. When the magnetic field is included in the simulation and the IPD is originated inside the critical points, the IPD contains a forward shock at its leading edge followed by large-amplitude, nonlinear, MHD waves which are convected outward by the solar wind. Unlike shock pairs, MHD waves are often observed in the solar wind. Hence, we conclude that physically realistic studies of the propagation of IPD which are assumed to originate near the solar surface must (1) initiate the IPD inside the critical points and (2) include the magnetic field. Although this conclusion is based on a one-dimensional analysis, we speculate that it would be equally valid in multi-dimensions.     

Unsteady isothermal flow of a gas behind an exponential shock in magnetogasdynamics

A self-similar flow of a perfect gas behind a strong shock driven out by a propelling contact discontinuity surface moving with time according to an exponential law in the presence of axial component of the magnetic field is investigated. The flow between the shock and the inner-expanding surface is assumed to be isothermal. The infinite electrically conductive and uniform medium has been taken into consideration.     

Equatorial propagation of axisymmetric magnetogasdynamic shocks with thermal radiation,I

Similarity solutions, for one-dimensional unsteady of a perfect gas behind a spherical shock wave produced on account of a sudden explosion or driven out by an expanding piston including the effects of radiative cooling and an idealised azimuthal magnetic field, are studied. The shock is assumed to be strong and it is propagating into a transparent medium at rest with varying density. The magnetic field is proportional tor ^?1. The total energy of the wave is time dependent obeying a power law.     

Magnetorotational supernovae. Magnetorotational instability. Jet formation

2D numerical simulations of magnetorotational (MR) supernova mechanism are described. It is shown that magnetic field is amplified due to the differential rotation after core collapse. When magnetic pressure reaches some level, a compression wave starts to move outwards. Moving along steeply decreasing density profile the compression wave transforms quickly into fast MHD shock. The magnetorotational instability (MRI) was found in our simulations. MRI leads to the exponential growth of the components of the magnetic field. The MRI significantly reduces MR supernova explosion time. Configuration of the initial magnetic field qualitatively defines the shape of MR supernova explosion. For the quadrupole-like initial poloidal field the MR supernova explosion develops mainly along equatorial plane, the dipole-like initial field results in MR supernova developing as mildly collimated jet along axis of rotation. The explosion energy of MR supernova found in our simulations is ∼0.5–0.6×10⁵¹ erg.     

Solar coronal heating by magnetosonic waves

Solar coronal heating by magnetohydrodynamic (MHD) waves is investigated. ultraviolet (UV) and X-ray emission lines of the corona show non-thermal broadenings. The wave rms velocities inferred from these observations are of the order of 25–60 km s⁻¹ . Assuming that these values are not negligible, we solved MHD equations in a quasi-linear approximation, by retaining the lowest order non-linear term in rms velocity. Plasma density distribution in the solar corona is assumed to be inhomogeneous. This plasma is also assumed to be permeated by dipole-like magnetic loops. Wave propagation is considered along the magnetic field lines. As dissipative processes, only the viscosity and parallel (to the local magnetic field lines) heat conduction are assumed to be important. Two wave modes emerged from the solution of the dispersion relation. The fast mode magneto-acoustic wave, if originated from the coronal base can propagate upwards into the corona and dissipate its mechanical energy as heat. The damping length-scale of the fast mode is of the order of 500 km. The wave energy flux associated with these waves turned out to be of the order of 2.5×10⁵ ergs cm⁻² s⁻¹ which is high enough to replace the energy lost by thermal conduction to the transition region and by optically thin coronal emission. The fast magneto-acoustic waves prove to be a likely candidate to heat the solar corona. The slow mode is absent, in other words cannot propagate in the solar corona.     

Features of the Non-Plane-Polarized Interaction ofMagnetohydrodynamic (MHD) Shock Waves

The features of the non-plane-polarized interaction of two plane MHD shock waves colliding at an arbitrary nonzero angle in the presence of an arbitrary magnetic field are considered. The problem is solved over a wide range of key parameters. When the key parameters of the problem vary continuously, there are no sudden restructurings (catastropies) of the flow pattern characteristic of the plane-polarized case. As distinct from the plane-polarized case, in the flow developed always there are two Alfvén discontinuities of different intensities with circular polarization. The presence of a magnetic field along the line of intersection of the shock fronts smoothers variation of pressure on the contact discontinuity C as a function of the angles of inclination of the magnetic field, the pressure on C being less than that in the plane-polarized case by several times. The velocity acquired by the medium as a result of the interaction depends significantly on the inclination of the magnetic field. This revised version was published online in July 2006 with corrections to the Cover Date.     

Linear MHD Wave Propagation in Time-Dependent Flux Tube

The propagation of magnetohydrodynamic (MHD) waves is an area that has been thoroughly studied for idealised static and steady state magnetised plasma systems applied to numerous solar structures. By applying the generalisation of a temporally varying background density to an open magnetic flux tube, mimicking the observed slow evolution of such waveguides in the solar atmosphere, further investigations into the propagation of both fast and slow MHD waves can take place. The assumption of a zero-beta plasma (no gas pressure) was applied in Williamson and Erdélyi (Solar Phys. 2013, doi: 10.1007/s11207-013-0366-9 , Paper I) is now relaxed for further analysis here. Firstly, the introduction of a finite thermal pressure to the magnetic flux tube equilibrium modifies the existence of fast MHD waves which are directly comparable to their counterparts found in Paper I. Further, as a direct consequence of the non-zero kinetic plasma pressure, a slow MHD wave now exists, and is investigated. Analysis of the slow wave shows that, similar to the fast MHD wave, wave amplitude amplification takes place in time and height. The evolution of the wave amplitude is determined here analytically. We conclude that for a temporally slowly decreasing background density both propagating magnetosonic wave modes are amplified for over-dense magnetic flux tubes. This information can be very practical and useful for future solar magneto-seismology applications in the study of the amplitude and frequency properties of MHD waveguides, e.g. for diagnostic purposes, present in the solar atmosphere.     

Energy, angular momentum and wave action associated with density waves in a rotating magnetized gas disc

Both fast and slow magnetohydrodynamic (MHD) density waves propagating in a thin rotating magnetized gas disc are investigated. In the tight-winding or WKBJ regime, the radial variation of MHD density-wave amplitude during wave propagation is governed by the conservation of wave action surface density which travels at a relevant radial group speed C _g. The wave energy surface density and the wave angular momentum surface density are related to by = and = m respectively, where is the angular frequency in an inertial frame of reference and the integer m , proportional to the azimuthal wavenumber, corresponds to the number of spiral arms. Consequently, both wave energy and angular momentum are conserved for spiral MHD density waves. For both fast and slow MHD density waves, net wave energy and angular momentum are carried outward or inward for trailing or leading spirals, respectively. The wave angular momentum flux contains separate contributions from gravity torque, advective transport and magnetic torque. While the gravity torque plays an important role, the latter two can be of comparable magnitudes to the former. Similar to the role of gravity torque, the part of MHD wave angular momentum flux by magnetic torque (in the case of either fast or slow MHD density waves) propagates outward or inward for trailing or leading spirals, respectively. From the perspective of global energetics in a magnetized gas sheet in rotation, trailing spiral structures of MHD density waves are preferred over leading ones. With proper qualifications, the generation and maintenance as well as transport properties of MHD density waves in magnetized spiral galaxies are discussed.