Structure of weak shock wave discontinuities in magnetohydrodynamics

In this paper, we study the propagation of a weak shock wave in a medium of initially constant fluid velocity, magnetic field and thermodynamic parameters. The structure of discontinuities for such a shock in real cases will be analyzed. By examining the change in variables inside the relaxation transition region, the length of the latter, i.e. of the disturbed region will be obtained. In order to derive the physical model explaining the finite shock length, several assumptions have been made: the medium has been treated as a very large layer of non-negligible viscosity and thermal conductivity. Starting from basic MHD relations, the invariants on the shock fronts, taking into consideration the process inside the disturbed region, have been calculated. Modified Rankine-Hugoniot equation discussing the process inside the relaxation region has been derived therefrom. Finally, the dependence of pressure upon distance has been examined under the assumptions: the fluid is considered as polytropic. Hence, by approximate integration of an obtained transcendental function, we get the length of relaxation region and discuss the result obtained.     

The effect of Alfvén waves on MHD fast shocks

The Rankine-Hugoniot equations for hydromagnetic shocks are extended to include the energy and momentum flux due to Alfvén waves incident on the shock. The shock relations are solved numerically for a wide variety of parameters typical of interplanetary conditions. The presence of the waves can cause appreciable changes in the structure of fast shocks of low Mach number.     

Jump relations across a shock in non-ideal gas flow

Generalized forms of jump relations are obtained for one dimensional shock waves propagating in a non-ideal gas which reduce to Rankine-Hugoniot conditions for shocks in idea gas when non-idealness parameter becomes zero. The equation of state for non-ideal gas is considered as given by Landau and Lifshitz. The jump relations for pressure, density, temperature, particle velocity, and change in entropy across the shock are derived in terms of upstream Mach number. Finally, the useful forms of the shock jump relations for weak and strong shocks, respectively, are obtained in terms of the non-idealness parameter. It is observed that the shock waves may arise in flow of real fluids where upstream Mach number is less than unity.     

On the possibility of radio emission from quasi-parallel and quasi-perpendicular propagation of shocks

A set of 21 solar type II radio bursts observed using Hiraiso radio spectrograph have been analysed to study the direction of propagation of coronal shocks. A simple analysis is carried out to find the approximate angle between the shock normal and magnetic field by solving the Rankine-Hugoniot MHD relation with assumption of Alfven speed and plasma beta. From this analysis, it is suggested that both quasi-parallel shocks (favourable) and quasi-perpendicular shocks can generate type II bursts depending upon the circumstances of the corona.     

Shock jump relations for a dusty gas atmosphere

This paper presents simplified forms of jump relations for one dimensional shock waves propagating in a dusty gas. The dusty gas is assumed to be a mixture of a perfect gas and spherically small solid particles, in which solid particles are continuously distributed. The simplified jump relations for the pressure, the temperature, the density, the velocity of the mixture and the speed of sound have been derived in terms of the upstream Mach number. The expressions for the adiabatic compressibility of the mixture and the change-in-entropy across the shock front have also been derived in terms of the upstream Mach number. Further, the handy forms of shock jump relations have been obtained in terms of the initial volume fraction of small solid particles and the ratio of specific heats of the mixture, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. The simplified shock jump relations reduce to the Rankine-Hugoniot conditions for shock waves in an ideal gas when the mass fraction (concentration) of solid particles in the mixture becomes zero. Finally, the effects due to the mass fraction of solid particles in the mixture, and the ratio of the density of solid particles to the initial density of the gas are studied on the pressure, the temperature, the density, the velocity of the mixture, the speed of sound, the adiabatic compressibility of the mixture and the change-in-entropy across the shock front. The results provided a clear picture of whether and how the presence of dust particles affects the flow field behind the shock front. The aim of this paper is to contribute to the understanding of how the shock waves behave in the gas-solid particle two-phase flows.     

The termination shock in a striped pulsar wind

The origin of radio emission from plerions is considered. Recent observations suggest that radio-emitting electrons are presently accelerated rather than having been injected at early stages of the plerion evolution. The observed flat spectra without a low-frequency cut-off imply an acceleration mechanism that raises the average particle energy by orders of magnitude but leaves most of the particles at an energy of less than approximately a few hundred MeV. It is suggested that annihilation of the alternating magnetic field at the pulsar wind termination shock provides the necessary mechanism. Toroidal stripes of opposite magnetic polarity are formed in the wind emanating from an obliquely rotating pulsar magnetosphere (the striped wind). At the termination shock, the flow compresses and the magnetic field annihilates by driven reconnection. Jump conditions are obtained for the shock in a striped wind. It is shown that the post-shock magnetohydrodynamic parameters of the flow are the same as if the energy of the alternating field had already been converted into plasma energy upstream of the shock. Therefore, the available estimates of the ratio of the Poynting flux to the matter energy flux, σ, should be attributed not to the total upstream Poynting flux but only to that associated with the average magnetic field. A simple model for the particle acceleration in the shocked striped wind is presented.     

Dynamical feedback of self-generated magnetic fields in cosmic ray modified shocks

We present a semi-analytical kinetic calculation of the process of non-linear diffusive shock acceleration (NLDSA) which includes the magnetic field amplification due to cosmic ray induced streaming instability, the dynamical reaction of the amplified magnetic field and the possible effects of turbulent heating. The approach is specialized to parallel shock waves, and the parameters we chose are the ones appropriate to forward shocks in supernova remnants. Our calculation allows us to show that the net effect of the amplified magnetic field is to enhance the maximum momentum of accelerated particles while reducing the concavity of the spectra, with respect to the standard predictions of NLDSA. This is mainly due to the dynamical reaction of the amplified field on the shock, which notably reduces the modification of the shock precursor. The total compression factors which are obtained for parameters typical of supernova remnants are   R _tot∼ 7–10  , in good agreement with the values inferred from observations. The strength of the magnetic field produced through excitation of streaming instability is found in good agreement with the values inferred for several remnants if the thickness of the X-ray rims is interpreted as due to severe synchrotron losses of high-energy electrons. We also discuss the relative role of turbulent heating and magnetic dynamical reaction in driving the reduction of the precursor modification.     

Faraday Rotation Response to Coronal Mass Ejection Structure

We present the results from modeling the coronal mass ejection (CME) properties that have an effect on the Faraday rotation (FR) signatures that may be measured with an imaging radio antenna array such as the Murchison Widefield Array (MWA). These include the magnetic flux rope orientation, handedness, magnetic-field magnitude, velocity, radius, expansion rate, electron density, and the presence of a shock/sheath region. We find that simultaneous multiple radio source observations (FR imaging) can be used to uniquely determine the orientation of the magnetic field in a CME, increase the advance warning time on the geoeffectiveness of a CME by an order of magnitude from the warning time possible from in-situ observations at L ₁, and investigate the extent and structure of the shock/sheath region at the leading edge of fast CMEs. The magnetic field of the heliosphere is largely “invisible” with only a fraction of the interplanetary magnetic-field lines convecting past the Earth; remote sensing the heliospheric magnetic field through FR imaging from the MWA will advance solar physics investigations into CME evolution and dynamics.     

MHD simulations of rayleigh-taylor instability in young supernova remnants

Radio observations shows that young supernova remnants such as Tycho and Cas A generally exhibit a circular clumpy shell. This shell shows a radial magnetic field whose equipartition strength is 2 to 3 orders of magnitude higher than the interstellar field. A simple compression of the ambient field by the shock can explain neither of these observations. We show that the Rayleigh-Taylor instability which occurs at the ejecta/ISM interface can explain these observations. We have done MHD simulations of the instability in the shell of Type-I supernova remnants for the first time by utilizing moving grid technique. Our simulation shows that Rayleigh-Taylor and Kelvin-Helmholtz instabilities amplify ambient magnetic fields locally and produce the clumpy radio shell. Strong magnetic field lines draped around the Rayleigh-Taylor fingers produce the radial B-vector polarization, whereas thermal bremsstrahlung from the dense fingers themselves produce the clumpy X-ray emission.     

Jump relations for magnetohydrodynamic shock waves in non-ideal gas flow

The generalized jump relations across the magnetohydrodynamic (MHD) shock front in non-ideal gas are derived considering the equation of state for non-ideal gas as given by Landau and Lifshitz. The jump relations for pressure, density, and particle velocity have been derived, respectively in terms of a compression ratio. Further, the simplified forms of the MHD shock jump relations have been obtained in terms of non-idealness parameter, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. Finally, the cases of strong and weak shocks are explored under two distinct conditions viz., (i) when the applied magnetic field is strong and, (ii) when the field is weak. The aim of this paper is to contribute to the understanding of how shock waves behave in magnetized environment of non-ideal gases.     

The Temperature – Magnetic Field Relation in Observed and Simulated Sunspots

Observations of the relation between continuum intensity and magnetic field strength in sunspots have been made for nearly five decades. This work presents full-Stokes measurements of the full-split (\(g = 3\)) line Fe i 1564.85 nm with a spatial resolution of \(0.5^{\prime\prime}\) obtained with the GREGOR Infrared Spectrograph in three large sunspots. The continuum intensity is corrected for instrumental scattered light, and the brightness temperature is calculated. Magnetic field strength and inclination are derived directly from the line split and the ratio of Stokes components. The continuum intensity (temperature) relations to the field strength are studied separately in the umbra, light bridges, and penumbra. The results are consistent with previous studies, and it was found that the scatter of values in the relations increases with increasing spatial resolution thanks to resolved fine structures. The observed relations show trends common for the umbra, light bridges, and the inner penumbra, while the outer penumbra has a weaker magnetic field than the inner penumbra at equal continuum intensities. This fact can be interpreted in terms of the interlocking comb magnetic structure of the penumbra. A comparison with data obtained from numerical simulations was made. The simulated data generally have a stronger magnetic field and a weaker continuum intensity than the observations, which may be explained by stray light and limited spatial resolution of the observations, and also by photometric inaccuracies of the simulations.     

A statistical study on property of spatial magnetic field for solar active region

Magnetic fields dominate most solar activities, there exist direct relations between solar flare and the distributions of magnetic field, and also its corresponding magnetic energy. In this paper, the statistical results about the relationships between the spatial magnetic field and solar flare are given basing on vector magnetic field observed by the Solar Magnetic Field Telescope (SMFT) at Huairou Solar Observing Station (HSOS). The spatial magnetic fields are obtained by extrapolated photosphere vector magnetic field observed by SMFT. There are 23 active regions with flare eruption are chosen as data samples, which were observed from 1997 to 2007. The results are as follows: 1. Magnetic field lines become lower after flare for 16 (69 %) active regions; 2. The free energy are decreased after flare for 17 (74 %) active regions. It can conclude that for most active regions the changes of magnetic field after solar flare re coincident with the previous observations and studies.     

The magnetic field near Mars: A comparison between a hybrid model, Mars Global Surveyor and Mars Express observations

Mars Express (MEX) does not carry its own magnetometer which complicates interpretation of ASPERA-3/MEX ion measurements. The direction of the interplanetary magnetic field (IMF) is especially important because it, among other things, determines the direction of the convective electric field and orientation of the cross tail current sheet and tail lobes. In this paper we present a case study to show the properties of the magnetic field near Mars in a quasi-neutral hybrid (QNH) model at the orbits where the Mars Global Surveyor (MGS) has made measurements, present a method to derive the IMF clock angle by comparing fields in a hybrid model and the direction of the magnetic field measured by MGS by deriving the IMF clock angle. We also use H⁺ ring velocity distribution observations upstream of the bow shock measured by the IMA/ASPERA-3 instrument on board MEX spacecraft. These observations are used to indirectly provide the orientation of the IMF. We use a QNH model (HYB-Mars) where ions are modeled as particles while electrons form a mass-less charge neutralizing fluid. We found that the direct MGS and non-direct IMA observations of the orientation magnetic field vectors in non-crustal magnetic field regions are consistent with the global magnetic field draping pattern predicted by the global model.     

Probability distribution functions of microscale magnetic fluctuations during quiet conditions

A statistical study of microscale magnetic fluctuations in the interplanetary and magnetosheath region during quiet conditions is approached from the concept of probability distribution function. Magnetic field data from Explorer 34 were used to reconstruct the distribution functions and to calculate some of their moments. The distribution functions are found to be nearly tri-Maxwellian as the background field is relatively quiet. The direction of maximum fluctuations is found to be nearly perpendicular to that of the background magnetic field, but the fluctuations are rarely circularly polarized. Across the Earth's bow shock, the degree of fluctuation anisotropy increases, but no noticeable change in relative fluctuation intensity has been observed.     

Anomalous deformation of the Earth's bow shock in the lunar wake: Joint measurement by Chang’E-1 and SELENE

Because the solar wind (SW) flow is usually super-sonic, a fast-mode bow shock (BS) is formed in front of the Earth's magnetosphere, and the Moon crosses the BS at both dusk and dawn flanks. On the other hand, behind of the Moon along the SW flow forms a tenuous region called lunar wake, where the flow can be sub-Alfvénic (and thus sub-sonic) because of its low-density status. Here we report, with joint measurement by Chang’E-1 and SELENE, that the Earth's BS surface is drastically deformed in the lunar wake. Despite the quasi-perpendicular shock configuration encountered at dusk flank under the Parker-spiral magnetic field, no clear shock surface can be found in the lunar wake, while instead gradual transition of the magnetic field from the upstream to downstream value was observed for a several-minute interval. This finding suggests that the ‘magnetic ramp’ is highly broadened in the wake where a fast-mode shock is no longer maintained due to the highly reduced density. On the other hand, observations at the 100 km altitude on the dayside show that the fast-mode shock is maintained even when the width of the downstream region is smaller than a typical scale length of a perpendicular shock. Our results suggest that the Moon is not so large to eliminate the BS at 100 km altitude on the dayside, while the magnetic field associated with the shock structure is drastically affected in the lunar wake.     

Energy build-up and release mechanisms in solar and auroral flares

The 80 and 160 MHz radioheliograph observations of a flare-associated outburst in June 1973 reveal three distinctive type IV continuum sources: a flare continuum, an isolated moving continuum and a storm continuum, in that time sequence. The observed characteristics of the three sources and their relations in space and time are described. The observed characteristics and the interrelations between the three continuum sources are explained in terms of energetic electrons trapped and accelerated in, and ejecta moving through, an arch-like magnetic field. It is also suggested that the isolated moving source - in the present event and in similar ones - is probably quite independent of the MHD shock wave which is responsible for the preceding type II burst.     

一类偶发物质抛射事件的观测和数值模拟物理解释

研究了2000年紫金山天文台赣榆观测站观测到的在太阳上7个中小抛射事件，认为它们的特点是不伴随发亮现象，长1—2．5万公里，宽3—5千公里，寿命3—7分钟，产生在弱磁场处远离大黑子的地方，用一维沿磁弧流动的流体力学方程的数值模拟来解释这种抛射，结果显示，与Suematsu等和Shibata等模拟针状物和日浪不同，不是激波或反弹激波将光球色球密度量级的物质推向日冕，而是重联后的连续物质流动形成这类抛射的，大约5分钟的演化，即可达到流体力学稳定解。     

Plasma electron signatures of magnetic connection to the Jovian bow shock: Ulysses observations

Ulysses plasma electron observations of bidirectional and enhanced unidirectional electron heat fluxes within 4500 R_J (0.8 a.u. or 3 months on either side of closest approach) of Jupiter are presented as evidence for the magnetic connection of the spacecraft to the Jovian bow shock. These bursts of suprathermal electrons (> 30 eV) are observed when the interplanetary magnetic field points roughly parallel or antiparallel to the Jupiter-spacecraft line. Ninety-eight possible connection events were found over the 6 month period centered on the closest approach to Jupiter. The frequency of occurrence peaked with proximity to the bow shock, with most events occurring post-encounter. These are the first observations of backstreaming suprathermal electrons made in the vicinity of the Jovian bow shock.     

On the comparison of radio-astronomical measurements of the height structure of magnetic field with results of model approximations

The results of microwave observations of the polarized emission of active regionsmade with the RATAN-600 radio telescope are used to develop the method for determining the structure of the magnetic field of these regions at coronal heights. About 1000-G-strong magnetic fields are observed in the solar atmosphere at rather high altitudes (from 10 to 25 Mm). This result is confirmed fairly well by the ultraviolet observations of magnetic loops, it is consistent with earlier radio-astronomical observations of the magnetic field at the height of the transition region, and it corresponds as well, if interpreted in terms of the dipole magnetic field model, to the vertical gradients of the photospheric magnetic field.     

The effect of heavy ions on the formation and structure of cometary bow shocks

We investigate the interaction of heavy cometary ions with the solar wind and the formation of a bow shock in front of a comet by means of a hybrid (particle ion, fluid electron) simulation code that solves self-consistently for the electromagnetic fields and the motion of the charged particles. This kinetic treatment of the solar wind protons and the heavy cometary ions allows us to examine two important issues. One is the effect of the velocity distribution function of the heavy ions on the shock formation and structure, and the other is the degree of coupling between the two ion species. The result of this study indicate that at high Mach numbers the shock structure is highly dependent upon the velocity distribution of the heavy ions. For example, when the newly created ions comprise a ring distribution in the solar wind frame, most of them turn around downstream of the shock surface and reenter the upstream region to form a large foot that extends about a heavy ions gyroradius upstream of the shock. On the other hand, heavy ions which have been picked up by the solar wind and possesses a Maxwellian distribution can mostly penetrate the shock without returning upstream and affecting the shock structure as much. In either case, however, at high Mach numbers the shock strength is the same. At low Mach numbers, where the shock is weak, the velocity distribution of heavy ions has a smaller effect on the formation of shock and its structure. In this regime, the degree of coupling between the cometary ions and the solar wind protons and the corresponding critical Mach number (at which a shock should begin to form) are determined from a set of Rankine-Hugoniot relations. The results of the simulations suggest that some coupling does occur (evidently, through the electromagnetic fields, since there are no particle collisions in the calculations), but less than that expected from magnetohydrodynamics. For low Mach numbers, it is also shown that shocks have a transitory nature, where they are continuously formed by the protons and subsequently destroyed by the heavy ions.