Flare-produced coronal MHD-fast-mode wavefronts and Moreton's wave phenomenon

The propagation characteristics of MHD fast-mode disturbances, which can emanate from flare regions, are computed for realistic conditions of the solar corona at the times of particular flares. The path of a fast-mode disturbance is determined by the large-scale (global) coronal distributions of magnetic field and density, and can be computed by a general raytracing procedure (eikonal equation) adapted to MHD. We use the coronal (electron) density distribution calculated from daily K-coronameter data, and the coronal magnetic field calculated under the current-free approximation from magnetograph measurements of the photospheric magnetic field. We compare the path and time-development of an MHD fast-mode wavefront emitted from the flare region (as calculated from a realistic model corona for the day of the observed Moreton wave event) with actual observations of the Moreton wave event, and find that the Moreton wave can be identified with the rapidly moving intersection of the coronal fast-mode wavefront and the chromosphere (as hypothesized in our previous paper); the directivity (anisotropic propagation), as well as other characteristics of the propagation of the Moreton wave can be successfully explained.sponsored by the National Science Foundation.     

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.     

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.     

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.     

MHD studies on the free convection and hall effects on waves in a semi-infinite plasma

In this paper, analytical MHD studies are made on the propagation of oscillatory waves in a semi-infinite plasma which is exposed to an applied magnetic field. The oscillatory wave is introduced into the plasma environment by temperature perturbation.The phase speeds of the resultant disturbance are discussed in terms Grashof, Prandtl, and Eckert numbers (free-convection parameters), Hall parameter, Alfvén parameter, and frequences. Expansion about small Eckert number is made to solve the very nonlinear coupled partial differential equations for the field variables. The appearance of steady streaming at all times in the first order expansion is mentioned.     

Oblique propagation and dissipation of Alfvén waves in coronal holes

We investigate the effect of viscosity and magnetic diffusivity on the oblique propagation and dissipation of Alfvén waves with respect to the normal outward direction, making use of MHD equations, density, temperature and magnetic field structure in coronal holes and underlying magnetic funnels. We find reduction in the damping length scale, group velocity and energy flux density as the propagation angle of Alfvén waves increases inside the coronal holes. For any propagation angle, the energy flux density and damping length scale also show a decrement in the source region of the solar wind (< 1.05 R_⊙) where these may be one of the primary energy sources, which can convert the inflow of the solar wind into the outflow. In the outer region (> 1.21 R_⊙), for any propagation angle, the energy flux density peaks match with the peaks of MgX 609.78 Å and 624.78 Å linewidths observed from the Coronal Diagnostic Spectrometer (CDS) on SOHO and the non-thermal velocity derived from these observations, justify the observed spectroscopic signature of the Alfvén wave dissipation.     

MHD instability due to non-homogeneity and non-uniformity of magnetic field in gravitating medium and its consequences in the central region of galaxies

The MHD wave instabilities due to non-uniform magnetic field and non-homogeneity of density have been studied. The reference (coordinate) system considered here is cylindrical type. The General Dispersion Relation (GDR) for the wave propagation in a gravitating but non-relativistic region has been derived. Similar to common knowledge, the said non-uniformities have been found to be responsible for the instability of the system. But interestingly many instability factors are produced due to presence of two types of non-uniformities simultaneously. This theory may add more clues for the event of instabilities, formation of hot plasma-bed in Galactic Central Region, and mass out-flow from there. Many conditions for instabilities could be obtained from GDR deduced here. However, a few conditions for critical wavelength of the MHD wave have been obtained in terms of system parameters (like gradient of magnetic field and rotation). This theory, in turn, may be helpful for the better understanding of the Explosion Theory of formation of outer structure of Galaxies like ours.     

Effects of the magnetic field model and wave polarisation on the estimation of proton number densities in the magnetosphere using field line resonances

The cold, core plasma mass density in the Earth's magnetosphere may be deduced from the resonant behaviour of ultra-low frequency (ULF; 1–100 mHz), magnetohydrodynamic (MHD) waves. Ground-based magnetometers are the most widely used instruments for recording the signature of ULF wave activity in the magnetosphere. For a suitable model of the background magnetic field and a functional form for the variation of the proton number density with radial distance, the resonant frequencies of ULF waves provide estimates of the equatorial plasma mass density. At high latitudes, the magnetic field model becomes critical when estimating the plasma mass density from FLR data. We show that a dipole field model is generally inadequate for latitudes greater than ∼65° geomagnetic compared with models that are keyed to magnetic activity, interplanetary magnetic field and solar wind properties. Furthermore, the method often relies on the detection of the fundamental ULF resonance, which changes frequency depending on the polarisation of the oscillation. Using idealised toroidal and poloidal oscillation modes, the range of the derived densities as the ULF wave polarisation changes is of the same order as changing the density function from a constant value throughout the magnetosphere to assuming constant Alfven speed in a dipole geometry.     

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.     

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.     

Driven waves in a two-fluid plasma

We study the physics of wave propagation in a weakly ionized plasma, as it applies to the formation of multifluid, magnetohydrodynamics (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 behaviour 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.     

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.     

Numerical simulations of fast MHD waves in a coronal plasma

The temporal evolution of ducted waves under coronal conditions is studied in the framework of linearized low MHD by means of numerical simulations. Coronal loops are represented by smoothed slabs of enhanced gas density embedded within a uniform magnetic field. The simulations show that for a smoothed density profile there is an energy leakage from the slab, associated with the propagation of sausage and kink waves. Wave energy leakage in the kink wave is generally small, whereas the wave energy in sausage waves leaks more strongly for long wavelengths and smoother slabs.     

Excess heating of corona and chromosphere above magnetic regions by non-linear Alfvén waves

Excess heating of the active region solar atmosphere is interpreted by the decay of MHD slow-mode waves produced in the corona through the non-linear coupling of Alfvén waves supplied from subphotospheric layers. It is stressed that the Alfvén-mode waves may be very efficiently generated directly in the convection layer under the photosphere in magnetic regions, and that such magnetic regions, at the same time, provide the ‘transparent windows’ for Alfvén waves in regard to the Joule and frictional dissipations in the photospheric and subphotospheric layers. Though the Alfvén waves suffer considerable reflection in the chromosphere and in the transition layer, a certain fraction of this large flux is propagated out to the corona, and a large velocity amplitude exceeding the local Alfvén velocity is attained during the propagation along the magnetic tubes of force into a region of lower density and weaker magnetic field. The otherwise divergence-free velocity field in Alfvén waves gets involved in such a case with a compressional component (slow-mode waves) which again is of considerable velocity amplitude relative to the local acoustic velocity when estimated by using the formulation for non-linear coupling between MHD wave modes derived by Kaburaki and Uchida (1971). Therefore, the compressional waves thus produced through the non-linear coupling of Alvén waves will eventually be thermalized to provide a heat source. The introduction of this non-linear coupling process and the subsequent thermalization of thus produced slow-mode waves may provide means of converting the otherwise dissipation-free Alfvén mode energy into heat in the corona. The liberated heat will readily be redistributed by conduction along the magnetic lines of force, with higher density as a consequence of increased scale height, and thus the loop-like structure of the coronal condensations (or probably also the thread-like feature of the general corona) may be explained in a natural fashion.     

Effect of rotation and self-gravity on the propagation of MHD waves

Magnetohydrodynamics waves and instabilities in rotating, self-gravitating, anisotropic and collision-less plasma were investigated. The general dispersion relation was obtained using standard mode analysis by constructing the linearized set of equations. The wave mode solutions and stability properties of the dispersion relations are discussed in the propagations transverse and parallel to the magnetic field. These special cases are discussed considering the axis of rotation to be in transverse and along the magnetic field. In the case of propagation transverse to the magnetic field with axis of rotation parallel to the magnetic field, we derived the dispersion relation modified by rotation and self-gravitation. In the case of propagation parallel to the magnetic field with axis of rotation perpendicular to the magnetic field, we obtained two separate modes affected by rotation and self-gravitation. This indicates that the Slow mode and fire hose instability are not affected by rotation. Numerical analysis was performed for oblique propagation to show the effect of rotation and self-gravitation. It is found that rotation has an effect of reducing the value of the phase speeds on the fast and Alfven wave modes, but self-gravitation affect only on the Slow modes, thereby reducing the phase speed compare to the ideal magneto hydrodynamic (MHD) case.     

Electron-acoustic instability driven by a crossfield hot electron-beam

On the basis of kinetic theory, the electron-acoustic instability is studied in a three component plasma consisting of a hot electron-beam and stationary cool electrons and ions. The transformation of the instability into the modified two-stream instability for wave propagation oblique to the confining magnetic field is also investigated. In our model both the electrons and ions are magnetized, with the beam drifting across the external magnetic field. The dependence of the growth rate on plasma parameters, such as electron-beam density, electron-beam speed, magnetic field strength and propagation angle, is examined. In addition, we investigate the effect of anisotropies in the velocity distributions of the hot electron-beam and the cool electrons on the instability growth rate.     

火星磁层中O^＋离子分布的理论研究

对火星磁层中背阳面区来自电离层的Ｏ＋离子沿磁力线的密度和通量密度分布进行了理论研究．设火星的磁场由内禀磁场和感应磁场相叠加而成,结合不同的内禀磁矩条件进行了计算．结果表明：（１）随着火心距离的增大,火星磁层中Ｏ＋离子的密度和通量密度沿磁力线都呈现出下降趋势;（２）随着Ｚ坐标的增大,火星磁层中Ｏ＋离子的密度和通量密度先呈现出下降趋势,后又逐渐上升;（３）火星的内禀磁场越强,Ｏ＋离子的密度和通量密度沿磁力线下降得越快;（４）在火星磁尾一定距离处,Ｏ＋离子的密度和通量密度随磁矩的增大而减小．这样,可通过探测火星磁层中离子的密度和通量密度分布来确定火星内禀磁场的强弱     

Possible Role of mhd Waves in Heating the Solar Corona

Heating of the solar corona by MHD waves has been investigated. Taking account of dissipation mechanisms self-consistently, a new general dispersion relation has been derived for waves propagating in a homogeneous plasma. Solution of this sixth-order dispersion relation provides information on how the damping of both slow and fast mode waves depends upon the plasma density, temperature, field strength, and angle of propagation relative to the background magnetic field. Wave quantities with and without dissipation are presented. In particular, we consider one of the most important clues from space observations that viscosity of coronal plasma may be orders of magnitude different from its classical value in heating of the corona by MHD waves.     

Hypersonic beam driven by high-energy particles in extragalactic radio sources

A mechanism is proposed for the formation of collimated beams in radio galaxies. The collimated flows which are non-thermally driven by high energy particles and magneto-hydrodynamic (MHD) waves are presented. The galactic nucleus surrounded by a cool gas is investigated. The cool gas accretes onto the nucleus and the accretion matter can confine the wave zone around the nucleus in which the high energy particles are completely locked to the MHD waves. When a quasi-radial magnetic field is embedded in the accretion flow, the MHD wave packets are collimated into the direction of symmetry axis of the galactic nuclear disc. The fluid around the nucleus is considered to be accelerated and heated by the MHD waves and ejected along the axis.A complete set of hydrodynamic equations which contain the energy transfers of high energy particles and MHD waves is presented. One-dimensional flows which are in pressure equilibrium with the surrounding accretion matter are calculated. When the energy density of the MHD waves is higher than that of the thermal energy, the fluid flow is strongly collimated in a narrow beam. When the MHD waves are strongly damped by the resistivity of the fluid at the great distance from the galactic centre, the collimated beam broadly reexpands. On the basis of the collimated beams driven by high energy particles, the radio morphology of the double radio sources is discussed.     

Axisymmetric and non-axisymmetric modulated MHD waves in magnetic flux tubes

Nonlinear modulated both axisymmetric and non-axisymmetric MHD wave propagation in magnetic flux tubes is studied. In the cylindrical coordinates, ordinary differential equation with cubic nonlinearity is derived. In both cases of symmetry, the equation has solitary solutions. Modulation stability of the solutions is studied. The results of the study show that the propagation of axisymmetric soliton causes rising of plasma temperature in peripheral regions of a magnetic flux tube. In the non-axisymmetric case, it gives also temperature rising effect. Results of theoretical study are examined on idealized model of chromospheric spicule.