Wave propagation in a magnetically structured atmosphere

The solar atmosphere, from the photosphere to the corona, is structured by the presence of magnetic fields. We consider the nature of such inhomogeneity and emphasis that the usual picture of hydromagnetic wave propagation in a uniform medium may be misleading if applied to a structured field. We investigate the occurrence of magnetoacoustic surface waves at a single magnetic interface and consider in detail the case where one side of the interface is field-free. For such an interface, a slow surface wave can always propagate. In addition, a fast surface wave may propagate if the field-free medium is warmer than the magnetic atmosphere.     

Wave diagrams for MHD modes in a magnetically structured atmosphere

Phase-speed diagrams, showing the allowable spectrum of surface and body waves in a magnetically structured atmosphere, are constructed for the interface and the slab. The diagrams (illustrated for photospheric flux tubes, photosphere-chromosphere magnetic canopy, and coronal conditions) classify disturbances for both the normal modes of a structure and incident wave propagation on a structure, allowing a simple application once sufficiently detailed observations of waves become available.     

Long nonlinear waves in a compressible magnetically structured atmosphere

The propagation of nonlinear slow sausage small-amplitude waves in a magnetic slab in a magnetic environment is considered. The equation for surface waves that is allied form of the Benjamin-Ono equation and the equation for body waves that is allied form of the equation for body waves in the slab are derived with the use of the method of stretching variables. The solutions of the equation for surface waves in the form of solitary waves are obtained numerically.     

Long nonlinear waves in a compressible magnetically structured atmosphere

The Benjamin-Ono equation is derived for long slow sausage waves propagating in a vertical magnetic slab embedded into a stratified atmosphere, provided that the slab thickness is much smaller than the scale height of the atmosphere. The soliton propagation in a nonstratified atmosphere is discussed. The approximate formulas describing the slow evolution of the amplitude and the length of a soliton propagating in a very weakly stratified atmosphere are obtained. The exact soliton-like solution for an atmosphere with a linearly growing temperature is found.     

Long nonlinear waves in a compressible magnetically structured atmosphere

The Hohlov-Zabolotskaja equation with an additional boundary condition is shown to describe long nonlinear small-amplitude fast sausage surface waves in a magnetic slab embedded in magnetic environment. It is proved that the obtained boundary problem has no solutions in the form of solitary waves. Approximate solution in the form of nonlinear stationary wave is found with the use of expansion in the power series of small amplitude. Second harmonic generation by a sinusoidal wave is studied. The law of energy conservation is obtained. Results of numerical computations are presented. They show that a sinusoidal disturbance does not overturn. The possibility of transmission of wave energy into corona along a magnetic slab is discussed in connection with these results.     

Wave propagation in a non-isothermal atmosphere and the solar five-minute oscillations

This paper presents a detailed discussion of the properties of linear, periodic acoustic waves that propagate vertically in a non-isothermal atmosphere. In order to retain the basic feature of the solar atmosphere we have chosen a temperature profile presenting a minimum. An analytical solution of the problem is possible if T/, being the mean molecular weight, varies parabolically with height. The purpose of this study is to point out the qualitative differences existing between the case treated here and the customary analysis based on a locally isothermal treatment. The computed velocity amplitude and the temperature-perturbation as functions of the wave period exhibit a sharp peak in the region between 180 and 300 s, thus showing the possibility of interpreting the five-minute oscillations as a resonant phenomenon. The propagating or stationary nature of the waves is investigated by a study of the phase of the proposed analytical solution.     

Waves in a magnetically structured slab configuration

The problem of wave-propagation in a magnetically structured compressible slab configuration is investigated, allowing for different magnetic field strengths inside and outside the slab and also a general orientation of the field vectors relative to each other and to the propagation vector. Several magnetic field geometries such as equal parallel, and equal orthogonal fields are considered. Properties of body and surface waves both for symmetric and asymmetric modes of perturbation propagating along and normal to the slab field are investigated idealising the slab to be incompressible, or considering the limiting case of wide and slender compressible slab. Numerical results are also obtained for a compressible slab of finite thickness for a specific choice of sound and Alfvén speeds involved.     

Propagation of MHD body and surface waves in magnetically structured regions of the solar atmosphere

The fact that magnetically structured regions exist in the solar atmosphere has been known for a number of years. It has been suggested that different kinds of magnetohydrodynamic (MHD) waves can be efficiently damped in these regions and that the dissipated wave energy may be responsible for the observed enhancement in radiative losses. From a theoretical point of view, an important task would be to investigate the propagation and dissipation of MHD waves in these highly structured regions of the solar atmosphere. In this paper, we study the behavior of MHD body and surface waves in a medium with either a single or double (slab) magnetic interface by use of a nonlinear, two-dimensional, time-dependent, ideal MHD numerical model constructed on the basis of a Lagrangean grid and semi-implicit scheme. The processes of wave confinement and wave energy leakage are discussed in detail. It is shown that the obtained results depend strongly on the type of perturbations imposed on the interface or slab and on the plasma parameter, . The relevance of the obtained results to the heating problem of the upper parts of the solar atmosphere is also discussed.     

Wave propagation in a magnetic cylinder

The nature of oscillations in a magnetic cylinder embedded in a magnetic environment is investigated. It is shown that the standard slender flux tube analysis of a kink mode in a cylinder excludes the possibility of a second mode, which arises under photospheric conditions. Under coronal conditions, two widely separated classes of oscillation can be freely sustained, one on an acoustic time-scale and the other on an Alfvénic time-scale. The acoustic-type oscillations are always present, but the much shorter period, Alfvénic-type, oscillations arise only in high density (strictly, low Alfvén velocity) loops. An application to waves in fibrils is also given, and suggests (following Wentzel, 1979) that they are fast kink waves propagating in a density enhancement.     

Dissipating the energy of magnetoacoustic waves in a structured atmosphere

The distances over which magnetohydrodynamic waves will propagate in a non-ideal, magnetic, compressible medium, representing the solar corona structured by the presence of loops of denser material, are considered. The waves are damped by ion viscosity and electron heat conduction in a radiating, optically thin atmosphere. Waves which lose their energy of propagation in distances of less than our criterion value of 4 × 10⁹ cm are regarded as candidates for contributing towards coronal heating. Alfvénic-type waves only dissipate in this way in weak ( 15 G) magnetic fields and when they have periods of a few seconds (210 s). Acoustic-type waves can also be dissipated and we give typical values of magnetic field strength, density and temperature for which the dissipation could occur. Dissipating acoustic-type waves have periods that range from tens to hundreds of seconds (15–225 s).Calculations show that reliable measurements of velocity amplitudes will be invaluable in deciding whether these dissipating waves can contribute to heating the corona. We suggest that the waves that survive dissipation may account for some of the observed coronal oscillations.     

Wave propagation in the photosphere

Using a 32 minutes sequence of observation, brightness and velocity fluctuations in the wings of the Mgi line at 5172.7 Å and Fe ii line at 5197.578 Å are analysed. The analysis of phase shifts and amplitude ratios leads to the following conclusions:

Wave reflections in the solar atmosphere

The small phase-lag between velocities observed at different chromospheric levels is interpreted as being due to acoustic waves reflected by the very hot atmospheric layers of the chromosphere-corona transition zone. We consider first an isothermal slab, then a realistic solar atmospheric model and calculate weighting functions for velocities in Ca ii lines. It is shown that taking into account these functions and integrating over horizontal wave numbers leads to a good agreement with previous observations (Mein, 1977) in the case of 8498 and 8542 Ca ii lines. For the K line, the less good agreement shows that magnetoacoustic waves become important in the upper chromospheric layers.     

Dissipating waves in a hot,compressible, magnetic,structured atmosphere

The damping of ducted, fast, magnetohydrodynamic (MHD) waves by ion viscosity and electron heat conduction in a radiating, optically thin, warm, structured atmosphere has been evaluated. Dissipation is more effective in a warm plasma than in a cold one but, for waves ducted by solar coronal loops, dissipation is only efficient if the periods of the waves are shorter than a few tens of seconds and only if the background magnetic field is less than about 15 G. It appears that MHD waves of longer periods and in stronger magnetic fields will survive the dissipative mechanisms considered here and may be manifest as observable coronal oscillations.     

Wave propagation in two-fluids self-gravitating plasma

Wave propagation is considered in self-gravitating collisionless magnetized plasma, when the Larmor frequency exceeds the plasma frequency. The external magnetic field is assumed to be strong and a modified two-fluids theory is used to describe the plasma. We find that there are three modes of wave propagation parallel to the magnetic field. The condition of hose instability is affected. The change in the dispersion relation due to the two-fluids theory is also discussed.     

Wave propagation in intense flux tubes

The nature of non-adiabatic wave propagation in a slender magnetic flux tube is explored. The results of the theory are compared with the observations of Giovanelli et al. (1978), and found to be in general agreement. Those observations, of tubes in the photosphere-chromosphere, show outwardly propagating waves, with periods of 300 s, which take some 19 s to propagate from one level of line formation to another level higher in the atmosphere. In sharp contrast to this, is the time of 7 s for a similar disturbance outside the tube to propagate between the same two levels of line formation, estimated to be some 600 km apart in the field-free atmosphere. It is argued that the sharply contrasting propagation times for the tube and its environment is principally due to the elasticity of the tube and its subsequent propensity for propagation. A non-adiabatic disturbance may be essentially propagating within the tube but essentially non-propagating outside, with considerably slower phase speeds thus arising inside the tube. The theory suggests that the observed disturbances are non-adiabatic, acoustic-gravity waves channelled along a magnetic flux tube and modulated by external pressure variations.     

Wave propagation in the magnetosphere of Jupiter

The magnetosphere of Jupiter has been the subject of extensive research in recent years due to its detectable radio emissions. Observations in the decimetric radio band have been particular helpful in ascertaining the general shape of the Jovian magnetic field, which is currently believed to be a dipole with minor perturbations. Although there is no direct evidence for thermal plasma in the magnetosphere of Jupiter, theoretical considerations about the physical processes that must occur in the ionosphere and magnetosphere surrounding Jupiter have lead to estimates of the thermal plasma distribution. These models of the Jovian magnetic field and thermal plasma distribution, specify the characteristic plasma and cyclotron frequencies in the magnetosplasma and thereby provide a basis for estimating thelocal electromagnetic and hydromagnetic noise around Jupiter. Spatial analogs of the well-known Clemmow-Mullaly-Allis (CMA) diagrams have been constructed to identify the loci of electron and ion resonances and cutoffs for the different field and plasma models. Regions of reflection, mode coupling, and probable amplification are readily identified. The corresponding radio noise properties may be estimated qualitatively on the basis of these various electromagnetic and hydromagnetic wave mode regions. Frequency bands and regions of intense natural noise may be estimated. On the basis of the models considered, the radio noise properties around Jupiter are quite different from those encountered in the magnetosphere around the Earth. Wave particle interactions are largely confined to the immediate vicinity of the zenographic equatorial plane and guided propagation from one hemisphere to the other apparently does not occur, except for hydromagnetic modes of propagation. The characteristics of these local signals are indicative of the physical processes occurring in the Jovian magnetosphere. Thus, as a remote sensing tool, their observation will be a vital asset in the exploration of Jupiter.     

Wave propagation in the quiet solar chromosphere

In order to precise previous results about wave propagation in the quiet chromosphere (N. Mein and P. Mein, 1976), we study the behaviour of Doppler shifts and intensity fluctuations in 3 lines of Ca ii. We use the same observation as in our previous work, that is to say a sequence of spectra lasting 27 mn, taken at Sacramento Peak Observatory solar tower. Results can be summarized as follows:

1. Phase-lag between intensity fluctuations and dopplershifts is always near 90° in the Ca ii lines, even for frequencies as high as 15 mHz, and whatever is the location in the chromospheric network.
2. Magneto-acoustic waves propagating vertically in a vertical or horizontal magnetic field could account for the observations only if they were, on one hand reflected in the upper atmosphere, on the other hand propagating with a very high sound or Alfvén speed. The lower limit for the speed (70 km s^-1) does not seem to be realistic. Oblique waves could be investigated for better agreement.

     

Reflectionless propagation of acoustic waves in the solar atmosphere

The possibility that vertical acoustic waves with frequencies lower than the cutoff frequency corresponding to the temperature minimum pass this minimum is investigated. It is shown that the averaged temperature profile in the solar atmosphere can be approximated by several so-called reflectionless profiles on which the acoustic waves propagate without internal reflection. The possibility of the penetration of vertical acoustic waves, including low-frequency ones, into the solar corona is explained in this way.     

The propagation of strong-plane magnetogasdynamic shock waves in an optically-thin atmosphere

The propagation of plane magnetogasdynamic shock waves in an optically-thin grey atmosphere of non-uniform density has been discussed by the use of the similarity method, by use of Planck's diffusion approximation. The distribution of pressure, density, magnetic field, velocity, temperature, and radiation flux have been illustrated through graphs. The numerical integration has been done on a DEC-1090 computer under a RKGS programme.     

Tunnel-effect and propagation of 5-min oscillations in the solar atmosphere

Summary Tunneling of surface waves (which are also called non-propagating or evanescent mode) in isothermal atmosphere is considered. Tunneling of 5-min oscillations in solar atmosphere is discussed. Phase lead of chromospheric oscillations with respect to photospheric oscillations (Tanenbaum et al., 1971) can be explained by tunneling only.