Fast MHD Waves Research Articles

Classification of Magnetoatmospheric Modes in Sunspot Umbrae

We examine the wave modes in a sunspot umbra. Assuming a stratification, based on a model atmosphere in a sunspot, the normal mode spectrum is determined. The modes are classified using a scheme based on a Helmholtz decomposition of the displacements into l(longitudinal) and t(transverse) components. In certain cases these can be related to the usual fast and slow MHD waves. We compute the theoretical eigenfrequencies and note the existence of umbral oscillations with periods in the range 2-3 min, which are interpreted as slow and mixed modes. The frequencies of the Alfvén waves are also calculated. It is suggested that these modes might also have been observed.

Evolution of interplanetary slow shocks

The possible existence of traveling forward slow shocks, their global geometry and their transition to forward fast shocks have been discussed in a recent paper. The decrease in the Alfven speed at increasing heliocentric distance causes the evolution of a forward slow shock into a forward fast shock. During the transition the shock system consists of a slow shock, a fast shock, and a rotational discontinuity. This paper continues to discuss three aspects about the evolution of interplanetary slow shocks. We first present a survey of slow shock solutions in a three‐dimensional A,θ,β parameter space. Here A = Un/(a cos θ) is the shock Alfven number, Un the normal component of the relative shock speed, a the Alfven speed, θ the acute angle between the shock normal and the magnetic field, and β the ratio of the thermal pressure p to the magnetic pressure B²/8π. In a region where the plasma β value is on the order of 1 or greater, the jumps in thermodynamic properties across a slow shock are small but the directional changes for the magnetic field and the relative flow velocity are not necessarily small. On the other hand, in the region where the plasma β value is on the order of 0.1 or less, the jumps of all physical properties across a slow shock may vary over a wide range of magnitudes. Next, we discuss that at the onset of the transition process an interplanetary slow shock smoothly converts to a system consisting of a slow shock, a very weak rotational discontinuity (an Alfven wave), and a very weak fast shock (a fast MHD wave). We also show that during the transition, the amplitude of fluctuations in flow velocity and magnetic fields are large in the turbulent region behind the fast shock.

Resonant interactions between cometary ions and low frequency electromagnetic waves

We explore the conditions for resonance between cometary pick-up ions and parallel propagating electromagnetic waves. A model ring—beam distribution for the pick-up H 2O + ions is adopted which allows a direct comparison of the source of free energy for growth from either the beam or the gyrating ring in the limit near marginal stability. Under average solar wind conditions in the inner solar system, the gyrating ring provides the dominant contribution to wave growth. The presence of a field-aligned beam is only important to allow resonance with R-mode waves which occur in two distinct frequency bands either well above or below the pick-up ion gyrofrequency. The most unstable mode is the low frequency R-mode or fast MHD wave, though higher frequency whistlers or low frequency L-mode waves may also be excited by the same source of free energy. The nature of the unstable waves is strongly influenced by the inclination α of the interplanetary field. For α ≲ 3° the rate of the low frequency R-mode growth is dramatically reduced and resonant L-mode waves should experience net ion beam damping. Conversely for α ≳ 75°, the ion beam velocity will be insufficient to allow resonant R-mode instability; L-mode waves should therefore predominate. The low frequency fast MHD mode should experience the most rapid amplification for intermediate inclination; 30° ≲ α ≲ 75°. In the frame of the solar wind such waves must propagate along the field in the direction upstream towards the Sun with a phase speed lower than the beaming velocity of the pick-up ions. The waves are consequently blown back away from the Sun and would thus be detected with a left-hand polarization by an observer in the cometary frame. We consider this the most likely mechanism to account for the interior MHD waves observed by satellites over an extended spatial region surrounding comets Giacobini-Zinner and Halley.

Spatial and temporal variations of solar coronal loops

Skylab EUV observations of an active region near the solar limb were analyzed. Both cool (T 106 K) loops were observed in this region. For the hot loops the observed intensity variations were small, typically a few percent over a period of 30 min. The cool loops exhibited stronger variations, sometimes appearing and disappearing in 5 to 10 min. Most of the cool material observed in the loops appeared to be caused by the downward flow of coronal rain and by the upward ejection of chromospheric material in surges. The frequent EUV brightenings observed near the loop footpoints appear to have been produced by both in situ transient energy releases (e.g. subflares) and the infall/impact of coronal rain. The physical conditions in the loops (temperatures, densities, radiative and conducting cooling rates, cooling times) were determined. The mean energy required to balance the radiative and conductive cooling of the hot loops is approximately 3 × 10−3 erg cm−3 s−1. One coronal heating mechanism that can account for the observed behavior of the EUV emission from McMath region 12634 is heating by the dissipation of fast mode MHD waves.

Nonlinear evolution of slow waves in the solar wind

We show by numerical simulation using a hybrid code that comparison of the nonlinear steepening rate, calculated from fluid theory, with the linear collisionless damping rate, defines reasonably well the parameters for which fast and slow MHD waves should steepen. Our results indicate that, whereas fast modes should ordinarly steepen, steepened slow waves should occur rarely in the solar wind near 1 AU.

Some characteristics of propagation of flare- or CME-associated interplanetary shock waves

Many interplanetary shock waves have a fast mode MHD wave Mach number between one and two and the ambient solar wind plasma and magnetic field are known to fluctuate. Therefore a weak, fast, MHD interplanetary shock wave propagating into a fluctuating solar wind region or into a solar wind stream will be expected to vary its strength. It is possible that an interplanetary shock wave, upon entering such a region will weaken its strength and degenerate into a fast-mode MHD wave. It is even possible that the shock may dissipate and disappear. A model for the propagation of a solar flare - or CME (Coronal Mass Ejections) - associated interplanetary shock wave is given. A physical mechanism is described to calculate the probability that a weak shock which enters a turbulent solar wind region will degenerate into a MHD wave. That is, the shock would disappear as an entropy-generate entity. This model also suggests that most interplanetary shock waves cannot propagate continuously with a smooth shock surface. It is suggested that the surface of an interplanetary shock will be highly distorted and that parts of the shock surface can degenerate into MHD waves or even disappear during its global propagation through interplanetary space. A few observations to support this model will be briefly described. Finally, this model of shock propagation also applies to corotating shocks. As corotating shocks propagate into fluctuating ambient solar wind regions, shocks may degenerate into waves or disappear.

Magnetohydrodynamic behaviour of a finite amplitude disturbance in the solar magnetic field

In this paper, dynamic processes in the solar atmosphere are studied numerically from a complete set of MHD equations. Dynamic evolution of the non-linear magnetic field is produced by the finite amplitude of the azimuthai magnetic field at the base of the flux tube of the solar atmosphere. It is assumed that the initial configuration of the magnetic field is a force-free and potential field, the magnetic field is disturbed at the base, the plasma is driven and a part of the magnetic energy is transformed into the kinetic energy of the plasma. The compressed flow of the plasma has the features of fast MHD waves. The computation results give quantitatively the non-linear evolution of strong magnetic fields. These results could be used in an explanation of coronal transients, surge, spray and eruptive prominence events in the solar atmosphere, as well as in a modelling of plasma behaviour in high-β structure experiments in the laboratory.

Comment on the paper ?a new resonance in the solar atmosphere? by Joseph V. Hollweg

In the absence of genuine forcing terms, there is no resonance between linear fast mhd and gravito-acoustic waves.

Heating of coronal loops by fast mode MHD waves

A possible mechanism for the formation and heating of coronal loops through the propagation and damping of fast mode waves is proposed and studied in detail. Loop-like field structures are represented by a dipole field with the point dipole at a given distance below the solar surface. The density of the medium is determined by hydrostatic equilibrium along the field lines in an isothermal atmosphere. The fast mode waves propagating outward from the coronal base are refracted into regions with a low Alfven speed and suffer collisionless damping when the gas pressure becomes comparable to the magnetic pressure. The propagation and damping of these waves are studied for three different cases: a uniform density at the coronal base, a density depletion within a given flux tube, and a density enhancement within a given flux tube. The fast mode waves are found to be important in the formation and heating of the loops if the wave energy flux density is of the order 105 ergs cm-2 s-1 at the coronal base.

Resonant interactions between fast particles and collision-dominated MHD waves

The theory of resonant interactions between particles and MHD waves (in collision-dominated plasmas) is shown to be equivalent to the corresponding theory for waves in collisionless plasmas provided that the wave properties are described in a suitable way. Slow-mode waves (as well as fast mode waves and Alfven waves) might contribute to the scattering of cosmic rays in the interstellar medium.