Alfvén-magnetosonic waves interaction in the solar corona

The nonlinear propagation of the Alfvén and magnetosonic waves in the solar corona is investigated in terms of model equations. Due to viscous effects taken into account the propagation of the fast wave itself is governed by Burgers type equations possessing both expansion and compression shock solutions. Numerical simulations show that both parallely and perpendicularly propagating fast waves can steepen into shocks if their amplitudes are in excess of some sizeable fraction of the Alfvén velocity. However, if the magnetic field changes linearly in the perpendicular direction, then formation of perpendicular shocks can be hindered. The Alfvén waves exhibit a tendency to drive both the slow and fast magnetosonic waves whose propagation is described by linearized Boussinesq type equations with ponderomotive terms due to the Alfvén wave. The limits of the slow and fast waves are investigated.     

Nonlinear dissipation of Alfvén waves

Alfvén waves are generated easily in many cosmic plasmas, but they possess no linear damping mechanism since they are not compressive. The most prominent nonlinear damping occurs when one Alfvén wave decays into another plus a slow magnetosonic wave, or two Alfvén waves combine into one fast magnetosonic wave; the resulting magnetosonic waves can then be dissipated. The nonlinear coupling rates are presented, with special emphasis on the astrophysically important case of sound speed Alfvén speed. Streaming cosmic rays generate Alfvén waves moving in the direction of streaming, but they reabsorb the backward moving waves then produced by wave decay. The possible steady states for this system of cosmic rays and Alfvén waves turn out to be highly restricted.Supported by NSF grant GP-15218.     

Alfvén Wave Phase Mixing as a Source of Fast Magnetosonic Waves

The nonlinear excitation of fast magnetosonic waves by phase mixing Alfvén waves in a cold plasma with a smooth inhomogeneity of density across a uniform magnetic field is considered. If initially fast waves are absent from the system, then nonlinearity leads to their excitation by transversal gradients in the Alfvén wave. The efficiency of the nonlinear Alfvén–fast magnetosonic wave coupling is strongly increased by the inhomogeneity of the medium. The fast waves, permanently generated by Alfvén wave phase mixing, are refracted from the region with transversal gradients of the Alfvén speed. This nonlinear process suggests a mechanism of indirect plasma heating by phase mixing through the excitation of obliquely propagating fast waves.     

Cosmic-Ray Momentum Diffusion in Magnetosonic versus Alfvénic Turbulent Field

Energetic particle transport in a finite amplitude magnetosonic and Alfvénic turbulence is considered using the Monte Carlo particle simulations, which involve integration of particle equations of motion. We show that in the low- plasma the cosmic-ray acceleration can be the most important damping process for magnetosonic waves. Assuming such conditions we derive the momentum diffusion coefficient Dp, for relativistic particles in the presence of anisotropic finite-amplitude turbulent wave fields, for flat and Kolmogorov-type turbulence spectra, respectively. We confirm the possibility of larger values of Dp occurring due to transit-time damping resonance interaction in the presence of isotropic fast-mode waves in comparison to the Alfvén waves of the same amplitude (cf. Schlickeiser and Miller, 1997). The importance of quasi-perpendicular fast-mode waves is stressed for the acceleration of high velocity particles.     

Obliquely Propagating Shear Alfvén Waves Excited by Newborn Ions in the Chromosphere – Corona Transition Region

A source mechanism for the generation of shear Alfvén waves in the low solar corona is suggested. It is attributed to newly created ions associated with the ionization of neutral atoms in the chromosphere – corona transition region. In the present discussion attention is mainly paid to the excitation of shear Alfvén waves rather than compressional Alfvén waves, i.e., fast and slow magnetosonic waves. A kinetic instability, which amplifies Alfvén waves propagating in an arbitrary direction, due to the newborn ions, is studied. In the present analysis heavy ion species are emphasized.     

Impulsively generated MHD waves and their detectability in solar coronal loops

Impulsively generated magnetohydrodynamic waves in solar coronal loops, with arbitrary plasma , are studied numerically by a flux-corrected transport algorithm. Numerical results show that the total reflection which occurs in the region of low Alfvén speed leads to trapped fast kink magnetosonic waves. These waves propagate along the slab and exhibit periodic, quasi-periodic, and decay phases. As a consequence of the difference in wave propagation speeds, the time signatures of the slow magnetosonic waves are delayed in time in comparison to the time signatures of the fast magnetosonic and Alfvén waves. An interaction between the waves can generate a longer lasting and complex quasi-periodic phase of the fast wave. We discuss also the observational detectability of such MHD waves in optical, radio, and soft X-ray wavelenghts.     

On the mean free path of solar cosmic rays – I. Protons

The spatial transport of charged particles in the presence of pure slab Alfvén waves, pure isotropic magnetosonic waves and their mixture is considered using Monte Carlo particle simulations. We show that the mean free path of solar cosmic ray protons strongly depends on the assumed spectrum and amplitude of MHD turbulence but much less on the type of the considered waves. It is demonstrated that, for realistic solar wind parameters, the presented wide range wave spectrum models can reproduce the observed mean free path in a particular SEP event but not in a wide range of rigidity characterized by the Palmer's `consensus'.     

A Two-Dimensional Alfvén-Wave-Driven Solar Wind Model

This paper presents a two-dimensional, Alfvén-wave-driven solar wind model, in which the wave energy is assumed to cascade from the low-frequency Alfvén waves to high-frequency ion cyclotron waves and to be transferred to the solar wind protons by cyclotron resonance at the Kolmogorov rate. A typical structure in the meridional plane consisting of a coronal streamer near the Sun, a fast wind in high latitudes, and a slow wind across the heliospheric current sheet, is found. The fast wind obtained in the polar region is essentially similar to that derived by previous one-dimensional flow-tube models, and its density profile in the vicinity of the Sun roughly matches relevant observations. The proton conditions at 1 AU are also consistent with observations for both the fast and slow winds. The Alfvén waves appear in the fast- and slow-wind regions simultaneously and have comparable amplitudes, which agrees with Helios observations. The acceleration and heating of the solar wind by the Alfvén waves are found to occur mainly in the near-Sun region. It is demonstrated in terms of one-dimensional calculations that the distinct properties of the fast and slow winds are mainly attributed to different geometries of the flow tubes associated with the two sorts of winds. In addition, the 2-D and 1-D simulations give essentially the same results for both the fast and the slow winds.     

Alfvén wave plasma turbulence during solar wind-comet interaction

The large differences in drift velocities between the solar wind protons and the picked-up ions of cometary origin cause the Alfvén waves (among others) to become unstable and generate turbulence. A self-consistent treatment of such instabilities has to take into account that these cometary ions affect the solar wind plasma in a decisive way. With the help of a previously developed formalism one finds the correct Alfvén instability criterion, which is here nondispersive, in contrast to recent calculations where the cometary ions are treated as a low-density, high-speed, and non-neutral beam through an otherwise undisturbed solar wind. The true bulk speed of the combined solar wind plus cometary ion plasma clearly shows the mass-loading and deceleration of the solar wind near the cometary nucleus, indicating a bow shock. The instability criterion is also used to determine the region upstream where the Alfvén waves can be unstable, based upon recent observations near comet Halley.     

Low-frequency plasma turbulence during solar wind-comet interaction

The pick up cometary ion distributions are shown to excite Alfvénic mode instabilities, slow ion-acoustic mode instability and a lower hybrid instability during solar wind-comet interaction. The growth rates of all these instabilities become larger as the comet is approached. The lower hybrid instability is shown to account for the low-frequency 0–300 Hz electrostatic turbulence observed near comet Halley. The Alfvén modes can grow to large amplitudes and become modulationally unstable, in the presence of low-frequency density fluctuations, going over to envelope Alfvén solitons. A model consisting of a gas of Alfvén solitons is suggested to explain the hydromagnetic turbulence observed near comet Halley and comet Giacobini-Zinner.     

Alfvén waves in the solar atmosphere

The nonlinear propagation of Alfvén waves on open solar magnetic flux tubes is considered. The flux tubes are taken to be vertical and axisymmetric, and they are initially untwisted. The Alfvén waves are time-dependent axisymmetric twists. Their propagation into the chromosphere and corona is investigated by solving numerically a set of nonlinear time-dependent equations, which couple the Alfvén waves into motions parallel to the initial magnetic field (motion in the third coordinate direction is artificially suppressed). The principal conclusions are: (1) Alfvén waves can steepen into fast shocks in the chromosphere. These shocks can pass through the transition region into the corona, and heat the corona. (2) As the fast shocks pass through the transition region, they produce large-velocity pulses in the direction transverse to B _o. The pulses typically have amplitudes of 60 km s^–1 or so and durations of a few tens of seconds. Such features may have been observed, suggesting that the corona is in fact heated by fast shocks. (3) Alfvén waves exhibit a strong tendency to drive upward flows, with many of the properties of spicules. Spicules, and the observed corrugated nature of the transition region, may therefore be by-products of magnetic heating of the corona. (4) It is qualitatively suggested that Alfvén waves may heat the upper chromosphere indirectly by exerting time-dependent forces on the plasma, rather than by directly depositing heat into the plasma.     

Kinetic Alfvén waves in extended radio sources

We study a model of extended radio sources (ERS), in particular, extragalactic jets and radio lobes, which are inhomogeneous and where noncompressive Alfvén and surface Alfvén waves (and not shocks and magnetosonic waves) are primarily excited. We assume that a negligible thermal population exists (i.e., the ion density at the low-energy cut-off of the power law distribution is greater than the ion density of the thermal population, if present). Due to internal instabilities and/or the interaction of the ERS with the ambient medium, surface Alfvén waves (SAW) are created. We show that even very small amplitude SAW are mode converted to kinetic Alfvén waves (KAW) which produce large moving accelerating potentials , parallel to the magnetic field. Neglecting nonlinear perturbations, and for typical physical parameters of ERS, we obtaine1 MeV. Wesuggest that these potentials are important in acceleration (e.g., injection energy) and reacceleration of electrons in ERS. We show that energy losses by synchrotron radiation can be compensated by reacceleration by KAW. The relation between KAW acceleration, and previously studied cyclotron-resonance acceleration by Alfvén waves, is discussed.     

Wave reflection and wave disorder in the solar transition zone and corona

The reflection coefficient for sound or Alfvén waves reaching the transition zone is evaluated. A family of temperature profiles, including T ^5/2 dT/dz = constant, permits analytical solutions for the velocity and yields the reflection coefficient as a function of both the wavelength and the temperature jump across the zone. When the temperature jump is large, even waves appreciably shorter than the zone thickness are reflected efficiently.Wave reflection disorders the waves in and below the transition zone, because rising waves there interact with reflected waves in a manner more similar to turbulence than to shock steepening.The distribution in directions of hydromagnetic waves is determined by the non-uniformity of their sources. Most inhomogeneities in the wave source cause the waves to resemble isotropic fastmode waves more than Alfvén waves. This places severe restrictions on possible sources of Alfvén waves.     

The Oscillations of Coronal Loops Including the Shell

We investigate the MHD waves in a double magnetic flux tube embedded in a uniform external magnetic field. The tube consists of a dense hot cylindrical cord surrounded by a co-axial shell. The plasma and the magnetic field are taken to be uniform inside the cord and also inside the shell. Two slow and two fast magnetosonic modes can exist in the thin double tube. The first slow mode is trapped by the cord, the other is trapped by the shell. The oscillations of the second mode have opposite phases inside the cord and shell. The speeds of the slow modes propagating along the tube are close to the tube speeds inside the cord and the shell. The behavior of the fast modes depends on the magnitude of Alfvén speed inside the shell. If it is less than the Alfvén speed inside the cord and in the environment, then the fast mode is trapped by the shell and the other may be trapped under the certain conditions. In the opposite case when the Alfvén speed in the shell is greater than those inside the cord and in the environment, then the fast mode is radiated by the tube and the other may also be radiated under certain conditions. The oscillation of the cord and the shell with opposite phases is the distinctive feature of the process. The proposed model allows to explain the basic phenomena connected to the coronal oscillations: i) the damping of oscillations stipulated in the double tube model by the radiative loss, ii) the presence of two different modes of perturbations propagating along the loop with close speeds, iii) the opposite phases of oscillations of modulated radio emission, coming from the near coronal sources having sharply different densities.     

Solar p-modes oscillations and heating of the corona

The properties of the resonator are considered for fast magnetoacoustic waves. It is shown that tunnel penetration of waves from the resonator leads either to heating of the medium in the Alfvén resonance vicinity (if the inclination angle of the magnetic field is smaller than the critical angle), or to excitation of Alfvén waves at the Alfvén resonance (if the inclination angle is larger than the critical angle). This suggests that non-radiative heating of the corona can be due to solar p-mode oscillations.     

Nonlinear propagation of Alfvén waves in cometary plasmas

Large-amplitude Alfvén waves propagating along the guide magnetic field in a three-component plasma are shown to be spatially localized due to their nonlinear interaction with nonresonant electrostatic density fluctuations. A new class of subsonic Alfvén soliton solutions are found to exist in the three-component plasma. The Alfvén solitons can be relevant in explaining the properties of hydromagnetic turbulence near the comets.     

Tunneling and interference of Alfvén waves

The propagation and interference of Alfvén waves in magnetic regions is studied. A multilayer approximation of the standard models of the solar atmosphere is used. In each layer, there is a linear law of temperature variation and a power law of Alfvén velocity variation. The analytical solutions of a wave equation are stitched at the layer boundaries. The low-frequency Alfvén waves (P > 1 s) are able to transfer the energy from sunspots into the corona by tunneling only. The chromosphere is not a resonance filter for the Alfvén waves. The interference and resonance of Alfvén waves are found to be important to wave propagation through the magnetic coronal arches. The transmission coefficient of Alfvén waves into the corona increases sharply on the resonance frequences. To take into account the wave absorption in the corona, a method of equivalent schemes is developed. The heating of a coronal arch by Alfvén waves is discussed.     

Nonlinear wave-wave interactions in astrophysical and space plasmas

We discuss nonlinear mode-mode coupling phenomena in cosmic plasmas. Four problems are considered: (1) nonlinear three-wave processes in the planetary magnetosphere involving the interaction of auroral Langmuir, Alfvén and whistler waves, (2) nonlinear three-wave processes in the solar wind involving the modulation of Langmuir and electromagnetic waves by ion-acoustic waves, (3) order and chaos in nonlinear four-wave processes in cosmic plasmas, and (4) regular and chaotic dynamics of the relativistic Langmuir turbulence and its application to pulsar and AGN emissions. The observational evidence in support of nonlinear wave-wave interactions in space and astrophysical plasmas is presented.     

Coupling equations for a flow-wave field used to faculae heating

In a binary system of a background fluid-wave field, the wave effect may be important in some cases. From general properties of thermodynamics of the medium, we derive the coupling equations for the mean flow-wave field. For six wave modes (Langmuir wave, ion-acoustic oscillations, whistlers, Alfvén waves, magneto-acoustic oscillations, and transverse plasma wave) the corresponding representation of the wave stress tensor is found. Finally, the representation for the Alfvén waves is applied to the faculae heating and a result consistent with observations is obtained.