Nonlinear coherent four‐wave interaction in space plasma

According to a widespread point of view, intensive electrostatic structures in the E‐region of the auroral ionosphere can be a consequence of the excitation of the modified two‐stream or Farley‐Buneman (FB) plasma turbulence. But in spite of the successes of the theoretical and experimental research of the auroral radar scattering, it is impossible to explain the existence of auroral echoes with large aspect angles (> 2 deg.), the wave propagation perpendicular to the electron drift velocity and wave scales less than 1 m. In this paper the coherent nonlinear interactions of three and four electrostatic FB‐waves are considered analytically and numerically. The evolution of the nonlinear waves is described by a system of magnetohydrodynamic equations. 1) It is shown that the interaction of three and four coherent waves is the main physical mechanism which leads to the saturation of the FB‐instability. 2) If no dissipative and dispersive effects occur, an explosive instability may be excited. 3) The main result of the interaction of coherent waves is the generation of nonlinear waves and nonlinear structures when the waves are damped linearly and propagate perpendicular to the electron drift velocity. This region corresponds to large aspect angles of the small‐scale waves. 4) Further, the wave interaction causes a nonlinear stabilization of the growth of the high‐frequency waves and a formation of local density structures of the charged particles. The results of the numerical models allow to analyse the possibility of scenarios of the two‐stream plasma instability in the collisional auroral E‐region.     

Acceleration of the solar wind by whistler waves from coronal holes

We investigate the possibility of an additional acceleration of the high speed solar wind by whistler waves propagating outward from a coronal hole. We consider a stationary, spherically symmetric model and assume a radial wind flow as well as a radial magnetic field. The energy equation consists of (a) energy transfer of the electron beam which excites the whistler waves, and (b) energy transfer of the whistler waves described by conservation of wave action density. The momentum conservation equation includes the momentum transfer of two gases (a thermal gas and an electron beam). The variation of the temperature is described by a polytropic law. The variation of solar wind velocity with the radial distance is calculated for different values of energy density of the whistler waves. It is shown that the acceleration of high speed solar wind in the coronal hole due to the whistler waves is very important. We have calculated that the solar wind velocity at the earth's orbit is about equal to 670 km/sec (for wave energy density about 10^?4 erg cm^?3 at 1.1R⊙). It is in approximate agreement with the observed values.     

Transmission of Alfvén waves through the rotational discontinuity at magnetopause

The reflection and refraction of MHD waves through an “open” magnetopause (rotational discontinuity) is studied. It is found that most of the incident wave energy can be transmitted through the open magnetopause. A transverse Alfvén wave (or a compressional magnetosonic wave) from the solar wind incident upon the open magnetopause would generally lead to the generation of both the transverse Alfvén and compressional magnetosonic waves in the magnetosphere. Transmission of Alfvén waves in the coplanar rotational discontinuity is studied in detail. The integral power of the Alfvén-wave transfer is found to be proportional to the open magnetic flux of the magnetosphere and is typically ～ 1% of the power of the total electromagnetic energy transfer through the open magnetopause. The transmitted wave power may contribute significantly to the geomagnetic pulsations observed on the ground, especially in the open-field-line region.     

Alfvén turbulence in collisionless plasmas

The evolution of Alfvén turbulence due to three-wave interactions is discussed using kinetic theory for a collisionless, thermal plasma. In particular, we consider decay of Alfvén waves through three-wave coupling with an ion sound mode in the random-phase approximation. Two decay processes are of particular interest: an Alfvén wave decays into a backward propagating Alfvén wave and a forward propagating ion sound wave, and an Alfvén wave decays into a backward propagating fast magnetoacoustic wave and a forward ion sound wave. The former was widely discussed in the literature, particularly under the coherent wave assumption. The latter was not well explored and is discussed here.     

Characteristics of oceanic impact‐induced large water waves—Re‐evaluation of the tsunami hazard

Abstract— The potential hazard of a meteorite impact in the ocean is controversial with respect to the destructive power of generated large ocean waves (tsunamis). We used numerical modeling of hypervelocity impact to investigate the generation mechanism and the characteristics of the resulting waves up to a distance of 100–150 projectile radii. The wave signal is primarily controlled by the ratio between projectile diameter and water depth, and can be roughly classified into deep‐water and shallow‐water impacts. In the latter, the collapse of the crater rim results in a wave signal similar to solitary waves, which propagate and decay in agreement with shallow‐water wave theory. The much more likely scenario for an asteroid impact on Earth is a relatively small body (much smaller than the water depth) striking the deep sea. In this case, the collapse of the transient crater results in a significantly different and much more complex wave signal that is characterized by strong nonlinear behavior. We found that such waves decay much more rapidly than previously assumed and cannot be treated as long waves. For this reason, the shallow‐water theory is not applicable for the computation of wave propagation, and more complex models (full solution of the Boussinesq equations) are required.     

Nonlinear break up of an infinite cylinder in the presence of a uniform axial magnetic field

A third-order theory has been developed to study the instability of an infinite cylinder in the presence of a uniform axial magnetic field. By use of strained coordinates, the growth of the surface waves is calculated for wave numbers less than the critical wave number. It is observed that the perturbed surface of an infinite cylinder assumes a non-sinusoidal shape resulting in secondary waves due to energy transfer between the harmonics of different orders.Department of Chemical Engineering and Technology.Department of Mathematics.     

Damping of slow magnetoacoustic waves in an inhomogeneous coronal plasma

We study the propagation and dissipation of slow magnetoacoustic waves in an inhomogeneous viscous coronal loop plasma permeated by uniform magnetic field. Only viscosity and thermal conductivity are taken into account as dissipative processes in the coronal loop. The damping length of slow-mode waves exhibit varying behaviour depending upon the physical parameters of the loop in an active region AR8270 observed by TRACE. The wave energy flux associated with slow magnetoacoustic waves turns out to be of the order of 10⁶ erg cm^?2 s^?1 which is high enough to replace the energy lost through optically thin coronal emission and the thermal conduction below to the transition region. It is also found that only those slow-mode waves which have periods more than 240s provide the required heating rate to balance the energy losses in the solar corona. Our calculated wave periods for slow-mode waves nearly match with the oscillation periods of loop observed by TRACE.     

Equations for transfer of radiation in plasma at decay interactions with ionacoustic waves

Equations for spectral energy densities of waves are obtained describing transfer of high frequency radiation through plasma without magnetic field at the decay of electromagnetic waves into electromagnetic and ionacoustic ones, as well as the decay of Langmuir waves into Langmuir and ionacoustic ones in case of isotropic distributions of all the above waves.     

Ulysses observations of nonlinear wave-wave interactions in the source regions of type III solar radio bursts

The Ulysses Unified Radio and Plasma Wave Experiment (URAP) has observed Langmuir, ion-acoustic and associated solar type III radio emissions in the interplanetary medium. Bursts of 50–300 Hz (in the spacecraft frame) electric field signals, corresponding to long-wavelength ion-acoustic waves are often observed coincident in time with the most intense Langmuir wave spikes, providing evidence for the electrostatic decay instability. Langmuir waves often occur as envelope solitons, suggesting that strong turbulence processes, such as modulational instability and soliton formation, often coexist with weak turbulence processes, such as electrostatic decay, in a few type III burst source regions.     

Dissipation mechanism of interplanetary alfvenic fluctuation

Observations on board Helios 1 and 2 have shown that, in 0.3–0.9 AU, the decay of the Alfvenic fluctuations is greater than is calculated by the WBK solution of the propagation of Alfven waves. The additional decay can be expressed by an exponential factor with a “dissipation length” λ, which varies with the frequency but is approximately constant for frequencies higher than 0.01 Hz. In this paper, we deduce the analytical expression for the dissipation length in both the wave energy cascade model, given in a previous work [7] and the viscous decay model [8]. After inserting the observed values of the solar wind parameters, we find the dissipation length given by the cascade model agrees with the observed length both in size and in its variation with frequency, while the one given by the viscous decay model differs greatly from the observations.     

Propagation of sonic waves in an optically thick medium in the presence of magnetic field

This paper studies sonic waves in an optically thick medium under the influence of a magnetic field. The conductivity of the medium has been taken to be infinite. The effects of radiation, radiation energy density, radiative heat transfer and magnetic field have been taken into account. It has been obtained that the magnetic field has significant effect on sonic velocity. The fundamental differential equations governing the growth and decay of sonic waves are determined and solved.     

Fluctuations of density and waves in nonlinear nuclear reactions in stellar cores

The space correlation of fluctuation of density in the nuclear reaction system inside the stars is investigated by using the theory of a generating function. Referring to the dynamical rate equation, we have introduced the gravitational force and temperature gradient terms into master equation of the probability distribution function of density, and a generalized master equation has been obtained. We take P-PI reactions of hydrogen-burning in the solar core as an example to solve this master equation for infinite medium. A series of waves have been obtained. The first branch is the average density wave which has already been obtained from the dynamical rate equation. Other branches describe the propagation of the fluctuation moments of the local density. They represent the propagation processes of the local distortion of the probability distribution function. Stability of the system may be related to an increase and decay of the waves. We have analysed the phase velocity of these waves.     

Test Particle Simulations of Interaction Between Monochromatic Chorus Waves and Radiation Belt Relativistic Electrons

Chorus waves have been suggested to be effective in acceleration of radiation belt electrons. Here we perform gyro-averaged test-particle simulations to calculate the bounce-averaged pitch angle and energy diffusion coefficients for parallel-propagating monochromatic chorus waves, and perform a comparison of test-particle (TP) model with quasi-linear (QL) theory to evaluate the influence of nonlinear processes. For small amplitude chorus waves, the diffusion coefficients of TP and QL models are in good agreement. As the wave amplitude reaches a threshold value, two nonlinear processes (phase trapping and phase bunching) start to occur, especially at large equatorial pitch angles. Phase trapping yields rapid increases in pitch angle and kinetic energy. In contrast, phase bunching causes overall decreases in pitch angle and kinetic energy. For the waves with amplitudes slightly above the threshold value, the average behavior is dominated by the phase trapping, and TP diffusion coefficients are larger than QL ones. As wave amplitude increases, TP diffusion coefficients become smaller than QL ones, indicating that phase trapping gradually reduces the dominance over phase bunching.     

Nonlinear excitation of small-scale Alfvén waves by fast waves and plasma heating in the solar atmosphere

We study a nonlinear mechanism for the excitation of kinetic Alfvén waves (KAWs) by fast magneto-acoustic waves (FWs) in the solar atmosphere. Our focus is on the excitation of KAWs that have very small wavelengths in the direction perpendicular to the background magnetic field. Because of their small perpendicular length scales, these waves are very efficient in the energy exchange with plasmas and other waves. We show that the nonlinear coupling of the energy of the finite-amplitude FWs to the small-scale KAWs can be much faster than other dissipation mechanisms for fast wave, such as electron viscous damping, Landau damping, and modulational instability. The nonlinear damping of the FWs due to decay FW = KAW + KAW places a limit on the amplitude of the magnetic field in the fast waves in the solar corona and solar-wind at the level B/B ₀∼10⁻². In turn, the nonlinearly excited small-scale KAWs undergo strong dissipation due to resistive or Landau damping and can provide coronal and solar-wind heating. The transient coronal heating observed by Yohkoh and SOHO may be produced by the kinetic Alfvén waves that are excited by parametric decay of fast waves propagating from the reconnection sites.     

On the linear transformation and resonant absorption of Alfvén p-modes in sunspots

We analyse the linear transformation of Alfvén p-modes into quasisurface waves and the resonant absorption of Alfvén p-waves in a slowly varying medium with a density gradient, parallel to the ambient homogeneous magnetic field. It is pointed out, that the energy transfer from Alfvén p-waves to quasisurface waves appear to take place in sunspots. The results obtained also suggest that Alfvén p-waves generated by overstability in sunspots may be absorbed in deep layers under sunspots. Moreover, it is very likely that part of the downward wave flux is reflected and hence it is possibble that essentially the energy from sunspots is transported outward by magnetogravitational waves, to which Alfvén p-waves are transformed.     

Stochastic wave growth, power balance, and beam evolution in type III solar radio sources

Energy-balance arguments are combined with the stochastic-growth theory of type III radio sources to determine the properties of the source in average dynamical equilibrium with the beam, and the beam's long-term evolution. Purely linear stochastic-growth theory has previously emphasized that the beam evolves to a state close to marginal stability. Small mean residual deviations from marginal stability are present at dynamical equilibrium and these lead to residual energy flows that feed the waves observed in situ and by remote receivers; consequently the beam energy is depleted. Here, dynamical equilibrium beam and wave levels are estimated for the first time and it is found that the main sink of beam-driven Langmuir waves is either via electrostatic decay into product Langmuir and ion-sound waves or via scattering by short-wavelength density fluctuations, depending on the conditions. Improved estimates of energy branching ratios imply that, at 1 AU from the Sun, typically 20% of the beam energy is converted to Langmuir waves that are scattered off low-frequency density fluctuations and then dissipated, with almost all the remaining waves undergoing electrostatic decay, although as little as one-third of the Langmuir waves may decay in atypical circumstances. Of order 10^–3 of the beam energy is converted into sound waves, which are mostly dissipated, and of order 10^–5 is converted into potentially observable electromagnetic waves. The mean lifetime of the Langmuir waves at 1 AU is 1–40 s, while that of the beam is of order 1000 s. The beam density decreases relative to that of the background as the beam propagates. For most parameters, analysis of energy losses from the beam to the waves shows that the beam velocity decreases at roughly the same rate as the thermal velocity of the background plasma. It is argued from these considerations, and from in situ observations at 1 AU, that these trends imply that only the densest and fastest type III beams will be able to penetrate much past 1 AU from the Sun. This implies a low-frequency cutoff to type III emission at roughly 10 kHz, in good agreement with recent Ulysses remote observations, showing their consistency with in situ measurements.     

Hydromagnetic-gravity wave critical levels in the solar atmosphere

It is shown that the discontinuous jump in the vertical wave energy flux of slow hydromagnetic-gravity waves, occurring at a critical level, which is accompanied by wave absorption, and the existence of a reflection point imply that slow waves are trapped in the solar atmosphere. Thus such a system behaves as a leaky wave guide.     

Particle acceleration and the decay of soft X-ray non-thermal line broadening in solar flares

The relationship between the production of -ray emitting particles and non-thermal soft X-ray line broadening is investigated. A model of particle acceleration via the stochastic interaction with MHD turbulence is assumed and the time development of the wave energy density derived under the condition of energy conservation between waves and particles. The inferred numbers and energy distribution of accelerated protons for four -ray flares are used to define the wave energy density and its temporal development. The presence of Alfvén wave turbulence is considered as the source of the non-thermal motions in the ambient plasma. These motions are observed as excess widths in the soft X-ray line emission from these events. The decay of the waves via the particle acceleration process is compared with the observed decays of this non-thermal line broadening. Our results show that both the -ray emission and excess soft X-ray line widths in these flares can be explained by the single physical phenomenon of Alfvén wave turbulence.     

Parametric Decay of a Circularly Polarized Electromagnetic Wave in an Electron-Positron Magnetized Plasma

We study the parametric decays of an electromagnetic wave propagating along an external magnetic field in an electron-positron plasma. We include weakly relativistic effects on the particle motions in the wave field, and the nonlinear ponderomotive force. We find resonant and nonresonant wave couplings. These include, ordinary decay instabilities, in which the pump wave decays into an electro-acoustic mode and a sideband wave. There are also nonresonant couplings involving two sideband waves, and a nonresonant modulational instability in which the pump wave decays into two sideband modes. Depending on the parameters involved, there is a resonant modulational instability involving a forward propagating electro-acoustic mode and a sideband daughter wave.     

Decay instability of kinetic Alfvén waves in preflare plasmas of the loops in active solar regions

We examine the physical conditions for the origin of the decay instability of kinetic Alfvén waves in loop plasmas at the early flare stages. The synchronism conditions are used to derive a modified expression for the nonlinear growth rate of the process of the decay of the primary kinetic Alfvén wave (KAW) into an ion-acoustic wave and a secondary KAW. The threshold amplitude of the primary KAW is calculated in units of the background magnetic field strength in the chromospheric section of loop current circuit.