Nonlinear treatment for solar radio spikes

We emphasize that a nonlinear treatment is required to realize the diagnostic potentiality of solar spiky emission. The observational constraints including the latest data on the harmonic structure, degree, and sense of polarization are discussed. A set of coupled equations for energy density of high-frequency normal modes of a magneto-active plasma involving the most important nonlinear effects within the three-wave approximation is deduced. The equations include both previously known and new effects. The qualitative evaluations of the equations obtained have provided a few new findings: (i) quasi-linear relaxation of fast electrons on quasi-potential waves (_) occurs in a characteristic time scale of the order of 10 ms if the frequency,f, is about 1 GHz; (ii) the stimulated scattering of the transverse waves on the background plasma particles is shown to be important if the brightness temperature of the spiky emission exceeds 10¹⁵–10¹⁶ K; (iii) the Raman scattering of the transverse waves on background plasma density inhomogeneities may suppress the electron cyclotron maser instability if n _e ² /n _e ² 3 × (10^–4–10^–5).     

Populations of highly excited atoms and ions in the optically thin plasma

Treating it as a boundary-value problem, the equations of highly excited state populations of atoms and ions are theoretically studied in case of recombining plasma. Scattering and spontaneous transitions as well as those induced by background radiation, are taken into account in the kinetic equations. The kinetic coefficients for inelastic scattering of incident charged particles on highly excited atoms and ions have been calculated in the asymptotically exact case: 1.6×10⁵ (z/n)²)T _e ^–1 1.The distribution functions over the Rydberg states, analytically found, allow to determine amplification factor and optical depth of radio-recombination lines as functions of cosmic plasma parameters.     

Electromagnetic velocity gradient instabilities in the magnetosphere

The velocity gradients of the contrastreaming electron beams observed in the Earth's magnetosphere can excite three types of ordinary mode instabilities, namely (i) B-resonance electron instability, (ii) ion cyclotron instability, and (iii) unmagnetized ion instability. The B-resonance electron instability occurs at small values of the shear parameter 10^–4<S<10^–3, whereS = [(1/e){dU _o(x)}/(dx)] (U ₀(x) and _e being the streaming velocity of the electron beams and the electron cyclotron frequency, respectively). Near the equatorial plane of the bouncing electron beams region, this instability can generate electromagnetic waves having frequenciesf(0.045–0.2) Hz and wavelentghs (0.5–10)km, and the wave magnetic field is polarised in a radial direction. This instability can also occur in the plasma sheet region during the earthwards and tailwards plasma flows events and can generate waves, with wave magnetic field polarised along north-south direction, in the frequency rangef(0.007–0.02) Hz with (10–100)km nearR=–35R _E . For 10^–3<S<10^–2, the ion cyclotron instability is excited and it can generate waves up to 5th harmonic or so of ion cyclotron frequency. ForS>10^–2, the unmagnetized ion instability is excited which can generate electromagnetic waves having frequences from 5 to 50 Hz and typical wavelengths (0.5–6)km. The growth rates of all the three velocity shear driven instabilities are reduced in the presence of cold background plasma. The turbulence generated by these instabilities may give rise to enhanced effective electron-electron and electron-ion collisions and broaden the bouncing electron beams.     

Generation of a d.c. field by nonlinear electromagnetic waves in relativistic plasmas

A finite amplitude linearly polarized electromagnetic wave propagating in a relativistic plasma, is found to generate the longitudinal d.c. as well as the oscillating electric field at the second harmonic. In a plasma consisting of only electrons and positrons, these fields cannot be generated.The evolution of the electromagnetic waves is governed by the non-linear Schrödinger equation which shows that the electromagnetic solitons are always possible in ultra-relativistic plasmas (electron-ion or electron-positron) but in a plasma with relativistic electrons and nonrelativistic ions, these solitons exist only if 1(KT _e/m_eC²)<(2m _i/15m_e);m _e andm _i being the electron and ion mass andT _e the electron temperature. Both the d.c. electric field and the solitons provide a nonlinear mechanism for anomalous acceleration of the particles. This model has direct relevance to some plasma processes occurring in pulsars.     

Modulational instability of nonlinear waves in the relativistic plasma with account of the nonlinear Landau damping

The modulational instability of the weakly nonlinear longitudinal Langmuir as well as the transverse electromagnetic waves, propagation in the relativistic plasma without the static fields is described. The nonlinear Schrödinger equation taking account of the nonlinear Landau damping for these waves has been derived by means of the relativistic Vlasov and Maxwell equations. The plasma with the weakly relativistic temperature and that with an ultrarelativistic one has been investigated. In the first case, for the electron-proton plasma with the temperature more than 2.3 KeV we found the regional change of the wave numbers for which the soliton of two types, subsonic and supersonic, can exist. The soliton of the transverse waves can exist when the group velocity of the waves is between the thermal velocity of the electron and ion and the length of the linear waves is less than 2c/ _pi .In the second case the regions of the wave numbers, with the solitons of the Langmuir and transverse waves have been determined.The nonlinear waves in the electron-positron plasma and the waves with the phase velocity, which is about the light one, are also considered in the following paper.     

Ion acoustic instability in the presence of plasma turbulence in the solar wind

The adiabatic theory of interaction between high and low frequency waves has been studied for the case of electron plasma oscillations and ion acoustic waves and the results are applied to the solar wind. The modified dispersion relation for ion acoustic waves has been derived, taking a Gaussian distribution for plasmons. Two limiting cases of the spectrum are studied. For a broad spectrum, the plasma turbulence has a destabilising effect by introducing a growth rate denoted by turbulence, which is positive for k ₀ > (m _e/ m _i )^1/2 _De ^–1 , k ₀ being the central wave numger of the spectrum, _De the electron Debye length. Also, even for v _d(drift velocity between electrons and ions) < c _s, we arrive at unstable ion acoustic modes. For narrow spectrum, the plasma turbulence has a stabilising effect.     

Dynamics of a cloud of fast electrons travelling through the plasma

A simulation of normal type III radio bursts has been made in a whole frequency range of about 200 MHz to 30 kHz by the usage of the semi-analytical method as developed in previous papers for the plasma waves excited by a cloud of fast electrons. Three-dimensional plasma waves are computed, though the velocities of fast electrons are assumed to be one-dimensional. Many basic problems about type III radio bursts and associated solar electrons have been solved showing the following striking or unexpected results.Induced scattering of plasma waves, by thermal ions, into the plasma waves with opposite wave vectors is efficient even for a solar electron cloud of rather low number density. Therefore, the second harmonic radio emission as attributed to the coalescence of two plasma waves predominates in a whole range from meter waves to km waves. Fundamental radio emission as ascribed to the scattering of plasma waves by thermal ions is negligibly small almost in the whole range. On the other hand, third harmonic radio emission can be strong enough to be observed in a limited frequency range.If, however, the time integral of electron flux is, for example, 2 × 10¹³ cm^–2 (>5 keV) or more at the height of 4.3 × 10¹⁰ cm ( _p = 40 MHz) above the photosphere, the fundamental may be comparable with or greater than the second harmonic, but an effective area of cross-section of the electron beam is required to be very small, 10¹⁷ cm² or less, and hence much larger sizes of the observed radio sources must be attributed to the scattering alone of radio waves.The radio flux density expected at the Earth for the second harmonic can increase with decreasing frequencies giving high flux densities at low frequencies as observed, if x-dependence of the cross-sectional area of the electron beam is x ^1.5 or less instead of x ², at least at x 2 × 10¹² cm.The second harmonic radio waves are emitted predominantly into forward direction at first, but the direction of emission may reverse a few times in a course of a single burst showing a greater backward emission at the low frequencies.In a standard low frequency model, a total number of solar electrons above 18 keV arriving at the Earth orbit reduces to 12% of the initial value due mainly to the collisional decay of plasma waves before the waves are reabsorbed by the beam electrons arriving later. However, no deceleration of the apparent velocity of exciter appears. A change in the apparent velocity, if any, results from a change in growth rate of the plasma waves instead of the deceleration of individual electrons.Near the Earth, the peak of second harmonic radio flux as emitted from the local plasma appears well after the passage of a whole solar electron cloud through this layer. This is ascribed to the secondary and the third plasma waves as caused in non-resonant regions by the induced scattering of primary plasma waves in a resonant region.     

Neutralization and stabilization of particle streams in the corona and type III radio bursts

The processes by which streams of charged particles become charge and current neutralized in the corona are investigated. It is shown that a large amplitude plasma wave, which is related to precursor phenomenon in type III bursts and possibly plasma radiation from type IV bursts, will be excited at the head of the stream. The energy extracted from the stream to produce this plasma wave is computed and used to set conservative upper limits on the densities of possible excitors for type III bursts. For electron streams the density n _s < 10^–5 n _e, where n _e is the density of the background plasma. For proton streams n _s < 1.8 × 10^–2 n _e. The energy extracted from the stream is also used to set upper limits on the lifetimes of relativistic electrons stored in the corona and it is concluded that for n _e > 10² cm^–3 this loss must be taken into account. Since electron streams cannot produce their own stabilizing ionacoustic waves because they would violate the condition n _s < 10^–5 n _e, other mechanisms for producing ion-acoustic waves in the corona are examined. Another stabilization mechanism due to velocity inhomogeneity is investigated.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Negative ions in comets

The primary negative ion sources in comets are shown to be: for the inner coma—both polar photodissociation of HCN, electron attachment of OH and collisions with alkalis; in the vicinity of the nucleus—plasma, excavated during interplanetary dust impacts on the nucleus; for both the contaminated solar wind region and sporadic discharges in the non-homogeneous inner coma plasma—dissociative electron attachment and charge inversion during keV positive ion scattering by cometary dust are also significant sources. Negative ion abundance for Halley's Comet has been estimated to be from 10^–6 to 10^–10 of electron densities. However, this ratio may be more due to the formation of clusters A^–(H₂O)_n. Some possible cometary plasma effects, caused by negative ions, have also been discussed.     

Effects of the non-extensive parameter on the propagation of ion acoustic waves in five-component cometary plasma system

Some important evolution nonlinear partial differential equations are derived using the reductive perturbation method for unmagnetized collisionless system of five component plasma. This plasma system is a multi-ion contains negatively and positively charged Oxygen ions (heavy ions), positive Hydrogen ions (lighter ions), hot electrons from solar origin and colder electrons from cometary origin. The positive Hydrogen ion and the two types of electrons obey \(q\)-non-extensive distributions. The derived equations have three types of ion acoustic waves, which are soliton waves, shock waves and kink waves. The effects of the non-extensive parameters for the hot electrons, the colder electrons and the Hydrogen ions on the propagation of the envelope waves are studied. The compressive and rarefactive shapes of the three envelope waves appear in this system for the first order of the power of the nonlinearity strength with different values of non-extensive parameters. For the second order, the strength of nonlinearity will increase and the compressive type of the envelope wave only appears.     

On the problem of the formation of quasar emission lines by the Cherenkov mechanism

In a series of papers of You, Cheng, et al. (cf., for example, [2–4]) the Cherenkov mechanism of radiation was proposed as the explanation of the wide emission lines in the spectra of quasars. This mechanism acts because the refractive index of the plasma in a certain frequency range near a spectral line can exceed one. It has been found that the role of Cherenkov radiation becomes significant for an optically thick medium when the density of the packet of relativistic electrons ñ_e is 10⁴–10⁶ cm^–3. However, the question of the formation of a spectral line as the result of ordinary (recombination and collision) processes under the same physical conditions has not been considered, and hence no comparison has been made between the intensities of lines formed by different mechanisms. Moreover, a large number of effects that may have significant influence on the profile of a line (multiple scattering in the medium, redistribution of radiation over frequencies within a line, redistribution of energy between a line and the continuous spectrum) have remained unexamined by these authors.The present work aims at sharpening some of the formulas used in [2–4] and filling up some of these gaps. We pose the classical problem of formation of a spectral line taking account of the action of the Cherenkov radiation mechanism and give an exact solution of it. The computations are carried out for the line L. It is shown that under the values presently accepted for the electron temperature for an average quasar (T_e 1.5 · 10⁴ K) the influence of the Cherenkov mechanism becomes noticeable only for implausibly high densities of relativistic electrons (10¹¹ cm^–3, The geometric model proposed in [4] for quasar radiation in a line encounters insuperable difficulties involving the energy of the quasar and the sizes of the radiating regions.Translated fromAstrofizika, Vol. 37, No. 3, 1994.     

Acceleration and radiation processes around active galactic nuclei

It is proposed that the region containing fast particles, electrostatic and electromagnetic fields, around active galactic nuclei is responsible for generating electromagnetic emissions from -rays to radio waves. The electrons are accelerated by Langmuir turbulence originating through the process of Raman forward scattering (RFS). The radiation mechanism is stimulated Raman backward scattering (RBS) where the fast electron beam loses energy by scattering over spatially periodic magnetic field. The spatially periodic magnetic field results from the magnetic modulational instability of the Langmuir waves. This model accounts well for the large luminosities observed in active galactic nuclei over -rays to radio waves and in addition it relates physically the emission regions at different wavelengths.     

Towards a theory for type III solar radio bursts

The mechanisms for the transformation of plasma waves into radiation near the fundamental and second harmonic of the plasma frequency are reviewed and equations are given for both the emission and absorption coefficients for these mechanisms. Near the fundamental the process is the scattering of plasma waves on the polarization clouds of ions and the absorption coefficient can be negative, i.e. the radiation can be amplified. Near the second harmonic the process is the combination of two excited plasma waves for which the absorption coefficient can only be positive. These results are applied to construct models of the radiation source for type III solar radio bursts both at high frequencies where the fundamental is dominant and at low frequencies where the second harmonic is dominant using two model plasma wave spectra, one being one-dimensional, the other isotropic. At high frequencies second harmonic radiation is used to determine the source area for a given energy density in plasma waves W _p . The source size and W _p are detrmined uniquely for a given plasma wave spectrum by tracing rays in a model source taking into account amplification of the fundamental. The results for a strong source at the 80 MHz plasma level with a ratio of emissivities of the fundamental to second harmonic P(ω _p )/P(2ω _p ) ≈ 10 are that the source with a one-dimensional plasma wave spectrum is about 14000 km in diameter and W _p = 10^?6.52 erg cm^?3, and the source with an isotropic distribution of plasma waves is about 200 km in diameter and W _p = 10^?6.3 erg cm^?3. It is shown that at low frequencies, where amplification of the fundamental is no longer possible, second harmonic radiation must be dominant and thus very little information about the source can obtained from the radiation.     

Dust-acoustic solitary and rogue waves in a Thomas-Fermi degenerate dusty plasma

The formation and propagation of dust-acoustic (DA) solitary and rogue waves are studied in a non-relativistic degenerate Thomas-Fermi thermal dusty plasma incorporating transverse velocity perturbation effects. The electrons and ions are described by the Thomas-Fermi density distributions, whereas the dust grains are taken as dynamic and classical. By using the reductive perturbation technique, the cylindrical Kadomtsev-Petviashvili (CKP) equation is derived, which is then transformed into a Korteweg-deVries (KdV) equation by using appropriate variable transformations. The latter admits a solitary wave solution. However, when the carrier waves frequency is much smaller than the dust plasma frequency, the DA waves evolve into the nonlinear modulation instability, generating modulated wave packets in the form of Rogue waves. For the study of DA-rogue waves, the KdV equation is transformed into a self-focusing nonlinear Schrödinger equation. The variation of dust temperature and the electron density affects the nonlinearity and dispersion coefficients which suppress the amplitudes of the DA solitary and rogue waves. The present results aim to describe the nonlinear electrostatic excitations in astrophysical degenerate dense plasma.     

Monte Carlo calculation of comptonization effects in spherical accretion onto black holes

Spherical accretion onto black holes at high accretion rates leads to temperatures and optical depths for which Comptonization of the emerging radiation plays an important role, altering both the plasma temperature and the emergent spectrum. In this paper the nonlocal effects of Comptonization are accounted for by numerically modeling the scattering process with Monte Carlo techniques. Calculations are performed for black hole masses ranging from 10¹–10⁹ M and are compared with the local scattering model of Ipser and Price (1983). It is found that the local scattering approximation underestimates the energy in the X-ray portion of the spectrum. Monte Carlo calculations shows that the spectrum flattens and the spectral index decreases to values about 20% below those obtained by using the local scattering approximation.     

Dust ion acoustic travelling waves in the framework of a modified Kadomtsev-Petviashvili equation in a magnetized dusty plasma with superthermal electrons

For the critical values of the parameters q and V, the work (Samanta et al. in Phys. Plasma 20:022111, 2013b) is unable to describe the nonlinear wave features in magnetized dusty plasma with superthermal electrons. To describe the nonlinear wave features for critical values of the parameters q and V, we extend the work (Samanta et al. in Phys. Plasma 20:022111, 2013b). To extend the work, we derive the modified Kadomtsev-Petviashvili (MKP) equation for dust ion acoustic waves in a magnetized dusty plasma with q-nonextensive velocity distributed electrons by considering higher order coefficients of ?. By applying the bifurcation theory of planar dynamical systems to this MKP equation, the existence of solitary wave solutions of both types rarefactive and compressive, periodic travelling wave solutions and kink and anti-kink wave solutions is proved. Three exact solutions of these above waves are determined. The present study could be helpful for understanding the nonlinear travelling waves propagating in mercury, solar wind, Saturn and in magnetosphere of the Earth.     

Stationary equations of hydrogen excitation and ionization in prominences

The statistical equilibrium equations for the continuum and first 10 levels of a hydrogen atom show that the radiation of a bright prominence (the brightness of the H line has attained 56 mÅ of the disc centre spectrum) is completely due to scattering of the Sun radiation. The basic unknowns are separated with certainty: electron concentration (n _e = 3.0 × 10¹⁰ cm^–3), effective thickness (l = 4.2 × 10⁸ cm) and electron temperature (T _e = 5000 K).Radiation of a very bright prominence (A (H) = 213 mÅ; T _e = 7300 K; n _e = 5.0 × 10¹¹ cm^–3; l = 1.3 × 10⁷ cm) is on account of electron impacts (40%) and the Sun radiation scattering (60%).The parameters are shown to depend greatly on the prominence optical thickness in the lines of the first subordinate series of a hydrogen atom. In the course of determination all the parameters and 100 interconnected integral equations of the radiation diffusion have been thickness-averaged; the population of levels has been calculated by observations using the self-absorption factors.     

Excitation of high-frequency Alfvén waves by plasma outflows from coronal reconnection events

We study a kinetic excitation mechanism for high-frequency dispersive Alfvén waves in the solar corona by magnetic reconnection events. The ion-cyclotron and Cerenkov kinetic effects are important for these waves which we call the ion-cyclotron kinetic Alfvén waves (IC KAWs). The plasma outflowing from the reconnection site sets up a neutralized proton beam in the surrounding plasma, providing free energy for the excitation of waves. The dependence of the phase velocity of the IC KAW on the parallel wavenumber is different from that on the perpendicular wavenumber. The phase velocity is an increasing function of the perpendicular wavenumber and overtakes the Alfvén velocity for sufficiently large values of k . However, the phase velocity is a decreasing function of k , and sufficiently large values of k result in a phase velocity below the Alfvén velocity. As a result, the IC KAWs can undergo the Cerenkov resonance with both super- and sub-Alfvénic particles, and for the waves to be excited the outflow velocity does not need to be super-Alfvénic, as for KAWs, but the beam/Alfvén velocity ratio can span a wide range of values. High growth rates of the order of 10⁴ s^–1 are found for the values of the plasma parameters typical for the low solar corona. The waves excited by (sub-)Alfvénic beams are damped mainly due to kinetic wave-particle interactions with ions at the cyclotron resonance (ion-cyclotron damping), and with ions and electrons at the Cerenkov resonance (Landau damping). Therefore, IC KAWs can heat the plasma species of the corona in both the parallel and perpendicular direction, giving rise to an anisotropic heating of the ions. The observational consequences of the processes under study are discussed.     

Non-inductive current driven by Alfvén waves in solar coronal loops

It has been shown that Alfvén waves can drive non-inductive current in solar coronal loops via collisional or collisionless damping. Assuming that all the coronal-loop density of dissipated wave power (W= 10–3 erg cm^–3 s^–1), which is necessary to keep the plasma hot, is due to Alfvén wave electron heating, we have estimated the axial current density driven by Alfvén waves to be jz 10³–10⁵ statA cm^–2. This current can indeed support the quasi-stationary equilibrium and stability of coronal loops and create the poloidal magnetic field up to B 1–5 G.