Ray-type spectra of plasma turbulence in coronal magnetic loops

The problem of stationary spectra of Langmuir, l, and electromagnetic, t, waves excited in a magnetic trap (loop) by a group of suprathermal electrons, whose velocity distribution includes a loss cone, is considered. Within the framework of weak turbulence theory, accurate spectra of l- and t-waves are found. These spectra have the form of thin rays in wavevector space. Forms of plasma emission radio lines of a homogeneous source near the plasma frequency and its second harmonic are determined.     

Combination Scattering by Anisotropic Langmuir Turbulence with Application to Solar Radar Experiments

We develop a theory for radar signal scattering by anisotropic Langmuir turbulence in the solar corona due to a t+l ⇄ t process. Langmuir turbulence is assumed to be generated within a cone by a narrow type III burst electron beam. Using wave-kinetic theory we obtain expressions for the frequency shift, scattering cross-section of the turbulence, coefficient of absorption (due to scattering) and optical depth. On the basis of those expressions we give some estimates for an echo spectrum. We show that the minimum radar echo frequency shift is determined by the minimal phase velocity of the Langmuir waves, the maximum shift is determined by the electron beam velocity, but in any case it can not exceed −wt/2 (decay) and wt (coalescence), where wt is the frequency of a radar signal. The angular characteristics of the scattered signal differ dramatically for the cases of coalescence and decay. The signal is scattered into a narrow cone high above the specular reflection point (wp ≪ wt), but in the vicinity of wp ∼ wt/2 the red-shifted echo is scattered isotropically, while the blue-shifted echo is scattered into a even narrower cone. We show that absorption (due to scattering) increases with increasing radar frequency. The dependence of the absorption on the local plasma frequency is strongly determined by the Langmuir turbulence spectrum. Our theory shows that the role of the nonlinear scattering process t+l ⇄ t is essential and that such process can be used for radar studies of the spectral energy density of anisotropic Langmuir turbulence.     

Resonant Transition Radiation and Solar Radio Bursts

This paper presents general relations for the intensity of the resonant transition radiation (RTR) and their detailed analysis. This analysis shows that the spectrum amplitude of the x-mode at some frequencies for high-energy electrons can grow with the magnetic field increase in some interval from zero value; it can even dominate over that for the o-mode. With further magnetic field increase, the intensity of the RTR x-mode decreases in comparison with the intensity of the o-mode and this decrease is higher for higher velocities of energetic electrons. The polarization of the RTR depends on the velocity of energetic electrons, too. For velocities lower than some velocity limit v<v _i the RTR emission is unpolarized in a broad interval of magnetic field intensities in the radio source. For reasonable values of indices of the power-law distribution functions of energetic electrons, the RTR is broadband in frequencies (df/f≈0.2−0.4). Furthermore, we show various dependencies of the RTR and its spectral characteristics. Assuming the same radio flux of the transition radiation and the gyro-synchrotron one at the Razin frequency, we estimate the limit magnetic field in the radio source of the transition radiation. Then, we analyze possible sources of small-scale inhomogeneities (thermal density fluctuations, Langmuir and ion-sound waves), which are necessary for the transition radiation. Although the small-scale inhomogeneities connected with the Langmuir waves lead to the plasma radiation, which is essentially stronger than RTR, the inhomogeneities of the ion-sound waves are suitable for the RTR without any other radiation. We present the relations describing the RTR for anisotropic distribution functions of fast electrons. We consider the distribution functions of fast electrons in the form of the Legendre polynomials which depend on the pitch-angle. We analyze the influence of the degree of the anisotropy (an increase of the number of terms in the Legendre polynomial) on spectral characteristics of the RTR. A comparison with previous studies is made. As an example of the use of the derived formulas for the RTR, the 24 December 1991 event is studied. It is shown that the observed decimetric burst can be generated by the RTR in the plasma with the density inhomogeneities at the level 〈ΔN ²〉/N ²=2.5⋅10⁻⁵.     

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.     

Beam propagation and Langmuir wave generation in a plasma with κ distribution function

Using a kappa velocity distribution function for the electrons of the background plasma, the dynamics of a beam of hot electrons streaming through the plasma and the generation of Langmuir waves are investigated in the frame work of quasilinear theory. It is shown that the Langmuir waves are strongly damped by high energy tail of the Kappa distribution function. The spatial expansion of the beam is reduced and the spectral density of Langmuir waves becomes narrower. The height of the plateau in the beam distribution function increases at small velocities and the average velocity of beam is larger than that of a Maxwellian distribution. The influence of Kappa velocity distribution function on the gasdynamical parameters is investigated. It is found that, the height of plateau in the beam distribution function, and its lower velocity boundary are enhanced while, the local beam width in velocity space decreases.     

Numerical simulation of electromagnetic emissions in the solar wind plasma with non-thermal electron distribution

Dynamics of fundamental and second harmonic electromagnetic emissions are simulated in the solar wind plasma in the presence of non-thermal electron distribution function in which primary Langmuir waves are driven by an electron beam. The electron velocity distribution function is separated into two distributions representing the distribution of the ambient electrons (Maxwellian) and the suprathermal electrons (non-thermal electrons). The effects of the non-thermal electrons on the generation of primary Langmuir waves, emission rates of the fundamental (F) and harmonic waves (H) and their distributions are investigated. The both of the F and H emissions are sensitive to the characterizes of the non-thermal electrons. It is found that in the presence of non-thermal electrons the production of the Langmuir waves decreases and consequently the levels of fundamental and second harmonic waves are reduced. The emission rate of the fundamental transverse waves decreases and its peak moves slightly toward smaller wave-numbers.     

Plasma emission and the decimetre portion of type-IV solar bursts

An attempt is made to account for the decimetre portion of the Type-IV solar radio bursts by plasma emission. Non-thermal electrons (E ～ 500 keV) trapped in a magnetic mirror (IV_dm, burst source) having loss-cone gap distribution excite plasma waves which are transformed into transverse waves through non-linear scattering by ions. A good agreement was reached between the calculated spectrum and the observed fluxes for the event of 1972 August 2. A distribution of the number of non-thermal electrons with height, and a total number of 10³², were obtained. Also it was found that the Langmuir waves can accelerate some background thermal electrons to the MeV range.     

Dust acoustic shock waves in a suprathermal dusty plasma with dust charge fluctuation

The properties of small but finite amplitude dust acoustic (DA) shock waves are studied in a charge varying dusty plasma with ions and electrons having kappa velocity distribution. We obtain the global Debye length including the influence of suprathermality effects and dust charge fluctuations. It is shown that the effects of suprathermality of ions/electrons and dust charge fluctuation significantly modify the basic properties of DA shock wave. We observe that only negative DA shock waves will be excited in this model. The amplitude of DA shock wave increases with deviation of electrons or ions from Maxwellian distribution via decrease of spectral index, κ _j (j=i,e denotes, ions and electrons, respectively). Also, it is indicated that the amplitude and steepness of the shock front decreases with an increase in the ion temperature.     

A relationship between the brightness temperatures for type III bursts

Type III bursts often have brightness temperatures at the fundamental greater than 10⁹K. If the fundamental emission is due to scattering of Langmuir waves into transverse waves by thermal ions, this implies that induced scattering dominates over spontaneous scattering, which in turn requires that the energy density in Langmuir waves be greater than some minimum value, e.g. W ^l > 3 × 10^-10 erg cm^-3 for bursts at f _p = 100 MHz. Such Langmuir waves become isotropic on a time-scale shorter than the rise-time of type III bursts, e.g. < l s at f _p = 100 MHz. Consequently, their coalescence, leading to emission at the second harmonic, proceeds. The above inequalities would imply a brightness temperature at the second harmonic in excess of 10⁹K at f = 200 MHz.The predicted values of the brightness temperatures _T1 ^t and _T2 ^t (at the fundamental and second harmonic respectively) can be expressed in terms of an optical depth . After is eliminated a functional relation between _T1 ^t , _T2 ^t and the plasma frequency, f _p , remains. The form of this relation is not dependent on a quantitative theory of how the Langmuir waves are generated by the stream of electrons. Consequently, comparison with observed quantities should provide further insight into the detailed properties of the emission processes.     

Ion acoustic solitary waves in a weakly relativistic plasma with <Emphasis Type="Italic">q</Emphasis>-nonextensive electrons and thermal positrons

Nonlinear ion acoustic solitary waves (IASWs) are addressed in a weakly relativistic plasma consisting of cold ion fluid, q-nonextensive electron velocity distribution and Boltzmann distributed positron. The Korteweg-de Vries- (KdV) equation is derived by reductive perturbation method. We investigate the effect of nonextensive electrons on solitary waves in this medium. It is found that only compressive solitons can be appeared in the existence of nonextensive electrons. It is shown that the structure of soliton depend sensitively on the q-nonextensive parameter.     

Quasi-linear relaxation of electrons interacting with an inhomogeneous distribution of Langmuir waves

Quasi-linear theory, describing the diffusion of electrons in velocity space due to resonant interaction with Langmuir waves, is generalized to treat the case where the waves are distributed inhomogeneously (in clumps). The method used is a generalization of an approach developed by Morales and Lee (1974) to treat the interaction of electrons with a distribution of solitons. It is shown that quasi-linear theory, specifically the diffusion of electrons in velocity space due to resonant interaction with Langmuir waves, applies irrespective of how the waves are distributed in space, provided that an electron has multiple encounters with clumps of Langmuir waves, and that the evolution of the distribution of electrons is considered only on a time-scale long compared with the time between such encounters. This generalization of quasi-linear theory is of relevance to type III solar radio bursts, where the Langmuir waves are known to be distributed inhomogeneously, and yet the electron distribution is consistent with that expected from a balance between ballistic effects and quasi-linear relaxation.     

Numerical simulation of the weak turbulence excited by a beam of electrons in the interplanetary plasma

The electron distribution functions measured at 1 AU in an electron stream passing the ISEE-3 spacecraft (Lin et al., 1981) are used as input data to a programme which simulates in a one-dimensional model the interaction between fast electrons and plasma waves (quasi-linear relaxation) together with the plasma wave scattering off the background ions. While the computed spectral energy density of the plasma waves excited in resonance with the streaming of electrons is below Zakharov's threshold of strong turbulence, it is sufficiently high to undergo a fast induced scattering off the background ions. The resulting spectrum is concentrated around the wave vector k = 0. Some simple analytic considerations show that this stage leads necessarily to the crossing of Zakharov's threshold and therefore this indirect excitation of strong turbulence seems to play an essential role in understanding the Langmuir turbulence generated by the motion of fast electron beams in the interplanetary plasma.     

Steady heat conduction in coronal loop unstable against plasma instability

The Fokker-Planck equation is numerically solved to study the electron velocity distribution under steady heat conduction with an applied axial electric current in a model coronal loop.If the loop temperature is so high that the electron mean-free path is longer than the local temperature scale height along the loop, a velocity hump appears at about the local thermal electron velocity. The hump is attributed to cooler electrons moving up the temperature gradient to compensate for the runaway electrons moving down the gradient. If the ratio between the mean free path and temperature scale height is greater than about 2, negative absorption for the plasma waves can appear (waves grow). This effect is enhanced by the presence of axial electric current in the half of the coronal loop in which the electrons carrying the current are drifting up the temperature gradient. Thus, the plasma instability may occur in the coronal elementary magnetic flux tubes. Although the present paper is limited to show the critical condition and linear growth rate of the instability, the following scenarios may be inferred.If the flux tubes change from marginally stable to unstable against the plasma instability, due to an increase in the loop temperature, anomalous resistivity may suddenly appear because of the growth of plasma waves. Then a high axial electric field is induced that may accelerate particles. This could be the onset of impulsive loop flares.For a low electric current, if the loop temperature is sufficiently high to give the negative absorption for the plasma waves in a large part of the coronal loop, steady plasma turbulence may originate. This could be a source for the type I radio noise storm.     

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.     

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.     

Generation of intermediate drift bursts in solar type IV radio continua through coupling of whistlers and Langmuir waves

The possible generation of intermediate drift bursts in type IV dm continua through coupling between whistler waves, traveling along the magnetic field, and Langmuir waves, excited by a loss-cone instability in the source region, is elaborated. We investigate the generation, propagation and coupling of whistlers. It is shown that the superposition of an isotropic background plasma of 10⁶K and a loss-cone distribution of fast electrons is unstable for whistler waves if the loss-cone aperture 2α is sufficiently large (sec α?4); a typical value of the excited frequencies is 0.1 ω _ce (ω _ce is the angular electron cyclotron frequency). The whistlers can travel upwards through the source region of the continuum along the magnetic field direction with velocities of 21.5–28 v _A (v _A is the Alfvén velocity). Coupling of the whistlers with Langmuir waves into escaping electromagnetic waves can lead to the observed intermediate drift bursts, if the Langmuir waves have phase velocities around the velocity of light. In our model the instantaneous bandwith of the fibers corresponds to a frequency of 0.1–0.5 ω _ce and leads to estimates of the magnetic field strength in the source region. These estimates are in good agreement with those derived from the observed drift rate, corresponding to 21.5–28 v _A, if we use a simple hydrostatic density model.     

Vlasov – Maxwell,Self-consistent Electromagnetic Wave Emission Simulations in the Solar Corona

1.5D Vlasov – Maxwell simulations are employed to model electromagnetic emission generation in a fully self-consistent plasma kinetic model for the first time in the context of solar physics. The simulations mimic the plasma emission mechanism and Larmor-drift instability in a plasma thread that connects the Sun to Earth with the spatial scales compressed appropriately. The effects of spatial density gradients on the generation of electromagnetic radiation are investigated. It is shown that a 1.5D inhomogeneous plasma with a uniform background magnetic field directed transverse to the density gradient is aperiodically unstable to the Larmor-drift instability. The latter results in a novel effect of generation of electromagnetic emission at plasma frequency. The generated perturbations consist of two parts: i) non-escaping (trapped) Langmuir type oscillations, which are localised in the regions of density inhomogeneity, and are highly filamentary, with the period of appearance of the filaments close to electron plasma frequency in the dense regions; and ii) escaping electromagnetic radiation with phase speeds close to the speed of light. When the density gradient is removed (i.e. when plasma becomes stable to the Larmor-drift instability) and a low density super-thermal, hot beam is injected along the domain, in the direction perpendicular to the magnetic field, the plasma emission mechanism generates non-escaping Langmuir type oscillations, which in turn generate escaping electromagnetic radiation. It is found that in the spatial location where the beam is injected, standing waves, oscillating at the plasma frequency, are excited. These can be used to interpret the horizontal strips (the narrow-band line emission) observed in some dynamical spectra. Predictions of quasilinear theory are: i) the electron free streaming and ii) the long relaxation time of the beam, in accord with the analytic expressions. These are corroborated via direct, fully-kinetic simulation. Finally, the interplay of the Larmor-drift instability and plasma emission mechanism is studied by considering a dense electron beam in the Larmor-drift unstable (inhomogeneous) plasma. The latter case enables one to study the deviations from the quasilinear theory.     

Investigation on spectral character of ELF electromagnetic radiations during Leonid 2009 meteor shower

The problem of solitary electron acoustic (EA) wave propagation in a plasma with nonthermal hot electrons featuring the Tsallis distribution is addressed. A physically meaningful nonextensive nonthermal velocity distribution is outlined. It is shown that the effect of the nonthermal electron nonextensivity on EA waves can be quite important. Interestingly, we found that the phase speed of the linear EA mode increases as the entropic index q decreases. This enhancement is weak for q>1, and significant for q<1. For a given nonthermal state, the minimum value of the allowable Mach numbers is lowered as the nonextensive nature of the electrons becomes important. This critical limit is shifted towards higher values as the nonthermal character of the plasma is increased. Moreover, our plasma model supports rarefactive EA solitary waves the main quantities of which depend sensitively on q. This dependency (for q>1) becomes less noticeable as the nonthermal parameter decreases. Nevertheless, decreasing α yields for q<0 a different result, a trend which may be attributed to the functional form of the nonthermal nonextensive distribution. Our study (which is not aimed at putting the ad hoc Cairns distribution onto a more rigorous foundation) suggests that a background electron nonextensivity may influence the EA solitons.     

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.