Solitary waves in a dusty plasma with negatively (positively) charged dust grains and non-thermal electrons

For an unmagnetized multicomponent dusty plasma, the effects of non-thermal electron distribution, ion temperature and two oppositely charged dust grains are incorporated in the study of arbitrary amplitude solitary waves. An energy-like integral equation involving Sagdeev potential is derived, and the existence, formation and basic properties of solitons are studied. It is also found a definite interval for the Mach number for which solitary waves exist and depends sensitively upon the population of fast or non-thermal electrons present. Our results should be useful to understand the properties of localized electrostatic disturbances that may occur in space dusty plasma.     

Electrostatic compressive and rarefactive shocks and solitons in relativistic plasmas occurring in polar regions of pulsar

The electrostatic shocks and solitons are studied in weakly relativistic and collisional electron-positron-ion plasmas occurring in polar regions of pulsar. The plasma system is composed of relativistically streaming electrons, positrons while ions are taken to be stationary. Dissipative effects in the system are due to collision phenomena among the constituents of relativistic plasma. Nonlinear dynamics of the dissipation and dispersion dominated relativistic plasma systems are governed by Korteweg-de Vries Burger (KdVB) and Korteweg-de Vries (KdV) equations respectively. Numerical results, exploring the effects of plasma parameters on the profile of nonlinear waves are expedited graphically for illustration. Positron to electron temperature ratio plays the role of a decisive parameter. It is noticed that compressive shocks and solitons evolve in the system if the positron to electron temperature ratio is less than a critical value. However, there exists a threshold value of positron to electron temperature ratio beyond which the system supports the rarefactive shocks and solitons. The results may have importance in the relativistic plasmas of pulsar magnetosphere.     

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.     

Evolution of the Electron Distribution Function in the Whistler Wave Turbulence of the Solar Wind

The electron distribution functions from the solar corona to the solar wind are determined in this paper by considering the effects of the external forces, of Coulomb collisions and of the wave – particle resonant interactions in the plasma wave turbulence. The electrons are assumed to be interacting with right-handed polarized waves in the whistler regime. The acceleration of electrons in the solar wind seems to be mainly due to the electrostatic potential. Wave turbulence determines the electron pitch-angle diffusion and some characteristics of the velocity distribution function (VDF) such as suprathermal tails. The role of parallel whistlers can also be extended to small altitudes in the solar wind (the acceleration region of the outer corona), where they may explain the energization and the presence of suprathermal electrons.     

Magnetospheric substorms and solar flares

Assuming that basic plasma processes associated with magnetospheric substorms and solar flares are similar and thus assuming also that a flare ribbon is produced by the impact of field-aligned current-carrying electrons on the chromosphere, a chain of processes leading to solar flares is considered, including the dynamo process in the photospheric level in the vicinity of bipolar sunspots, the formation of a sheet current in the lower coronal level, the interruption of the sheet current, the subsequent diversion of it to the chromosphere, the development of a potential drop along magnetic field lines, the acceleration of current-carrying electrons and their impact on the chromosphere, producing a pair of flare ribbons.     

Simulation studies of electron acceleration by ion ring distributions in solar flares

Using a 2 1/2-D fully relativistic electromagnetic particle-in-cell code (PIC) we have investigated a potential electron acceleration mechanism in solar flares. The free energy is provided by ions which have a ring velocity distribution about the magnetic field direction. Ion rings may be produced by perpendicular shocks, which could in turn be generated by the super-Alfvénic motion of magnetic flux tubes emerging from the photosphere or by coronal mass ejections (CMEs). Such ion distributions are known to be unstable to the generation of lower hybrid waves, which have phase velocities in excess of the electron thermal speed parallel to the field and can, therefore, resonantly accelerate electrons in that direction. The simulations show the transfer of perpendicular ion energy to energetic electrons via lower hybrid wave turbulence. With plausible ion ring velocities, the process can account for the observationally inferred fluxes and energies of non-thermal electrons during the impulsive phase of flares. Our results also show electrostatic wave generation close to the plasma frequency: we suggest that this is due to a bump-in-tail instability of the electron distribution.     

Ion-cyclotron instability and electron acceleration in coronal loops

Quasi-electrostatic electron and ion-cyclotron instabilities are studied. The result indicates that the higher harmonic ion cyclotron instabilities (ICI) can be excited while the fast ions produced from reconnection are injected into a coronal loop. Part of the energetic ions can be dragged out of the magnetic mirror turning points and a negative plasma potential is generated. The plasma potential may directly accelerate the electrons up to the relativistic velocity within a short time. This acceleration is similar to the processes occurring in the magnetic mirror devices of controlled thermonuclear fusion. The spectrum and flux of accelerated electrons have also been obtained. Some observational results during the solar flare might be explained by this acceleration mechanism.     

Gardner solitons in dusty plasmas with nonextensive ions and two-temperature superthermal electrons

Nonlinear propagation of dust-acoustic waves in an unmagnetized dusty plasma consisting of negatively charged mobile dust, nonextensive ions following nonextensive q-distribution and two distinct temperature superthermal electrons following superthermal kappa distribution each, is investigated by employing lower and higher order nonlinear equations, namely the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV) and the Gardner equations. The characteristic features of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two superthermal temperature electrons and ions nonextensivity on the basic characteristics of DA K-dV, mK-dV and Gardner solitons have also been investigated. It has been found that the DA Gardner solitons exhibit either negative or positive potential solitons only for q<q _c where, q _c is the critical value of the nonextensive parameter q. The possible applications of our results in understanding the localized nonlinear electrostatic structures existing in solar atmosphere, Saturn’s magnetosphere etc. (where the tails of the high energetic particles at different temperatures follow power-law like distribution) are also briefly discussed.     

Korteweg-de Vries equation for ion acoustic soliton with negative ions in the presence of nonextensive electrons

Korteweg-de Vries (KdV) equation for electrostatic ion acoustic wave in a three component plasma containing positive and negative ions along with the nonextensive electrons is derived. Fast and slow ion acoustic modes which propagate with different velocities are excited. The effects of variation of quantities like q (nonextensive parameter), Q (mass ratio of positive to negative ion), μ (electron to positive ion number density ratio), θ _i (positive ion to electron temperature ratio) and θ _n (negative ion to electron temperature ratio) have been presented for fast and slow ion acoustic modes. Both compressive and rarefactive solitons are observed. It is found that the solitary excitations strongly depend on the mass and density ratios of the positive and negative ions as well as on nonextensive electron parameter.     

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.     

Solar Impulsive Hard X-Ray Emission and Two-Stage Electron Acceleration

Heating and acceleration of electrons in solar impulsive hard X-ray (HXR) flares are studied according to the two-stage acceleration model developed by Zhang for solar 3He-rich events. It is shown that electrostatic H-cyclotron waves can be excited at a parallel phase velocity less than about the electron thermal velocity and thus can significantly heat the electrons (up to 40 MK) through Landau resonance. The preheated electrons with velocities above a threshold are further accelerated to high energies in the flare-acceleration process. The flare-produced electron spectrum is obtained and shown to be thermal at low energies and power law at high energies. In the non-thermal energy range, the spectrum can be double power law if the spectral power index is energy dependent or related. The electron energy spectrum obtained by this study agrees quantitatively with the result derived from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) HXR observations in the flare of 2002 July 23. The total flux and energy flux of electrons accelerated in the solar flare also agree with the measurements.     

Particle beams in the solar atmosphere: General overview

An overview of particle beams in the solar atmosphere is separated into discussions of (i) current-carrying beams, (ii) current-neutralized electron beams, and (iii) ion beams. The Alfvén-Lawson limit on an electric current implies some severe limitations including the following: the current flowing into the corona cannot exceed about 10¹² A; if the current density is near threshold for a current instability then the current must flow in thin layers; and, the primary electrons and ions cannot be accelerated simply by the particles falling down a parallel potential drop. Considerable progress has been made in understanding how electron beams in type III solar radio events propagate in a way that is consistent with the generation of Langmuir waves, but a completely consistent picture has not yet emerged. Such beams, and more importantly the electron beams that generate hard X-ray bursts require current neutralization; how the required return current is set up is still not entirely clear. There is direct evidence for ion beams with energies 10 MeV per nucleon from -ray line emission; there is no unambiguous evidence for ion beams of lower energy. A mechanism is suggested for bulk energization of electrons due to dissipation of a parallel current in solar flares. Some outstanding problems concerning particle beams are identified.     

K-dV and mK-dV equations for solitary waves in negative ion plasmas with non-Maxwellian electrons

Ion-acoustic (IA) solitons in a collisionless plasma consisting of positive and negative ions and superthermal electrons are studied by using the reductive perturbation method. The basic set of fluid equations is reduced to Korteweg-de Vries (K-dV) and modified Korteweg-de Vries (mK-dV) equations. It is found that both compressive and rarefactive solitons can be propagated in this system. Also it is shown that at critical concentration of positive ions mK-dV solitons coexist. The effects of spectral index kappa, positive to negative ion density ratio and mass ratio of positive to negative ions on IA solitons structure are also discussed.     

Spherical electron acoustic solitary waves in plasma with suprathermal electrons

A reductive perturbation technique is employed to solve the fluid-Poisson equations in spherical geometry describing a weakly nonlinear electron–acoustic (EA) waves in unmagnetized plasma consisting of stationary ions, cold electrons and kappa distributed hot electrons. It is shown that a variable coefficient Kadomtsev–Petviashvili (KP) equation governs the evolution of scalar potential describing propagation of EA waves. The influence of suprathermality and geometry effects on propagation of EA solitary waves is investigated. We found that when electrons evolve toward their thermodynamic equilibrium, EA solitons are generated with large amplitudes. Also it is shown that EA solitary structures can be significantly modified by transverse perturbations.     

Electron surfing acceleration by electrostatic waves in current sheet

The electron surfing acceleration in the current sheet with perpendicular propagating electrostatic waves is studied using analytical theories and test particle simulations. The trapped electron moving with the phase velocity v _p of wave may be accelerated effectively in the outflow direction by force until the electron is de-trapped from the wave potential. A criterion K>0 for the electron surfing acceleration is obtained. The electron will escape from the boundary of current sheet quickly, if this criterion does not hold. The maximum velocity of surfing acceleration is about the same as the electric drift velocity. Superposed longitudinal magnetic field along the wave propagation is favorable for the electron surfing acceleration in the current sheet.      

Nonlinear propagation of ion-acoustic waves in an electron-positron-ion plasma

A theoretical investigation has been made of electrostatic solitary structures in an electron-positron-ion (e-p-i) plasma, taking nonextensive electrons and nonextensive positrons. By employing the reductive perturbation method, the basic characteristics of ion-acoustic (IA) solitary waves (SWs) in a three-component e-p-i plasma (consisting of negatively charged nonextensive electrons, positively charged nonextensive positrons, and ions) have been addressed. The Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and Gardner equations are derived and their numerical solutions are obtained. It has been shown that the combined effects of electron nonextensivity, positron nonextensivity, and ions significantly modify the behavior of these electrostatic solitary structures that have been found to exist with positive and negative potential in this plasma model. The present analysis may be useful to understand and demonstrate the dynamical properties of IA SWs in different astrophysical and cosmological scenarios (viz. stellar polytropes, hadronic matter and quark-gluon plasma, protoneutron stars, dark-matter halos, etc.).     

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.     

Electrostatic ion cyclotron waves in an anisotropic plasma

In the solar wind, electrostatic ion cyclotron waves can be excited, by electrons or ions when the flow velocity becomes supersonic. The instability of these waves is investigated for a situation in which ions are streaming in opposite directions along the interplanetary magnetic field in a uniform background of relatively stationary electrons. Many modes become unstable under the existing conditions. It is conjectured that the excitation of this instability may lead to a steady state electrostatic turbulence in the solar wind.     

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.