Non-isothermal Electrons Research Articles

Dust voids (holes) in a charge-varying complex plasma with non-isothermal trapped electrons

AbstractThe recent analysis of dust voids (Mamun, A. A. and Shukla, P. K. 2005 J. Plasma Phys.71, 143) is extended to include self-consistent electron trapping and dust charge variation. It is found that under certain conditions the effect of dust charge variation can be quite important. In particular, it may be noted that the dust charge variation leads to an additional enlargement of the nonlinear dust voids. The effects of ion/electron temperature and trapping parameter on the properties of these nonlinear dust voids are briefly discussed. As the dust particle number density is increased, the depth, as well as the width, of the dust void decreases and the additional enlargement (due to dust charge perturbations) becomes less pronounced. Furthermore, these dust voids exhibit smaller widths than those involving isothermal electrons.

Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 1. Stability of solitary waves

Abstract.Weakly nonlinear waves in strongly magnetized plasma with slightly non-isothermal electrons are governed by a modified Zakharov–Kuznetsov (ZK) equation, containing both quadratic and half-order nonlinear terms, which we refer to as the Schamel–Korteweg–de Vries–Zakharov–Kuznetsov (SKdVZK) equation. We present a method to obtain an approximation for the growth rate, γ, of sinusoidal perpendicular perturbations of wavenumber, k, to SKdVZK solitary waves over the entire range of instability. Unlike for (modified) ZK equations with one nonlinear term, in this method there is no analytical expression for kc, the cut-off wavenumber (at which the growth rate is zero) or its corresponding eigenfunction. We therefore obtain approximate expressions for these using an expansion parameter, a, related to the ratio of the nonlinear terms. The expressions are then used to find γ for k near kc as a function of a. The approximant derived from combining these analytical results with the ones for small k agrees very well with the values of γ obtained numerically. It is found that both kc and the maximum growth rate decrease as the electron distribution becomes progressively less peaked than the Maxwellian. We also present new algebraic and rarefactive solitary wave solutions to the equation.

The influence of non-isothermal electrons and neutral wind structures on the doppler properties of vertical m-size field-aligned irregularities in the low latitude E-region

Meter size irregularities are routinely studied with radars in the equatorial and low latitude regions. In both instances echoes from the E-region (90 to 120 km altitude) are a common occurrence. The resulting echoes are labeled as so-called Type I or Type II according to their spectral signature. In this paper we show that the phase velocity of Type I echoes increases with decreasing altitude owing to thermal feedback effects taking place in the growth process. We also show that Type II echoes can be influenced by atmospheric neutral winds to the point of revealing the presence of Kelvin- Helmholtz billows, as shown by a recently studied example taken from the Gadanki radar in India.

Modulated dust-acoustic wave packets in a plasma with non-isothermal electrons and ions

Nonlinear self-modulation of the dust acoustic waves is studied, in the presence of non-thermal (non-Maxwellian) ion and electron populations. By employing a multiple scale technique, a nonlinear Schrodinger-type equation (NLSE) is derived for the wave amplitude. The influence of non-thermality, in addition to obliqueness (between the propagation and modulation directions), on the conditions for modulational instability to occur is discussed. Different types of localized solutions (envelope excitations) which may possibly occur are discussed, and the dependence of their characteristics on physical parameters is traced. The ion deviation from a Maxwellian distribution comes out to be more important than the electron analogous deviation alone. Both yield a de-stabilizing effect on (the amplitude of) DAWs propagating in a dusty plasma with negative dust grains. The opposite effect, namely a tendency towards amplitude stabilization, is found for the case of positively charged dust presence in the plasma.

The stability of obliquely-propagating solitary-wave solutions to a modified Zakharov–Kuznetsov equation

In the context of ion-acoustic waves in a magnetized plasma comprising cold ions and non-isothermal electrons, the present authors have previously shown small amplitude, weakly nonlinear waves to be governed by a modified version of the Zakharov–Kuznetsov equation. In this paper, we consider a plane solitary travelling-wave solution to this equation that propagates at an angle , there is excellent agreement between the analytical and numerical results. The results in this paper agree qualitatively with those of Allen and Rowlands for the Zakharov–Kuznetsov equation.

Modulation of electromagnetic electron cyclotron waves in the presence of nonisothermal electrons in plasmas

Nonlinear interactions between electromagnetic electron cyclotron (EMEC) waves and ion-acoustic perturbations involving nonisothermal electrons and cold inertial ions are considered. Following standard methods, a reduced wave equation for the slowly varying EMEC wave envelope is derived, including nonlinear effects associated with relativistic electron mass variation and electron density changes caused by the EMEC ponderomotive force and trapped electrons in the ion-acoustic perturbations which modulate the EMEC waves. The governing equations are employed to investigate the influence of trapped electrons on the modulational instability and envelope EMEC solitons. It is found that the static magnetic field intensifies the reduction of the growth rate, and makes the conditions for constructing envelope soliton solutions harder.

Higher-order stability analysis of ion-acoustic solitons in a multispecies plasma consisting of non-isothermal electrons

The modified Kadomtsev–Petviashvili (KP) (1970) equation, describing the long-time evolution of weakly nonlinear and weakly dispersive ion-acoustic waves in a multispecies plasma consisting of non-isothermal electrons, admits soliton solutions having a sech4 profile. The higher-order stability analysis of this soliton is made using the method developed by Allen and Rowlands [J. Plasma Phys.50, 413 (1993); 53, 63 (1995)]. Though there is stability at the order is the wave number of a long-wavelength plane-wave perturbation. This instability occurs when the dimensionless width of the soliton exceeds a critical value.

Ion-acoustic solitons in a plasma consisting of positive and negative ions with nonisothermal electrons

In this research paper, the authors study the propagation of ion-acoustic solitons in a plasma consisting of warm positive and negative ions with different concentration of masses, charged states, and nonisothermal electrons. To account for the full nonlinearity of plasma equations, a quasipotential method is used here. The potential so obtained is characterized for solitons as a function of Mach number, positive and negative ions temperature, nonisothermal electrons, different concentration of negative and positive ions over a wide range of parameter space. Corresponding to isothermal case with β=1, coexistence of compressive and rarefactive solitons is obtained. For non-negative β≠1, only compressive solitons are observed. The prediction, that with introduction of negative ions there exists a critical ion concentration below which compressive solitons exist and above which rarefactive solitons exist, is ruled out for nonisothermal electrons.

Nonlinear oscillations in dusty plasmas in the presence of nonisothermal trapped electrons

The recent analysis of the excitation of new dust Bernstein–Greene–Kruskal (DBGK) modes in a noncollisional dusty plasma [Tribeche et al., Phys. Plasmas 7, 4013 (2000)] is extended to include self-consistently the effects of trapped electrons. A kinetic analysis is presented. Highly nonlinear differential equations are obtained and solved numerically leading to some new and original results. The dust density is found to be highly perturbed in the region of the DBGK soliton localization. The dust particles are locally expelled and pushed out of this region, a phenomenon which can generate intense and spiky electric fields in the medium. Furthermore, the results show that under certain conditions double layers (DLs) as well as localized cusped solitons are found to coexist. Such two-level structures are unique to the influence of dust and reflected particles and usually the DLs and the solitons do not coexist in the same parameter regime.

Stability of solitary-wave solutions to a modified Zakharov–Kuznetsov equation

In the context of ion-acoustic waves in a magnetized plasma comprising cold ions and non-isothermal electrons, small-amplitude, weakly nonlinear waves have been shown previously by Munro and Parkes to be governed by a modified version of the Zakharov–Kuznetsov equation. In this paper, we consider solitary travelling-wave solutions to this equation that propagate along the magnetic field. We investigate the initial growth rate γ(k) of a small transverse sinusoidal perturbation of wavenumber k. The instability range is shown to be 0 < k < 3. We use the multiple-scale perturbation method developed by Allen and Rowlands to determine a consistent expansion of γ about k = 0 and k = 3. By combining these results in the form of a Padé approximant, an analytical expression for γ is found that is valid for 0 < k < 3. γ is also determined by using the variational method developed by Bettinson and Rowlands. The two results for γ are compared with a numerical determination.

Third-order contributions to ion-acoustic solitons in a plasma with two types of cold positive ions and two-temperature non-isothermal electrons

Higher-order nonlinear and dispersive effects on ion-acoustic solitons in a plasma consisting of two types of cold positive ions and two-temperature non-isothermal electrons are studied using a reductive perturbation method. An integrated form of the basic sets of fluid equations consisting of two types of positive ions and two types of non-isothermal electrons is derived in terms of a pseudo-potential. A perturbation solution of this equation is obtained by the Bogoliubov–Mitropolsky method. At the lowest order, we obtain a modified Korteweg–de Vries solitary-wave solution, which has a sech4 profile. Calculations are carried out at the next two higher orders. The secularity-removing condition at each order gives a correction to the velocity of the solitary wave at the corresponding order. The variations of Mach number and width of the ion-acoustic soliton with amplitude at each order are shown graphically for plasmas with H+ and He+ or with He+ and Ar+ ions, with two-temperature non-isothermal electrons.

Large-amplitude solitary waves in a relativistic nonisothermal plasma with warm ions

Large amplitude solitary waves in a relativistic plasma with non-isothermal electrons and finite ion temperature are studied using Sagdeev's pseudopotential technique. It is found that there exists a critical value of beta, the ratio of the temperatures of the free and trapped electrons respectively, beyond which soliton solutions cease to exist. This critical value depends on other parameters. Also the relativistic effect and finite ion temperature restrict the region of existence of solitary waves. A small amplitude expansion of the pseudopotential is derived to find different kinds of solitary waves.PACS Nos.: 52.35 Fp, 52.35 Sb, 52.35 Tc

Solitary wave structures in presence of nonisothermal ions in a dusty plasma

The nonlinear properties of solitary wave structures in the presence of non-isothermal ions, electrons, and charged dust grains are reported. The modification in the amplitude and the width of the solitary wave structures due to the inclusion of the effects of reflected ions and charged dust grains are investigated.

Stability of ion-acoustic solitons in a multispecies plasma consisting of non-isothermal electrons

A modified Kadomtsev–Petviashvili equation is derived for ion-acoustic waves in a multispecies plasma consisting of non-isothermal electrons. This equation is used to investigate the stability of modified KdV solitons against long-wavelength plane-wave perturbation using the small-k perturbation expansion method of Rowlands and Infeld. It is found that modified KdV solitons are stable.

Three-dimensional stability of ion-acoustic solitary waves in a magnetized plasma consisting of non-isothermal electrons

A stability analysis is performed for solitary ion-acoustic waves in a magnetized plasma in which the electrons are non-isothermal. Including the effect of ion drift velocity and magnetic perturbation, a three-dimensional mKdV equation is derived for ion-acoustic waves. The solitary-wave solution of this equation is found to have a sech4 profile. A stability analysis of this solitary wave is performed using the small-k perturbation expansion method of Rowlands and Infeld. A condition for the onset of instability is obtained. The growth rate of the instability is found to attain a maximum for perturbations in the plane perpendicular to the direction of propagation of the solitary wave.

The derivation of a modified Kadomtsev–Petviashvili equation and the stability of its solutions

A modified Kadomtsev–Petviashvili (MKP) equation is proposed. The equation is a weakly two-dimensional generalisation of the Schamel equation. It is shown that one form of this equation arises in the context of the propagation of ion-acoustic waves in a plasma with non-isothermal electrons. The stability of certain plane periodic and solitary travelling wave solutions of the MKP equation to two-dimensional long wavelength perturbations is investigated using the method of Rowlands and Infeld. The results obtained are compared with those for the standard KP equation; some qualitative differences are found.

Higher-order contributions to ion-acoustic solitary waves in a multicomponent plasma consisting of warm ions and two-component nonisothermal electrons.

An integrated form of the governing equations in terms of pseudopotential higher-order nonlinear and dispersive effects is obtained by applying the reductive perturbation method for ion-acoustic solitary waves in a collisionless unmagnetized multicomponent plasma having warm ions and two-component nonisothermal electrons. The present method is advantageous because instead of solving an inhomogeneous second-order differential equation at each order, as in the standard procedure, we solve a first-order inhomogeneous equation at each order except at the lowest. The expressions of both Mach number and width of the solitary wave are obtained as a function of the amplitude of the wave for third-order nonlinear and dispersive effects. The variations of potential, width, and Mach number against soliton amplitude are shown graphically, taking into consideration the nonisothermality of two-component electrons in the plasma.

Theory of weak dust acoustic double layers

We present a theoretical model to investigate the existence of small amplitude dust acoustic double layers in a plasma consisting of highly charged mobile dust grains in the background of hot electrons and ions. We show that in the presence of isothermal hot electrons a double layers solution can exist only when dust particles are positively charged. On the other hand, in case of nonisothermal hot electrons double layers can exist only when dust particles are negatively charged. In both cases only a compressive type of double layers solution is found to occur.

A numerical study of the transient behaviors of solitary waves in relativistic plasmas

The authors study the transient behaviors of solitary waves in a relativistic plasma with nonisothermal electrons. In particular, the modified Korteweg-de Vries (K-dV) equation is solved numerically with a Gaussian function as the initial condition. In addition, it is found that the time evolution of solitons from the initial profile is quite similar to that of a K-dV equation with the exception that the soliton speeds are faster. It is also found that the relativistic ions and the nonisothermal electrons tend to have a similar effect on the soliton behavior of the wave, making nonisothermal electrons more noticeable.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonlinear ion-acoustic solitons in a warm plasma with adiabatic positive and negative ions and hot non-isothermal electrons

The propagation of an ion-acoustic soliton in a collisionless plasma with adiabatic positive and negative ions (with equal ion temperature) and hot non-isothermal electrons is studied by use of the renormalization method introduced by Kodama and Taniuti in the reductive perturbation method. The basic set of fluid equations describing the system is reduced to a Korteweg-de Vries (K-dV)-type equation for the first-order perturbed potential and to a linear inhomogeneous differential equation to the second-order of the perturbed potential. A stationary solution of the coupled equations is obtained.