Two-electron Temperature Plasma Research Articles

Soliton interaction in a two-temperature electron plasma with trapping and superthermality effects

Head-on collision of the two small-amplitude electron-acoustic (EA) solitons is studied in an unmagnetized collisionless plasma in the presence of superthermal (hot) trapped electrons. For this purpose, using a well-known extended Poincare–Lighthill–Kuo (PLK) method, a pair of the trapped Korteweg–de Vries (tKdV) equations is derived to investigate the soliton trajectories and phase shifts. The latter are found dependent on amplitudes of the interacting solitons, effectively altering with hot-electron superthermality and plasma parameters. Typical parameters for the electron diffusion region (EDR) and day-side auroral zone have been selected to examine the impact of hot-electron superthermality, trapping parameter, hot-to-cold electron number density ratio, and cold-to-hot electron temperature ratio on the profiles of potential excitations and phase shifts of interacting solitons. It is found that phase speed of the EA waves becomes altered by varying the κ–parameter, strongly modifying the nonlinearity and dispersive coefficients in a superthermal trapped plasma. However, particle trapping phenomenon does not affect the linear phase speed but introduces a fractional nonlinearity in the tKdV equations of two interacting solitons. The impact of the adiabatic and isothermal pressures is also highlighted to show new modifications in the propagation characteristics of two interacting solitons.

Behavior of ion acoustic solitons in a two-electron temperature plasma of a multi-pole line cusp plasma device (MPD)

This article presents the experimental observations and characterization of ion acoustic solitons (IASs) in a unique multi-pole line cusp plasma device (MPD), in which the magnitude of the pole-cusp magnetic field can be varied. In addition, by varying the magnitude of the pole-cusp magnetic field, the proportion of the two-electron-temperature components in the filament-produced plasmas of the MPD can be varied. The solitons are experimentally characterized by measuring their amplitude-width relation and Mach numbers. The nature of the solitons is further established by making two counter-propagating solitons interact with each other. Later, the effect of the two-temperature electron population on soliton amplitude and width is studied by varying the magnitude of the pole cusp-magnetic field. It has been observed that different proportions of two-electron-temperature significantly influence the propagation of IASs. The amplitude of the solitons has been found to be inversely proportional to the effective electron temperature (Teff).

Study of two-electron temperature plasma sheath using non-extensive electron distribution in presence of an external magnetic field

In this study, the physics of sheath formation in a collisional two-electron temperature plasma in the presence of an oblique external magnetic field has been investigated. At first, a comparative study among the fluid electron model, Boltzmann electron model, and the non-extensive electron model has been carried out and a suitable range of non-extensive parameter q has been predicted. In the latter part, a collisional two-electron temperature plasma is considered. Both the hot and cold electron densities are described using the non-extensive distribution, whereas cold ions are described by the fluid equations. The properties of the sheath are investigated in different collisional regimes by varying the non-extensive parameter (q) and the hot to cold electron densities and temperatures. The magnetic field inclination angle is varied in the limit 1° ≤ α ≤ 5°. It is observed that electron distribution significantly deviates from Boltzmann distribution for nearly parallel magnetic field. Moreover, collision enhanced flux deposition for highly magnetized case is a significant finding of the study. The results obtained in this study can enhance the understanding of plasma–matter interaction processes where multiple electron groups with near parallel magnetic field are found.

Formation and interaction of multi-dimensional electrostatic ion-acoustic solitons in two-electron temperature plasmas

Ion-acoustic waves are investigated in an unmagnetized collisionless plasma comprising dynamical ions and inertialess cold and hot (C–H) electrons expressed by Maxwellian, kappa, and (r, q) distributions. The reductive perturbation theory is applied for deriving a modified Kadomtsev–Petviashvili (mKP) equation to examine the characteristics of ion-acoustic structures (solitary waves, IASWs). The Hirota bilinear formalism is used to investigate the propagation of a single soliton and the interaction of two solitons with special reference to space plasmas. It is found that ratio of number density of cold to hot electrons and non-Maxwellian nature of cold electrons not only affect the propagation characteristics of single mKP solitons but also alter the interaction time of the IASWs. It is found that the swiftness of the interaction of solitons for flat-topped distribution surpasses both kappa and Maxwellian distributions. It is also found that the bipolar and tripolar structures depend on the ratio of the propagation vectors. The ranges of electric field amplitude for the IASWs are calculated for C–H electron distributions corresponding to Saturn's B-ring and the region just beyond terrestrial magnetopause, and are shown to agree with Cassini wideband receiver observational data and wideband plasma wave instrument's waveform data.

Symmetry analysis and conservation laws of the modified Korteweg–de Vries equation with a quartic nonlinear term

In this paper, a modified Korteweg–de Vries equation with a quartic nonlinear term in two-electron temperature plasmas is studied. Firstly, the symmetries are constructed using the generalized symmetry method. In addition, the potential equation is studied, it can been found that this equation does not posses potential symmetries. Meanwhile, the symmetry reduction and group-invariant solutions are derived rely on the one-dimensional optimal system of subalgebras. Finally, conservation laws are showed resort by the multipliers method, three polynomial type conserved quantities are presented, also the Hamiltonian form is obtained. In particular, reciprocal Bäcklund transformations for conservation laws are obtained for the first time.

Experimental study on controlled production of two-electron temperature plasma

A two-electron temperature plasma is produced by the method of diffusion of two different plasmas with distinct temperatures and densities. The method is simple and provides an adequate control over the plasma parameters. The study reveals that the temperature and density of both the electron groups can be effectively controlled by just changing the discharge currents of both the plasmas. An ion-acoustic wave is excited in the plasma and is detected using a planar Langmuir probe. The damped amplitude of the wave is measured and is used as a diagnostic tool for establishing the presence of two-electron components. This production method can be helpful in controlling the hot electron density and temperature in plasma processing industries.

Observations of a mix of cold and warm electrons by RPC-MIP at 67P/Churyumov-Gerasimenko

Context. The Mutual Impedance Probe (MIP) of the Rosetta Plasma Consortium (RPC) onboard the Rosetta orbiter which was in operation for more than two years, between August 2014 and September 2016 to monitor the electron density in the cometary ionosphere of 67P/Churyumov-Gerasimenko. Based on the resonance principle of the plasma eigenmodes, recent models of the mutual impedance experiment have shown that in a two-electron temperature plasma, such an instrument is able to separate the two isotropic electron populations and retrieve their properties. Aims. The goal of this paper is to identify and characterize regions of the cometary ionized environment filled with a mix of cold and warm electron populations, which was observed by Rosetta during the cometary operation phase. Methods. To reach this goal, this study identifies and investigates the in situ mutual impedance spectra dataset of the RPC-MIP instrument that contains the characteristics of a mix of cold and warm electrons, with a special focus on instrumental signatures typical of large cold-to-total electron density ratio (from 60 to 90%), that is, regions strongly dominated by the cold electron component. Results. We show from the observational signatures that the mix of cold and warm cometary electrons strongly depends on the cometary latitude. Indeed, in the southern hemisphere of 67P, where the neutral outgassing activity was higher than in northern hemisphere during post-perihelion, the cold electrons were more abundant, confirming the role of electron-neutral collisions in the cooling of cometary electrons. We also show that the cold electrons are mainly observed outside the nominal electron-neutral collision-dominated region (exobase), where electrons are expected to have cooled down. This which indicates that the cold electrons have been transported outward. Finally, RPC-MIP detected cold electrons far from the perihelion, where the neutral outgassing activity is lower, in regions where no electron exobase was expected to have formed. This suggests that the cometary neutrals provide a more frequent or efficient cooling of the electrons than expected for a radially expanding ionosphere.

Electrostatic Steepening of Whistler Waves.

We present surprising observations by the NASA Van Allen Probes spacecraft of whistler waves with substantial electric field power at harmonics of the whistler wave fundamental frequency. The wave power at harmonics is due to a nonlinearly steepened whistler electrostatic field that becomes possible in the two-temperature electron plasma due to the whistler wave coupling to the electron-acoustic mode. The simulation and analytical estimates show that the steepening takes a few tens of milliseconds. The hydrodynamic energy cascade to higher frequencies facilitates efficient energy transfer from cyclotron resonant electrons, driving the whistler waves, to lower energy electrons.

Formation of solitary waves and oscillatory shocklets in a two-temperature electron κ–distributed plasma

Large-amplitude electron acoustic (EA) waves and shocklets are investigated in a two-temperature electron plasma. For this purpose, dynamical cold electrons are described by the fully nonlinear continuity and momentum equations, while superthermal (hot) inertialess electrons are described by the κ–distribution function with a neutralizing background of static positive ions. The fluid equations along with a quasineutrality equation are solved to obtain a set of two characteristic wave equations that admit analytical and numerical solutions. It is shown that variation due to hot electron superthermality and hot-to-cold electron density ratio strongly affects the profiles of nonlinear EA structures in terms of negative potential, cold electron velocity and density. In particular, at time τ=0, symmetric solitary pulses are formed, which develop into oscillatory shocklets with the course of time. Our results should be useful for understanding solitary excitations and associated nonstationary large-amplitude shocklets in laboratory κ–distributed plasmas, where superthermal (hot) energetic electrons exist.

Modified Korteweg–de Vries solitons at supercritical densities in two-electron temperature plasmas

The supercritical composition of a plasma model with cold positive ions in the presence of a two-temperature electron population is investigated, initially by a reductive perturbation approach, under the combined requirements that there be neither quadratic nor cubic nonlinearities in the evolution equation. This leads to a unique choice for the set of compositional parameters and a modified Korteweg–de Vries equation (mKdV) with a quartic nonlinear term. The conclusions about its one-soliton solution and integrability will also be valid for more complicated plasma compositions. Only three polynomial conservation laws can be obtained. The mKdV equation with quartic nonlinearity is not completely integrable, thus precluding the existence of multi-soliton solutions. Next, the full Sagdeev pseudopotential method has been applied and this allows for a detailed comparison with the reductive perturbation results. This comparison shows that the mKdV solitons have slightly larger amplitudes and widths than those obtained from the more complete Sagdeev solution and that only slightly superacoustic mKdV solitons have acceptable amplitudes and widths, in the light of the full solutions.

Self-similar two-electron temperature plasma expansion into vacuum

AbstractA theoretical model is developed to describe self-similar plasma expansion into vacuum with two different electron temperature distribution functions. The cold electrons are modeled with a Maxwellian distribution while the hot ones are supposed to be non-thermal obeying a kappa distribution function. It is shown that ion density and velocity profiles depend only on cold electron distribution in early stage of expansion whereas ion acceleration is mainly governed by the hot electrons at the ion front and is strongly enhanced with the proportion of kappa distributed electrons. It is also found that when the kappa index is decreasing, the critical value of temperature ratio Teh/Tec, limiting the application of quasi-neutrality, becomes larger than the $5 + \sqrt {24} \approx 9.9$ value obtained in the two-electron Maxwellian Bezzerides model [Bezzerides, B., Forslund, D. W. & Lindman, E. L. (1978). Phys. Fluids21, 2179–2185].

Ion-acoustic solitons in plasma: an application to Saturn’s magnetosphere

Soliton formation in plasma is addressed. Nonlinear acoustic waves in plasma where the combined effects of bounded spherical geometry and the transverse perturbation are dealt with, in two-temperature electron plasma are studied. Using the perturbation method, a spherical Kadomtsev-Petviashvili equation (SKP) that describes the ion acoustic waves is derived. The plasma is modeled by a kappa distribution function for both electrons components as found in Saturn’s magnetosphere. It is found that parameters taken into account have significant effects on the properties of nonlinear waves. The model is applied to Saturn’s magnetosphere, where two temperature superthermal electrons are present. Hence, ion acoustic waves are deduced for three regions, namely, the inner, the intermediate and the outer Saturn’s magnetosphere. We point out, that this work has been motivated by recent observations of Saturn’s magnetosphere.

Freak waves in Saturn’s magnetosphere

Properties of planar as well as nonplanar ion acoustic freak waves that propagate in a plasma composed of warm ions and two-temperature electron plasma having kappa-distribution are reported. The dynamics of the nonlinear freak waves is governed by a modified nonlinear Schrodinger equation. The possible region for the freak waves to exist is defined precisely for typical parameters of Saturn’s magnetosphere. For planar case, stability/instability analyses reveals that there is a critical value (f cr ) of f (i.e., the equilibrium density ratio of the hot-to-cold electron species) exists for low wave number k. For large wave number k, the stability domain is always a decreasing function in f. Low κ values, which indicate that an excess of suprathermal particles in the tail of the distribution, shifts f cr to higher values. Also, there exists a modulation instability period for the cylindrical and spherical envelope excitations, which does not exist in the one-dimensional case. Furthermore, cylindrical and spherical freak waves are investigated numerically. Spherical ion-acoustic freak waves are found to grow faster than the cylindrical waves.

Solitary Langmuir waves in two-electron temperature plasma

Nonlinear interaction of Langmuir and ion-acoustic waves in two-electron temperature plasma is investigated. New integrable wave interaction regime was discovered, this regime corresponds to the Langmuir soliton with three-hump amplitude, propagating with a speed close to the ion–sound speed in the conditions of strong non-isothermality of electronic components. It was discovered that besides the known analytical solution in the form of one- and two-hump waves, there exists a range of solutions in the form of solitary waves, which in the form of envelope has multi-peak structure and differs from the standard profiles described by hyperbolic functions. In case of fixed plasma parameters, different group velocities correspond to the waves with different number of peaks. It is found that the Langmuir wave package contains both even and uneven numbers of oscillations. Low-frequency potential here has uneven number of peaks. Interrelation of obtained and known earlier results are also discussed.

Shielding effect and wakefield pattern of a moving test charge in a non-Maxwellian dusty plasma

By using the Vlasov-Poisson equations, we calculate an expression for the electrostatic potential caused by a test charge in an unmagnetized non-Maxwellian dusty plasma, whose constituents are the superthermal hot-electrons, the mobile cold-electrons with a neutralizing background of cold ions, and charge fluctuating isolated dust grains. The superthermality effects due to hot electrons not only modify the dielectric constant of the electron-acoustic waves but also significantly affect the electrostatic potential. The latter can be decomposed into the Debye-Hückel and oscillatory wake potentials. Analytical and numerical results reveal that the Debye-Hückel and wakefield potentials converge to the Maxwellian case for large values of superthermality parameter. Furthermore, the plasma parameters play a vital role in the formation of shielding and wakefield pattern in a two-electron temperature plasma. The present results should be important for laboratory and space dusty plasmas, where hot-electrons can be assumed to follow the non-Maxwellian distribution function.

Acoustic nonlinear periodic (cnoidal) waves and solitons in pair-ion plasmas

Electrostatic acoustic nonlinear periodic (cnoidal) waves and solitons are investigated in unmagnetized pair-ion plasmas consisting of the same mass ion species with different temperatures. It is found that the temperature difference between negatively and positively charged ions appropriates the dispersion property to linear acoustic waves and this difference has a decisive role in nonlinear dynamics as well. Using a reductive perturbation method and appropriate boundary conditions the Korteweg–de Vries equation is derived. Both cnoidal wave and soliton solutions are discussed in detail. In the special case, it is revealed that the amplitude of a soliton may become larger than what is allowed by the nonlinear stationary wave theory, which is equal to the quantum tunneling by a particle through a potential barrier effect. The serious flaw in the results obtained for ion acoustic nonlinear periodic waves by Yadav et al (1995 Phys. Rev. E 52 3045) in two-electron temperature plasmas and Chawla and Misra (2010 Phys. Plasmas17 102315) in electron–positron–ion plasmas is also pointed out.

Ion acoustic solitons in a plasma with two-temperature kappa-distributed electrons

Existence domains and characteristics of ion acoustic solitons are studied in a two-temperature electron plasma with both electron components being kappa-distributed, as found in Saturn’s magnetosphere. As is the case for double-Boltzmann electrons, solitons of both polarities can exist over restricted ranges of fractional hot electron density ratio for this plasma model. Low κ values, which indicate increased suprathermal particles in the tail of the distribution, yield a smaller domain in the parameter space of hot density fraction and normalized soliton velocity (f, M), over which both soliton polarities are supported for a given plasma composition (the coexistence region). For some density ratios that support coexistence, solitons occur even at the lowest (critical) Mach number (i.e., at the acoustic speed), as found recently for a number of other plasma models. Like Maxwellians, low-κ distributions also support positive potential double layers over a narrow range of low fractional cool electron density (<10%).

Nonplanar Ion Acoustic Solitary Waves in a Two-Electron Temperature Plasma

Linear and non-linear properties of ion acoustic wave (IAW) propagating in a two-electron temperature plasma are investigated from both analytical and numerical perspectives by employing the fluid theory. A one-dimensional modified Korteweg de Vries equation is derived for the IAW using the reductive perturbative technique in a nonplanar geometry. It is observed that the ion acoustic soliton in a two-temperature plasma admits rarefactive (dip like) solitons. In the limit that the cold electron population goes to zero, it is observed that the ion acoustic soliton yields compressive (hump like) solitons. The variation of the ion acoustic soliton with different plasma parameters is also shown. The present investigation may be beneficial to explain some aspects of ion acoustic rarefactive solitary structures observed in space environments where two-electron temperature plasmas have been observed.

Effects of density gradient and dust concentration on ion acoustic solitons in multicomponent plasmas

The ion acoustic solitons have been investigated in an inhomogeneous two-temperature electron plasma in the presence of immobile dust particles. The modified Korteweg–de Vries equation with an additional term due to density gradients is deduced by employing reductive perturbation technique. It is noticed that the amplitude of the soliton is increased with the decrease in the positively charged dust concentration, while the soliton amplitude is increased with the increase in negatively charged dust concentration in such inhomogeneous plasmas. The equilibrium density profile is taken exponential type and density gradient effects on soliton formation are also studied. The numerical results are shown for illustration.

Sheath structure in front of an electron emitting electrode immersed in a two-electron temperature plasma: a fluid model and numerical solutions of the Poisson equation

A one-dimensional fluid model of sheath formation in front of a large, planar, floating, electron emitting electrode (collector) immersed in a two-electron temperature plasma is presented. For certain values of the parameters the Bohm criterion is triple valued. Three methods to select the correct Bohm velocity are compared. The simplest is to find the parameters, where the floating potentials that correspond to the high and to the low Bohm velocity are equal. But sometimes—when the electron emission is small—such parameters cannot be found. The second method is the ‘maximum positive ion flux criterion’, proposed recently by Fernández Palop et al (2002 J. Appl. Phys. 91 2587), for electronegative plasmas. In this work it is modified for a two-electron temperature plasma with emitted electrons and applied successfully. This method is sometimes—when the electron emission from the collector is increased—not applicable because the positive ion flux as a function of potential has only 1 maximum. The third method is a numerical solution of the Poisson equation. The transition from the low to the high Bohm velocity occurs at the parameters where the numerically found space charge density profile indicates the formation of a double layer in the sheath. These parameters are always identical to the parameters found with the maximum positive ion flux method, when the latter can be applied. The ‘shooting method’ for the correct determination of electric field at the collector is presented. This method reveals the existence of regular and irregular numerical solutions of the Poisson equation. The irregular solutions of the Poisson equation fulfill only one of the two sheath edge conditions and they correspond to the solutions of the fluid model, that are not physically acceptable. The parameters, where the numerical solutions of the Poisson equation become irregular, are identical to those found with the ‘positive square of electric field’ test, which is also presented.