Langmuir Solitons Research Articles

Langmuir solitons in plasma with κ-deformed Kaniadakis distributed electrons in the kinetic regime

The dynamics of Langmuir solitons in plasma with κ-deformed Kaniadakis distributed electrons is studied. First, a Zakharov-type equation describing the evolution of the fields of Langmuir and ion-acoustic wave is derived in a kinetic regime. Then, in the one-dimensional case, the Zakharov-type equation is reduced to the well-known nonlinear Schrödinger equation that is applied to investigate the characteristics of modulated Langmuir wave packets. It is shown that there are two types of solitons, one is bright soliton in the subsonic regime and the other is dark soliton in the supersonic regime. It also found that when the amplitudes of both types of solitons are fixed, the width of bright soliton increases, while the width of dark soliton decreases, with increased distribution index κ. The present work may serve as a preliminary investigation into the nonlinearity of the κ-deformed Kaniadakis distributed plasma system.

Dynamical energy effects in subsonic collapsing electrostatic Langmuir soliton

The nonlinear characteristic of subsonic Langmuir collapsing waves and energy has been explored using a mathematical system for plasma fluids. New electrostatic Langmuir structures such as supersolitary, breather dissipative, and supersoliton structures have been obtained via a mathematical robust solver. The obtained structures become important in constrained relation between the nonlinearity, dispersion, and dissipative effects in the model. It was discovered that the type of Langmuir structures controlled the collapsing energy for density turbulence. Breather shock forms in time are used to characterize the collapsing Langmuir dissipative waves. This structure mainly affects the electric field and related densities in the subsonic case. Finally, the results explored here may be applicable to the observation of energy collapsing Langmuir solar wind waves.

The envelope soliton for the nonlinear interaction of Langmuir waves with electron acoustic waves in the Earth's inner magnetosphere

The nonlinear coupling of Langmuir waves with electron-acoustic waves is investigated using the kinetic theory, where the hot electron component is modeled by the kappa distribution with an exponential cutoff at high energy tail, i.e., the cutoff kappa distribution. The one dimensional structure of envelope Langmuir solitons is analyzed by the numerical calculation with parameters typical of the Earth's inner magnetosphere. In the case of hot electrons with a cutoff kappa distribution, envelope Langmuir solitons have larger width and slower speed than that in the case of hot electrons with a Maxwellian distribution. The envelop Langmuir soliton with density depletion obtained in the Earth's inner magnetosphere propagates at a speed lower than the electron-acoustic velocity. At a given amplitude of electrostatic field, the envelope Langmuir soltions have a speed comparable with the ones of electron-acoustic wave solitons, but a wider scale in the case of hot electrons with a cutoff kappa distribution.

Pulsar radio emission mechanism – II. On the origin of relativistic Langmuir solitons in pulsar plasma

ABSTRACT Observations suggest that coherent radio emission from pulsars is excited in a dense pulsar plasma by curvature radiation from charge bunches. Numerous studies propose that these charge bunches are relativistic charge solitons that are solutions of the non-linear Schrödinger equation (NLSE) with a group velocity dispersion (G), cubic non-linearity (q), and non-linear Landau damping (s). The formation of stable solitons crucially depends on the parameters G, q, and s as well as the particle distribution function (DF). In this work, we use realistic pulsar plasma parameters obtained from observational constraints to explore the parameter space of NLSE for two representative DFs of particles’ momenta: Lorentzian (long-tailed) and Gaussian (short-tailed). The choice of DFs critically affects the value of |s/q|, which, in turn, determines whether solitons can form. Numerical simulations show that well-formed solitons are obtained only for small values of |s/q| ≲ 0.1, while for moderate and higher values of |s/q| ≳ 0.5 soliton formation is suppressed. Small values for |s/q| ∼ 0.1 are readily obtained for long-tailed DF for a wide range of plasma temperatures. On the other hand, short-tailed DF provides these values only for some narrow range of plasma parameters. Thus, the presence of a prominent high-energy tail in the particle DF favours soliton formation for a wide range of plasma parameters. Besides pair plasma, we also include an iron ion component and find that they make a negligible contribution in either modifying the NLSE coefficients or contributing to charge separation.

Definite integral of a hyperbolic quotient function expressed in terms of the Lerch function

In applied sciences it is always useful to improve the catalogue of definite integrals available in tables. In this paper the authors derived definite integrals used in research concerned with perturbation analysis of single Langmuir solitons, proving the Riemann Hypothesis and the Goldbach conjecture and the LPM effect in sequential bremsstrahlung. We also derived new results and summarized these formulae in a table of integrals.

Detection of Extreme and Exceptional Langmuir Wave Packets in Solar Type III Radio Bursts

AbstractWe report the STEREO observations of two extreme and exceptional Langmuir wave packets, which are the most intense wave packets ever detected in solar type III bursts; their peak intensities Et∼ 215 and ∼ 161 mVm−1 beat out the previous 107 mVm−1 record, reported by Thejappa and MacDowall (2018a; https://doi.org/10.3847/1538-4357/aaca3b). These observations provide new evidence for (1) the four‐wave interaction called the oscillating two‐stream instability (OTSI), which is the coupling of two beam‐excited Langmuir waves with an ion sound wave yielding downshifted and upshifted side bands, and (2) Langmuir solitons formed as a result of OTSI, and (3) density cavities created by their ponderomotive forces. The fast Fourier transform spectra of these wave packets provide what is believed to be the first evidence for harmonics of the electron plasma frequency, fpe up to the order of 5 with peak intensities falling off with increasing harmonic number. The higher order spectral analysis indicates that these harmonics probably correspond to the electromagnetic waves excited as a result of various three‐wave interactions. We argue that although the observed characteristics also indicate that these wave packets could be collapsing wave packets formed as a result of nucleation instability, the observed evidence for OTSI and Langmuir solitons trapped inside the self‐generated density cavities strongly favor the OTSI as the route for the spatial collapse of Langmuir waves in the present case. The implication of these findings for theories of solar type III radio bursts is discussed.

Propagation of isolated waves of coupled nonlinear (2 + 1)-dimensional Maccari System in plasma physics

In this article we have presented the analytical analysis of coupled integrable (2 + 1)-dimensional Maccari System with the aid of newly developed technique named as an extended modified auxiliary equation mapping method. As a result we have found a variety of new families of exact traveling wave solutions including triangular-type solutions, periodic and doubly periodic like solutions, combined soliton like solutions, kink and anti kink type soliton like solutions with the help of three parameters which is the key importance of this method. Maccari System is a well known model to define the dynamics of isolated waves, localized in a very small part of space in different fields of physics such as quantum mechanics, hydrodynamics, plasma physics, quantum field theory to study the dynamics of Langmuir solitons which are appearing in the nonlinear optics. For physical description of our newly obtained solutions we have expressed them graphically using Mathematica 10.4 to explain more efficiently the behavior of different shapes of solutions. Also the computational work and efficiency of the method demonstrates the reliability, straightforwardness, and simplicity of the method for solving other nonlinear complicated partial differential equations.

Characteristics of a Langmuir Soliton Observed in a Solar Type III Burst

We present the high time resolution in situ observations of a Langmuir wave packet obtained by the STEREO WAVES experiment in the source region of a solar type III radio burst. This wave packet is unique in the sense that it occurs as an intense localized one-dimensional magnetic field aligned wave packet with peak intensity well in excess of the threshold for the oscillating two stream instability (OTSI), soliton formation and related strong turbulence processes. Most importantly, the measured half-width of this wave packet is approximately equal to the expected half-width of a Langmuir soliton with the same peak intensity as that of the wave packet. Furthermore, a density cavity is created by the ponder-motive force of this wave packet as expected of a Langmuir soliton. These findings indicate that the observed wave packet is most likely a Langmuir soliton formed as a result of the balance between the non-linearity related self-compression and the dispersion related spreading. We discuss the implication of these observations for theories of solar type III radio bursts.

Diagnostic of Langmuir Solitons in Plasmas Using Hydrogenic Spectral Lines

The development of various spectroscopic diagnostics of relatively weak Langmuir waves in plasmas and their successful implementation have a history of over 50 years. As for spectroscopic diagnostics of Langmuir solitons (i.e., relatively strong Langmuir waves) in plasmas, there have only been very few theoretical papers. The most promising result so far was based on using satellites of the dipole-forbidden spectral lines of He, Li, or He-like and Li-like ions. It was shown that, in the case of Langmuir solitons, the peak intensity of the satellites of the dipole-forbidden lines can be significantly enhanced—by orders of magnitude—compared to the case of non-solitonic Langmuir waves. This distinctive feature of satellites under Langmuir solitons allows them to be distinguished from non-solitonic Langmuir waves. In the present paper, we perform a general study of the effects of Langmuir solitons on arbitrary spectral lines of hydrogen or hydrogen-like ions. Then, using the Ly-beta line as an example, we compare the main features of the profiles for the case of the Langmuir solitons with the case of the non-solitonic Langmuir waves of the same amplitude. We also show how the line profiles depend on the amplitude of the Langmuir solitons and on their separation from each other within the sequence of the solitons.

Electron Heating by Langmuir Soliton on Electrostatic Vlasov–Poisson Simulation

The wave-particle interaction has been studied in the presence of Langmuir solitons with non-Maxwellian distribution function electrons. The numerical simulation is based on the phase space volume conserving splitting scheme by Cheng and Knorr. By employing graphics processing unit computing, the calculation speed has increased. Time evolution of the electron distribution function by providing the initial distribution function with the kappa distribution function has been compared with the nominal case starting with the Maxwellian.

Self-adjustment and disintegration threshold of Langmuir solitons in inhomogeneous plasmas

Dynamics of Langmuir solitons in the presence of a background density gradient is investigated numerically, including cases with steep gradients to the extent the solitons can disintegrate. The disintegration threshold is explained by regarding the electric field part of the soliton as a point mass moving along the self-generated potential well corresponding to the density cavity. On the other hand, it is demonstrated that the Langmuir solitons are robust when the density gradient is below the threshold. During the acceleration phase toward low density regions, Langmuir solitons adjust themselves to balance the electric field pressure and the negative plasma pressure by expelling the imbalanced portion as density cavities at the sound velocity. When the density gradient is below the disintegration threshold, the electric field part of the soliton bounces back and forth within the potential well suggesting the solitons have internal structures.

Latest advances in the semiclassical theory of the Stark broadening of spectral lines in plasmas

Spectral lines continue to be used as an important practical tool for diagnosing various laboratory and astrophysical plasmas. As experiments move to very high electron densities of plasmas or to strongly magnetized plasmas, new physical phenomena have to be taken into account while calculating Stark broadening of hydrogen spectral lines. As for spectral lines having dipole-forbidden components (such as, He-, He-like-, Li-, Li-like-lines), it is shown that they provide the best way for diagnosing Langmuir solitons in plasmas.

New and more exact traveling wave solutions to integrable (2+1)-dimensional Maccari system

In this article, new and general exact traveling wave solutions including soliton-like solutions, triangular-type solutions, single and combined nondegenerate Jacobi elliptic wave function-like solutions, doubly periodic-like solutions are obtained for integrable (2+1)-dimensional Maccari system. This system is frequently introduced to define the motion of the isolated waves, localized in a very small part of space, in many fields such as quantum field theory, hydrodynamics, in plasma physics to describe the behavior of the sonic Langmuir solitons, and also in nonlinear optics. Based on the generalized elliptic equation, an algebraic method is used to construct a series of exact solutions. Being concise and straightforward, the calculations demonstrate the effectiveness and convenience of the method for solving other nonlinear partial differential equations.

On the Nonlinear Plasma Waves in the High-Frequency Wave Heating of the Ionosphere

In the O-mode high-frequency (HF) heating of the ionosphere, parametric instabilities were excited to generate plasma waves. Among those, Langmuir waves and ion acoustic waves were evidenced by the HF enhanced plasma lines and HF enhanced ion lines in the recorded spectra of the ultra high frequency (UHF)/very high frequency (VHF) backscatter radars. These waves can grow to large amplitudes and become nonlinear waves. The nonlinear Schrodinger equation and Korteweg-de Vries equation governing the nonlinear evolution of Langmuir waves and ion acoustic waves are derived and solved. It is shown that the solutions of these equations can be either periodic or solitary depending on the physical conditions. The analyses show the conditions of generating Langmuir soliton and ion acoustic soliton.

OVERVIEW OF IONOSPHERIC MODIFICATION BY HIGH FREQUENCY (HF) HEATERS-THEORY

The scenarios of achieving efiective ionospheric modiflcation are summarized and the likely physical processes engaging linear and nonlinear mode conversions through plasma inhomogeneity and nonlinearity are revealed. Parametric instabilities, which are the directly relevant processes to achieve efiective heating of the ionospheric F region, are formulated and analyzed. The threshold flelds and growth rates of instabilities are obtained. The nonlinear Schrodinger equation governing the nonlinear evolution of Langmuir waves is derived and analyzed. The nonlinear periodic and solitary solutions of the equation are obtained. The analyses illustrate the conditions for the generation of Langmuir soliton and nonlinear periodic Langmuir 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.

Stable Langmuir solitons in plasma with diatomic ions

Abstract. We study stable axially and spherically symmetric spatial solitons in plasma with diatomic ions. The stability of a soliton against collapse is provided by the interaction of induced electric dipole moments of ions with the rapidly oscillating electric field of a plasmoid. We derive the new cubic-quintic nonlinear Schrödinger equation, which governs the soliton dynamics and numerically solve it. Then we discuss the possibility of implementation of such plasmoids in realistic atmospheric plasma. In particular, we suggest that spherically symmetric Langmuir solitons, described in the present work, can be excited at the formation stage of long-lived atmospheric plasma structures. The implication of our model for the interpretation of the results of experiments for the plasmoids generation is discussed.

Kinetic description of the Langmuir solitons in ultra-relativistic electron-positron plasmas

The nonlinear interaction between the high frequency Langmuir wave and the low frequency density fluctuation in ultrarelativistic isothermal electron positron plasmas is investigated from kinetic Vlasov equation. One dimensional Langmuir solitons are obtained, the width of which is so large that it is not relevant to the coherent pulsar radio emission.

Arbitrary amplitude Langmuir solitons in a relativistic electron–positron plasma

AbstractThe arbitrary amplitude Langmuir solitons are investigated in an unmagnetized, warm, relativistic plasma, consisting of electrons and positrons. Both the species are considered to have equal non-relativistic temperatures, but can have arbitrary relativistic drift speeds, and their dynamics are governed by fluid equations. Using the Sagdeev psuedo-potential approach, the effects of drift speed, Mach number, and thermal temperature on the amplitude and width of the Langmuir solitons are investigated. For the parameters considered, only rarefactive solitons are found. These solitons represent dip in electron density or electron holes in the configuration space. Existence domain of the Langmuir solitons is limited by the minimum and maximum Mach numbers for given parameters. An increase in the electron (positron) temperature leads to an increase in the Langmuir soliton amplitude and their half-widths. On the other hand, increasing the electron (positron) drift speeds results in decreasing soliton amplitudes and their half-widths. For some typical parameters corresponding to the pulsar magnetosphere, namely electron density ~106 cm−3 and electron thermal velocity of one-tenth of the velocity of light, the electric field of the Langmuir solitons can be of the order of (3–24)kV/m. The presence of such large amplitude electrostatic solitary structures may accelerate electrons and positrons and also produce fine structures of (1–5) microseconds in pulsar radio emissions.

Langmuir solitons in plasma with κ-distributed electrons in the kinetic regime

Superthermal electrons are often observed in space and astrophysics, and can be appropriately modeled by the family of kappa distribution functions. The Langmuir solitons are studied in the plasma with kappa-distributed electrons based on the Zakharov equation in the kinetic regime. It is shown that the presence of additional superthermal particles does not make qualitative changes to the important aspect of soliton behavior, but modifies the thickness of solitons.