Maxwellian Ions Research Articles

Magnetosonic Waves Excited by Maxwellian Ring Protons in Space Plasma Environment

A comprehensive theoretical model for a homogeneous plasma system of hot, tenuous Maxwellian ring-distributed protons and the cold background of Maxwellian ions and electrons is used to study the resonant instabilities of magnetosonic (MS) waves. The perpendicular velocity integrals associated with the Maxwellian ring distribution have no analytical solution, hence, are solved numerically, while the parallel velocity integrals are solved analytically by invoking series expansion of the plasma dispersion function. For the plasma parameters relevant to Earth’s inner magnetosphere, the theoretical model generates MS waves with frequencies from 5 times the local proton cyclotron frequency to above the lower hybrid frequency for a propagation angle of 89.5°. Hydrogen (H+) band electromagnetic ion cyclotron waves are also excited by the Maxwellian ring protons for the same set of plasma parameters. A detailed analysis reveals that a sufficiently large ring velocity, as well as a smaller perpendicular and parallel thermal velocity, can enhance the MS wave growth. The study also explores the role of background plasma parameters in modulating the waves. The present theoretical model reproduces the harmonics of the MS waves observed by the Van Allen Probes in the Earth’s inner magnetosphere. Further, the model can generate MS waves in other plasma environments, e.g., Mars, where the presence of ring protons has been established by MAVEN in connection with the MS wave observations.

Dust acoustic solitons in a positively charged dust plasma with regularized-κ distributed electrons in the presence of generalized polarization force

The propagation features of dust acoustic waves in a three-component plasma system composed of regularized Kappa distributed electrons, Maxwellian ions, and dust grains carrying positive charges are investigated. The reductive perturbation technique is employed to derive the KdV equation. A generalized expression for the polarization force is derived and the effect of the polarization force is taken into consideration as well. The bifurcation analysis is used, and the solitary wave solution was investigated. The critical value of the superthermal spectral index κ is introduced at which the solitonic structure turns up from rarefactive to compressive. It is found that in the range 0<κ<2.23, a rarefactive structure is obtained while the compressive structure appears for κ>2.23. In addition, it is found that by increasing the value of cutoff parameter α, the polarization strength increases too. All the obtained results are helpful to investigate the characteristics of the nonlinear wave propagating in the mesosphere region.

Effects observed in numerical simulation of high-beta plasma with hot ions in an axisymmetric mirror machine

We present the results of numerical simulation by two-dimensional hybrid particle-in-cell code of high-beta plasma with hot ions in an axisymmetric mirror machine. Two particular effects are discussed: the self-rotating of plasma with Maxwellian ions in regime of diamagnetic confinement and the excitation of axisymmetric magnetosonic waves in a high-beta plasma with sloshing ions.

A comparative study of ion beam and velocity shear driven resonant instability of kinetic Alfvén waves with [formula omitted]-electrons

A comparative analysis is carried out between the ion beam and velocity shear as the possible source of free energy in the generation of kinetic Alfvén waves (KAWs) through a three-component theoretical model. The model consists of Kappa electrons, Maxwellian background ions, and drifting-Maxwellian beam ions as the constituent species. The ion beam and velocity shear-driven resonant instabilities of KAWs are investigated and the results are compared on a one-to-one basis. In the presence of κ-electrons, velocity shear is found to be a more effective source of free energy as compared to ion beam in the generation of KAWs. The threshold value of both energy sources in the excitation of KAWs is found numerically for a fixed set of plasma parameters. The characteristics of KAWs such as real frequency, parallel and perpendicular wavelength range, wave unstable region, growth rate, etc. are examined for both cases and the results are compared with the observed values relevant to Earth’s magnetotail.

Kinetic Alfvén Waves Excited by Multiple Free Energy Sources in the Magnetotail

The generation of kinetic Alfvén waves (KAWs) is investigated through a three-component theoretical model incorporating ion beam and velocity shear as the sources of free energy in a non-Maxwellian κ-distributed plasmas. The model considers Maxwellian distributed background ions, drifting-Maxwellian beam ions, and κ-electrons as its constituent species. It is found that the combination of either positive velocity shear with counter-streaming beam ions or parallel streaming beam ions with negative velocity shear favors the excitation of KAWs. The effect of the κ-parameter on the excitation of KAWs under the combined energy sources is explored. The effect of plasma parameters such as number density, propagation angle, and temperature of plasma species on the real frequency and the growth rate of KAWs are examined. For the plasma parameters pertinent to the magnetotail region of Earth’s magnetosphere, the model is able to produce KAWs in the frequency range of ≈(5–67) mHz, which matches well with the recent ‘Time History of Events and Macroscale Interactions during Substorms (THEMIS)’ observations in the near-Earth magnetotail region.

The attributes of the dust-acoustic solitary and periodic structures in the Saturn's inner magnetosphere

Nonlinear characteristics of dust-acoustic (DA) structures including the localized and periodic waves in a plasma having Maxwellian ions and superthermal two-temperature electrons are investigated. The wave equations, including both Kadomtsev–Petviashvili (KP) and modified KP (mKP) equations, are derived using the reductive perturbation technique (RPT). The quantitative and qualitative characteristics of both compressive and rarefactive structures are studied. The Jacobi elliptic function expansion method (JEFEM) is employed for the purpose of quantitative analysis, while the qualitative behavior is studied by the dint of the dynamical system approach. The solutions to the mKP equation hold under a critical condition where the quadratic nonlinearity ceases to exist. It is noticed that the KP equation admits only rarefactive solitary waves (SWs), whereas the mKP equation admits both compressive and rarefactive SWs. It is found that the profile (amplitude and width) of both DA solitary and periodic structures are different at different radii of Saturn's inner magnetosphere. The effect of the kappa spectral index is studied, and it is found that when the population of energetic cold electrons is decreased, the solitary structure gets energized. Our study is applied to Saturn's inner magnetosphere where kappa distributed two-temperature electrons and dust grains with negative charge are observed by various satellite missions.

Energy Spectra of 3He, 4He, C, O, and Fe Suprathermal Ions per 1 AU in Particle Flows from Coronal Holes in the 23rd and 24th Solar Cycles

The energy spectra of ions 3He, 4He, C, O and Fe with energies of 0.04–2 MeV/nucleon were studied at 1 AU in solar-wind streams from near-equatorial coronal holes during the decline of solar activity in cycle 23 according to the information of the ULEIS, SWICS, and SWEPAM instruments installed onboard the ACE spacecraft. The results of this work show that suprathermal ions from coronal holes are Maxwellian solar-wind ions accelerated on the Sun and/or in interplanetary space and form a high-energy contribution to solar-wind ions (a suprathermal “tail” in the energy distribution of solar-wind ions). The energy spectra of accelerated “tail” ions have different dependences on energy, which indicates different mechanisms of their acceleration. The relationship between the intensity of suprathermal ions and the speed of the solar wind indicates the effectiveness of the acceleration of Maxwellian solar-wind ions.

Landau damping of ion‐acoustic waves with simultaneous effects of non‐extensivity and non‐thermality in the presence of hybrid Cairns‐Tsallis distributed electrons

AbstractThe dispersion properties and Landau damping rate of ion‐acoustic waves (IAWs) with the hybrid Cairns‐Tsallis distributed (CTD) electrons and Maxwellian ions are investigated using the plasma kinetic model based on Vlasov‐Poisson's equations. For both super‐extensive (q < 1) and sub‐extensive (q > 1) plasmas, the dielectric response function, real frequency, and Landau damping rate of IAWs are derived. By taking the effect of θi, e (ion‐to‐electron temperature ratio) into account, it is found that with the increase of ion temperature, the real frequency and wave dispersion effects increase as well (for both super‐extensive and sub‐extensive cases). Exploring the properties of the Landau damping rate of IAWs with the simultaneous presence of non‐thermal parameter α and non‐extensive parameter q, a comparison of numerical and analytical results is presented. It is found that in different ranges of θe, i (electron‐to‐ion temperature ratio), on decreasing the values of the non‐extensive parameter and increasing values of the non‐thermal parameter, the weak damping rate is observed (vice versa) in super‐extensive or super‐thermal plasma, although the trend of the damping rate in sub‐thermal plasma is similar (as in the case of super‐thermal plasma) but is less weak. It is further revealed that the damping rate of IAWs in thermal plasmas (Maxwellian) is stronger than the damping rate of IAWs in the case of non‐thermal plasmas (CTD). The current study is applicable to provide deep insight and further allow the exploration of electrostatic plasma modes in different space and laboratory plasma environments where the hybrid CTD plasma exists.

Dust charge fluctuation and ion acoustic wave propagation in dusty plasma with q-nonextensive hot and Maxwellian cold electrons

We have employed the self-consistent kinetic theory to study the linear dispersion relation of ion acoustic waves in a four-component plasma consisting of nonextensive hot electrons, Maxwellian cold electrons, positive ions, and dust particles. The dust charging process with the modified ion acoustic wave damping, as well as its unstable mode, has been graphically illustrated. It is found that the dust charging mechanism depends on the density of hot electrons, the degree of nonextensive electron distribution, and the temperature ratio of hot to cold electrons. It is shown that the damping and instability rates of ion acoustic waves due to dust charge fluctuations explicitly depend on the choice of electron distribution and the magnitude of dusty plasma parameters. In addition, we have studied the ion acoustic Landau damping in the absence of dust particles. It is found that the weak damping region broadens, while the strong damping region shrinks and is shifted toward the short wavelength region for the increase in the temperature ratio of hot to cold electrons.

Nonlinear dynamics in the jupiter magnetosphere: implications of dust-acoustic cnoidal mode

Different types of waves and their nature in the Jovian middle magnetosphere are still not clear or specified. For this purpose, a generalized hydrodynamic model for an arbitrary amplitude dust-acoustic waves is built for true Jovian magnetosphere. The plasma system consists of positive dust grains, Maxwellian ions and electrons. An evolution equation containing a Sagdeev potential is derived, and its numerical analysis is presented. Unexpectedly, the given data yielded cnoidal waves only with positive potential. The effect of the external magnetic field, Mach number, and directional cosine parameters are studied and manipulated. We think that the present results are important in realizing the main waves in the Jovian magnetosphere, and the possible correlation to its particles’ stability and pole acoustic waves.

Kinetic Alfvén Waves in Space Plasma Environment with κ-electrons

Abstract A resonant instability of kinetic Alfvén waves (KAWs) driven by ion beam is discussed through a theoretical model encompassing Maxwellian background ions and beam ions and non-Maxwellian κ-electrons. The ion beam velocity alone as a source is able to excite the KAWs up to a significant growth. The non-Maxwellian parameter κ impedes the growth of KAWs by restricting the wave unstable region. The effects of other plasma parameters such as propagation angle, temperature of the plasma species, and ion plasma beta on the excitation of KAWs are also examined. The present model can generate waves with frequencies in the range of ≈6.6–51.2 mHz, which are relevant to explaining the observed ultralow frequency waves at auroral ionospheric altitudes. Theoretical model predictions will also be applicable to other planetary environments where ion beams and non-Maxwellian κ-electrons are present.

An unmagnetized strongly coupled plasma: heavy ion acoustic shock wave excitations

The propagation of heavy ion-acoustic shock waves (HIASWs) are studied in an unmagnetized strongly coupled plasma having inertial positively charged heavy ions (HIs) fluid and inertia-less (α, q)-distributed electrons and Maxwellian light ions (MLIs). To examine such phenomena, the Burgers equation (BE), modified Burgers equation (mBE), and mixed mBE (mmBE) are derived without considering the stretching of viscosity coefficient of HIs via the reductive perturbation technique (RPT). In addition, the appropriate stationary shock wave solutions of the nonlinear equations, particularly, mBE and mmBE is formulated for the first time. With the changes of plasma parameters, the basic features of HIASWs are examined in both of strongly coupled regime (SCR) and weakly coupled regime (WCR). It is described that the basic features (viz., polarity, amplitude, width, etc.) of the HIASWs are remarkably modified, and for that the adiabatic HIs, (α, q)-distributed electrons, MLIs and viscosity coefficient of HIs played an important role. The presented investigation might be beneficial to comprehend and predict the behavior of HIASWs structures in space and astrophysical environments (SAEs) and the future experimental studies in plasma laboratory (PL).

Nonplanar dust acoustic waves in a four-component dusty plasma with double spectral distributed electrons: modulational instability and rogue waves

A theoretical investigation of nonplanar (cylindrical and spherical) amplitude modulation of dust acoustic waves (DAWs) in a four component dusty plasma including positive and negative dusts, Maxwellian ions and double spectral electron distribution (DSED) is carried out. The focusing modified nonlinear Schrödinger equation (MNLSE) is derived using the derivative expansion perturbation technique (DEPT). The limit of DSED to Maxwell distribution is discussed. The effects of the two spectral indices, r and q , on the modulational instability (MI) growth rate are examined and it is deduced that increasing the value of r and q raises the MI growth rate. Additionally, the structure of the first and second-order dust acoustic (DA) rogue waves in the modulational unstable region is analyzed. The influences of both of r and q on the rogue wave amplitude (energy) are investigated. We found that increasing the value of r enhances the rogue wave amplitude while the opposite behavior is found by increasing q values. The findings of the present study are useful to interpret some physical phenomena in various plasma situations that found in space regions, such as Titan (the largest moon) of Saturn, auroral region and asteroid zones, where the effectiveness of non-Maxwellian particles such as DSED is existed.

Polarization force in an opposite polarity dusty plasma with hybrid Cairns–Tsallis distributed electrons

AbstractThe effect of polarization force acting on oppositely charged dust grains in magnetized plasma is analysed for obliquely propagating low frequency electrostatic waves with Maxwellian ions, and non‐Maxwellian electrons following the hybrid Cairns–Tsallis velocity distribution. It is shown that the polarization force acting on positively charged dust grain is different from the one acting on negatively charged dust grain in the presence of hybrid Cairns–Tsallis distributed electrons. A nonlinear equation in the form of Zakharov–Kuznetsov equation is derived via perturbation analysis for the description of electrostatic solitary structures in the limit of weak‐amplitude. A parametric investigation determines the modifications arising in the propagation of dust acoustic soliton due to the presence of polarization force and hybrid Cairns–Tsallis distributed electrons. It is also found that the effect of polarization force is more pronounced for heavier dust grain with high charge number. Finally, there is a lower limit found for the q‐nonextensive parameter, below which modifications in soliton profile cease to exist due to the presence of hybrid Cairns–Tsallis distributed electrons.

TEST PARTICLE SIMULATIONS FOR NON-MAXWELLIAN PLASMA TRANSPORT: DISCRETIZED COLLISIONAL OPERATOR

The plasma observed in modern fusion devices is very often characterized by strongly non Maxwellian distribution function. That is the direct result of inevitable application of plasma heating techniques, such as neutral beam injection (NBI) and ion/electron cyclotron resonance frequency (ICRF/ECRF) heating, which induce the non Maxwellian fast ions. Another cause of transfer from Maxwellian to non Maxwellian is the reconnection of magnetic field lines followed by formation of magnetic resonant structures like magnetic islands and stochastic layers. One of the basic approaches used to simulate fusion plasma is test particle approach based on a solution of the equations of test particle motion. To make this approach more comprehensive one should take care of plasma particle interactions, i.e. Coulomb collisions in non Maxwellian environment. In present paper the expressions for the discretized collision operator of a general Monte Carlo equivalent form in terms of expectation values and standard deviation for an arbitrary non Maxwellian bulk distribution function are derived. The modification of transport coefficients of impurity ions caused by the transition from the background Maxwellian to non Maxwellian plasma is studied by means of this discretized collision operator. On this purpose, the set of monoenergetic neon test impurities is followed in a toroidal plasma consisting of bulk deuterons and electrons. The non Maxwellian distribution of the bulk is obtained by adding a fraction of energetic particles of the same species. It is demonstrated that a change of collision frequencies of impurities takes place in presence of this energetic fraction leading to a change of impurity neoclassical transport regime.

Dust-Ion-Acoustic waves in unmagnetized 4-component plasma

A theoretical study is presented for the propagation of Dust Ion Acoustic Waves in an unmagnetized four-component plasma, consisting of Maxwellian negative ions, cold mobile positive ions, κ-distributed electrons and positively charged dust grains. Based on the characteristics of Sagdeev pseudopotential and phase portraits, three types of nonlinear waves are observed – solitons, double layers and supersolitons. The conditions for the existence of such nonlinear waves are highly sensitive to the plasma parameters. The results obtained in this study may be of wide relevance in the field of space plasma as well as ultrasmall semiconductor devices in the laboratory.

Study of Dust-Acoustic Multisoliton Interactions in Strongly Coupled Dusty Plasmas

The effect of the structure parameter on the compressibility of dust grains and soliton behavior in a dusty plasma system consisting of Maxwellian electrons, ions, and dust grains charged with a negative charge has been studied. In the theoretical study, a reductive perturbation technique was used to derive the Korteweg-de Vries (KdV) equation and employ the Hirota bilinear method to obtain multisoliton solution. It is found that coupling and structure parameters have a clear effect on the compressibility. These changes in the compressibility affected the amplitude and width of interactive solitons, in addition to the phase shifts resulting from the interaction. These results can be used to understand the behavior of solitary waves that occur in various natural and laboratory plasma environments with dust impurity situations.

Soliton turbulence in electronegative plasma due to head-on collision of multi solitons

Abstract Head-on interaction of four dust ion acoustic (DIA) solitons and the statistical properties of the wave field due to head-on interaction of solitons moving in opposite direction is studied in the framework of two Korteweg de Vries (KdV) equations. The extended Poincaré–Lighthill–Kuo (PLK) method is applied to obtain two opposite moving KdV equations from an unmagnetized four component plasma model consisting of Maxwellian negative ions, cold mobile positive ions, κ-distributed electrons and positively charged dust grains. Hirota’s bilinear method is adopted to obtain two-soliton solutions of both the KdV equations and accordingly act of soliton turbulence is presented due to head-on collision of four solitons. The amplitude and shape of the resultant wave profile at the point of strongest interaction are obtained. To see the effect of head-on collision on the statistical properties of wave field the first four moments are computed. It is observed that the head-on collision has no effect on the first integral moment while the second, third and fourth moments increase in the dominant interaction region of four solitons, which is a clean indication of soliton turbulence.

New method for rekindling the explosive waves in Maxwellian space plasmas

Our interest is to study the nonlinear wave phenomena in complex plasma constituents with Maxwellian electrons and ions. The main aim is to use a new method known as the (G′/G) method to exhibit the effects of dust charge fluctuations on the evolution of nonlinear waves. The coherent features of the shock and solitary waves along with the generation of high-energy waves have been amplified through the solution of the Korteweg–de Vries–Burgers equation, and the different natures of the waves were found successfully. Results are discussed graphically with the thoughtful choice of typical plasma parameters from different space plasma environments, exactly those found in cosmic dusty plasmas laden in ionospheric auroral region, radial spokes of Saturn’s rings, planetary nebulae and solar F-corona region. All conclusions are in good accordance with the actual occurrences and could be of interest to further investigations of space. Moreover, the applicability of the present method is hoped to be a great enhancement by its use as ingenious mechanism used to evaluate the soliton dynamics and Burgers shock waves.

A New Approach for Solving the Undamped Helmholtz Oscillator for the Given Arbitrary Initial Conditions and Its Physical Applications

In this paper, a new analytical solution to the undamped Helmholtz oscillator equation in terms of the Weierstrass elliptic function is reported. The solution is given for any arbitrary initial conditions. A comparison between our new solution and the numerical approximate solution using the Range Kutta approach is performed. We think that the methodology employed here may be useful in the study of several nonlinear problems described by a differential equation of the form z ″ = F z in the sense that z = z t . In this context, our solutions are applied to some physical applications such as the signal that can propagate in the LC series circuits. Also, these solutions were used to describe and investigate some oscillations in plasma physics such as oscillations in electronegative plasma with Maxwellian electrons and negative ions.