Superthermal Ions Research Articles

Scattering of Superthermal Ions at Shocks: Dependence on Energy

Diffusive shock acceleration requires the production of backstreaming superthermal ions (injection) as a first step. Such ions can be generated in the process of scattering of ions in the superthermal tail off the shock front. Knowledge of the scattering of high-energy ions is essential for matching conditions of upstream and downstream distributions at the shock transition. Here we analyze the generation of backstreaming ions as a function of their initial energy in a model stationary shock and in a similar rippled shock. Rippling substantially enhances ion reflection and the generation of backstreaming ions for slightly and moderately superthermal energies, and thus is capable of ensuring ion injection into a further diffusive shock acceleration process. For high-energy ions, there is almost no difference in the fraction of backstreaming ions produced and the ion distributions between the planar stationary shock and the rippled shock.

The effect of dust streaming on arbitrary amplitude solitary waves in superthermal polarized space dusty plasma

Abstract The impact of dust streaming and polarization force on dust acoustic solitary waves (DASWs) is examined in a non-magnetized dusty plasma made up of negatively charged dust, superthermal ions, and Maxwellian electrons. In the linear limit, the dispersion relation is derived and numerically analyzed. In order to explore the characteristics of arbitrary amplitude DASWs, a Sagdeev potential technique is used. It is explored how the existence domain and characteristics of the DASWs are affected by the polarization force connected to the superthermality index of ions and dust streaming. The relevance of the present study to space dusty plasma, in particular to Saturn’s F-ring, is highlighted.

Theoretical analysis of low frequency dust cyclotron waves with dust charge variations

The propagation of nonlinear dust cyclotron (DC) cnoidal waves having superthermal distributed electrons and ions in the presence of external magnetic field and adiabatic dust charge variation is investigated. The effect of dust charge variation is profoundly modified due to the presence of the superthermal electrons and ions. The dust charge variation parameter decreases with an increase in the superthermality index of ions. Adopting the reductive perturbation approach, it is shown that the dynamics of the cnoidal structure is modeled by a Korteweg–de Vries equation. It is found that only negative potential DC cnoidal and solitary structures are observed in such a plasma. The results further reveal that the cnoidal structures strongly depend on the degree of superthermality, dust charge variation parameter, temperature and number density of fluid particles, angle of obliqueness, as well as on the magnetic field strength. The numerical results confirm that as the dust charge variation enters the picture, amplitude as well as the width of the cnoidal waves enhances. Furthermore, the analysis is performed through Sagdeev potential, plane phase plot and spatial variation of potential to elucidate various aspects of the cnoidal wave dynamics in the presence of the adiabatic dust charge variation.

On the analytical approximations to the nonplanar damped Kawahara equation: Cnoidal and solitary waves and their energy

In this work, the non-integrable nonplanar (cylindrical and spherical) damped Kawahara equation (ndKE) is solved and analyzed analytically. The ansatz method is implemented for analyzing the ndKE in order to derive some high-accurate and more stable analytical approximations. Based on this method, two-different and general formulas for the analytical approximations are derived. The obtained solutions are applied for studying the distinctive features for both cylindrical and spherical dissipative dressed solitons and cnoidal waves in a complex plasma having superthermal ions. Moreover, the accuracy of the obtained approximations is numerically examined by estimating the global maximum residual error. Also, a general formula for the nonplanar dissipative dressed solitons energy is derived in detail. This formula can recover the energy of the nonplanar dissipative dressed solitons, the planar dressed solitons, the planar damped dressed solitons, and the nonplanar dressed solitons. Both the suggested method and obtained approximations can help a large sector of authors interested in studying the nonlinear and complicated phenomena in various fields of science such as the propagating of nonlinear phenomena in physics of plasmas, nonlinear optics, communications, oceans, and seas.

Effect of dust charge polarization on the propagation characteristics of nonlinear Dust-acoustic solitons and double layers in superthermal un-magnetized complex plasma

The propagation characteristics of solitons and double layers associated with the dust-acoustic waves (DAWs) are studied in superthermal un-magnetized plasma through solitary and double layer solutions of the nonlinear Korteweg–de Vries (KdV) and the modified Korteweg–de Vries (mKdV) equations, respectively. The plasma constituents are superthermal electrons, superthermal ions, and dust particles. The electrons and ions follow the generalized Lorentzian velocity distribution while the dust particles are considered inertial and bear the charge polarization effect. In the small amplitude limit, we found that the phase velocity of the DAWs varies inversely with the polarization force. The effects of the polarization force and superthermality index on the properties of the solitons and double layer structures are also traced in the small but finite amplitude limit. It is found that the strong superthermality and dust charge polarization decrease the soliton’s energy. A study of the phase portrait is also carried out to investigate the propagation features of the solitary waves through parametric dependence of the configured plasma. It is found that for a selected set of configured parameters, the plasma system supports only rarefactive solitons. Furthermore, the amplitude of double layers has been observed to vary inversely with both the superthermality and the polarization force.

Formation of electrostatic solitary and periodic waves in dusty plasmas in the light of Voyager 1 and 2 spacecraft and Freja satellite observations

Motivated by the observations of Voyager 1 and 2 spacecraft and Freja satellite observations in Saturn’s magnetosphere, the formation of dust-acoustic (DA) localized and periodic waves in a complex plasma having superthermal electrons and ions are reported. In this regard, a modified Kadomtsev–Petviashvili (mKP) equation is derived by employing the weak turbulence theory for studying the characteristics of the nonlinear dust-acoustic waves (DAWs) in the model under consideration. The localized and periodic wave solutions to the mKP equation are derived using ansatz method in terms of Jacobi elliptic functions (JEFs). It is reported that the phase velocity of the DAWs in the Saturn’s magnetosphere is lower for kappa distributed ions and electrons by comparison with regions of space plasmas where the electrons and ions follow the Maxwellian distribution. The conditions for the existence of both localized and periodic waves are also presented. Estimates are also given of the spatial scales over which the dust-acoustic solitary/periodic structures form in Saturn’s magnetosphere.

The model of particles modes. I. A paradigm for phase synchronization in tokamak turbulence

Superthermal energetic particles may alter the kinetic and resonant nature of zonal flows by leading to new types of instabilities. Here, we study the effects induced by superthermal energetic ions on trapped-ion modes (TIM) by using a reduced Hamiltonian gyrokinetic model, where both fast scales (cyclotron and bounce or transit motions) are gyro-averaged. In particular, we analyze the enhancement of resonant processes induced by energetic ions associated with nonlinear phase synchronization, in an extended version of the TIM model including circulating ions. Once an energetic particle mode is driven unstable, a rich nonlinear dynamics is observed, which encompasses a frequency chirping associated with a synchronization process driven by TIM and a transition scenario. An equivalence with the classic Kuramoto model—the paradigm describing the synchronization of a system of coupled oscillators—explains much of this phenomenology.

Evolution of cylindrical/spherical shock formation in a dusty plasma with nonadiabatic dust charge variation

Cylindrical/spherical dust acoustic shock waves are studied in an unmagnetized plasma consisting of Maxwellian electrons, superthermal ions under the effect of nonadiabatic dust charge fluctuation. The dissipation is introduced in the system via nonadiabaticity, a new mechanism for the formation of shock waves. Using standard reductive perturbation method, nonplanar equation namely Korteweg–de Vries Burgers (KdVB) equation is derived and solution is obtained using the Weighted residual method. By use of weighted residual method, a progressive wave solution to nonplanar modified KdV Burgers equation is presented. It is shown that dust charge fluctuation produces dissipation which is responsible for shock formation. The solution shows that as one goes towards the axis of the cylinder or center of the sphere, the wave attenuates faster and the effects are shown in some 2D figures. We have studied various parametric influences on such shock structure and also showed how the gradual variations of these parameter affect the generation and structure of the shocks in their respective domain. Our results should be applicable to the formation of nonlinear DIA shock wave structures in regions in which dust grain is embedded in a Kappa distributed plasma, such as Saturn's magnetosphere.

Kinetic Alfvénic cnoidal waves in Saturnian magnetospheric plasmas

The characteristics of kinetic Alfvénic cnoidal waves (KACWs) in Saturn's magnetosphere plasma composed of two temperature superthermal electrons and inertial ions are presented. The Korteweg–de Vries (KdV) equation and its cnoidal wave solution are derived by adopting reductive perturbation technique. Only positive potential kinetic Alfvénic cnoidal and solitary waves are evolved in Saturnian magnetospheric plasma. The influence of superthermality of cold electrons, concentration of hot electrons, plasma beta and angle of propagation of the wave with respect to the magnetic field has been analyzed on the characteristics of KACWs. The findings of this investigation may shed the light on the possible existence of KACWs and acceleration as well as energy transportation in space plasmas especially in Saturn's magnetosphere.

Modulational Instability of Dust Acoustic Waves in an Opposite Polarity Dusty Plasma in the Presence of Generalized Polarization Force with Superthermal Electrons and Ions

Modulational Instability of Dust Acoustic Waves in an Opposite Polarity Dusty Plasma in the Presence of Generalized Polarization Force with Superthermal Electrons and Ions

Kinetic instability of twisted ion-acoustic mode with superthermal species of plasma

The electrostatic twisted ion-acoustic waves with finite orbital angular momentum states and associated kinetic instability are investigated in an electron-ion plasma. The plasma consisting of superthermal electrons and ions is modeled by using a non-gyrotropic Kappa distribution function in which the free energy source for wave excitation is provided by the relative directed motion of streaming electrons with respect to the ions. In the frame work of kinetic theory, the Vlasov-Poisson equations are employed to derive the expressions for dispersion relation and Landau damping rate under paraxial approximation. The results are analyzed for threshold condition of wave dispersion and instability growth rate in the presence of helical electric field structure. The relevance of study to the observed situations is also described.

Propagation of dust-acoustic nonlinear waves in a superthermal collisional magnetized dusty plasma

The nonlinear features of dust-acoustic waves (DAWs) propagating in a multicomponent, collisional, magnetized dusty plasma whose constituents are negative dust grains, superthermal ions, and electrons are investigated. The hydrodynamic fluid equations are reduced to a damped Zakharov–Kuznetsov (DZK) equation, using the reductive perturbation technique. The DZK equation is solved using both the generalized $$(G^{{\prime }}/G)$$ –expansion method and the Painleve analysis method. Each method gives a class of solutions. This indicates that these methods are sufficient to give all possible solutions of the DZK equation. These solutions successfully describe different kinds of nonlinear waves such as explosive, soliton, shocklike, periodical, and cnoidal waves. Additionally, the effects of different plasma parameters such as relative densities and temperatures as well as superthermality parameters of ions and electrons on the behavior of the obtained diverse waves are investigated. The relevance of the present investigation can be used to understand the cosmic dust-laden plasmas.

Adomian decomposition method for modelling the dissipative higher-order rogue waves in a superthermal collisional plasma

A reductive perturbation technique (the derivative expansion technique (DET)) is employed to derive a linear damped nonlinear Schrödinger equation (LDNLSE) for investigating the feature properties of the dissipative modulated nonlinear dust-acoustic wavepacket including rogue waves (RWs) in an electron-ion dusty plasma having superthermal electrons and ions. The modulational instability (MI) of the dissipative envelope structures is investigated and the (un)stable domain of the modulated structures is mapped precisely. The LDNLSE is solved numerically using Adomian decomposition method (ADM) in order to study the impact of the related plasma parameters on the features of the dissipative RWs. The influence of superthermal parameters and the dust-neutral collisional frequency on the profile of the dissipative dust-acoustic RWs is numerically investigated. Moreover, the accuracy of the numerical solutions is examined by estimating the global residual error in the whole space-time domain.

Kinetic modelling of parallel ion transport in the scrape-off layer and divertor of inter-edge localised mode JET high radiative H-mode plasma

KInetic code for Plasma Periphery (KIPP) was used to assess the importance of kinetic effects of parallel ion transport in the scrape-off layer (SOL) and divertor of JET high radiative H-mode inter-edge localised mode plasma conditions with strong nitrogen (N2) injection, leading to partial detachment at divertor targets. Plasma parameter profiles along the magnetic field from one of the EDGE2D-EIRENE simulation cases were used as an input for KIPP runs. The profiles were maintained by particle and power sources. This work is a continuation of the previous study carried out for electrons (Chankin et al 2018 Plasma Phys. Control. Fusion 60 115011).In this modelling KIPP calculated ion distribution functions and ion parallel power fluxes. In the main SOL kinetic effects lead to a reduction of heat (conductive power) fluxes compared to Braginskii fluxes by factors 3−4 (‘heat flux limiting’). In the divertor, on the contrary, a strong ‘heat flux enhancement’, by up to two orders of magnitude above Braginskii’s, was found. Similar to cases for electrons, high ion heat flux enhancement factors, in particular near targets, are attributed to a non-local transport of super-thermal ions originating from positions along field lines with the highest ion temperature, resulting in the appearance of bump-on-tail features on ion heat flux density profiles. Despite ion heat flux enhancement factors at the target being much higher than for electrons, total power fluxes, ion plus electron, were dominated by ion and electron convection and electron conduction, with ion conductive fluxes playing a secondary role. This must be attributed to lower ion (than electron) velocities (factor ∼ reduction), which are not compensated by kinetic effects of lower ion upstream collisionality.

Spatial channeling in toroidal plasmas: overview and new results

Energy and momentum transfer by eigenmodes in tokamaks and stellarators, which arises when eigenmodes are destabilized by superthermal ions in a region that does not coincide with the damping region, is considered. This phenomenon, named spatial channeling (SC), may play an important role in toroidal plasmas. It may affect plasma energy confinement, plasma rotation, heating of the electron and ion components, and features of eigenmodes. The work contains both an overview and new results. In particular, it is found that SC may affect structure of Toroidicity-induced Alfvén Eigenmodes (TAE modes); the analysis is carried out for a low-mode-number TAE. It is concluded that high-frequency modes, with frequencies above and around the ion cyclotron frequency (fast magnetoacoustic modes and Alfvén modes), are more likely to affect plasma energy balance for reasonable values of mode amplitudes than low-frequency Alfvén modes. SC can also have strong influence on sheared rotation for reasonable values of mode amplitudes, and this effect does not depend on mode frequency. The overview is restricted to modes naturally occurring in unstable plasmas.

A study of Chandrasekhar limits in adiabatic degenerate plasmas with superthermal ions

A theoretical investigation has been done to find the impacts of Chandrasekhar limits (ultra-relativistic and non-relativistic) in adiabatic plasmas with the presence of superthermal ions. To do so, a dust-acoustic solitary wave (DASW) equation propagating in adiabatic degenerate plasmas has been derived employing the reductive perturbation method. The effects of the external magnetic field on the wave propagation and its instability have also been scrutinized. However, the plasma parameters, used in this present theoretical analysis, correspond to white dwarfs but it is possible to apply results for neutron stars and other compact objects.

Mechanisms of energetic-particle transport in magnetically confined plasmas

Super-thermal ions and electrons occur in both space and fusion plasmas. Because these energetic particles (EP) have large velocities, EP orbits necessarily deviate substantially from magnetic surfaces. Orbits are described by conserved constants of motion that define topological boundaries for different orbit types. Electric and magnetic field perturbations produced by instabilities can disrupt particle orbits, causing the constants of motion to change. The statistics of the “kicks” associated with these perturbations determines the resulting cross field transport. A unifying theme of this tutorial is the importance of the perturbation’s phase at the particle’s position Θ=k·r−ωt, where k and ω are the wavevector and frequency of the perturbation, r is the EP position, and t is the time. A distinction is made between field perturbations that resonate with an aspect of the orbital motion and those that do not. Resonance occurs when the wave phase returns to its initial value in an integer multiple of an orbital period. Convective transport occurs when resonant particles experience an unvarying wave phase. Alternatively, multiple wave-particle resonances usually decorrelate the phase, resulting in diffusive transport. Large orbits increase the number of important resonances and can cause chaotic orbits even for relatively small amplitude waves. In contrast, in the case of non-resonant perturbations, orbital phase averaging reduces transport. Large field perturbations introduce additional effects, including nonlinear resonances at fractional values of the orbital motion. In summary, large orbits are a blessing and a curse: For non-resonant modes, orbit-averaging reduces transport but, for resonant transport, large orbits facilitate jumps across topological boundaries and enhance the number of important resonances.

Impact of dust kinematic viscosity on the breathers and rogue waves in a complex plasma having kappa distributed particles

In this paper, a numerical examination of propagating nonlinear dissipative dust-acoustic breathers and rogue waves (RWs) in electron depleted dusty plasmas having two superthermal ions of different temperature has been made. An important ingredient in this study is the inclusion of the dissipative effect due to the viscosity of the dust grains in the evolution wave equation. Accordingly, a damped/modified nonlinear Schrödinger equation (DNLSE), i.e. the standard nonlinear Schrödinger equation (NLSE) in addition to the damping term, is obtained using a reductive perturbation (the derivative expansion) method. Without taking into account the effect of dust viscosity, the standard NLSE is also examined, and the effect of relevant physical parameters on the breathers and rogue waves is examined. Moreover, the impact of dust kinetic viscosity on both breather structures and RWs is investigated by solving DNLSE numerically with the Dirichlet boundary conditions. This model may be useful to understand the excitation of dust-acoustic waves in the Earth's magnetotail.

The evolution of rogue wave triplets and super rogue waves in superthermal polarized space dusty plasma

This present investigation has been instigated to examine the impact of polarization force on modulational instability of dust acoustic (DA) waves and transition of rogue wave triplets to super rogue waves in dusty plasma composed of negative dust as fluid, Boltzmannian electrons, and superthermal ions. The presence of superthermal ions has remarkably altered the impact of polarization force. An increment in ion superthermality index restricts the polarization parameter toward smaller values. By adopting the reductive perturbation technique, the nonlinear Schrödinger equation (NLSE) is procured that determines the modulational instability of the dust acoustic waves. It is observed that the effect of polarization force is constricted by the wavenumber domain in the advent of the instability region. The rational solution of NLSE describes the evolution of dust acoustic rogue wave triplets, which further transform into the super rogue waves by means of superposition of triplets. It is remarked that the amalgamation of polarization force and superthermal ions have an explicit impact on the characteristics of different kinds of dust acoustic rogue waves. It is intensified that our present theoretical pronouncements may shed light on the salient features of different kinds of DA rogue waves in laboratory experiments and space/astrophysical regions, especially in Saturn's magnetosphere, planetary rings, and comet tails, etc.

Stability of three-dimensional dust acoustic waves in a strongly coupled dusty plasma including kappa distributed superthermal ions and electrons

A rigorous theoretical investigation of multi-dimensional instability of dust acoustic (DA) solitary waves in strongly coupled dusty plasma (SCDP) composed of superthermal distributed ions and electrons is presented. The dynamics of linear and nonlinear electrostatic excitations are studied. The dispersion properties of linear DA solitary waves are discussed in details. A nonlinear Zakharov-Kuznetsov (ZK) equation adequate for describing DA solitary waves is also derived. At the vicinity of the critical phase velocity, an extended ZK (EZK) equation is derived. The effects of the electrons and ions superthermality, the strongly and weakly coupling cases, and the ion-to-electron temperature ratio are discussed. The growth rate of the produced waves is calculated. It is found that the DA phase velocity decreases as the ion-to-electron temperature ratio increases. The contrary is occurred for strongly coupled system. The instability growth rate increases (decreases) by increasing the ion-to-electron temperature ratio (the superthermal parameters). The present investigation could be helpful in understanding the propagation and the instability of the detected DA solitary waves in laboratory, space and astrophysics mediums where superthermal particles are present.