Sagdeev Pseudopotential Technique Research Articles

A Mechanism for Slow Electrostatic Solitary Waves in the Earth’s Plasma Sheet

An analysis of the Magnetospheric Multiscale (MMS) spacecraft data shows the presence of slow electrostatic solitary waves (SESWs) in the Earth’s plasma sheet, which have been interpreted as slow electron holes (SEHs). An alternative mechanism based on slow ion-acoustic solitons is proposed for these SESWs. The SESWs are observed in the region where double humped ion distributions and hot electrons co-exist. Our theoretical model considers the plasma in the SESW region to consist of hot electrons with a vortex distribution, core Maxwellian protons drifting parallel to the magnetic field, B and beam protons drifting anti-parallel to B. Parallel propagating nonlinear ion-acoustic waves are studied using the Sagdeev pseudopotential technique. The analysis yields four types of modes, namely, two slow ion-acoustic (SIA1 and SIA2) solitons and two fast ion-acoustic (FIA1 and FIA2) solitons. All solitons have positive potentials. Except the FIA1 solitons which propagate parallel to B; the other three types propagate anti-parallel to B. Good agreement is found between the amplitudes of electrostatic potential, the electric field, the widths and speed of SIA1 and SIA2 solitons, and the observed properties of SESWs by the MMS spacecraft.

On the dynamics of large-amplitude ion-acoustic waves in a non-Maxwellian plasma with nonthermal electrons and an electron beam

This work investigates the characteristics of nonlinear large-amplitude ion-acoustic waves that occur and propagate in a non-Maxwellian plasma consisting of inertial ions and electrons beam as well as inertialess Cairns-distributed electrons. For this purpose, this inquiry utilizes a two-fluid model with the Sagdeev pseudopotential technique. By utilizing the Sagdeev pseudopotential, a mathematical equation similar to an energy balance equation is derived. The effects of the related physical parameters, including the inertialess electron concentration, the electron beam concentration, and the electron beam velocity, on the existence region of the solitary waves (SWs), and accordingly, the properties of ion-acoustic SWs (IASWs) are examined. Also, the Cairns distribution of electrons can significantly affect the features of large-amplitude IASWs, depending on the parameter that controls the distribution (the inertialess electron nonthermality). Additionally, the distinctive features of the solitary waves and their existence domain in connection with the relevant plasma parameters are also addressed.

A Mechanism for Large-Amplitude Parallel Electrostatic Waves Observed at the Magnetopause

Large-amplitude electrostatic waves propagating parallel to the background magnetic field have been observed at the Earth’s magnetopause by the Magnetospheric Multiscale (MMS) spacecraft. These waves are observed in the region where there is an intermixing of magnetosheath and magnetospheric plasmas. The plasma in the intermixing region is modeled as a five-component plasma consisting of three types of electrons, namely, two counterstreaming hot electron beams and cold electrons, and two types of ions, namely, cold background protons and a hot proton beam. Sagdeev pseudo-potential technique is used to study the parallel propagating nonlinear electrostatic solitary structures. The model predicts four types of modes, namely, slow ion-acoustic mode, fast ion-acoustic mode, slow electron-acoustic mode and fast electron-acoustic modes. Except the fast ion-acoustic mode, all other modes support solitons. Whereas slow ion-acoustic solitons have positive potentials, both slow and fast electron-acoustic solitons have negative potentials. For the case of 4% cold electron density, the slow ion-acoustic solitons have electric field ∼(40–120) mV m−1. The fast Fourier transforms (FFT) of slow ion-acoustic solitons produce broadband frequency spectra having peaks between ∼100 Hz to 1000 Hz. These theoretical predictions are in good agreement with the observations. The slow and fast electron-acoustic solitons could be relevant in explaining the low-intensity high (>1 kHz) frequency waves which are also observed at the same time.

Study of hydromagnetic solitary waves in the Earth's inner magnetosphere via the Adlam-Allen model

Solitary hydromagnetic waves propagating perpendicular to the ambient magnetic field are nonlinear structures that were first analysed by Adlam and Allen in 1958. Although they were first studied for electron-ion plasmas in the controlled thermonuclear reaction experiment, they can also occur in other plasma media. Satellite observations have confirmed that these large-amplitude hydromagnetic waves are ubiquitous in many space plasma environments. In this paper, using Sagdeev pseudopotential technique, we study the properties of large amplitude hydromagnetic waves using the physical model employed by Adlam-Allen. It is confirmed that the waves exist with Mach numbers within the range from 1 to 2. Applications to observations of di-polarization fronts (DFs) in the Earth's inner magnetosphere are discussed.

Arbitrary amplitude ion-acoustic supersolitons in negative ion plasmas with two-temperature superthermal electrons

Arbitrary amplitude ion-acoustic supersolitons are investigated with two-temperature superthermal electrons in an unmagnetized negative ion plasma. In this study, we have considered the plasma containing two cold ion species with different masses, ion concentration and charge multiplicity, and two superthermal (non-Maxwellian) electrons. The energy integral equation has been derived by using the Sagdeev pseudopotential technique. We have investigated that both negative and positive potential supersolitons and solitons can exist in the selected domain of Mach number. A numerical analysis shows that the ion-acoustic supersolitons appear below the acoustic speed (Ms). The amplitude of the supersoliton is found larger than the soliton. The formation of solitons and supersolitons (both polarity) is analyzed by phase portrait of the dynamic of the plasma system. The plasma system also supports the coexistence of compressive and rarefactive solitons for a particular set of plasma parameters. The present study is focused on ion-acoustic solitary and supersolitary waves in the D-and F-regime of Earth's ionosphere and experimentally produced plasmas (Ar+, F−) and (Ar+, SF−6) ion species. The present investigation may be helpful in understanding the nonlinear behavior of supersoliton and soliton in space and laboratory plasmas, where negative ions are present with superthermal electrons at two temperatures.

Large-amplitude electrostatic fluctuations at the Earth’s magnetopause with a vortex-like distribution of hot electrons

Large-amplitude electrostatic solitary waves (ESWs) associated with asymmetric magnetic reconnection at the Earth’s magnetopause are studied in a four-component plasma composed of a mixture of the magnetosheath and magnetosphere plasma of a cold, warm and hot electron populations, and background ions. The species are modeled as adiabatic fluids except for the hot electrons which have a kinetic vortex-like velocity distribution. The hybrid model uses the Sagdeev pseudopotential technique to study the arbitrary amplitude ion- and electron-acoustic solitons and double layers. The numerical computations reveal that for the parameters corresponding to magnetosphere side of the ion diffusion region, only slow electron-acoustic solitons and double layer can exist. On the magnetosheath side of the ion diffusion region, only the electron-acoustic/beam solitons can exist. The electric field amplitude of the electrostatic solitary waves (ESWs) predicted by our model are consistent with the Magnetospheric Multiscale (MMS) observations.

A mechanism for electrostatic solitary waves observed in the reconnection jet region of the Earth’s magnetotail

• An ion-acoustic soliton model for the ESWs in the reconnection jet region. • Observed plasma parameters used as input for the model, there is no free parameter. • Slow and fast ion-acoustic solitons can exist in the reconenction jet plasma. • Good agreement between theoretical predictions and observed properties of ESWs. Electrostatic solitary waves (ESWs) have been observed in the reconnection jet region in the Earth’s magnetotail by the Magnetospheric Multiscale spacecraft (MMS). A mechanism for the reconnection jet ESWs is proposed in terms of slow and fast ion-acoustic solitons. At the time of occurrence of ESWs, no hot plasmasheet ions were observed. Based on the observations, the reconnection jet plasma is modeled by a three-component magnetized plasma consisting of hot electrons and two cold ion beams streaming parallel and anti-parallel to the magnetic field, B respectively. The model is based on the Sagdeev pseudopotential technique, and it predicts four types of ion-acoustic solitons, namely, two fast and two slow ion-acoustic solitons, where one of each type propagates parallel and another anti-parallel to the ambient magnetic field, respectively. The theoretical model predicts bipolar electric fields with amplitudes in the range of ≈ (3–69) mV m −1 , positive potentials with amplitudes of ≈ (51–539) V, and the soliton widths of ≈ (4.5–10.3) Debye lengths. These predictions are in good agreement with the observed characteristics of ESWs in the reconnection jet region.

Arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless magnetized plasma consisting of non-thermal and isothermal electrons

Abstract Using Sagdeev pseudo-potential technique, we have studied the arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless plasma consisting of adiabatic warm ions, non-thermal hot electrons and isothermal cold electrons immersed in an external uniform static magnetic field. We have used the phase portraits of the dynamical system describing the non-linear behaviour of ion acoustic waves to confirm the existence of different solitary structures. We have found that the system supports (a) positive potential solitons, (b) negative potential solitons, (c) coexistence of both positive and negative potential solitons, (d) negative potential double layers, (e) negative potential supersolitons and (f) positive potential supersolitons. Again, we have seen that the amplitude of the positive potential solitons decreases or increases with increasing n ch according to whether 0 < n c h < n c h ( c ) $0{< }{n}_{ch}{< }{n}_{ch}^{\left(c\right)}$ or n c h ( c ) < n c h ≤ 1 ${n}_{ch}^{\left(c\right)}{< }{n}_{ch}\le 1$ , where n c h ${n}_{ch}$ is the ratio of isothermal cold and non-thermal hot electron number densities, and n c h ( c ) ${n}_{ch}^{\left(c\right)}$ is a critical value of n ch . Also, we have seen that the amplitude of the positive potential solitons decreases with increasing β e , where β e is the non-thermal parameter. We have also investigated the transition of different negative potential solitary structures: negative potential soliton (before the formation of negative potential double layer) → negative potential double layer → negative potential supersoliton → negative potential soliton (after the formation of negative potential double layer) by considering the variation of θ only, where θ is angle between the direction of the external uniform static magnetic field and the direction of propagation of the ion acoustic wave.

Propagation of Large-Amplitude Ion-Acoustic Double Layers in Warm Negative Ion Plasmas

Employing the Sagdeev pseudopotential technique, we have investigated ion-acoustic double layers (IADLs) in multicomponent plasma comprising adiabatic ions (positive and negative) with Maxwellian electron distribution. We have numerically calculated the occurrence range of IADLs in negative ion plasmas and studied the influence of various parameters on Mach number ( $M$ ). The existence of large-amplitude IADLs and corresponding phase portrait is investigated analytically. Our system also supports the coexistence of compressive and rarefactive DLs for certain set of parameters. This present model is applied to study the large-amplitude IADLs in the plasmas containing (Xe $^{+}$ , $\text{F}^{-}$ ), (CS $^{+}$ , Cl $^{-}$ ), (Ar $^{+}$ , $\text{F}^{-}$ ), and ( $\text{H}^{+}\,\,\text{H}^{-}$ ) ion species. Our theoretical predications are found to be a good agreement with the experimental observations of large-amplitude IADLs in (Ar $^{+}$ , SF $_{6}^{-}$ ) negative ion plasma. Present investigations may be helpful to understand the DLs in laboratory and space plasma, where negative ions are present with Maxwellian electrons.

A new class of Ion-acoustic solitons that can exist below critical Mach number

It is commonly believed that ion-acoustic solitons can only exist above the critical Mach number in a plasma system. A new class of ion-acoustic solitons that can exist below the critical Mach number is reported for the first time in a three-component plasma consisting of hot Maxwellian electrons, and two counterstreaming ion beams. The analysis is based on the Sagdeev pseudopotential technique, and considers a simple case of two counterstreaming proton beams with equal density and streaming velocity. Linear stability analysis shows that the slow ion-acoustic modes become unstable due to ion beam instability when the beam velocity normalized with the ion acoustic speed, U0, is in the range of 0.55 ≤ U0 ≤ 1.14. It is shown that when the normalized streaming velocity is below or at a threshold value, Uth = 1.14, only the regular solitons having Mach numbers greater than critical Mach number can exist. However, when the streaming velocity exceeds the threshold value (all modes are stable), both regular and the new class of ion-acoustic solitons can exist. A special case of unequal ion densities and unequal streaming velocities of the counterstreaming beams is considered in , and similar effects are found. Hence, the new class of slow ion-acoustic solitons can exist in the parametric regime where the system is stable to counterstreaming ion beams instability. The results could be useful in the interpretation of slow electrostatic solitary waves (ESWs) observed in the magnetosphere.

Combined effect of Kappa and Cairns distributed electrons on ion acoustic solitary structures in a collisionless magnetized dusty plasma

Starting from one dimensional Kappa distribution for electrons, we have systematically developed the combined Kappa-Cairns distribution. We have found the effective bounds of both nonthermal parameters $\kappa $ and $\beta _{e}$ for the combined Kappa-Cairns distribution. This distribution can generate more highly energetic particles in comparison with both Kappa and Cairns distributions. We have investigated ion acoustic solitary structures in a collisionless magnetized plasma composed of negatively charged static dust grains, adiabatic warm ions and a population of highly energetic electrons generated from the combined Kappa-Cairns distribution. Sagdeev pseudo-potential technique has been considered to investigate the arbitrary amplitude steady state solitary structures including double layers and supersolitons. We have developed a computational scheme to draw the existence domains showing the nature of existence of different solitary structures. Different solitary structures of both positive and negative polarities have been observed for different values of $\kappa $ and $\beta _{e}$. We have seen two important transitions of solitary structures for negative polarity, viz., soliton before the formation of double layer → double layer → supersoliton → soliton after the formation of double layer, and soliton before the formation of supersoliton → supersoliton → soliton. For the second case, we have a supersoliton structure without the formation of double layer and this case is completely new one for magnetized plasma. Different solitary structures supported by the system have been investigated with the help of compositional parameter spaces and the phase portraits of the dynamical systems describing different solitary structures.

Effect of Landau damping on ion acoustic solitary waves in a collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons

We have used the Sagdeev pseudo-potential technique to investigate the arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless magnetized plasma consisting of adiabatic warm ions, isothermal cold electrons and nonthermal hot electrons immersed in an external uniform static magnetic field. We have used the phase portraits of the dynamical system describing the nonlinear behaviour of ion acoustic waves to confirm the existence of different solitary structures. We have also investigated the transition of different solitary structures: soliton (before the formation of double layer) $\rightarrow$ double layer $\rightarrow$ supersoliton $\rightarrow$ soliton (soliton after the formation of double layer) by considering the variation of $\theta$ only, where $\theta$ is the angle between the direction of the external uniform static magnetic field and the direction of propagation of the wave.

Folded double layer: a novel nonlinear ion acoustic wave propagating obliquely in a magnetized plasma

A novel nonlinear structure is reported with a ‘near-unipolar’ solution which is obtained analytically by using Sagdeev pseudopotential technique for a three component magnetized plasma. The plasma is consisting of warm fluid ions and two types of electrons having Maxwell Boltzmann distributions. The structure is an amalgamation of the newly discovered super solitary wave and a conventional double layer. Because of the extra ‘wiggle’ or ‘fold’ in the usual monopolar electric field, it is named as ‘Folded Double Layer’. The presence of the extra wiggle, or ‘fold’, in the otherwise monopolar pulse may well modify the particle acceleration processes which remains hitherto unknown, or unnoticed, during the satellite observations.

Effect of nonextensivity on the characteristics of supersolitons in a two‐temperature electron plasma

AbstractIon‐acoustic supersolitons are investigated in an unmagnetized two‐temperature electron plasma comprising cold fluid ions, hot nonextensive electrons, and cool Maxwellian electrons by using the Sagdeev pseudopotential technique. Existence domain of positive polarity supersolitons in terms of Mach number is computed, which is found to exist for Mach numbers beyond the existence of positive double layers. The domain of existence of supersolitons diminishes with the decrease of the nonextensive parameter (q). The amplitude and width of the supersolitons are dependent on the cool‐to‐hot electron temperature ratio (τ), cool electron density (f), and nonextensive parameter (q). The increase of cool electron density increases the amplitude of the supersolitons. For fixed values of f, q, and Mach numbers, the decrease of τ exhibits more distinct wiggles in the electric fields of supersolitons. The present work may be helpful for further study of supersolitons in the auroral plasma.

Gravitoelectrostatic excitations in an opposite polarity complex plasma

The linear and nonlinear properties of gravitoelectrostatic mode, in a plasma system consisting of inertial opposite polarity charged dust grains as well as inertialess nonextensively q-distributed ions and electrons (including the effect of polarization force on the massively charged dust grains), have been investigated. A general dispersion relation has been derived yielding only one eigen wave mode. It is found that the polarization force and the nonextensively distributed ions effects play directly a destabilizing role in Jeans instability. Moreover, a new pair of gravitoelectrostatically coupled energy integral equation has been obtained by applying the Sagdeev pseudopotential technique. Also, a small-amplitude approximation is considered for the self-gravitational potential. It is reported that the fluctuations dynamics of the dust grains evolve self-gravitational rarefactive soliton pulses and electrostatic compressive soliton-like patterns. Applying the phase plane analysis, the phase portraits of the dynamical system have been presented and also the corresponding wave solutions. Our results could be applicable for different space and astrophysical plasma systems, particularly for dust molecular clouds of H-II region.

Dust Ion Acoustic Solitary Structures at the Acoustic Speed in the Presence of Nonthermal Electrons and Isothermal Positrons

The Sagdeev pseudo-potential technique and the analytic theory developed by Das et al. [J. Plasma Phys. 78, 565 (2012)] have been used to investigate the dust ion acoustic solitary structures at the acoustic speed in a collisionless unmagnetized dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions, nonthermal electrons and isothermal positrons. The present system supports both positive and negative potential solitary waves at the acoustic speed, but the system does not support the coexistence of solitary structures of opposite polarity at the acoustic speed. The system also supports negative potential double layer at the acoustic speed, but does not support positive potential double layer. Although the system supports positive potential supersoliton at the supersonic speed, but there does not exist supersoliton of any polarity at the acoustic speed. Solitary structures have been investigated with the help of compositional parameter spaces and the phase portraits of the dynamical system describing the nonlinear behaviour of the dust ion acoustic waves at the acoustic speed. For the case, when there is no positron in the system, there exist negative potential double layer and negative potential supersoliton at the acoustic speed and for such case, the mechanism of transition of supersoliton to soliton after the formation of double layer at the acoustic speed has been discussed with the help of phase portraits. The differences between the solitary structures at the acoustic speed and the solitary structures at the supersonic speed have been analysed with the help of phase portraits.

Ion acoustic super solitary waves in a magnetized plasma

Ion acoustic super solitary waves have been derived for a three component magnetized plasma consisting of warm fluid ions and two different temperature electrons having Boltzmann distributions by using the Sagdeev pseudopotential technique. The result exhibits similar traits of the recently reported electron acoustic super solitary wave in a magnetized plasma [Kamalam et al., J. Plasma Phys. 84, 905840406 (2018)]. This is the first report of super solitary waves for a low frequency wave in a magnetized plasma. This prediction might be useful to analyze the non-conventional structures in the low altitude auroral regions in the Earth's magnetosphere.

Existence of electron acoustic solitary waves in relativistic limit

The nonlinear relativistic dynamics of electron acoustic waves (EAWs) in collisionless, unmagnetized plasma comprising cold inertial electrons, hot Boltzmann distributed electrons, and stationary ions are studied. The Sagdeev pseudopotential technique is employed to discuss the effect of equilibrium plasma species density and temperature of the hot electrons on the relativistic solitary wave solutions. In exploring the electron acoustic soliton characteristics, we encounter only negative polarity solitons which are found to exist in a restricted range of the physical parameter space of the system. In addition, we extend our analysis to demonstrate the wave breaking phenomena of EAW and estimate the maximum sustainable electric field amplitude of this mode considering the relativistic electron mass variation effect.

Arbitrary amplitude dust–ion acoustic solitary structures in electronegative plasma

In the present study existence domains of large amplitude dust–ion acoustic (DIA) solitary structures are analyzed in an unmagnetized and collisionless, electronegative plasma containing inertial positive and negative ions, inertialess superthermal electrons with two different temperatures and negatively charged stationary dust. Using the Sagdeev pseudopotential technique, the energy-balance equation has been derived and the critical values (lower and upper limits) of the Mach number are also determined. The effect of different physical parameters has been analyzed for the formation of these nonlinear structures. Also the critical values of different physical parameters have been determined to establish parametric regimes for the existence of positive/negative potential DIA solitary structures.

Electron acoustic super solitary waves in a magnetized plasma

An electron acoustic super solitary wave has been derived using the Sagdeev pseudopotential technique for a four component magnetized plasma consisting of the beam and bulk fluid electrons and two ions with Maxwell Boltzmann distributions. This is the first theoretical report of a super solitary wave in a magnetized plasma which has no direct association with the singularity of the pseudopotential. It shows a narrow and spiky subwell near the low potential which causes the lateral inversion of the wiggle for the bipolar electric field vis-á-vis the unmagnetized plasma. An analytical formalism was developed to identify these novel kinds of super solitary waves and their transition processes have been characterized. It was observed that the super solitary wave is directly influenced by the singularity of the pseudopotential lying in the vicinity of the solution. The first ever prediction of the electron acoustic super solitary wave raises the possibility of its application to the interpretation of the satellite observations of the electrostatic field data.