Electron Inertia Research Articles

The impact of electron beams on the arbitrary amplitude electron–acoustic solitons in a nonthermal plasma

This study examines the nonlinear dynamics of high-frequency electron–acoustic waves (EAWs) in a collisionless, unmagnetized plasma consisting of several components, including inertial cold electrons, an inertial electron beam, and inertialess Cairns-distributed hot electrons in addition to background stationary ions. We use a nonlinear pseudopotential (Sagadeev potential) method to investigate the possibility of stationary-profile electron–acoustic solitons (EASs). In this study, the nonthermal parameter, the temperature ratio between hot and cold electrons, density ratios, and electron beam parameters are carefully examined to see how they change the features of EASs. As the nonthermality of hot electrons rises, the beam speed decreases, the density ratio of the beam to the cold electron increases, and the existence domain for EASs gets bigger. The current theoretical model shows a link between the wideband noise seen in Geotail satellites and the plasma sheet boundary layer in Earth's magnetosphere.

Effects of electron inertia and finite-Larmor radius correction on Jeans instability of quantum plasma with the impact of cosmic pressure

We present a theoretical investigation of the Jeans instability in quantum plasma, taking into consideration cosmic ray (CR) pressure and diffusion effects using a generalized magneto-hydrodynamic (MHD) model. Our analysis incorporates finite electron inertia, finite electrical resistivity, and finite Larmor radius (FLR) correction. By applying the normal mode technique, we derive a unique form of a generalized dispersion relation that describes the behavior of the system. We further discuss this dispersion relation under different limiting cases. Interestingly, we find that all considered parameters have distinct impacts on the growth rate of the system in various scenarios. Additionally, our exploration reveals that both CR-driven acoustic speed as well as quantum parameter influence the conditions for Jeans instability while the remaining parameters do not have any impact on it. Consequently, when combined with the quantum parameter, electron inertia and FLR correction act as stabilizing agents to suppress instability. This research sheds light on the intricate processes involved in structure formation in the universe, highlighting the significance of considering quantum corrections, electron inertia, and FLR to accurately model the dynamics and stability of cosmic plasma systems.

The magnetised plasma Richtmyer–Meshkov instability: elastic collisions in an ion–electron multifluid plasma

The influence of an applied magnetic field on the collisional plasma Richtmyer–Meshkov instability (RMI) is investigated through numerical simulation. The instability is studied within the five-moment multifluid plasma model without any simplifying assumptions such as infinite speed of light, negligible electron inertia or quasineutrality. The plasma is composed of ion and electron fluids, and elastic collisions are modelled with the Braginskii transport coefficients. A collisional regime is investigated and the magnetic field is applied in the direction of shock propagation, which is perpendicular to the density interface. The primary instability is influenced by several terms affecting the evolution of circulation, the most significant of which are the baroclinic, magnetic field torque and intraspecies collisional terms. The applied magnetic field results in a reduction of interface perturbation growth, agreeing qualitatively with previous numerical simulations for the case of an ideal multifluid plasma RMI. The only major difference in the present case's instability mitigation by applied magnetic field, relative to the ideal case with applied magnetic field, is that the elastic collisions replace and obstruct the secondary vorticity suppression mechanism through collisional dissipation of vorticity. Additionally the collisions, influenced by the combination of self-generated and the applied magnetic field, introduce anisotropy to the problem. The primary suppression mechanism for the RMI is unchanged relative to the ideal case, i.e. the magnetic field torque resisting baroclinic deposition of vorticity in the ion fluid.

Post-disruption reconnection event driven by a runaway current

The role of a runaway current in a post-disruption plasma is investigated through numerical simulations in an asymmetric magnetic reconnection event. We first reproduce the known linear results on the growth rate, the rotation frequency, and the formation of a microlayer smaller than the resistive one as found in Liu et al. [Physics of Plasmas 27, 092507 (2020)] and then focus on the nonlinear regime where are our main findings. We find that while the resistive layer controls the transition of the island from the linear to the nonlinear stage, the microlayer width controls the transition of the runaway current from the linear to the nonlinear phase. This latter transition is accompanied by a redistribution of runaways according to a spiral-like structure within the island. The same structure is also found in the thermal electron distribution when the electron inertia effects into the Ohm's law are taken into account. Finally, nonlinear simulations show that the island rotation frequency tends toward zero when the saturation is reached.

Nonlinear dynamics of small-scale Alfvén waves

We study the nonlinear evolution of very oblique small-scale Alfvén waves with k⊥di≳1. At these scales, the waves become significantly compressive, unlike in magnetohydrodynamics, due to the Hall term in the equations. We demonstrate that when frequencies are small compared to the ion gyrofrequency and amplitudes are small compared to unity, no new nonlinear interaction appears due to the Hall term alone at the lowest non-trivial order, even when k⊥di∼1. However, at the second non-trivial order, we discover that the Hall physics leads to a slow but resonant nonlinear interaction between co-propagating Alfvén waves, an inherently three-dimensional effect. Including the effects of finite temperature, finite frequency, and electron inertia, the two-fluid Alfvén wave also becomes dispersive once one or more of k⊥ρs, k⊥de, or k∥di becomes significant: for oblique waves at low β as studied here, this can be at a much smaller scale than di. We show that the timescale for one-dimensional steepening of two-fluid Alfvén waves is only significant at these smaller dispersive scales, and also derive an expression for the amplitude of driven harmonics of a primary wave. Importantly, both new effects are absent in gyrokinetics and other commonly used reduced two-fluid models. Our calculations have relevance for the interpretation of laboratory Alfvén wave experiments, as well as shedding light on the physics of turbulence in the solar corona and inner solar wind, where the dominant nonlinear interaction between counter-propagating waves is suppressed, allowing these new effects to become important.

Electron inertia effects in 3D hybrid-kinetic collisionless plasma turbulence

The effects of the electron inertia on the current sheets that are formed out of kinetic turbulence are relevant to understand the importance of coherent structures in turbulence and the nature of turbulence at the dissipation scales. We investigate this problem by carrying out 3D hybrid-kinetic Particle-in-Cell simulations of decaying kinetic turbulence with our CHIEF code. The main distinguishing feature of this code is an implementation of the electron inertia without approximations. Our simulation results show that the electron inertia plays an important role in regulating and limiting the largest values of current density in both real and wavenumber Fourier space, in particular, near and, unexpectedly, even above electron scales. In addition, the electric field associated with the electron inertia dominates most of the strongest current sheets. The electron inertia is thus important to accurately describe the properties of current sheets formed in turbulence at electron scales.

Impact of temperature asymmetry and small fraction of static positive ions on the relaxed states of a relativistic hot pair plasma

Abstract The relaxed state of a magnetized relativistic hot plasma composed of inertial electrons and positrons having different relativistic temperatures and a fraction of static positive ions is studied. From the steady-state solutions of vortex dynamics equations and the relation for current density, a non-force-free triple Beltrami (TB) relaxed state equation is derived. The TB state is characterized by three scale parameters that consequently provide three different self-organized structures. The analysis of the relaxed state shows that for specific values of generalized helicities, the disparity in relativistic temperature and the existence of a small fraction of static positive ions in pair plasma can transform the nature of scale parameters. Moreover, an analytical solution of the TB state for an axisymmetric cylindrical geometry with an internal conductor configuration demonstrates that due to asymmetries of temperature and density of plasma species, diamagnetic structures can transform into paramagnetic ones and vice versa. The present study will improve our understanding of pair plasmas in trap-based plasma confinement experiments and astrophysical environments.

Arbitrary amplitude electron acoustic solitary excitations with Cairns–Tsallis distributed hot electrons and positrons in magnetized space plasmas

A rigorous theoretical study is performed to understand the characteristics of nonlinear electron acoustic (EA) solitary waves propagating in collisionless magnetized plasma system comprising cold inertial electrons, nonthermal–nonextensive hot electrons and positrons and stationary ions. The propagation and evolution of two potential modes (fast and slow) are studied in the linear regime. By employing magnetic hydrodynamic equations and with the aid of travelling wave approximation, the nonlinear wave dynamics is demonstrated by the first integral of motion in the form of a pseudo-energy balance equation. In exploring the EA soliton characteristics, numerical results reveal that only negative polarity EA solitons exist in a restricted range of the physical parametric space of the plasma system. It is revealed that the effects of nonthermal and nonextensive parameters, hot to cold electron density ratio, Mach number and magnetic strength considerably modify the basic properties of solitary waves. The present results may be important in space plasmas as well as laboratory plasmas with non-Maxwellian particle population.

Kinetic simulation of a 50 mTorr capacitively coupled argon discharge over a range of frequencies and comparison to experiments

The effect of driving frequency in the range of 13.56–73 MHz on electron energy distribution and electron heating modes in a 50 mTorr capacitively coupled argon plasma discharge is studied using 1D-3V particle-in-cell simulations. Calculated electron energy probability functions exhibit three distinct “temperatures” for low-, mid-, and high-energy electrons at all the studied driving frequencies. When compared to published experimental data, the calculated probability functions show a reasonable agreement for the energy range resolved in the measurements (about 2–10 eV). Discrepancies due to limitations in experimental energy resolution outside this range lead to differences between computational and experimental values of the electron number density determined from the distribution functions, and the predicted effective electron temperature is within 25% of experimental values. The impedance of the discharge is interpreted in terms of a homogeneous equivalent circuit model, and the driving frequency dependence of the inferred combined sheath thickness is found to obey a known, theoretically derived, power law. The average power transferred from the field to the electrons (electron heating) is computed, and a region of negative heating near the sheath edge, particularly at higher driving frequencies, is identified. Analysis of the electron momentum equation shows that electron inertia, which on temporal averaging would be zero in a linear regime, is responsible for negative values of power deposition near the sheath edge at high driving frequencies due to the highly nonlinear behavior of the discharge.

Magnetospheric Multiscale measurements of turbulent electric fields in earth's magnetosheath: How do plasma conditions influence the balance of terms in generalized Ohm's law?

Turbulence is ubiquitous within space plasmas, where it is associated with numerous nonlinear interactions. Magnetospheric Multiscale (MMS) provides the unique opportunity to decompose the electric field (E) dynamics into contributions from different linear and nonlinear processes via direct measurements of the terms in generalized Ohm's law. Using high-resolution multipoint measurements, we compute the magnetohydrodynamic (EMHD), Hall (EHall), electron pressure (EPe), and electron inertia (Einertia) terms for 60 turbulent magnetosheath intervals, to uncover the varying contributions to the dynamics as a function of scale for different plasma conditions. We identify key spectral characteristics of the Ohm's law terms: the Hall scale, kHall, where EHall becomes dominant over EMHD; the relative amplitude of EPe to EHall, which is constant in the sub-ion range; and the relative scaling of the nonlinear and linear components of EMHD and of EHall, which are independent of scale. We find expressions for the characteristics as a function of plasma conditions. The underlying relationship between turbulent fluctuation amplitudes and ambient plasma conditions is discussed. Depending on the interval, we observe that EMHD and EHall can be dominated by either nonlinear or linear dynamics. We find that EPe is dominated by its linear contributions, with a tendency for electron temperature fluctuations to dominate at small scales. The findings are not consistent with existing linear kinetic Alfvén wave theory for isothermal fluctuations. Our work shows how contributions to turbulent dynamics change in different plasma conditions, which may provide insight into other turbulent plasma environments.

Characteristics of Magnetic Reconnection With a Finite X‐Line Length

AbstractThe characteristics of magnetic reconnection with a finite x‐line length are studied using three‐dimensional (3D) particle‐in‐cell (PIC) simulations. We simulate two cases: anti‐parallel reconnection and guide field reconnection. In both cases, reconnection is triggered by an initial perturbation that is localized in the current direction, and then, an active reconnection region extending around 20 ion inertia length along the current direction is developed. In both cases, the electron inertia term plays an important role in balancing the reconnection electric field near the two edges of the x‐line along the current direction. On the ion drifting side, ions are heated while electron heating is not significant; while on the electron drifting side, electrons are heated while ion heating is weak. In the anti‐parallel case, the out‐of‐plane Hall magnetic field on the ion and electron drifting side of the reconnection region shows reversed polarization, while in the guide field case, the in‐plane Hall electric field shows reversed polarization. These features can be used as identifications for reconnection with a finite x‐line length during observations in the magnetotail, they also provide an estimation of the satellite location in the dawn‐dusk direction of the reconnection region.

Overtaking interaction of electron-acoustic solitons in Saturn’s magnetosphere

The progression of nonlinear electron-acoustic waves (EAWs) in a magnetized and collision-free plasma made up of cold inertial electrons, inertialess superthermal electrons, and stationary background ions with special reference to Saturn’s magnetosphere (SMS) is explored. The method of reductive perturbation (MRP) is employed to obtain the evolution equation (i.e., Zakharov– Kuznetsov equation (ZKE)) that governs the propagation of electron acoustic solitons (EASs). Using the elegant and efficient Hirota bilinear method (HBM), multi-soliton solutions (MSSs) of the ZKE are determined. The impact of the effects of hot-to-cold electron density ratio, magnetic field (MF) strength, and superthermality on single as well as the interaction of EASs is examined. Estimates of the values of the electric field at several radii of SMS (i.e., 12 R s − 17.8 R s, where R s is the radius of Saturn) are presented, which are found in μV/ m to mV/ m range and are in perfect agreement with the data from Cassini radio and plasma wave science wideband receiver. Moreover, the influence of the relevant plasma parameters on the interaction time and spatial extent of the interacting EASs is also explored.

Time-dependent axial fluid model of the Hall thruster discharge and its plume

One-dimensional axial models of a Hall thruster give a good qualitative picture of the main physical phenomena in the discharge with small computational effort. Time-dependent models, in particular, are widely used for the analysis of low-frequency axial oscillations (i.e. the breathing mode). The standard time-dependent three-fluid model found in the literature is here enhanced by extending the physical domain beyond the cathodic surface into the far plume, and improving the modeling of some physical phenomena. A suite of five models is presented in this work with an increasing complexity of added physics; the most complete version accounting for ion and neutral energy evolution equations along with the partial inclusion of electron inertia. The added physics has a non negligible impact on both the dynamics of the breathing mode and the time-averaged response of the plasma. In particular, it is found that the onset of the instability is sensitive to both the level of modeled physics and the operational parameters. In some cases, the strong breathing mode oscillations can result in a weak plasma attachment to the anode, leading to the collapse of the normal anode sheath and to the subsequent failure of the model.

Asymptotic scalings of fluid, incompressible “electron-only” reconnection instabilities: Electron-magnetohydrodynamics tearing modes

We perform a numerical study of the scaling laws of tearing modes in different parameter regimes of incompressible fluid electron magnetohydrodynamics, both in the small and large wavelength limits, as well as for the fastest growing mode that can be destabilized in a large aspect ratio current sheet. We discuss the relevance of these results, also for the interpretation of the “electron-only reconnection regime,” recently identified in spacecraft measures and in numerical simulations of solar wind turbulence. We restrict here to a single parameter study, in which we selectively consider only one non-ideal effect among electron inertia, perpendicular resistivity, and perpendicular electron viscosity, and we also consider the cases in which a proportionality exists between the parallel and the perpendicular dissipative coefficients. While some known theoretical results are thus confirmed, in other regimes and/or wavelength limits, corrections are proposed with respect to some theoretical estimates already available in the literature. In other cases, the scalings are provided for the first time. All numerical results are justified in terms of heuristic arguments based on the measurement of the scaling laws of some new microscopic scales associated with the gradients of the eigenfunctions. The alternative scalings we have found are consistent with this interpretation.

Beltrami fields in partially ionized magnetized dusty plasma

The relaxed state of a magnetized four-component partially ionized dusty (PID) plasma is explored. PID plasma is composed of inertial electrons, positive ions, neutrals, and static negatively charged dust particles. When the neutrals are dragged along with the ions, the steady-state solution of vortex dynamic equations for inertial electron and ion species yields a triple Beltrami relaxed state, which is a linear combination of three single force-free fields and is characterized by three self-organized structures. The impact of plasma parameters such as Beltrami parameters and neutral (degree of ionization) and dust species densities on the nature of the relaxed state is investigated. Furthermore, the role of scale separation and its implication in space plasma are also presented. The present research will aid in elucidating the role of neutral and dust species in space, astrophysical, and laboratory plasmas.

An alternative justification for the stationary assumption made by many reduced models for nonlocal electron heat flow in plasmas

Nonlocal models are widely used for approximating kinetic effects on electron heat flow in fusion-relevant plasmas. Almost universally, such models have no explicit time dependence and are designed to make heat flow predictions based directly on instantaneous profiles of macroscopic plasma parameters. While this is usually justified by the claim that transient effects fade before temperature profiles evolve appreciably, a more rigorous justification of the stationarity assumption in terms of kinetic theory is desirable. In this Letter, such a justification is provided by demonstrating that nonstationary effects related to the time dependence of the isotropic part of the electron distribution function vanish up to third order in Chapman–Enskog theory (irrespective of ion charge state or presence of magnetic fields). However, it is found that the electron inertia term (whose appearance in Ohm's law stems from the time derivative of the anisotropic part of the electron distribution function) does have a small but finite third order effect that is most prominent for plasmas with low average ion charges. This Letter additionally provides a convenient analytic inverse for the isotropic part of the Landau electron–electron collision operator.

Rayleigh–Taylor stability of quantum magnetohydrodynamic plasma with electron inertia and resistivity

Abstract The analytical observation of the simultaneous impacts of electrical resistivity, finite Larmor radius (FLR) correction, and electron inertia on the magnetohydrodynamic Rayleigh–Taylor unstable mode of incompressible rotating quantum plasma is carried out. The perturbation formulations of the problem are derived by applying the QMHD model to obtain the dispersion equation for the stratified quantum hydrodynamic fluid plasma. The dispersion equation is analyzed graphically and numerically for the various cases. It is obtained that the simultaneous impacts of rotation, resistivity, FLR correction, electron inertia, and quantum correction modify the Rayleigh–Taylor (RT) unstable mode of the stratified magnetized fluid plasma. The graphical studies show that the rotational effect destabilizes or stabilizes the Rayleigh–Taylor (RT) instability of the magnetized quantum plasma, with or without the impacts of electrical resistivity and electron inertia. This result may be useful for studying the magnetic reconnection process and its applications, viz., supernova explosions, neutron stars, white dwarfs, etc.

Investigation of stochastic heating and its influence on plasma radial uniformity in biased inductively coupled Ar discharges by hybrid simulation

A bias power is usually applied in inductively coupled plasmas (ICP) to realize the separate control of the plasma density and the ion energy. In this research, a two-dimensional fluid/electron Monte Carlo hybrid model is developed to self-consistently investigate the bias effect on the stochastic heating and on the radial homogeneity in a biased argon ICP operated at low pressure (3 mTorr). The results show that the temporal evolution of the stochastic heating exhibits a plateau and a peak when the sheath collapses at high bias voltages, due to the limited sheath heating and the electron inertia. In addition, the plasma density in the diffusion chamber increases with bias voltage and bias frequency, because of the more pronounced stochastic heating both at the substrate and at the grounded wall. In the main discharge chamber, the plasma density decreases with bias voltage, due to the compression of the bulk plasma region, and this trend becomes less obvious at high bias frequency, because of the enhanced power absorption caused by the stochastic heating. Therefore, it is concluded that by tuning the bias voltage and bias frequency, the plasma radial uniformity could be modulated efficiently, which is very important for improving plasma processing.

The role of electron inertia on jeans instability of radiative quantum plasma with the impact of rotation and resistivity

With the use of the Quantum Magnetohydrodynamic (QMHD) model, we took into account the Jeans instability of rotating magnetized radiative quantum plasma under the impact of finite electron inertia and resistivity. The issue is set up and using the linearization method and normal mode technique, we can get the general dispersion relation, which is then described in terms of various modes of propagation. Within the prescribed boundaries, we also get the Jeans instability criteria. Plotting the curves between the system's growth rate and wave number for the investigation of the stability analysis of the system, which is then thoroughly explained.

Исследование влияния неоднородности плазмы с учётом тормозного и фоторекомбинационного излучений на поглощение альфвеновской волны

We numerically study the nonlinear absorption of a plane Alfven wave incident on a fixed boundary of a dissipative inhomogeneous plasma, which is caused by dissipative factors, including bremsstrahlung and photorecombination radiation. Density inhomogeneities specified using a Gaussian distribution are considered. The study is based on the equations of two-fluid electromagnetic hydrodynamics with full allowance for the inertia of electrons. The proposed implicit difference scheme for calculating plane-parallel flows of a two-fluid plasma made it possible to reveal a number of important absorption patterns. In particular, it is shown that absorption with allowance for bremsstrahlung and photorecombination radiation for an inhomogeneous plasma leads to blocking of the Alfven wave in a dissipative plasma. The dependences of the depth of penetration of the Alfven wave and the maximum temperatures of electrons and ions on the size of the density inhomogeneity are obtained.