Ion Time Scale Research Articles

Quantitative and qualitative analyses of the mKdV equation and modeling nonlinear waves in plasma

In this paper, nonlinear electrostatic structures on the ion time scale in plasma consisting of two populations of electrons (cold and hot), positrons, and warm adiabatic ions are investigated. The multiple scale method is used to derive the modified Korteweg–de Vries equation (mKdVE). The Jacobi elliptic function expansion method (JEFEM) is employed to find some exact analytical solutions such as periodic, solitonic, and shock solutions. It is shown that the variation in the plasma parameters of interest, for our model, allows the existence of solitary and periodic structures and no shocks. It is also shown that the most important plasma parameters for the plasma model under consideration are positron concentration, α, and the percentage of cold and hot electrons, represented by the parameters μ and ν, respectively. Additionally, the qualitative behavior of the mKdVE is studied using dynamical system theory. The topological structure of the solution is discussed in the phase plane. In this work, the phase plane analysis, which is restricted to the discrete values of the parameter, is extended to the continuous range of the parameter using a bifurcation diagram. Bifurcation diagrams are drawn to forecast the behavior of the solution for specifically chosen essential plasma parameters. The analytical solution and the qualitative behavior of the solution presented in this paper are shown to be compatible with each other. The results presented here are general and can be gainfully employed to study a variety of nonlinear waves in space, laboratory plasmas, and astrophysical plasmas.

Multicomponent Diffusion of Dusty Plasma in PMSE Including the Growth of Dust Particles

AbstractDusty plasma diffusion was applied to model the plasma response to perturbations in dust density, which yields small‐scale irregularities in electron density that are responsible for Polar Mesosphere Summer Echos. Previous diffusion models treated aerosols either as fixed‐charge dust or as multiple‐charge‐state dust using chemical rate equations. The growth of aerosol particles was previously considered in the study of layered structures in mesospheric clouds, but it has not been incorporated into dust diffusion. In this paper, a multicomponent diffusion of a dusty plasma, consisting of electrons, ions, and charged aerosols, is developed, accounting for the growth of the aerosols. It is shown that, for typical parameters in polar mesopause region, the evolution of the density structures of the dusty plasma undergoes an initial charging process (approximately 100 s), then an ambipolar diffusion process on ion time scale (approximately hundreds of seconds), and the aerosol diffusion on dust time scale (>104 s). Furthermore, the growth of the aerosols retards the dust diffusion and causes the transition from anticorrelation to correlation between the electron and ion density perturbations (contrary to only anticorrelation or correlation as in the case without considering the growth). The growth also bends the density profiles from upward shifting to downward sedimentation. In addition, larger initial grain radius and the width of the initial perturbation result in slower diffusion. The diffusion is much faster at 88 km than at 82 km.

Interaction of ion acoustic solitons for Zakharov Kuznetsov equation in relativistically degenerate quantum magnetoplasmas

Nonlinear electrostatic waves on the ion time scale have been studied in a quantum magnetoplasma in the presence of relativistically degenerate electrons. In this regard, Zakharov Kuznetsov (ZK) equation has been derived using the reductive perturbation technique. The single and two soliton solutions of the ZK equation have been obtained by employing Hirota formalism. The nonrelativistic and ultrarelativistic limits of the relativistically degenerate electrons have been studied and discussed in detail for important plasma parameters both for the single and two soliton solutions of the ZK equation. We have applied our study for the plasma parameters that are found in the white dwarfs. It has been noticed that the interaction of the ZK solitons depends on the propagation vectors in the predominant direction of propagation. Importantly, it has been found that the spatial and temporal scales over which the interaction of solitons occur are different for the nonrelativistic and ultrarelativistic cases.

Damped dust‐ion‐acoustic solitons in collisional magnetized nonthermal plasmas

AbstractA multispecies magnetized collisional nonthermal plasma system, containing inertial ion species, noninertial electron species following nonthermal ‐distribution, and immobile dust particles, is considered to examine the characteristics of the dissipative dust‐ion‐acoustic soliton modes, theoretically and parametrically. The electrostatic solitary modes are found to be associated with the low‐frequency dissipative dust‐ion‐acoustic solitary waves (DIASWs). The ion‐neutral collision is taken into account, and the influence of ion‐neutral collisional effects on the dynamics of dissipative DIASWs is investigated. It is reported that most of the plasma medium in space and laboratory are far from thermal equilibrium, and the particles in such plasma system are well fitted via the ‐nonthermal distribution than via the thermal Maxwellian distribution. The reductive perturbation approach is adopted to derive the damped KdV (dKdV) equation, and the solitary wave solution of the dKdV equation is derived via the tangent hyperbolic method to analyse the basic features (amplitude, width, speed, time evolution, etc.) of dissipative DIASWs. The propagation nature and also the basic features of dissipative DIASWs are seen to influence significantly due to the variation of the plasma configuration parameters and also due to the variation of the supethermality index in the considered plasma system. The implication of the results of this study could be useful for better understanding the electrostatic localized disturbances, in the ion length and time scale, in space and experimental dusty plasmas, where the presence of excess energetic electrons and ion‐neutral collisional damping are accountable.

Dispersion and the speed-limited particle-in-cell algorithm

This paper discusses temporally continuous and discrete forms of the speed-limited particle-in-cell (SLPIC) method first treated by Werner et al. [Phys. Plasmas 25, 123512 (2018)]. The dispersion relation for a 1D1V electrostatic plasma whose fast particles are speed-limited is derived and analyzed. By examining the normal modes of this dispersion relation, we show that the imposed speed-limiting substantially reduces the frequency of fast electron plasma oscillations while preserving the correct physics of lower-frequency plasma dynamics (e.g., ion acoustic wave dispersion and damping). We then demonstrate how the time step constraints of conventional electrostatic particle-in-cell methods are relaxed by the speed-limiting approach, thus enabling larger time steps and faster simulations. These results indicate that the SLPIC method is a fast, accurate, and powerful technique for modeling plasmas wherein electron kinetic behavior is nontrivial (such that a fluid/Boltzmann representation for electrons is inadequate) but evolution is on ion timescales.

Influence of secondary electron emission on plasma-surface interactions in the low earth orbit environment

The low earth orbit plasma experienced by exposed interconnect-dielectric junctions commonly found on spacecraft solar panel surfaces was modeled using a fully kinetic particle-in-cell (PIC) simulation of both ambient ions and electrons. From time-accurate simulations we observed that the plasma sheath had a formation time somewhere between the ion and electron time scales of 17 μs and 30 ps, respectively and electron and ion velocity distribution functions were observed to be highly non-Maxwellian. Comparison of the electron plasma sheath thickness with analytic cylindrical sheath models gave reasonable agreement if the embedded biased interconnect voltage was sufficiently high to cause the dielectric surface to act as a free electron flowing medium. Finally, it was found from the fully kinetic PIC simulations that the fundamental mechanism behind parasitic current is closely related to electron avalanche and the fraction of SEE emitted from different avalanche levels as well as the current collected at the interconnect could be modeled by a power law series for avalanche levels greater than two.

Interaction of Gardner solitons in plasmas: applications in the Saturn’s magnetosphere

Multi-soliton solutions of the Gardner equation (GE) have been obtained using the Hirota’s bilinear formalism and, to the best of our knowledge, have been studied in the context of plasmas for the first time. The results have been used to study the electrostatic waves on the ion time scale in a two-electron temperature (TET) kappa distributed plasma in the light of the data obtained from Saturn’s Magnetosphere. The most important result that has come out of the investigation of multi-soliton solution of GE is that both overtaking and head on interactions may occur owing to the simultaneous presence of quadratic and cubic nonlinearities in the GE. The plasma parameters of the system have been found to influence the spatial scale of interaction. The results of kappa distributed plasma have been compared with the Maxwellian case and the key differences with regard to the parametric regimes for the existence of ion acoustic Gardner solitons and the soliton interaction for the two cases have also been explored in detail.

(Invited) Zombie Lithium: Consequences of Remainder Lithium Metal in Lithium Ion Batteries

It is well understood that lithium metal should not exist in lithium ion batteries, but high energy/high rate lithium ion cells did not seem to have gotten this memorandum. Dissection of commercial cells often indicates direct and indirect evidence of metallic lithium present in the battery. This lithium is often called "dead" lithium as it is considered no longer active. In this presentation we motivate the nomenclature zombie lithium because it is, in this construction, truly undead. Lithium metal that is present in lithium ion batteries is never completely isolated from the other activities of the cell, and as the cell ages, without proper understanding, the "dead" lithium can suddenly arise and impact the cell is decidedly negative ways.In this presentation we will review and (try to) understand behavior of zombie lithium generated during the operation of a lithium ion battery and time scale and length scales of its impact across the cell and the system.

Multi-scale dynamics of atmospheric-pressure discharges ignited over liquid electrodes

A multiphase computational model of atmospheric-pressure gas discharges ignited over liquid electrodes is developed. The model takes into account both the liquid electrode motion under applied electric fields and plasma generation in the gas phase. The influence of the applied voltage and liquid properties (density, viscosity, and surface tension) on the liquid surface deformation is analyzed. It is shown that the shape of dynamic cones formed on the liquid surface differs from the static Taylor's cones. The influence of the liquid surface protrusions on gas breakdown dynamics is demonstrated. It is shown that the breakdown develops in two stages: first, a fast ionization wave propagates from the cathode to the anode, and then the cathode sheath collapses due to secondary electron emission from the liquid surface. It is shown that dynamics of the multiphase system containing gas, plasma, and liquid states is characterized by three disparate time scales: the fast electron time scale, the intermediate ion time scale, and the slow liquid dynamics time scale.

Electron Acceleration in a Magnetotail Reconnection Outflow Region Using Magnetospheric MultiScale Data

AbstractWe study Magnetospheric MultiScale observations in the outflow region of magnetotail reconnection. We estimate the power density converted via the three fundamental electron acceleration mechanisms: Fermi, betatron, and parallel electric fields. The dominant mechanism, both on average and the peak values, is Fermi acceleration with a peak power density of about +200 pW/m3. The magnetic field curvature during the most intense Fermi acceleration is comparable to the electron gyroradius, consistent with efficient electron scattering. The peak power densities due to the betatron acceleration are a factor of 3 lower than that for the Fermi acceleration, the average betatron acceleration is close to zero and slightly negative. The contribution from parallel electric fields is significantly smaller than those from the Fermi and betatron acceleration. However, the observational uncertainties in the parallel electric field measurement prevent further conclusions. There is a strong variation in the power density on a characteristic ion time scale.

Study on electron emission by a spherical object: dynamics of trapped particles

In this paper, the dynamics of electrons emitted by a spherical object when the total charge of the system is constant is studied in detail. In particular, the condition for which the total electron charge presents damped oscillations is deduced rigorously by considering a perturbation with respect to the steady-state solution. The results obtained can be of utility in simulating the expansion of a spherical plasma by separating the ion and electron time scales.

Radially ingoing and outgoing dispersive and dissipative structures in electron‐ion plasmas in the presence of electron trapping

In this article, non‐linear propagation of ingoing and outgoing electrostatic waves on the ion time scale in an unmagnetized, non‐relativistic electron‐ion (ei) plasma in the presence of warm ions, ion kinematic viscosity, and trapped Maxwellian electrons was examined in a non‐planar geometry. In the weak non‐linearity limit, modified soliton and shock equations were derived with the inclusion of electron trapping in cylindrical and spherical geometries. The finite difference method was used to solve all these equations in the non‐planar geometries using the planar versions of these equations as an initial input. The results were compared with their counterparts with quadratic non‐linearity and the main differences were expounded. It was shown that the spatio‐temporal scales over which the shocks form for the non‐planar trapped Burgers equation are much shorter by comparison with the shocks admitted by the non‐planar trapped Korteweg de Vries Burgers equation. It was also found that unlike their non‐linear shock counterparts, the solitary structures admitted by the non‐planar trapped Korteweg de Vries equation exhibit a phase shift.

Electrostatic shock structures in magnetorotating relativistic plasmas with non-Maxwellian electrons

Linear and nonlinear properties of electrostatic waves on the ion time scale in a collisional rotating magnetoplasma with warm relativistically streaming ions and non-Maxwellian electrons have been investigated here. In the weak nonlinearity limit, we have derived Zakharov-Kuznetsov-Burgers equation to study the shock wave propagation in dissipative magneto-rotating plasmas with non-Maxwellian electrons. It has been found that ion acoustic shock waves with kappa distributed electrons admit only compressive shock structures, however, the ones with Cairns distributed electrons have been shown to allow for the formation of both compressive and rarefactive structures. This change in behavior has been found to be closely linked with the difference in the shapes of both distribution functions. The dependence of the characteristics of ion acoustic shock structures on rotation, obliqueness, relativistic streaming, kinematic viscosity and non-Maxwellian electrons has also been explored in detail. The relevance of the work with regard to planetary magnetospheres and pulsars has also been pointed out.

Electrons in regions of high phase density exhibit uncanny traits in the study of linear and nonlinear drift waves in spatially non-uniform magnetoplasmas

Linear and nonlinear waves are examined on the ion time scale in a spatially inhomogeneous plasma having electrons that follow product bi (r,q) distribution. It has been shown that the linear dispersion relation for product bi (r,q) distribution undergoes appreciable changes as opposed to the one for the Maxwellian electrons. It has been found that the drift wave frequency is highest for flat-topped distribution, whereas it is lowest for the spiky distribution. It has been found that the drift solitary wave with flat-topped distribution (i.e., r > 0) is one of a kind and exhibits peculiar characteristics. It has been shown that Maxwellian and kappa-like electrons cannot alter the nature of the electrostatic drift waves under consideration; however, the spiky electrons can. The results obtained here are general and can be applied to many regions of space plasmas where the satellite missions have reported the presence of electron distribution functions that show deviation from the Gaussian behavior.

The structure of ion-acoustic waves in a low-frequency three-component electron–ion space plasma with two-electron populations

Low-frequency ion-acoustic waves are analysed on the ion time-scale, in a three-component electron–ion space plasma. The solitary waves propagate in the positive x direction relative to an ambient magnetic field $$\vec {B}_0$$ which forms static background for a configuration consisting of cool fluid ions and both warm and hot Boltzmann-distributed electrons with temperatures $$T_{ic},$$ $$T_{ew}$$ and $$T_{eh},$$ respectively. We derive linear dispersion relation for the waves by introducing first-order density, pressure and velocity perturbations into the ion fluid equations. Additionally, the variation in the nonlinear structure of the waves are investigated by carrying out a full parametric analysis utilising our numerical code. Our results reveal that ion-acoustic waves exhibit well-defined nonlinear spikes at speeds of $$M\ge 2.25$$ and an electric field amplitude of $$E_0=0.85.$$ It is also shown that low wave speeds $$(M\le 2),$$ higher densities of the hot electrons, antiparallel drifting of the cool fluid ions, and increased ion temperatures all lead to significant dispersive effects. The ion-acoustic plasma waves featured in this paper have forms that are consistent with those classified as the type-A and type-B broadband electrostatic noise (BEN) observed in the data obtained from earlier satellite missions.

Modeling heat dominated electric breakdown in air, with adaptivity to electron or ion time scales

We model heat dominated electrical breakdown in air in a short planar gap. We couple the discharge dynamics in fluid approximation with the hydrodynamic motion of the air heated by the discharge. To be computationally efficient, we derive a reduced model on the ion time scale, and we switch between the full model on the electron time scale and the reduced model. We observe an ion pulse reaching the cathode, releasing electrons by secondary emission, and these electrons create another ion pulse. These cycles of ion pulses might lead to electrical breakdown. This breakdown is driven by Ohmic heating, thermal shocks and induced pressure waves, rather than by the streamer mechanism of local field enhancement at the streamer tip.

Bursty emission of whistler waves in association with plasmoid collision

Abstract. A new mechanism to generate whistler waves in the course of collisionless magnetic reconnection is proposed. It is found that intense whistler emissions occur in association with plasmoid collisions. The key processes are strong perpendicular heating of the electrons through a secondary magnetic reconnection during plasmoid collision and the subsequent compression of the ambient magnetic field, leading to whistler instability due to the electron temperature anisotropy. The emissions have a bursty nature, completing in a short time within the ion timescales, as has often been observed in the Earth's magnetosphere. The whistler waves can accelerate the electrons in the parallel direction, contributing to the generation of high-energy electrons. The present study suggests that the bursty emission of whistler waves could be an indicator of plasmoid collisions and the associated particle energization during collisionless magnetic reconnection.

Can the downward current region of the aurora be simulated in the laboratory?

A laboratory plasma device is proposed to simulate the downward current region of the aurora. In this device, a discharge in neon is used as a plasma source to represent the hot plasma of the magnetosphere, and a sodium Q-machine source represents the ionospheric plasma. An electrostatic Vlasov model is used to simulate both the downward current region itself and the proposed laboratory analogue. All important phenomena that appear in the simulation of space are found in the laboratory simulation too: a double layer carries most of the potential difference; double layers are in constant motion in the direction of decreasing magnetic field; electron phase space holes appear on the high potential side of double layers and these holes carry a part of the potential difference during double layer disruptions. The ability to simulate auroral physics in the laboratory is better for the downward than the upward current region, because of the lower levels of ion acoustic-like waves in the laboratory model of the former region. Better laboratory-space agreement is found when the discharge and Q-machine ions are of similar masses. If the masses differ significantly, as they do when using helium together with sodium ions, waves on the ion time scale dominate the plasma on the low potential side of the double layer, and there is a tendency toward multiple double layers appearing simultaneously at different locations. The experiment is suitable for the study of heating processes that occur in the downward current region and to address the behaviour of the current–voltage relationship for low voltages.

One-dimensional particle-in-cell simulations of electrostatic Bernstein waves in plasmas with kappa velocity distributions

Electrostatic Bernstein waves that propagate exactly perpendicularly to a static magnetic field in an electron-ion plasma are investigated using one-and-two-halves dimensional particle-in-cell simulations. An ion-to-electron mass ratio of mi/me = 100 is used, allowing sufficient separation of the electron and ion time scales while still accounting for the ion dynamics without resorting to exceptionally long simulation run times. As a consequence of the mass ratio used, both the high frequency electron Bernstein wave and the lower frequency ion Bernstein wave are resolved within a single simulation run. The simulations presented here use isotropic three-dimensional kappa velocity distributions as well as the widely used Maxwellian velocity distribution, and the results from using each of these velocity distributions are analysed and compared. The behaviour of the Bernstein waves is found to be significantly dependent on the spectral index, κ, of the kappa distribution in all frequency domains of the Bernstein waves. In both the Maxwellian and kappa cases, spectral analysis of the electric field (wave) intensities, as a function of ω and k, show very good agreement between the simulation results and the linear dispersion relation for Bernstein waves. This agreement serves to validate the simulation techniques used, as well as the theory of Bernstein waves in plasmas with a kappa velocity distribution. The intensity of the field fluctuations in the simulations containing an abundance of superthermal particles, i.e., where the plasma has a kappa velocity distribution with a low kappa index, is slightly higher compared to the simulations of plasmas with higher kappa values. The plasmas with low kappa values also exhibit a broader region in frequency space of high intensity field fluctuations.

SEP ACCELERATION IN CME DRIVEN SHOCKS USING A HYBRID CODE

We preform hybrid simulations of super Alfvenic quasi-parallel shock, driven by a Coronal Mass Ejection (CME), propagating in the Outer Coronal or Solar Wind at distances of between 3 to 6 solar radii. The hybrid treatment of the problem enable the study of the shock propagation on the ion time scale, preserving ion kinetics and allowing for a self consistent treatment of the shock propagation and particle acceleration. The CME plasma drags the embedded magnetic field lines stretching from the sun, and propagates out into interplanetary space at a greater velocity than the in-situ solar wind, driving the shock, and producing very energetic particles. Our results show electromagnetic Alfven waves are generated at the shock front. The waves propagate upstream of the shock and are produced by the counter streaming ions of the solar wind plasma being reflected at the shock. A significant fraction of the particles are accelerated in two distinct phases: first, particles drift from the shock and are accelerated in the upstream region and, second, particles arriving at the shock get trapped, and are accelerated at the shock front. A fraction of the particles diffused back to the shock, which is consistent with the Fermi acceleration mechanism.