non-Maxwellian Velocity Distribution Research Articles

Ten-moment fluid model with heat flux closure for gasdynamic flows

The gasdynamic 10-moment equations are revisited, applying a Chapman-Enskog type expansion to achieve the closure for heat flux. The resulting gradient-based closure performs favorably against previously employed closures in regions of shocks when compared to the kinetic results obtained from Direct Simulation Monte Carlo simulations. The 10-moment model can capture finite kinetic effects due to non-Maxwellian velocity distribution functions, as compared to the 5-moment Navier-Stokes equations, and remains hyperbolic-parabolic with real wave speeds under all initial conditions. Self-consistent kinetic boundary conditions are derived without consideration of a distinct Knudsen layer. The model is applied to a number of canonical gasdynamics problems in one and two dimensions such as steady normal and oblique shocks, as well as the Sod shock tube problem.

Non-Maxwellian electron effects on the macroscopic response of a Hall thruster discharge from an axial–radial kinetic model

A 2D axial–radial particle-in-cell (PIC) model of a Hall thruster discharge has been developed to analyze (mainly) the fluid equations satisfied by the azimuthally-averaged slow dynamics of electrons. Their weak collisionality together with a strong interaction with the thruster walls lead to a non-Maxwellian velocity distribution function (VDF). Consequently, the resulting macroscopic response differs from a conventional collisional fluid. First, the gyrotropic (diagonal) part of the pressure tensor is anisotropic. Second, its gyroviscous part, although small, is relevant in the azimuthal momentum balance, where the dominant contributions are orders of magnitude lower than in the axial momentum balance. Third, the heat flux vector does not satisfy simple laws, although convective and conductive behaviors can be identified for the parallel and perpendicular components, respectively. And fourth, the electron wall interaction parameters can differ largely from the classical sheath theory, based on near Maxwellian VDF. Furthermore, these effects behave differently in the near-anode and near-exit regions of the channel. Still, the profiles of basic plasma magnitudes agree well with those of 1D axial fluid models. To facilitate the interpretation of the plasma response, a quasiplanar geometry, a purely-radial magnetic field, and a simple empirical model of cross-field transport were used; but realistic configurations and a more elaborate anomalous diffusion formulation can be incorporated. Computational time was controlled by using an augmented vacuum permittivity and a stationary depletion law for neutrals.

Generation of Subion Scale Magnetic Holes from Electron Shear Flow Instabilities in Plasma Turbulence

Magnetic holes (MHs) are coherent structures associated with strong magnetic field depressions in magnetized plasmas. They are observed in many astrophysical environments at a wide range of scales, but their origin is still under debate. In this work, we investigate the formation of subion scale MHs using a fully kinetic 2D simulation of plasma turbulence initialized with parameters typical of the Earth’s magnetosheath. Our analysis shows that the turbulence is capable of generating subion scale MHs from large scale fluctuations via the following mechanism: first, the nonlinear large scale dynamics spontaneously leads to the development of thin and elongated electron velocity shears; these structures then become unstable to the electron Kelvin–Helmholtz instability and break up into small scale electron vortices; the electric current carried by these vortices locally reduces the magnetic field, inducing the formation of subion scale MHs. The MHs thus produced exhibit features consistent with satellite observations and with previous numerical studies. We finally discuss the kinetic properties of the observed subion scale MHs, showing that they are characterized by complex non-Maxwellian electron velocity distributions exhibiting anisotropic and agyrotropic features.

Recovering non-Maxwellian particle velocity distribution functions from collective Thomson-scattered spectra

Collective optical Thomson scattering (TS) is a diagnostic commonly used to characterize plasma parameters. These parameters are typically extracted by a fitting algorithm that minimizes the difference between a measured scattered spectrum and an analytic spectrum calculated from the velocity distribution function (VDF) of the plasma. However, most existing TS analysis algorithms assume that the VDFs are Maxwellian, and applying an algorithm that makes this assumption does not accurately extract the plasma parameters of a non-Maxwellian plasma due to the effect of non-Maxwellian deviations on the TS spectra. We present new open-source numerical tools for forward modeling analytic spectra from arbitrary VDFs and show that these tools are able to more accurately extract plasma parameters from synthetic TS spectra generated by non-Maxwellian VDFs compared to standard TS algorithms. Estimated posterior probability distributions of fits to synthetic spectra for a variety of example non-Maxwellian VDFs are used to determine uncertainties in the extracted plasma parameters and show that correlations between parameters can significantly affect the accuracy of fits in plasmas with non-Maxwellian VDFs.

Fast dynamics and high effective dimensionality of liquid fluidity

Fluidity, the ability of liquids to flow, is the key property distinguishing liquids from solids. This fluidity is set by the mobile transit atoms moving from one quasi-equilibrium point to the next. The nature of this transit motion is unknown. Here, we show that flow-enabling transits form a dynamically distinct sub-ensemble where atoms move on average faster than the overall system, with a manifestly non-Maxwellian velocity distribution. This is in contrast to solids and gases where no distinction of different ensembles can be made and where the distribution is always Maxwellian. The non-Maxwellian distribution is described by an exponent alpha corresponding to high dimensionality of space. This is generally similar to extra synthetic dimensions in topological quantum matter, albeit higher dimensionality in liquids is not integer but is fractional. The dimensionality is close to 4 at melting and exceeds 4 at high temperature. alpha has a maximum as a function of temperature and pressure in liquid and supercritical states, returning to its Maxwell value in the solid and gas states.

Evidence of non-Maxwellian ion velocity distributions in spherical shock-driven implosions.

The ion velocity distribution functions of thermonuclear plasmas generated by spherical laser direct drive implosions are studied using deuterium-tritium (DT) and deuterium-deuterium (DD) fusion neutron energy spectrum measurements. A hydrodynamic Maxwellian plasma model accurately describes measurements made from lower temperature (<10keV), hydrodynamiclike plasmas, but is insufficient to describe measurements made from higher temperature more kineticlike plasmas. The high temperature measurements are more consistent with Vlasov-Fokker-Planck (VFP) simulation results which predict the presence of a bimodal plasma ion velocity distribution near peak neutron production. These measurements provide direct experimental evidence of non-Maxwellian ion velocity distributions in spherical shock driven implosions and provide useful data for benchmarking kinetic VFP simulations.

Non-field-aligned Proton Beams and Their Roles in the Growth of Fast Magnetosonic/Whistler Waves: Solar Orbiter Observations

The proton beam is an important population of the non-Maxwellian proton velocity distribution in the solar wind, but its role in wave activity remains unclear. In particular, the velocity vector of the proton beam and its influence on wave growth/damping have not been addressed before. Here we explore the origin and the associated particle dynamics of a kinetic wave event in the solar wind by analyzing measurements from Solar Orbiter and comparing them with theoretical predictions from linear Vlasov theory. We identify the waves as outward-propagating circularly polarized fast magnetosonic/whistler (FM/W) waves. The proton’s velocity distribution functions can destabilize FM/W waves. According to linear Vlasov theory, the velocity fluctuations of the core and the beam associated with FM/W waves render the original field-aligned background drift velocity non-field-aligned. This non-field-aligned drift velocity carrying the information of the velocity fluctuations of the core and the beam is responsible for the wave growth/damping. Specifically, for the FM/W waves we analyze, the non-field-aligned fluctuating velocity of the beam population is responsible for the growth of these unstable waves in the presence of a proton beam. In contrast, the core population plays the opposite role, partially suppressing the wave growth. Remarkably, the observed drift velocity vector between the core and the beam is not field aligned during an entire wave period. This result contrasts the traditional expectation that the proton beam is field aligned.

Inertial and anisotropic pressure effects on cross-field electron transport in low-temperature magnetized plasmas

In this paper, a one-dimensional (1D) particle-in-cell Monte Carlo collision (PIC-MCC) model is developed to investigate the effects of anisotropic pressure and inertial terms due to non-Maxwellian velocity distribution functions on cross-field electron transport. The conservation of momentum is evaluated by taking the moments of the first-principles gas-kinetic equation. A steady-state discharge is obtained without any low-frequency ionization oscillations by considering an anomalous electron scattering profile. The results obtained from the 1D PIC-MCC model are compared with fluid models, including the quasi-neutral drift-diffusion (DD), non-neutral DD, and full fluid moment models. The discharge current obtained from the PIC-MCC model is in good agreement with the fluid models. The cross-field electron transport due to the inertial terms, i.e. the gradient of axial and azimuthal drift, is evaluated. Moreover, PIC-MCC simulation results show non-zero, anisotropic, off-diagonal pressure tensor terms due to asymmetric non-Maxwellian electron velocity distribution function, potentially contributing to cross-field electron transport.

Hirota bilinear method and multi-soliton interaction of electrostatic waves driven by cubic nonlinearity in pair-ion–electron plasmas

Multi-soliton interaction of nonlinear ion sound waves in a pair-ion–electron (PIE) plasma having non-Maxwellian electrons including Kappa, Cairns, and generalized two spectral index distribution functions is studied. To this end, a modified Korteweg–de Vries (mKdV) equation is obtained to investigate the ion-acoustic waves in a PIE plasma at a critical plasma composition. The effects of temperature and density ratios and the non-Maxwellian electron velocity distributions on the overtaking interaction of solitons are explored in detail. The results reveal that both hump (positive peak) and dip (negative peak) solitons can propagate for the physical model under consideration. Two and three-soliton interactions are presented, and the novel features of interacting compressive and rarefactive solitons are highlighted. The present investigation may be useful in laboratory plasmas where PIE plasmas have been reported.

Constraints on ion velocity distributions from fusion product spectroscopy

Recent inertial confinement fusion experiments have shown primary fusion spectral moments which are incompatible with a Maxwellian velocity distribution description. These results show that an ion kinetic description of the reacting ions is necessary. We develop a theoretical classification of non-Maxwellian ion velocity distributions using the spectral moments. At the mesoscopic level, a monoenergetic decomposition of the velocity distribution reveals there are constraints on the space of spectral moments accessible by isotropic distributions. General expressions for the directionally dependent spectral moments of anisotropic distributions are derived. At the macroscopic level, a distribution of fluid element velocities modifies the spectral moments in a constrained manner. Experimental observations can be compared to these constraints to identify the character and isotropy of the underlying reactant ion velocity distribution and determine if the plasma is hydrodynamic or kinetic.

The collision frequencies of charged particles in the complex plasmas with the non-Maxwellian velocity distributions

We study the collision frequencies of charged particles in the complex plasmas with the two-parameter and three-parameter non-Maxwellian velocity distributions. The average collision frequencies of electron–ion, electron–electron and ion–ion for the distributions are derived, respectively. We show that the average collision frequencies in the complex plasmas depend strongly on the parameters in the non-Maxwellian distributions and thus are significantly different from those cases in the plasmas with a Maxwell velocity distribution. The significant effects of the non-Maxwell parameters on the average collision frequencies are numerically analyzed. The results have important impacts on the transport coefficients and transport properties of charged particles in the highly or fully ionized complex plasmas.

Excitation of long electrostatic solitary waves in ion beam neutralization process

Unusually long electrostatic solitary waves (ESWs) are discovered in a particle-in-cell simulation study of the process of ion beam neutralization by electron emission from a filament. These ESWs are long because the density perturbation responses to the potential wells created by the ESWs are very small. The density perturbation is small because the trapped (positive) and untrapped (negative) electron density perturbations nearly compensate each other because of a non-Maxwellian electron velocity distribution in the beam.

On the electron sheath theory and its applications in plasma–surface interactions

In this work, an improved understanding of electron sheath theory is provided using both fluid and kinetic approaches while elaborating on their implications for plasma–surface interactions. A fluid model is proposed considering the electron presheath structure, avoiding the singularity in electron sheath Child–Langmuir law which overestimates the sheath potential. Subsequently, a kinetic model of electron sheath is established, showing considerably different sheath profiles in respect to the fluid model due to non-Maxwellian electron velocity distribution function and finite ion temperature. The kinetic model is then further generalized and involves a more realistic truncated ion velocity distribution function. It is demonstrated that such a distribution function yields a super-thermal electron sheath whose entering velocity at the sheath edge is greater than the Bohm criterion prediction. Furthermore, an attempt is made to describe the electron presheath–sheath coupling within the kinetic framework, showing a necessary compromise between a realistic sheath entrance and the inclusion of kinetic effects. Finally, the secondary electron emissions induced by sheath-accelerated plasma electrons in an electron sheath are analysed and the influence of backscattering is discussed.

Laboratory Observations of Electron Heating and Non-Maxwellian Distributions at the Kinetic Scale during Electron-Only Magnetic Reconnection.

Non-Maxwellian electron velocity distribution functions composed of a warm bulk population and a cold beam are directly measured during electron-only reconnection with a strong out-of-plane (guide) magnetic field in a laboratory plasma. Electron heating is localized to the separatrix, and the electron temperature increases continuously along the separatrix. The measured gain in enthalpy flux is 70% of the incoming Poynting flux. The electron beams are oppositely directed on either side of the X point, and their velocities are comparable to, and scale with, the electron Alfvén speed. Particle-in-cell simulations are consistent with the measurements. The experimental results are consistent with, and go beyond, recent observations in the magnetosheath.

The power loss requirement in the non-thermal ³He-³He fusion plasma

The control of power loss is the most important issue in the plasma and it should be minimised by suitable selection of design parameters. This research is done with the aim of determining power loss and the parameters affecting the ³He-³He plasma with isotropic non-Maxwellian electron velocity distribution function (EVDF). In order to investigate the power loss requirement, bi-Maxwellian EVDF is considered. The results show that the rate of entropy production decreases as the electron density decreases and collision time increases. The ratio of the minimum power loss to the fusion power decreases as the electron temperature, and electron and helium-3 densities decrease, and the ion temperature increases. It is favourable to decrease the electron temperature lower than the thermal limit. Moreover, decreasing the electron temperature increases the fusion power.

Macroscopic plasma analysis from 1D-radial kinetic results of a Hall thruster discharge

A radial particle-in-cell model of the weakly-collisional plasma discharge in a Hall thruster, provides the non-Maxwellian velocity distribution functions (VDF) of ions and electrons. The model considers a radial magnetic field, secondary electron emission from the two walls, and phenomenological models of anomalous electron scattering. The electron VDF is used to assess the different terms in the macroscopic momentum and energy equations, identifying those differing from the standard fluid model for a near-Maxwellian VDF. The pressure tensor consists of an anisotropic gyrotropic part and a small gyroviscous part. Nonetheless, the gradient of this last one affects the cross-field electron current density, generating radial undulations that resemble those reported for near-wall conductivity. A gyroviscous energy flux is identified too. The heat flux parallel to the magnetic lines does not follow a conductive-type law but a convective-type one, already found in other weakly-collisional plasmas. The tails of the electron velocity distribution function are partially depleted due to wall collection, leading to reduced electron fluxes of particles and energy, which are characterized with parameters useful for fluid models. Differences in the plasma response for annular and planar channel geometries are highlighted. The levels of replenishment of the electron VDF and of the asymmetries in radial profiles differ for isotropic and anisotropic anomalous scattering models.

Free Energy Sources in Current Sheets Formed in Collisionless Plasma Turbulence

Abstract Collisionless dissipation of macroscopic energy into heat is an unsolved problem of space and astrophysical plasmas, e.g., solar wind and Earth’s magnetosheath. The most viable process under consideration is the turbulent cascade of macroscopic energy to kinetic scales where collisionless plasma processes dissipate the energy. Space observations and numerical simulations show the formation of kinetic scale current sheets in turbulent plasmas. Instabilities in these current sheets (CS) can provide collisionless dissipation and influence the turbulence. Spatial gradients of physical quantities and non-Maxwellian velocity distribution functions provide the free energy sources for CS plasma instabilities. To determine the free energy sources provided by the spatial gradients of plasma density and electron/ion bulk velocities in CS formed in collisionless turbulent plasmas with an external magnetic field B 0, we carried out two-dimensional particle-in-cell-hybrid simulations and interpret the results within the limitations of the simulation model. We found that ion-scale CS in a collisionless turbulent plasma are formed primarily by electron shear flows, i.e., electron bulk velocity inside CS is much larger than ion bulk velocity while the density variations through the CS are relatively small (&lt;10%). The electron bulk velocity and, thus, the current density inside the sheets are directed mainly parallel to B 0. The shear in the perpendicular electron and ion bulk velocities generates parallel electron and ion flow vorticities. Inside CS, parallel electron flow vorticity exceeds the parallel ion flow vorticity, changes sign around the CS centers, and peaks near the CS edges. An ion temperature anisotropy develops near CS during the CS formation. It has a positive correlation with the parallel ion and electron flow vorticities. Theoretical estimates support the simulation results.

Nature of Electrostatic Fluctuations in the Terrestrial Magnetosheath

Abstract The high cadence plasma, electric, and magnetic field measurements by the Magnetospheric MultiScale spacecraft allow us to explore the near-Earth space plasma with an unprecedented time and spatial resolution, resolving electron-scale structures that naturally emerge from plasma complex dynamics. The formation of small-scale turbulent features is often associated to structured, non-Maxwellian particle velocity distribution functions that are not at thermodynamic equilibrium. Using measurements in the terrestrial magnetosheath, this study focuses on regions presenting bumps in the power spectral density of the parallel electric field at subproton scales. Correspondingly, it is found that the ion velocity distribution functions exhibit beam-like features at nearly the local ion thermal speed. Ion-cyclotron waves in the ion-scale range are frequently observed at the same locations. These observations, supported by numerical simulations, are consistent with the generation of ion-bulk waves that propagate at the ion thermal speed. This represents a new branch of efficient energy transfer at small scales, which may be relevant to weakly collisional astrophysical plasmas.

The collision frequency of electron-neutral-particle in weakly ionized plasmas with non-Maxwellian velocity distributions

The collision frequencies of electron-neutral-particle in weakly ionized complex plasmas with the non-Maxwellian velocity distributions are studied. The average collision frequencies of electron-neutral-particle in plasmas are accurately derived. We find that these collision frequencies are significantly dependent on the power-law spectral indices of non-Maxwellian distribution functions and so they are generally different from the collision frequencies in plasmas with a Maxwellian velocity distribution, which will affect the transport properties of the charged particles in plasmas. Numerically analyses are made to show the roles of the spectral indices in the average collision frequencies respectively.

On the approximate solutions of a damped nonplanar modified Korteweg–de Vries equation for studying dissipative cylindrical and spherical solitons in plasmas

In this work, the effect of both nonplanar (cylindrical and spherical) geometry and the dust-neutral collision on the propagation of dissipative nonplanar electrostatic dust-acoustic solitary waves (DASWs) in a strongly coupled complex plasma (SCCP) is examined. The electrons and ions are assumed to follow a Maxwellian and non-Maxwellian trapped velocity distributions, respectively. The fluid governing equations of the plasma species are reduced to an evolution equation using the reductive perturbation technique (RPT). For describing the dynamical mechanism of the dissipative nonplanar DASWs, the evolution equation (the damped nonplanar Shamel Korteweg–de Vries (SKdV)) is solved numerically using both homotopy perturbation method (HPM) and the improved multistage homotopy perturbation method (MsHPM). The numerical solutions of the integrable planar Shamel-KdV (SKdV) equation using both HPM and MsHPM is compared with the exact solution of the SKdV. Also, the comparison between the numerical solutions of the damped nonplanar SKdV using both HPM and MsHPM is discussed. Moreover, the maximum global residual error for both HPM and MsHPM is estimated for measuring the accuracy of the obtained numerical solutions. Furthermore, the dependence of dissipative nonplanar solitons characteristics on various plasma parameters are investigated.