Collisional Fluid Research Articles

Self-organization in collisionless, high-β turbulence

The magnetohydrodynamic (MHD) equations, as a collisional fluid model that remains in local thermodynamic equilibrium (LTE), have long been used to describe turbulence in myriad space and astrophysical plasmas. Yet, the vast majority of these plasmas, from the solar wind to the intracluster medium (ICM) of galaxy clusters, are only weakly collisional at best, meaning that significant deviations from LTE are not only possible but common. Recent studies have demonstrated that the kinetic physics inherent to this weakly collisional regime can fundamentally transform the evolution of such plasmas across a wide range of scales. Here, we explore the consequences of pressure anisotropy and Larmor-scale instabilities for collisionless, $\beta \gg 1$ , turbulence, focusing on the role of a self-organizational effect known as ‘magneto-immutability’. We describe this self-organization analytically through a high- $\beta$ , reduced ordering of the Chew–Goldberger–Low-MHD (CGL-MHD) equations, finding that it is a robust inertial-range effect that dynamically suppresses magnetic-field-strength fluctuations, anisotropic-pressure stresses and dissipation due to heat fluxes. As a result, the turbulent cascade of Alfvénic fluctuations continues below the putative viscous scale to form a robust, nearly conservative, MHD-like inertial range. These findings are confirmed numerically via Landau-fluid CGL-MHD turbulence simulations that employ a collisional closure to mimic the effects of microinstabilities. We find that microinstabilities occupy a small ( ${\sim }5\,\%$ ) volume-filling fraction of the plasma, even when the pressure anisotropy is driven strongly towards its instability thresholds. We discuss these results in the context of recent predictions for ion-vs-electron heating in low-luminosity accretion flows and observations implying suppressed viscosity in ICM turbulence.

Ion flow and dust charging at the sheath boundary in dusty plasma with an electron-emitting surface: applications to laboratory and lunar dusty plasmas

In laboratory and space plasmas, the emission of electrons from the surface significantly affects the characteristics of the plasma sheath that forms at that surface, which is crucial to understanding the overall plasma-wall interaction mechanism. In this work, the collisional fluid model is used for laboratory dusty plasma, whereas the collisionless model is used for lunar dusty plasma. We have extended the Bohm sheath criterion for the formation of the stable plasma sheath due to electron emission from the surface, loss of ion flux, and the gas pressure of the collisional laboratory dusty plasmas. It is found that ion flow at the sheath boundary is considerably influenced by the concentration of electron emission, the ion loss term, and gas pressure. The evolution of the dust charge explicitly determines the magnitude of the ion flow at the sheath boundary. The plasma parameters adopted in the present case are reliable in laboratory and space dusty plasmas, especially the dusty plasma environment on the lunar surface. The lunar surface and dust grains on the Moon become electrically charged as a result of the interaction between solar wind plasma and photoemission electrons emitted from the lunar surface. In addition, the lunar plasma sheath characteristics, dust-charging process, and stable dust levitation in the sheath region have been studied.

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.

A collisional global sheath – Bulk model of argon plasma for semiconductor scale manufacturing

Plasma processes enhance the high-quality, semiconductor fabrication employed in large-scale industries. A crucial element in this process are the many gases that generate different reactive species at low temperatures. Capacitive plasma discharge radio frequency CCPs play a major role in semiconductor scale fabrication. The analysis of nonlinear dynamics in CCPs are complicated even under simple approaches. Therefore, we study self consistent collision fluid model, particle in cell simulation PIC, step approximation and finally the global model to find the accurate solution of merging plasma sheath -bulk region. For this purpose we study the self consistent collisional fluid model to find the accurate charge–voltage distribution V(Q) which controls the nonlinear dynamics of CCPs. The results against the PIC simulations and the more elaborate model step approximation is accomplished with higher accuracy. Consequently, the cubic polynomial formula V(Q) are applied in the global model. Accurate analytical global sheath-bulk calculations of the higher harmonic effect-exhibiting average power distributions, bulk potentials, and currents are obtained. This study provides an effective solution of collision regime for any arbitrary plasma reactor designs, including single-frequency and double frequency CCPs. Moreover, we used the argon gas as a good example in our study for a good ion etching. Finally, we can assist in achieving effective results that are consistent with experimental data and in large-scale applications in the semiconductor sector.

Modelling of edge plasma dynamics with active wall boundary conditions

AbstractA self‐consistent 2D model is presented for transport in boundary plasma and plasma‐facing material walls. Plasma dynamics in the domain is represented by a 2D collisional plasma fluid model in the edge‐plasma code UEDGE (Rognlien et al., J. Nucl. Mater. 196–198 (1992) 347), and transport of hydrogen and heat in the wall is represented by a system of reaction–diffusion equations in the 1D wall code FACE (Smirnov et al., Fusion Sci. Technol. 71 (2017) 75). To account for variation of parameters along the wall, in the coupled model multiple instances of the FACE code run in parallel. The coupled model provides a tool for investigating a range of dynamic plasma–material interactions phenomena in 2D. For demonstration of its capability, one application of particular interest is the role of active wall in tokamak strike point sweeping proposed for mitigation of divertor heat loads. In the present study, the coupled calculations are applied to investigation of the impact of heat and hydrogen transport in the material wall on the divertor plasma and target heat load during sweeping of the target strike point for parameters of a high‐power tokamak.

Generalized collisional fluid theory for multi-component, multi-temperature plasma using the linearized Boltzmann collision operator for scrape-off layer/edge applications

Grad’s method is used on the linearized Boltzmann collision operator to derive the most general expressions for the collision coefficients for a multi-component, multi-temperature plasma up to rank-2. In doing so, the collision coefficients then get expressed as series sum of pure coefficients of temperature and mass ratios multiplied by the cross-section dependent Chapman–Cowling integrals. These collisional coefficients are compared to previously obtained coefficients by Zhdanov (2002 Transport Processes in Multicomponent Plasma (London: Taylor and Francis)) for 13N-moment multi-temperature scheme. First, the differences in coefficients are compared directly, and then the differences in first approximation to viscosity and friction force are compared. For the 13N-moment multi-temperature coefficients, it is found that they behave reasonably similarly for small temperature differences, but display substantial differences in the coefficients when the temperature differences are high, both for the coefficients and for viscosity and friction force values. Furthermore, the obtained coefficients are compared to the 21N-moment single-temperature approximation provided by Zhdanov et al, and it is seen that the differences are higher than the 13N-moment multi-temperature coefficients, and have substantial differences even in the vicinity of equal temperatures, especially for the viscosity and friction force calculations.

Tunneling Transport of Unitary Fermions across the Superfluid Transition.

We investigate the transport of a Fermi gas with unitarity-limited interactions across the superfluid phase transition, probing its response to a direct current (dc) drive through a tunnel junction. As the superfluid critical temperature is crossed from below, we observe the evolution from a highly nonlinear to an Ohmic conduction characteristic, associated with the critical breakdown of the Josephson dc current induced by pair condensate depletion. Moreover, we reveal a large and dominant anomalous contribution to resistive currents, which reaches its maximum at the lowest attained temperature, fostered by the tunnel coupling between the condensate and phononic Bogoliubov-Anderson excitations. Increasing the temperature, while the zeroing of supercurrents marks the transition to the normal phase, the conductance drops considerably but remains much larger than that of a normal, uncorrelated Fermi gas tunneling through the same junction. We attribute such enhanced transport to incoherent tunneling of sound modes, which remain weakly damped in the collisional hydrodynamic fluid of unpaired fermions at unitarity.

Zonal profile corrugations and staircase formation: Role of the transport crossphase

Recently, quasi-stationary structures called E × B staircases were observed in gyrokinetic simulations, in all transport channels [Dif-Pradalier et al. Phys. Rev. Lett. 114, 085004 (2015)]. We present a novel analytical theory—supported by collisional drift-wave fluid simulations—for the generation of density profile corrugations (staircase), independent of the action of zonal flows: turbulent fluctuations self-organize to generate quasi-stationary radial modulations Δθk(r,t) of the transport crossphase θk between density and electric potential fluctuations. The radial modulations of the associated particle flux drive zonal corrugations of the density profile via a modulational instability. In turn, zonal density corrugations regulate the turbulence via nonlinear damping of the fluctuations.

Three-dimensional cross-field flows at the plasma-material interface in an oblique magnetic field

This article describes experimental evidence that the magnetic presheath is a fully three-dimensional structure modified by ion–neutral collisions. Velocity distributions of both ions and neutrals, obtained via laser-induced fluorescence, show that cross field ion drifts do not result from entrainment of ions in a flowing neutral background. Ion flows parallel to E×B arise and accelerate to as much as 0.2cs within several ion gyroradii of the boundary surface, where cs is the sound speed. Within measurement resolution, the onset of the E×B aligned flow occurs at the same distance to the surface that ions begin to deflect from travel along magnetic field lines. Collisional fluid and particle-in-cell simulations of the boundary region are compared to the experimental measurements. We find that, in contrast to the classical collisionless Chodura model, collisional effects between the ions and the non-flowing neutral population are essential to quantitatively predict the observed ion drift velocities. No momentum coupling between ions and neutrals, separable from noise and other effects, is observed in either signal. We discuss several explanations and implications of this observation.

Pathways to Dissipation in Weakly Collisional Plasmas

Abstract Observed turbulence in space and astrophysics is expected to involve cascade and subsequent dissipation and heating. Contrary to standard collisional fluid turbulence, the weakly collisional magnetized plasma cascade may involve several channels of energy conversion, interchange, and spatial transport, leading eventually to the production of internal energy. This paper describes these channels of transfer and conversion, collectively amounting to a complex generalization of the Kolmogorov cascade. Channels may be described using compressible magnetohydrodynamic (MHD) and multispecies Vlasov–Maxwell formulations. Key steps are conservative transport of energy in space, parallel incompressible and compressible cascades in scale, electromagnetic work on particles driving macroscopic and microscopic flows, and pressure–strain interactions, both compressive and shear-like, that produce internal energy. A significant contrast with the collisional case is that the steps leading to the disappearance of large-scale energy in favor of internal energy are formally reversible. This property motivates a discussion of entropy, reversibility, and the relationship between dissipation with collisions and in the Vlasov system without collisions. Where feasible, examples are given from MHD and Particle in Cell simulations and from MMS observations.

Effect of ion acceleration on a plasma potential profile formed in the expander of a mirror trap

We consider a flow of completely ionized magnetized plasma streaming along divergent magnetic field lines from an open magnetic trap. An analytical model is proposed that takes into account a transition from a collisional (fluid) regime to a collisionless kinetic regime as the flow expands. This allows for study of the formation of a plasma potential along the magnetic field and the acceleration of ions in a self-consistent way. We show that ion acceleration may influence the potential profile; in particular, it significantly reduces the potential gap inside the Debye sheath near the plasma collector. This positive effect predicts low arcing in plasma absorbing units, which is important for all large-scale fusion-aimed experiments in mirror machines. Applications of the theory to smaller table-top machines are also considered.

Constraints on Dark Matter Microphysics from the Milky Way Satellite Population

Abstract Alternatives to the cold, collisionless dark matter (DM) paradigm in which DM behaves as a collisional fluid generically suppress small-scale structure. Herein we use the observed population of Milky Way (MW) satellite galaxies to constrain the collisional nature of DM, focusing on DM–baryon scattering. We first derive conservative analytic upper limits on the velocity-independent DM–baryon scattering cross section by translating the upper bound on the lowest mass of halos inferred to host satellites into a characteristic cutoff scale in the linear matter power spectrum. We then confirm and improve these results through a detailed probabilistic inference of the MW satellite population that marginalizes over relevant astrophysical uncertainties. This yields 95% confidence upper limits on the DM–baryon scattering cross section of 6 × 10−30 cm2 (10−27 cm2) for DM particle masses m χ of 10 keV (10 GeV); these limits scale as m χ 1/4 for m χ ≪ 1 GeV and m χ for m χ ≫ 1 GeV. This analysis improves upon cosmological bounds derived from cosmic-microwave-background anisotropy measurements by more than three orders of magnitude over a wide range of DM masses, excluding regions of parameter space previously unexplored by other methods, including direct-detection experiments. Our work reveals a mapping between DM–baryon scattering and other alternative DM models, and we discuss the implications of our results for warm and fuzzy DM scenarios.

Finite Larmor radius regime: Collisional setting and fluid models

The subject matter of this paper concerns the derivation of fluid limits for gyro-kinetic models. The arguments apply for any collision kernel satisfying the usual conservations (mass, momentum, kinetic energy) and possessing a production entropy sign. We describe the set of equilibria in terms of several moments, we determine the average collision invariants, and we write the associated macroscopic equations and the entropy inequality.

A Lagrangian probability-density-function model for collisional turbulent fluid–particle flows

Inertial particles in turbulent flows are characterised by preferential concentration and segregation and, at sufficient mass loading, dense particle clusters may spontaneously arise due to momentum coupling between the phases. These clusters, in turn, can generate and sustain turbulence in the fluid phase, which we refer to as cluster-induced turbulence (CIT). In the present work, we tackle the problem of developing a framework for the stochastic modelling of moderately dense particle-laden flows, based on a Lagrangian probability-density-function formalism. This framework includes the Eulerian approach, and hence can be useful also for the development of two-fluid models. A rigorous formalism and a general model have been put forward focusing, in particular, on the two ingredients that are key in moderately dense flows, namely, two-way coupling in the carrier phase, and the decomposition of the particle-phase velocity into its spatially correlated and uncorrelated components. Specifically, this last contribution allows us to identify in the stochastic model the contributions due to the correlated fluctuating energy and to the granular temperature of the particle phase, which determine the time scale for particle–particle collisions. The model is then validated and assessed against direct-numerical-simulation data for homogeneous configurations of increasing difficulty: (i) homogeneous isotropic turbulence, (ii) decaying and shear turbulence and (iii) CIT.

Fluidization of collisionless plasma turbulence

In a collisionless, magnetized plasma, particles may stream freely along magnetic field lines, leading to "phase mixing" of their distribution function and consequently, to smoothing out of any "compressive" fluctuations (of density, pressure, etc.). This rapid mixing underlies Landau damping of these fluctuations in a quiescent plasma-one of the most fundamental physical phenomena that makes plasma different from a conventional fluid. Nevertheless, broad power law spectra of compressive fluctuations are observed in turbulent astrophysical plasmas (most vividly, in the solar wind) under conditions conducive to strong Landau damping. Elsewhere in nature, such spectra are normally associated with fluid turbulence, where energy cannot be dissipated in the inertial-scale range and is, therefore, cascaded from large scales to small. By direct numerical simulations and theoretical arguments, it is shown here that turbulence of compressive fluctuations in collisionless plasmas strongly resembles one in a collisional fluid and does have broad power law spectra. This "fluidization" of collisionless plasmas occurs, because phase mixing is strongly suppressed on average by "stochastic echoes," arising due to nonlinear advection of the particle distribution by turbulent motions. Other than resolving the long-standing puzzle of observed compressive fluctuations in the solar wind, our results suggest a conceptual shift for understanding kinetic plasma turbulence generally: rather than being a system where Landau damping plays the role of dissipation, a collisionless plasma is effectively dissipationless, except at very small scales. The universality of "fluid" turbulence physics is thus reaffirmed even for a kinetic, collisionless system.

Extension of Landau-fluid closure to weakly collisional plasma regime

Both collisionless and collisional Landau fluid (LF) closure have been developed and implemented in two-fluid plasma simulation framework BOUT++, taking full advantage of the fast non-Fourier method (Dimits, 2014). The spectral range of good fit can be conveniently extended to larger domain by adding more Lorentzians. The scaling for upper limit of wavenumber resolved in collisionless LF operator and the fitting coefficients for the collisional LF operator, the later is extended to weakly collisional regime (νe∗∼0.01), are presented in this paper. The flux limited expression q∥eFL is reduced to free streaming expression q∥eFS in collisionless limit and gives classical Spitzer–Härm result q∥eSH in collisional limit as we expected. The collisional LF closure recovers the classical Spitzer–Härm result q∥eSH in collisional limit and is same as the collisionless LF closure in collisionless limit. The test cases also obviously demonstrate the nonlocal effects from LF closures and responding to different boundary conditions in open surface region. This work will make it more applicable and possible to include the Landau damping kinetic effect in the fluid simulation of tokamak plasma.

An iterative algorithm of coupling the Kinetic Code for Plasma Periphery (KIPP) with SOLPS

Power exhaust is one of the critical issues for future fusion devices, e.g. ITER. The calculation of power deposition is critical for the divertor design. SOLPS is the main tool for predictions of the Scrape-off Layer (SOL) and divertor conditions in the future fusion device ITER, where parallel kinetic effects in the SOL will play an important role. SOLPS uses a collisional fluid model which does not take kinetic effects into account. The present work has enabled SOLPS in its 1D version to incorporate electron kinetic effects by coupling it with the Kinetic Code for Plasma Periphery (KIPP). An iterative algorithm, which is made as an automatic process, is investigated in this work.

Investigation of the short argon arc with hot anode. I. Numerical simulations of non-equilibrium effects in the near-electrode regions

The atmospheric pressure arcs have recently found application in the production of nanoparticles. The distinguishing features of such arcs are small length and hot ablating anode characterized by intensive electron emission and radiation from its surface. We performed a one-dimensional modeling of argon arc, which shows that near-electrode effects of thermal and ionization non-equilibrium play an important role in the operation of a short arc, because the non-equilibrium regions are up to several millimeters long and are comparable to the arc length. The near-anode region is typically longer than the near-cathode region and its length depends more strongly on the current density. The model was extensively verified and validated against previous simulation results and experimental data. The Volt-Ampere characteristic (VAC) of the near-anode region depends on the anode cooling mechanism. The anode voltage is negative. In the case of strong anode cooling (water-cooled anode) when the anode is cold, temperature and plasma density gradients increase with current density, resulting in a decrease of the anode voltage (the absolute value increases). Falling VAC of the near-anode region suggests the arc constriction near the anode. Without anode cooling, the anode temperature increases significantly with the current density, leading to a drastic increase in the thermionic emission current from the anode. Correspondingly, the anode voltage increases to suppress the emission, and the opposite trend in the VAC is observed. The results of simulations were found to be independent of sheath model used: collisional (fluid) or collisionless model gave the same plasma profiles for both near-anode and near-cathode regions.

Energy transfer, pressure tensor, and heating of kinetic plasma

Kinetic plasma turbulence cascade spans multiple scales ranging from macroscopic fluid flow to sub-electron scales. Mechanisms that dissipate large scale energy, terminate the inertial range cascade, and convert kinetic energy into heat are hotly debated. Here, we revisit these puzzles using fully kinetic simulation. By performing scale-dependent spatial filtering on the Vlasov equation, we extract information at prescribed scales and introduce several energy transfer functions. This approach allows highly inhomogeneous energy cascade to be quantified as it proceeds down to kinetic scales. The pressure work, −(P·∇)·u, can trigger a channel of the energy conversion between fluid flow and random motions, which contains a collision-free generalization of the viscous dissipation in collisional fluid. Both the energy transfer and the pressure work are strongly correlated with velocity gradients.

Exact collisional moments for plasma fluid theories

The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely, the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow, or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas that relies on the Chapman-Enskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rates.