Collisionless Regime Research Articles

Elastic response of the electron fluid in intrinsic graphene: The collisionless regime

The elastic response of an electron fluid at finite frequencies is defined by the electron viscosity $\eta(\omega)$. We determine $\eta(\omega)$ for graphene at the charge neutrality point in the collisionless regime, including the leading corrections due to the electron-electron Coulomb interaction. We find interaction corrections to $\eta(\omega)$ that are significantly larger if compared to the corresponding corrections to the optical conductivity. In addition, we find comparable contributions to the dynamic momentum flux due to single-particle and many-particle effects. We also demonstrate that $\eta(\omega)$ is directly related to the nonlocal energy-flow response of graphene at the Dirac point. The viscosity in the collisionless regime is determined with the help of the strain generators in the Kubo formalism. Here, the pseudo-spin of graphene describing its two sublattices plays an important role in obtaining a viscosity tensor that fulfills the symmetry properties of a rotationally symmetric system.

Collisionless dynamics in two-dimensional bosonic gases

We study the dynamics of dilute and ultracold bosonic gases in a quasi two-dimensional (2D) configuration and in the collisionless regime. We adopt the 2D Landau-Vlasov equation to describe a three-dimensional gas under very strong harmonic confinement along one direction. We use this effective equation to investigate the speed of sound in quasi 2D bosonic gases, i.e. the sound propagation around a Bose-Einstein distribution in collisionless 2D gases. We derive coupled algebraic equations for the real and imaginary parts of the sound velocity, which are then solved taking also into account the equation of state of the 2D bosonic system. Above the Berezinskii-Kosterlitz-Thouless critical temperature we find that there is rapid growth of the imaginary component of the sound velocity which implies a strong Landau damping. Quite remarkably, our theoretical results are in good agreement with very recent experimental data obtained with a uniform 2D Bose gas of $^{87}$Rb atoms.

Collisionless Sound in a Uniform Two-Dimensional Bose Gas.

Using linear response theory within the random phase approximation, we investigate the propagation of sound in a uniform two dimensional (2D) Bose gas in the collisionless regime. We show that the sudden removal of a static density perturbation produces a damped oscillatory behavior revealing that sound can propagate also in the absence of collisions, due to mean-field interaction effects. We provide explicit results for the sound velocity and damping as a function of temperature, pointing out the crucial role played by Landau damping. We support our predictions by performing numerical simulations with the stochastic (projected) Gross-Pitaevskii equation. The results are consistent with the recent experimental observation of sound in a weakly interacting 2D Bose gas both below and above the superfluid Berezinskii-Kosterlitz-Thouless transition.

Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials.

Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the collisionless regime (ℏω≫k_{B}T) in the vicinity of a relativistic quantum critical point, separating two-dimensional (d=2) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such a critical point, gapless fermionic and bosonic excitations are strongly coupled, leading to a universal suppression of the interband OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in 1/N_{f}- and ε expansions, where N_{f} counts the fermion flavor number and ε=3-d. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from nonperturbative gauge-gravity duality, for example.

Analysis of the high-energy electron population in surface-wave plasma columns in presence of collisionless resonant absorption

In surface-wave plasmas, the energy can be transferred to the plasma electrons through both ohmic (collisional) and collisionless heating mechanisms. At very low pressure, when the electron–neutral collision frequency is much lower than the wave frequency (collisionless regime), a resonance is excited close to the tube walls where the electron plasma frequency in the radially-inhomogeneous plasma column reaches the wave frequency. In such conditions, the sharp rise of the component of the surface-wave electric field perpendicular to the tube axis can induce transit-time heating. At the resonant point, the long-wavelength electromagnetic surface wave can also be converted into short-wavelength electrostatic Langmuir waves that propagate down the density gradient. In this work, spatially-resolved trace-rare-gases optical emission spectroscopy combined with collisional-radiative modeling is used to analyze the electron energy distribution function (EEDF) and wave–particle interactions in low-pressure argon plasma columns sustained by an electromagnetic surface wave at 600 MHz (over-dense plasma). The EEDF is found to depart from a Maxwellian with the presence of a high-energy tail. The relative population of high-energy electrons increases with the axial distance towards the end of the plasma column where the electron density decreases and the resonance point becomes closer to the discharge axis. Over the range of experimental conditions examined, the high-energy tail increases with the characteristic length of the plasma density gradient at the resonance point; a feature that can be linked to collisionless electron heating by Landau damping of Langmuir waves.

Regimes of magnetic reconnection in colliding laser-produced magnetized plasma bubbles

We conduct a multiparametric study of driven magnetic reconnection relevant to recent experiments on colliding magnetized laser-produced plasmas using particle-in-cell simulations. Varying the background plasma density, plasma resistivity, and plasma bubble geometry, the 2D simulations demonstrate a rich variety of reconnection behaviors and show the coupling between magnetic reconnection and the global hydrodynamical evolution of the system. We consider both the collision between two radially expanding bubbles where reconnection is seeded by the pre-existing X-point and the collision between two flows in a quasi-1D geometry with initially anti-parallel fields where reconnection must be initiated by the tearing instability. At a baseline case of low-collisionality and low background density, the current sheet is strongly compressed to below scale of the ion-skin-depth scale, and rapid, multi-plasmoid reconnection results. Increasing the plasma resistivity, we observe a collisional slow-down of reconnection and stabilization of plasmoid instability for Lundquist numbers less than approximately S ∼ 103. Second, increasing the background plasma density modifies the compressibility of the plasma and can also slow down or even prevent reconnection, even in completely collisionless regimes, by preventing the current sheet from thinning down to the scale of the ion-skin depth. These results have implications for understanding recent and future experiments, and signatures for these processes for proton-radiography diagnostics of these experiments are discussed.

On availability of the optimal regimes in a Knudsen Cs-Ba thermionic converter at high emitter temperatures

A thermionic energy converter (TIC) functioning in collisionless regime at high emitter temperatures demonstrates very high output performance. In practice, such a regime has been realized at moderate temperatures (up to 2300 K) when its inter-electrode gap is filled with Cs and Ba vapors. Changing the Ba vapor pressure, one can vary the emitter work function and obtain optimum output performances, moreover maximum output power being available with any emitter material. The higher the emitter temperature, the more pronounced a shift of this maximum is toward higher Ba pressure, and at high temperature a TIC happens to be working in the collision regime before the maximum power point. We have analysed some experimental data in the literature when studying the emission parameters of refractory metals in the presence of the Ba vapor as well as in the Cs-Ba TIC experiments. Through our analysis, as well as results on the TIC optimization, the Ba optimum pressure is evaluated to obtain maximum power at the high emitter temperature for a set of refractory metals. We conclude that the maximum output performance of the Knudsen TIC with W and Re emitters can be reached up to the emitter temperature as high as 2600 K.

Temperature gradient driven heat flux closure in fluid simulations of collisionless reconnection

Recent efforts to include kinetic effects in fluid simulations of plasmas have been very promising. Concerning collisionless magnetic reconnection, it has been found before that damping of the pressure tensor to isotropy leads to good agreement with kinetic runs in certain scenarios. An accurate representation of kinetic effects in reconnection was achieved in a study by Wang et al. (Phys. Plasmas, vol. 22, 2015, 012108) with a closure derived from earlier work by Hammett and Perkins (Phys. Rev. Lett., vol. 64, 1990, 3019). Here, their approach is analysed on the basis of heat flux data from a Vlasov simulation. As a result, we propose a new local closure in which heat flux is driven by temperature gradients. This way, a more realistic approximation of Landau damping in the collisionless regime is achieved. Previous issues are addressed and the agreement with kinetic simulations in different reconnection set-ups is improved significantly. To the authors’ knowledge, the new fluid model is the first to perform well in simulations of the coalescence of large magnetic islands.

Temps de cohérence d'un condensat de Bose–Einstein dans un gaz isolé harmoniquement piégé

We study the condensate phase dynamics in a low-temperature equilibrium gas of weakly interacting bosons, harmonically trapped and isolated from the environment. We find that at long times, much longer than the collision time between Bogoliubov quasiparticles, the variance of the phase accumulated by the condensate grows with a ballistic term quadratic in time and a diffusive term affine in time. We give the corresponding analytical expressions in the limit of a large system, in the collisionless regime and in the ergodic approximation for the quasiparticle motion. When properly rescaled, they are described by universal functions of the temperature divided by the Thomas-Fermi chemical potential. The same conclusion holds for the mode damping rates. Such universality class differs from the previously studied one of the homogeneous gas.

Observation of Spin Superfluidity in a Bose Gas Mixture.

The spin dynamics of a harmonically trapped Bose-Einstein condensed binary mixture of sodium atoms is experimentally investigated at finite temperature. In the collisional regime the motion of the thermal component is shown to be damped because of spin drag, while the two condensates exhibit a counterflow oscillation without friction, thereby providing direct evidence for spin superfluidity. Results are also reported in the collisionless regime where the spin components of both the condensate and thermal part oscillate without damping, their relative motion being driven by a mean-field effect. We also measure the static polarizability of the condensed and thermal parts and we find a large increase of the condensate polarizability with respect to the T=0 value, in agreement with the predictions of theory.

Collective modes of an imbalanced unitary Fermi gas

We study theoretically the collective mode spectrum of a strongly imbalanced two-component unitary Fermi gas in a cigar-shaped trap, where the minority species forms a gas of polarons. We describe the collective breathing mode of the gas in terms of the Fermi liquid kinetic equation taking collisions into account using the method of moments. Our results for the frequency and damping of the longitudinal in-phase breathing mode are in good quantitative agreement with an experiment by Nascimb\`ene et al. [Phys. Rev. Lett. 103, 170402 (2009)] and interpolate between a hydrodynamic and a collisionless regime as the polarization is increased. A separate out-of phase breathing mode, which for a collisionless gas is sensitive to the effective mass of the polaron, however, is strongly damped at finite temperature, whereas the experiment observes a well-defined oscillation.

Distribution functions for a family of general-relativistic hypervirial models in the collisionless regime

By considering the Einstein-Vlasov system for static spherically symmetric distributions of matter, we show that configurations with constant anisotropy parameter $\beta$ have, necessarily, a distribution function (DF) of the form $F=l^{-2\beta}\xi(\varepsilon)$, where $\varepsilon=E/m$ and $l=L/m$ are the relativistic energy and angular momentum per unit rest mass, respectively. We exploit this result to obtain DFs for the general relativistic extension of the Hypervirial family introduced by Nguyen and Lingam (2013), which Newtonian potential is given by $\phi(r)=-\phi_o /[1+(r/a)^{n}]^{1/n}$ ($a$ and $\phi_o$ are positive free parameters, $n=1,2,...$). Such DFs can be written in the form $F_{n}=l^{n-2}\xi_{n}(\varepsilon)$. For odd $n$, we find that $\xi_n$ is a polynomial of order $2n+1$ in $\varepsilon$, as in the case of the Hernquist model ($n=1$), for which $F_1\propto l^{-1}\left(2\varepsilon-1\right)\left(\varepsilon-1\right)^2$. For even $n$, we can write $\xi_n$ in terms of incomplete beta functions (Plummer model, $n=2$, is an example). Since we demand that $F\geq 0$ throughout the phase space, the particular form of each $\xi_n$ leads to restrictions for the values of $\phi_o$. For example, for the Hernquist model we find that $0\leq \phi_o \leq2/3$, i.e. an upper bounding value less than the one obtained for Nguyen and Lingam ($0\leq \phi_o \leq1$), based on energy conditions.

Electron parallel closures for the 3 + 1 fluid model

Linear closures are obtained for arbitrary collisionality for the 3 + 1 fluid model which includes the evolution of density, flow velocity, and pressure both parallel and perpendicular to a preferred direction, usually a magnetic field. A large set of 6400 moment equations is solved to provide closures that are accurate in the collisional regime and well into the collisionless regime. The closures in the collisionless limit are determined by solving the kinetic equation with a model collision operator. Simple fits for the kernel functions that define the closures are obtained for arbitrary collisionality in wave number space. The results are linearly accurate to within 3% across the entire range of collisionality.

Understanding the scaling of electron kinetics in the transition from collisional to collisionless conditions in microscale gas discharges

When gas discharge and plasma devices shrink to the microscale, the electrode distance in the device approaches the mean free path of electrons and they experience few collisions. As microscale gas discharge and plasma devices become more prevalent, the behavior of discharges at these collisionless and near-collisionless conditions need to be understood. In conditions where the characteristic length d is much greater than the mean free path λ (i.e., macroscopic conditions), electron energy distributions (EEDs) and rate coefficients scale with the reduced electric field E/p. However, when d is comparable with or much lower than λ, this E/p scaling breaks. In this work, particle-in-cell/Monte Carlo collision simulations are used to explore the behavior of the EED and subsequent reaction rate coefficients in microscale field emission-driven Townsend discharges for both an atomic (argon) and a molecular (hydrogen) gas. To understand the behavior, a pseudo-analytical model is developed for the spatially integrated EED and rate coefficients in the collisional to collisionless transition regime based on the weighted sum of a fully collisional, two-temperature Maxwellian EED and the ballistic EED. The theory helps clarify the relative contribution of ballistic electrons in these extreme conditions and can be used to more accurately predict when macroscopic E/p scaling fails at the microscale.

Chiral anomalous dispersion

The linearized Einstein equation describing graviton propagation through a chiral medium appears to be helicity dependent. We analyze features of the corresponding spectrum in a collision-less regime above a flat background. In the long wave-length limit, circularly polarized metric perturbations travel with a helicity dependent group velocity that can turn negative giving rise to a new type of an anomalous dispersion. We further show that this chiral anomalous dispersion is a general feature of polarized modes propagating through chiral plasmas extending our result to the electromagnetic sector.

Density and spin modes in imbalanced normal Fermi gases from collisionless to hydrodynamic regime

We study the mass- and population-imbalance effect on density (in-phase) and spin (out-of-phase) collective modes in a two-component normal Fermi gas. By calculating the eigenmodes of the linearized Boltzmann equation as well as the density/spin dynamic structure factor, we show that mass- and population-imbalance effects offer a variety of collective mode crossover behaviors from collisionless to hydrodynamic regimes. The mass-imbalance effect shifts the crossover regime to the higher-temperature, and a significant peak of the spin dynamic structure factor emerges only in the collisionless regime. This is in contrast to the case of mass- and population-balanced normal Fermi gases, where the spin dynamic response is always absent. Although the population-imbalance effect does not shift the crossover regime, the spin dynamic structure factor survives both in the collisionless and hydrodynamic regimes.

Identifying microturbulence regimes in a TCV discharge making use of physical constraints on particle and heat fluxes

Reducing the uncertainty on physical input parameters derived from experimental measurements is essential towards improving the reliability of gyrokinetic turbulence simulations. This can be achieved by introducing physical constraints. Amongst them, the zero particle flux condition is considered here. A first attempt is also made to match as well the experimental ion/electron heat flux ratio. This procedure is applied to the analysis of a particular Tokamak à Configuration Variable discharge. A detailed reconstruction of the zero particle flux hyper-surface in the multi-dimensional physical parameter space at fixed time of the discharge is presented, including the effect of carbon as the main impurity. Both collisionless and collisional regimes are considered. Hyper-surface points within the experimental error bars are found. The analysis is done performing gyrokinetic simulations with the local version of the GENE code, computing the fluxes with a Quasi-Linear (QL) model and validating the QL results with non-linear simulations in a subset of cases.

Optical conductivity of an interacting Weyl liquid in the collisionless regime

Optical conductivity (OC) can serve as a measure of correlation effects in a wide range of condensed matter systems. We here show that the long-range tail of the Coulomb interaction yields a universal correction to the OC in a three-dimensional Weyl semimetal $\sigma(\Omega)=\sigma_0(\Omega)\left[ 1+\frac{1}{N+1} \right]$, where of $\sigma_0(\Omega)=Ne^2_0 \Omega/(12 h v)$ is the OC in the non-interacting system, with $v$ as the actual (renormalized) Fermi velocity of Weyl quasiparticles at frequency $\Omega$, and $e_0$ is the electron charge in vacuum. Such universal enhancement of OC, which depends only on the number of Weyl nodes near the Fermi level ($N$), is a remarkable consequence of an intriguing conspiracy among the quantum-critical nature of an interacting Weyl liquid, marginal irrelevance of the long-range Coulomb interaction and the violation of hyperscaling in three dimensions, and can directly be measured in recently discovered Weyl as well as Dirac materials. By contrast, a local density-density interaction produces a non-universal correction to the OC, stemming from the non-renormalizable nature of the corresponding interacting field theory.

Three‐Phonon and Four‐Phonon Interaction Processes in a Pair‐Condensed Fermi Gas

AbstractWe study the interactions among phonons and the phonon lifetime in a pair‐condensed Fermi gas in the BEC‐BCS crossover in the collisionless regime. To compute the phonon‐phonon coupling amplitudes we use a microscopic model based on a generalized BCS Ansatz including moving pairs, which allows for a systematic expansion around the mean field BCS approximation of the ground state. We show that the quantum hydrodynamic expression of the amplitudes obtained by Landau and Khalatnikov apply only on the energy shell, that is for resonant processes that conserve energy. The microscopic model yields the same excitation spectrum as the Random Phase Approximation, with a linear (phononic) start and a concavity at low wave number that changes from upwards to downwards in the BEC‐BCS crossover. When the concavity of the dispersion relation is upwards at low wave number, the leading damping mechanism at low temperature is the Beliaev‐Landau process 2 phonons ↔ 1 phonon while, when the concavity is downwards, it is the Landau‐Khalatnikov process 2 phonons ↔ 2 phonons. In both cases, by rescaling the wave vectors to absorb the dependence on the interaction strength, we obtain a universal formula for the damping rate. This universal formula corrects and extends the original analytic results of Landau and Khalatnikov [ZhETF 19, 637 (1949)] for the 2↔2 processes in the downward concavity case. In the upward concavity case, for the Beliaev 1↔ 2 process for the unitary gas at zero temperature, we calculate the damping rate of an excitation with wave number q including the first correction proportional to q7 to the q5 hydrodynamic prediction, which was never done before in a systematic way.

Transition from Collisional to Collisionless Regimes in Interpenetrating Plasma Flows on the National Ignition Facility.

A study of the transition from collisional to collisionless plasma flows has been carried out at the National Ignition Facility using high Mach number (M>4) counterstreaming plasmas. In these experiments, CD-CD and CD-CH planar foils separated by 6-10mm are irradiated with laser energies of 250kJ per foil, generating ∼1000 km/s plasma flows. Varying the foil separation distance scales the ion density and average bulk velocity and, therefore, the ion-ion Coulomb mean free path, at the interaction region at the midplane. The characteristics of the flow interaction have been inferred from the neutrons and protons generated by deuteron-deuteron interactions and by x-ray emission from the hot, interpenetrating, and interacting plasmas. A localized burst of neutrons and bright x-ray emission near the midpoint of the counterstreaming flows was observed, suggesting strong heating and the initial stages of shock formation. As the separation of the CD-CH foils increases we observe enhanced neutron production compared to particle-in-cell simulations that include Coulomb collisions, but do not include collective collisionless plasma instabilities. The observed plasma heating and enhanced neutron production is consistent with the initial stages of collisionless shock formation, mediated by the Weibel filamentation instability.