Collisionless Regime Research Articles

Fluctuation-response relation as a probe of long-range correlations in nonequilibrium quantum and classical fluids.

The absence of a simple fluctuation-dissipation theorem is a major obstacle for studying systems that are not in thermodynamic equilibrium. We show that for a fluid in a nonequilibrium steady state characterized by a constant temperature gradient the commutator correlation functions are still related to response functions; however, the relation is to the bilinear response of products of two observables, rather than to a single linear response function as is the case in equilibrium. This modified fluctuation-response relation holds for both quantum and classical systems. It is both motivated and informed by the long-range correlations that exist in such a steady state and allows for probing them via response experiments. This is of particular interest in quantum fluids, where the direct observation of fluctuations by light scattering would be difficult. In classical fluids it is known that the coupling of the temperature gradient to the diffusive shear velocity leads to correlations of various observables, in particular temperature fluctuations, that do not decay as a function of distance, but rather extend over the entire system. We investigate the nature of these correlations in a fermionic quantum fluid and show that the crucial coupling between the temperature gradient and velocity fluctuations is the same as in the classical case. Accordingly, the nature of the long-ranged correlations in the hydrodynamic regime also is the same. However, as one enters the collisionless regime in the low-temperature limit the nature of the velocity fluctuations changes: they become ballistic rather than diffusive. As a result, correlations of the temperature and other observables are still singular in the long-wavelength limit, but the singularity is weaker than in the hydrodynamic regime.

Chiral hydrodynamics of expanding systems

We obtain equations of motion for the boost-invariant expansion of a system of chiral particles. Our analysis is based on the Boltzmann equation for left- and right-handed massless particles in the relaxation time approximation. We assume Bjorken symmetry, but allow for parity breaking. We generalize the relaxation time approximation to take into account the so-called side-jump effect, but we show that the ensuing correction happens to vanish for Bjorken symmetry. After expressing the conserved currents in terms of chiral moments, we derive equations of motion for these moments from the Boltzmann equation. After a suitable truncation, these equations allow us to study the transition from the early-time collisionless regime to the hydrodynamic regime at late time, where the parity-violating chiral moments decay exponentially. The truncation that we use for the parity-violating moments is shown to be identical to Israel-Stewart’s 14-moment approximation. Our final set of equations can be used to calculate the energy-momentum tensor, vector, and axial-vector currents with chiral degrees of freedom for possible applications in heavy-ion collisions. Published by the American Physical Society 2024

Collective excitations of a Bose-condensed gas: Fate of second sound in the crossover regime between hydrodynamic and collisionless regimes

Collective excitations of a Bose-condensed gas: Fate of second sound in the crossover regime between hydrodynamic and collisionless regimes

Experimental signatures of the transition from acoustic plasmon to electronic sound in graphene.

Fermi liquids respond differently to perturbations depending on whether their frequency is higher (collisionless regime) or lower (hydrodynamic regime) than the interparticle collision rate. This results in a different phase velocity between the collisionless zero sound and the hydrodynamic first sound. We performed terahertz photocurrent nanoscopy measurements on graphene devices, with a metallic gate close to the graphene layer, to probe the dispersion of propagating acoustic plasmons, the counterpart of sound modes in electronic Fermi liquids. We report the observation of a change in the plasmon phase velocity when the excitation frequency approaches the electron-electron collision rate that is compatible with the transition between the zero and the first sound mode.

Phase space dynamics of unmagnetized plasmas: Collisionless and collisional regimes

Eulerian electrostatic kinetic simulations of unmagnetized plasmas (kinetic electrons and motionless protons) with high-frequency equilibrium perturbations have been employed to investigate the phase space free energy transfer across spatial and velocity scales, associated with the resonant interaction of electrons with the self-induced electric field. Numerical runs cover a wide range of collisionless and weakly collisional plasma regimes. An analysis technique based on the Fourier–Hermite transform of the particle distribution function allows to point out how kinetic processes trigger the free energy cascade, which is instead inhibited at finer scales when collisions are turned on. Numerical results are presented and discussed for the cases of linear wave Landau damping, nonlinear electron trapping, and bump-on-tail and two-stream instabilities. A more realistic situation of turbulent Langmuir fluctuations is also discussed in detail. Fourier–Hermite transform shows a free energy spread, highly conditioned by collisions, which involves velocity scales more quickly than the spatial scales, even when nonlinear effects are dominant. This results in anisotropic spectra whose slopes are compatible with theoretical expectations. Finally, an exact conservation law has been derived, which describes the time evolution of the free energy of the system, taking into account the collisional dissipation.

Pressure anisotropy and viscous heating in weakly collisional plasma turbulence

Pressure anisotropy can strongly influence the dynamics of weakly collisional, high-beta plasmas, but its effects are missed by standard magnetohydrodynamics (MHD). Small changes to the magnetic-field strength generate large pressure-anisotropy forces, heating the plasma, driving instabilities and rearranging flows, even on scales far above the particles’ gyroscales where kinetic effects are traditionally considered most important. Here, we study the influence of pressure anisotropy on turbulent plasmas threaded by a mean magnetic field (Alfvénic turbulence). Extending previous results that were concerned with Braginskii MHD, we consider a wide range of regimes and parameters using a simplified fluid model based on drift kinetics with heat fluxes calculated using a Landau-fluid closure. We show that viscous (pressure-anisotropy) heating dissipates between a quarter (in collisionless regimes) and half (in collisional regimes) of the turbulent-cascade power injected at large scales; this does not depend strongly on either plasma beta or the ion-to-electron temperature ratio. This will in turn influence the plasma's thermodynamics by regulating energy partition between different dissipation channels (e.g. electron and ion heat). Due to the pressure anisotropy's rapid dynamic feedback onto the flows that create it – an effect we term ‘magneto-immutability’ – the viscous heating is confined to a narrow range of scales near the forcing scale, supporting a nearly conservative, MHD-like inertial-range cascade, via which the rest of the energy is transferred to small scales. Despite the simplified model, our results – including the viscous heating rate, distributions and turbulent spectra – compare favourably with recent hybrid-kinetic simulations. This is promising for the more general use of extended-fluid (or even MHD) approaches to model weakly collisional plasmas such as the intracluster medium, hot accretion flows and the solar wind.

Generic deformation channels for critical Fermi surfaces in the collisionless regime

Using a quantum Boltzmann equation framework, we analyse the nature of generic low-energy deformations of a critical Fermi surface, which exists at the non-Fermi liquid fixed point of a system consisting of fermions interacting with massless bosons. The non-Fermi liquid behaviour arises due to the itinerant quasiparticles of the Fermi surface interacting strongly with the massless bosons, which on the other hand undergo Landau damping as a result of the mutual interactions. Focussing on the collisionless regime, where we neglect the collision integral, we chalk out the possible excitations spanning the entire spectrum of angular momentum (ℓ) channels (i.e., including both small and large values of ℓ). The excitations are of two types: particle-hole like localized excitations forming an energy band (or continuum) and delocalized collective modes with discrete energies. Although we find a collective mode analogous to the zero sound of a Fermi liquid, its dispersion shows a crossover from a Ω∼|q|6/5 behaviour to the usual Ω∼|q| dependence, where Ω and q represent the frequency and momentum, respectively. We estimate the frequency scale at which this crossover takes place. We also determine the boundary for the particle-hole continuum in the Ω–q plane, and observe a crossover from Ω∼|q|3/2 to Ω∼|q| behaviour, determined by another crossover frequency scale.

Automated plasma probing system for laboratory experiments in high vacuum using closed loop control

The Inverse Mirror Experimental Plasma Device (IMPED) is constructed to study the behaviour of magnetized plasmas in both collisional and collision-less regimes. The device has multiple active probe diagnostics to investigate turbulence, flow dynamics, instabilities, and wave interactions. In the paper, we report the development of feedback-controlled, very accurate (±0.2 mm accuracy of positioning) probe drive system, that achieves its performance utilizing inexpensive major components including motor, drive controller, and digital scale, which is used for position verification. This could make it economically feasible for even the small-scale experiment to use a large number of such drives. This facilitates the studies, where high temporal and spatial resolution are required for simultaneous measurements made at widely separated axial and/or azimuthal locations. Precise positioning is achieved by properly tuned Proportional–Integral–Derivative (PID) control. PC-based automation of the probe drive is validated for vacuum integrity by a pressure gauge and length measurement by digital scale. The software is developed on LabVIEW for integration with the Data Acquisition System (DAQ) and Python for its application in other experiments. The system has achieved ±0.2 mm accuracy in a linear scan of 0 to 80 mm, under the vacuum of 10−6 mBar and background magnetic field of 120 mT.

Gyrokinetic simulations of plasma turbulence in a Z-pinch using a moment-based approach and advanced collision operators

The first nonlinear gyrokinetic simulations obtained using a moment approach based on the Hermite–Laguerre decomposition of the distribution function are presented, implementing advanced models for the collision operator. Turbulence in a two-dimensional Z-pinch is considered within a flux-tube configuration. In the collisionless regime, our gyromoment approach shows very good agreement with nonlinear simulations carried out with the continuum gyrokinetic code GENE, even with fewer gyromoments than required for the convergence of the linear growth rate. By using advanced linear collision operators, the role of collisions in setting the level of turbulent transport is then analysed. The choice of collision operator model is shown to have a crucial impact when turbulence is quenched by the presence of zonal flows. The convergence properties of the gyromoment approach improve when collisions are included.

In search of a data-driven symbolic multi-fluid ten-moment model closure

The inclusion of kinetic effects into fluid models has been a long standing problem in magnetic reconnection and plasma physics. Generally, the pressure tensor is reduced to a scalar which is an approximation used to aid in the modelling of large scale global systems such as the Earth's magnetosphere. This unfortunately omits important kinetic physics which have been shown to play a crucial role in collisionless regimes. The multi-fluid ten-moment model, however, retains the full symmetric pressure tensor. The ten-moment model is constructed by taking moments of the Vlasov equation up to second order, and includes the scalar density, the vector bulk-flow and the symmetric pressure tensor for a total of ten separate components. Use of the multi-fluid ten-moment model requires a closure which truncates the cascading system of equations. Here we look to leverage data-driven methodologies to seek a closure which may improve the physical fidelity of the ten-moment multi-fluid model in collisionless regimes. Specifically, we use the sparse identification of nonlinear dynamics (SINDy) method for symbolic equation discovery to seek the truncating closure from fully kinetic particle-in-cell simulation data, which inherently retains the relevant kinetic physics. We verify our method by reproducing the ten-moment model from the particle-in-cell (PIC) data and use the method to generate a closure truncating the ten-moment model which is analysed through the nonlinear phase of reconnection.

Collective modes in interacting two-dimensional tomographic Fermi liquids

We develop an analytically solvable model for interacting two-dimensional Fermi liquids with separate collisional relaxation rates for parity-odd and parity-even Fermi surface deformations. Such a disparity of collisional lifetimes exists whenever scattering is restricted to inversion-symmetric Fermi surfaces, and should thus be a generic feature of two-dimensional Fermi liquids. It implies an additional unanticipated "tomographic" transport regime (in between the standard collisionless and hydrodynamic regimes) in which even-parity modes are overdamped while odd-parity modes are collisionless. We derive expressions for both the longitudinal and the transverse conductivity and discuss the collective mode spectrum along the collisionless-tomographic-hydrodynamic crossover. Longitudinal modes cross over from zero sound in the collisionless regime to hydrodynamic first sound in the tomographic and hydrodynamic regime, where odd-parity damping appears as a subleading correction to the lifetime. In charged Fermi liquids with long-range Coulomb coupling, these modes reduce to plasmons with a strongly suppressed odd-parity correction to the damping. The transverse response, by contrast, has a specific tomographic transport regime with two imaginary odd-parity modes, one of which requires a finite repulsive interaction, distinct from both the shear sound in the collisionless regime and an overdamped diffusive current mode in the hydrodynamic limit. Our work demonstrates that there are deep many-body aspects of interacting Fermi liquids, which are often thought to be well understood theoretically, remaining unexplored.

Heat Transfer in a Non-Isothermal Collisionless Turbulent Particle-Laden Flow

To better understand the role of particle inertia on the heat transfer in the presence of a thermal inhomogeneity, Eulerian–Lagrangian direct numerical simulations (DNSs) have been carried out by using the point–particle model. By considering particles transported by a homogeneous and isotropic, statistically steady turbulent velocity field with a Taylor microscale Reynolds number from 37 to 124, we have investigated the role of particle inertia and thermal inertia in one- and two-way coupling collisionless regimes on the heat transfer between two regions at uniform temperature. A wide range of Stokes numbers, from 0.1 to 3 with a thermal Stokes-number-to-Stokes-number ratio equal to 0.5 to 4.43 has been simulated. It has been found that all moments always undergo a self-similar evolution in the interfacial region between the two uniform temperature zones, the thickness of which shows diffusive growth. We have determined that the maximum contribution of particles to the heat flux, relative to the convective heat transfer, is achieved at a Stokes number which increases with the ratio between thermal Stokes and Stokes number, approaching 1 for very large ratios. Furthermore, the maximum increases with the thermal Stokes-to-Stokes number ratio whereas it reduces for increasing Reynolds. In the two-way coupling regime, particle feedback tends to smooth temperature gradients by reducing the convective heat flux and to increase the particle turbulent heat flux, in particular at a high Stokes number. The impact of particle inertia reduces at very large Stokes numbers and at larger Reynolds numbers. The dependence of the Nusselt number on the relevant governing parameters is presented. The implications of these findings for turbulence modelling are also briefly discussed.

From moments of the distribution function to hydrodynamics: The nonconformal case

We study the one-dimensional boost-invariant Boltzmann equation in the relaxation-time approximation using special moments of the distribution function for a system with a finite particle mass. The infinite hierarchy of moments can be truncated by keeping only the three lowest moments that correspond to the three independent components of the energy-momentum tensor. We show that such a three-moment truncation reproduces accurately the exact solution of the kinetic equation after a simple renormalization that takes into account the effects of the neglected higher moments. We derive second-order Israel-Stewart hydrodynamic equations from the three-moment equations, and show that, for most physically relevant initial conditions, these equations yield results comparable to those of the three-moment truncation, albeit less accurate. We attribute this feature to the fact that the structure of Israel-Stewart equations is similar to that of the three-moment truncation. In particular, the presence of the relaxation term in the Israel-Stewart equations, yields an early-time regime that mimics approximately the collisionless regime. A detailed comparison of the three-moment truncation with second-order non-conformal hydrodynamics reveals ambiguities in the definition of second-order transport coefficients. These ambiguities affect the ability of Israel-Stewart hydrodynamics to reproduce results of kinetic theory.

Collective effects in an incompressible electronic liquid.

Starting from Landau's kinetic equation, we show that an electronic liquid in d = 2, 3 spatial dimensions depicted by a Landau-type effective theory will become incompressible on condition that the Landau parameters satisfy either (i) [Formula: see text] or (ii) [Formula: see text]. Condition (i) is the Pomeranchuk instability in the current channel and suggests a quantum spin liquid (QSL) state with a spinon Fermi surface; while condition (ii) means that the strong repulsion in the charge channel leads to a conventional charge and thermal insulator. In the collisionless regime (ωτ ≫ 1) and the hydrodynamic regime (ωτ ≪ 1), the zero and first sound modes have been studied and classified by symmetries, including the longitudinal and transverse modes in d = 2, 3 and the higher angular momentum modes in d = 3. The sufficient (and/or necessary) conditions of these collective modes have been revealed. It has been demonstrated that some of these collective modes will behave in quite different manners under incompressibility condition (i) or (ii). Possible nematic QSL states and a hierarchy structure for gapless QSL states have been proposed in d = 3.

Non-Kasha fluorescence of pyrene emerges from a dynamic equilibrium between excited states.

Pyrene fluorescence after a high-energy electronic excitation exhibits a prominent band shoulder not present after excitation at low energies. The standard assignment of this shoulder as a non-Kasha emission from the second-excited state (S2) has been recently questioned. To elucidate this issue, we simulated the fluorescence of pyrene using two different theoretical approaches based on vertical convolution and nonadiabatic dynamics with nuclear ensembles. To conduct the necessary nonadiabatic dynamics simulations with high-lying electronic states and deal with fluorescence timescales of about 100ns of this large molecule, we developed new computational protocols. The results from both approaches confirm that the band shoulder is, in fact, due to S2 emission. We show that the non-Kasha behavior is a dynamic-equilibrium effect not caused by a metastable S2 minimum. However, it requires considerable vibrational energy, which can only be achieved in collisionless regimes after transitions into highly excited states. This strict condition explains why the S2 emission was not observed in some experiments.

Laboratory observation of plasmoid-dominated magnetic reconnection in hybrid collisional-collisionless regime

Magnetic reconnection, breaking and reorganization of magnetic field topology, is a fundamental process for rapid release of magnetic energy into plasmas that occurs pervasively throughout the universe. In natural circumstances, the plasma properties on either side of the reconnection layer are almost asymmetric, in particular for the collision rates that critically determine the underlying reconnection mechanism. To date, all laboratory experiments on magnetic reconnections have been limited to purely collisional or collisionless regimes. Here, we report a well-designed experimental investigation on magnetic reconnections in a hybrid collisional-collisionless regime by interactions between laser-ablated copper and plastic plasmas. We directly observe the topology evolutions of the whole process of this asymmetric magnetic reconnection by highly-resolved proton radiography. Through this, we show that the growth rate of tearing instability in such a hybrid regime is still extremely large, resulting in rapid formation of multiple plasmoids and generation of plasmoid-dominated current sheet.

Laser cluster interaction in ambient magnetic fields for accelerating electrons in two stages without external injection

In the few-cycle pulse regime of laser-cluster interaction (intensity >10^{16},text{ W/cm}^{2}, wavelength > 780 nm), laser absorption is mostly collisionless and may happen via anharmonic resonance (AHR) process in the overdense (cluster) plasma potential. Many experiments, theory and simulation show average absorbed energy per cluster-electron ({mathcal {E}_A}) close to the electron’s ponderomotive energy (U_mathrm {p}) in the collisionless regime. In this work, by simple rigid sphere model (RSM) and detailed particle-in-cell (PIC) simulation, we show enhanced {mathcal {E}_A}approx 30–70U_mathrm {p}—a 15–30 fold increase—with an external (crossed) magnetic field near the electron-cyclotron resonance (ECR). Due to relativistic mass increase, electrons quickly deviate from the standard (non-relativistic) ECR, but time-dependent relativistic-ECR (RECR) happens which also contributes to enhanced {mathcal {E}_A}. Here laser is coupled to electrons in two stages, i.e, AHR and ECR/RECR. To probe further we retrieve the phase-difference Delta psi between the driving electric field and corresponding velocity component for each electron (in PIC and RSM). We find absorption by electron via AHR happens in a very short interval Delta tau for less than half a laser period where Delta psi remains close to pi (necessary condition for maximum laser absorption) and then Delta psi drops to its initial pi /2 (meaning no absorption) after such short-lived AHR. On the contrary, auxiliary magnetic field near the ECR modifies AHR scenario inside the cluster and also helps maintaining the required phase Delta psi approx pi for the liberated cluster-electron accompanied by frequency matching for ECR/RECR for a prolonged Delta tau (which covers 50–60% of the laser pulse through pulse maxima) even after AHR—leading to jump in {mathcal {E}_A}approx 30–70U_mathrm {p}. We note that to realize the second stage of enhanced energy coupling via ECR/RECR, the first stage via AHR is necessary.

Zero sound and plasmon modes for non-Fermi liquids

We derive the quantum Boltzmann equation (QBE) by using generalized Landau-interaction parameters, obtained through the nonequilibrium Green's function technique. This is a generalization of the usual QBE formalism to non-Fermi liquid (NFL) systems, which do not have well-defined quasiparticles. We apply this framework to a controlled low-energy effective field theory for the Ising-nematic quantum critical point, in order to find the collective excitations of the critical Fermi surface in the collisionless regime. We also compute the nature of the dispersion after the addition of weak Coulomb interactions. The zero angular momentum longitudinal vibrations of the Fermi surface show a linear-in-wavenumber dispersion, which corresponds to the zero sound of Landau's Fermi liquid theory. The Coulomb interaction modifies it to a plasmon mode in the long-wavelength limit, which disperses as the square-root of the wavenumber. Remarkably, our results show that the zero sound and plasmon modes exhibit the same behaviour as in a Fermi liquid, although an NFL is fundamentally different from the former.

Soft modes in Fermi liquids at arbitrary temperatures

We use kinetic-theory methods to analyze Landau Fermi-liquid theory, and in particular to investigate the number and nature of modes in Fermi liquids that are soft in the long-wavelength limit, both in the hydrodynamic and the collisionless regimes. In the hydrodynamic regime we show that Fermi-liquid theory is consistent with Navier-Stokes hydrodynamics at all temperatures, as expected. The soft modes are the ones familiar from classical hydrodynamics that are controlled by the five conservation laws; namely, two first-sound modes, two shear diffusion modes, and one heat diffusion mode. These modes have a particle-like spectrum and are soft, or scale invariant, at all temperatures. In the collisionless regime we show that the entire single-particle distribution function is soft with a continuous part of the spectrum. This continuous soft mode, which is well known but often not emphasized, has important physical consequences, e.g., for certain quantum phase transitions. In addition, there are the well-known soft zero-sound excitations that describe angular fluctuations of the Fermi surface; their spectra are particle-like. They are unrelated to conservation laws, acquire a mass at any nonzero temperature, and their number depends on the strength of the quasiparticle interaction. We also discuss the fates of these two families of soft modes as the temperature changes. With increasing temperature the size of the collisionless regime shrinks, the damping of the modes grows, and eventually all of the collisionless modes become overdamped. In their stead the five hydrodynamic modes appear in the hydrodynamic regime at asymptotically low frequencies. The two families of soft modes are unrelated and have very different physical origins. In charged Fermi liquids the first-sound modes in the hydrodynamic regime and the $\ensuremath{\ell}=0$ zero-sound modes in the collisionless regime get replaced by plasmons, all other modes remain soft.

Fluctuating quantum kinetic theory

We consider a quantum Langevin kinetic equation for a system of fermions. We first derive the Langevin force noise correlation functions in Landau's Fermi-liquid kinetic theory from general considerations. We then use the resulting equation to calculate the equilibrium dynamic structure factor in the collisionless regime at low temperatures. The result is in agreement with the conventional many-body result. We then use the theory to derive both the fluctuating Navier-Stokes equations for a quantum fluid and the fluctuating hydrodynamic equations for fermions in the presence of quenched disorder. We also discuss the modifications needed for the fluctuating hydrodynamic equations to describe an electron fluid with long-ranged interactions, and we prove an $H$ theorem for the nonlinear Landau kinetic equation.