Collisionless Turbulence Research Articles

On hydromagnetic wave interactions in collisionless, high-βplasmas

We describe the interaction of parallel-propagating Alfvén waves with ion-acoustic waves and other Alfvén waves, in magnetized, high-$\beta$collisionless plasmas. This is accomplished through a combination of analytical theory and numerical fluid simulations of the Chew–Goldberger–Low (CGL) magnetohydrodynamic (MHD) equations closed by Landau-fluid heat fluxes. An asymptotic ordering is employed to simplify the CGL-MHD equations and derive solutions for the deformation of an Alfvén wave that results from its interaction with the pressure anisotropy generated either by an ion-acoustic wave or another, larger-amplitude Alfvén wave. The difference in time scales of acoustic and Alfvénic fluctuations at high-$\beta$means that interactions that are local in wavenumber space yield little modification to either mode within the time it takes the acoustic wave to Landau damp away. Instead, order-unity changes in the amplitude of Alfvénic fluctuations can result after interacting with frequency-matched acoustic waves. Additionally, we show that the propagation speed of an Alfvén-wave packet in an otherwise homogeneous background is a function of its self-generated pressure anisotropy. This allows for the eventual interaction of separate co-propagating Alfvén-wave packets of differing amplitudes. The results of the CGL-MHD simulations agree well with these predictions, suggesting that theoretical models relying on the interaction of these modes should be reconsidered in certain astrophysical environments. Applications of these results to weak Alfvénic turbulence and to the interaction between the compressive and Alfvénic cascades in strong, collisionless turbulence are also discussed.

Statistics of pressure fluctuations in turbulent kinetic plasmas

ABSTRACTIn this study, we explore the statistics of pressure fluctuations in kinetic collisionless turbulence. A 2.5D kinetic particle-in-cell simulation of decaying turbulence is used to investigate pressure balance via the evolution of thermal and magnetic pressure in a plasma with β of order unity. We also discuss the behaviour of thermal, magnetic, and total pressure structure functions and their corresponding wavenumber spectra. The total pressure spectrum exhibits a slope of −7/3 extending for about a decade in the ion-inertial range. In contrast, shallower −5/3 spectra are characteristic of the magnetic pressure and thermal pressure. The steeper total pressure spectrum is a consequence of cancellation caused by density-magnetic field magnitude anti-correlation. Further, we evaluate higher order total pressure structure functions in an effort to discuss intermittency and compare the power exponents with higher order structure functions of velocity and magnetic fluctuations. Finally, applications to astrophysical systems are also discussed.

Magnetic Field Annihilation in a Magnetotail Electron Diffusion Region With Electron-Scale Magnetic Island.

We present observations in Earth's magnetotail by the Magnetospheric Multiscale spacecraft that are consistent with magnetic field annihilation, rather than magnetic topology change, causing fast magnetic‐to‐electron energy conversion in an electron‐scale current sheet. Multi‐spacecraft analysis for the magnetic field reconstruction shows that an electron‐scale magnetic island was embedded in the observed electron diffusion region (EDR), suggesting an elongated shape of the EDR. Evidence for the annihilation was revealed in the form of the island growing at a rate much lower than expected for the standard X‐type geometry of the EDR, which indicates that magnetic flux injected into the EDR was not ejected from the X‐point or accumulated in the island, but was dissipated in the EDR. This energy conversion process is in contrast to that in the standard EDR of a reconnecting current sheet where the energy of antiparallel magnetic fields is mostly converted to electron bulk‐flow energy. Fully kinetic simulation also demonstrates that an elongated EDR is subject to the formation of electron‐scale magnetic islands in which fast but transient annihilation can occur. Consistent with the observations and simulation, theoretical analysis shows that fast magnetic diffusion can occur in an elongated EDR in the presence of nongyrotropic electron effects. We suggest that the annihilation in elongated EDRs may contribute to the dissipation of magnetic energy in a turbulent collisionless plasma.

Importance of accurate consideration of the electron inertia in hybrid-kinetic simulations of collisionless plasma turbulence: The 2D limit

The dissipation mechanism of the magnetic energy in turbulent collisionless space and astrophysical plasmas is still not well understood. Its investigation requires efficient kinetic simulations of the energy transfer in collisionless plasma turbulence. In this respect, hybrid-kinetic simulations, in which ions are treated as particles and electrons as an inertial fluid, have begun to attract a significant interest recently. Hybrid-kinetic models describe both ion- and electron scale processes by ignoring electron kinetic effects so that they are computationally much less demanding compared to fully kinetic plasma models. Hybrid-kinetic codes solve either the Vlasov equation for the ions (Eulerian Vlasov-hybrid codes) or the equations of motion of the ions as macro-particles [Lagrangian particle-in-cell (PIC)-hybrid codes]. They consider the inertia of the electron fluid using different approximations. We check the validity of these approximations by employing our recently massively parallelized three-dimensional PIC-hybrid code Code Hybrid with Inertial Electron Fluid (CHIEF), which considers the electron inertia without any of the common approximations. In particular, we report the results of simulations of two-dimensional collisionless plasma turbulence. We conclude that the simulation results obtained using hybrid-kinetic codes, which use approximations to describe the electron inertia, need to be interpreted with caution. We also discuss the parallel scalability of CHIEF, to the best of our knowledge, the first PIC-hybrid code, which without approximations describes the inertial electron fluid.

Available Energy of Trapped Electrons and Its Relation to Turbulent Transport.

Any collisionless plasma possesses some "available energy" (AE), defined as that part of the thermal energy that can be converted into instabilities and turbulence. Here, we present a calculation of the AE carried by magnetically trapped electrons in a flux tube of collisionless plasma. The AE is compared with nonlinear simulations of the energy flux resulting from collisionless turbulence driven by trapped-electron modes in various magnetic geometries. The numerical calculation of AE is rapid and shows a strong correlation with the simulated energy fluxes, which can be expressed as a power law and understood in terms of a simple model.

Efficient generation of turbulent collisionless shocks in laser-ablated counter-streaming plasmas

Laser-ablated high-energy-density (HED) plasmas offer a promising route to study astrophysically relevant processes underlying collisionless shock formation, magnetic field amplification, and particle acceleration in the laboratory. Using large-scale, multi-dimensional particle-in-cell simulations, we explore the interpenetration of laser-ablated counter-streaming plasmas for realistic experimental flow profiles. We find that the shock formation and its structure are substantially different from those of more idealized and commonly considered uniform flows: shock formation can be up to 10 times faster due to the transition from small-angle scattering to magnetic reflection and the shock front develops strong corrugations at the ion gyroradius scale. These findings have important consequences for current experimental programs and open exciting prospects for studying the microphysics of turbulent collisionless shocks with currently available high-energy laser systems.

Identification and characterization of current sheets in collisionless plasma turbulence

Current sheets forming in an ion-kinetic turbulent collisionless plasma are characterized by utilizing the results of two-dimensional hybrid-kinetic numerical simulations (ions treated as kinetic species using particle-in-cell method and electrons treated as mass-less fluid). For this sake, the algorithm, proposed by Zhdankin et al. [Astrophys. J. 771, 124 (2013)] for the identification and characterization of current sheets forming in magnetohydrodynamic plasma turbulence, is extended to current sheets forming in a much noisier kinetic plasma turbulence. Effects of the algorithm parameters on the identification of current sheets in plasma turbulence are analyzed. Based on this analysis, appropriate values of algorithm parameters for the current sheet identification are chosen. Current sheets are statistically characterized in terms of their main properties—the peak current density, the peak current carrier velocity (mainly electrons), the thickness, the length, and also the aspect ratio (length/thickness). Results of the characterization show that the current sheets have a tendency to thin down to below ion inertial length scale until numerical (grid-resolution based) dissipation stops any further thinning. Simulations that include the physics at the electron inertial scales, e.g., hybrid simulations with electron inertia, are required to fully address the current sheet thinning processes and determination of the final thicknesses of current sheets.

Identification and characterization of current sheets in collisionless plasmas turbulence

Current sheets forming in an ion-kinetic turbulent collisionless plasma are characterized by utilizing the results of two-dimensional hybrid-kinetic numerical simulations (ions treated as kinetic species using particle-in-cell method and electrons treated as mass-less fluid). For this sake, the algorithm, proposed by Zhdankin et al. [Astrophys. J. 771, 124 (2013)] for the identification and characterization of current sheets forming in magnetohydrodynamic plasma turbulence, is extended to current sheets forming in a much noisier kinetic plasma turbulence. Effects of the algorithm parameters on the identification of current sheets in plasma turbulence are analyzed. Based on this analysis, appropriate values of algorithm parameters for the current sheet identification are chosen. Current sheets are statistically characterized in terms of their main properties—the peak current density, the peak current carrier velocity (mainly electrons), the thickness, the length, and also the aspect ratio (length/thickness). Results of the characterization show that the current sheets have a tendency to thin down to below ion inertial length scale until numerical (grid-resolution based) dissipation stops any further thinning. Simulations that include the physics at the electron inertial scales, e.g., hybrid simulations with electron inertia, are required to fully address the current sheet thinning processes and determination of the final thicknesses of current sheets.

Effects of the Background Turbulence on the Relaxation of Ion Temperature Anisotropy in Space Plasmas

Turbulence in space plasmas usually exhibits two regimes separated by a spectral break that divides the so called inertial and kinetic ranges. Large scale magnetic fluctuations are dominated by non-linear MHD wave-wave interactions following a −5/3 or −2 slope power-law spectrum. After the break, at scales in which kinetic effects take place, the magnetic spectrum follows a steeper power-law k−α shape given by a spectral index α > 5/3. Despite its ubiquitousness, the possible effects of a turbulent background spectrum in the quasilinear relaxation of solar wind temperatures are usually not considered. In this work, a quasilinear kinetic theory is used to study the evolution of the proton temperatures in an initially turbulent collisionless plasma composed by cold electrons and bi-Maxwellian protons, in which electromagnetic waves propagate along a background magnetic field. Four wave spectrum shapes are compared with different levels of wave intensity. We show that a sufficient turbulent magnetic power can drive stable protons to transverse heating, resulting in an increase in the temperature anisotropy and the reduction of the parallel proton beta. Thus, stable proton velocity distribution can evolve in such a way as to develop kinetic instabilities. This may explain why the constituents of the solar wind can be observed far from thermodynamic equilibrium and near the instability thresholds.

Ion versus Electron Heating in Compressively Driven Astrophysical Gyrokinetic Turbulence

The partition of irreversible heating between ions and electrons in compressively driven (but subsonic) collisionless turbulence is investigated by means of nonlinear hybrid gyrokinetic simulations. We derive a prescription for the ion-to-electron heating ratio $Q_\rmi/Q_\rme$ as a function of the compressive-to-Alfv\'enic driving power ratio $P_\compr/P_\AW$, of the ratio of ion thermal pressure to magnetic pressure $\beta_\rmi$, and of the ratio of ion-to-electron background temperatures $T_\rmi/T_\rme$. It is shown that $Q_\rmi/Q_\rme$ is an increasing function of $P_\compr/P_\AW$. When the compressive driving is sufficiently large, $Q_\rmi/Q_\rme$ approaches $\simeq P_\compr/P_\AW$. This indicates that, in turbulence with large compressive fluctuations, the partition of heating is decided at the injection scales, rather than at kinetic scales. Analysis of phase-space spectra shows that the energy transfer from inertial-range compressive fluctuations to sub-Larmor-scale kinetic Alfv\'en waves is absent for both low and high $\beta_\rmi$, meaning that the compressive driving is directly connected to the ion entropy fluctuations, which are converted into ion thermal energy. This result suggests that preferential electron heating is a very special case requiring low $\beta_\rmi$ and no, or weak, compressive driving. Our heating prescription has wide-ranging applications, including to the solar wind and to hot accretion disks such as M87 and Sgr A*.

Electron acceleration in laboratory-produced turbulent collisionless shocks

Astrophysical collisionless shocks are among the most powerful particle accelerators in the Universe. Generated by violent interactions of supersonic plasma flows with the interstellar medium, supernova remnant shocks are observed to amplify magnetic fields1 and accelerate electrons and protons to highly relativistic speeds2–4. In the well-established model of diffusive shock acceleration5, relativistic particles are accelerated by repeated shock crossings. However, this requires a separate mechanism that pre-accelerates particles to enable shock crossing. This is known as the ‘injection problem’, which is particularly relevant for electrons, and remains one of the most important puzzles in shock acceleration6. In most astrophysical shocks, the details of the shock structure cannot be directly resolved, making it challenging to identify the injection mechanism. Here we report results from laser-driven plasma flow experiments, and related simulations, that probe the formation of turbulent collisionless shocks in conditions relevant to young supernova remnants. We show that electrons can be effectively accelerated in a first-order Fermi process by small-scale turbulence produced within the shock transition to relativistic non-thermal energies, helping overcome the injection problem. Our observations provide new insight into electron injection at shocks and open the way for controlled laboratory studies of the physics underlying cosmic accelerators. In laser–plasma experiments complemented by simulations, electron acceleration is observed in turbulent collisionless shocks. This work clarifies the pre-acceleration to relativistic energies required for the onset of diffusive shock acceleration.

Electron and Ion Energization in Relativistic Plasma Turbulence.

Electron and ion energization (i.e., heating and nonthermal acceleration) is a fundamental, but poorly understood, outcome of plasma turbulence. In this work, we present new results on this topic from particle-in-cell simulations of driven turbulence in collisionless, relativistic electron-ion plasma. We focus on temperatures such that ions (protons) are subrelativistic and electrons are ultrarelativistic, a regime relevant for high-energy astrophysical systems such as hot accretion flows onto black holes. We find that ions tend to be preferentially heated, gaining up to an order of magnitude more energy than electrons, and propose a simple empirical formula to describe the electron-ion energy partition as a function of the ratio of electron-to-ion gyroradii (which in turn is a function of initial temperatures and plasma beta). We also find that while efficient nonthermal particle acceleration occurs for both species in the ultrarelativistic regime, nonthermal electron populations are diminished with decreasing temperature whereas nonthermal ion populations are essentially unchanged. These results have implications for modeling and interpreting observations of hot accretion flows.

Thermal disequilibration of ions and electrons by collisionless plasma turbulence

Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetized, turbulent plasma? And, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion disks around black holes. In the context of disks, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfvénic turbulence: Collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion-electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, [Formula: see text]: It ranges from [Formula: see text] at [Formula: see text] to at least 30 for [Formula: see text] This energy partition is approximately insensitive to the ion-to-electron temperature ratio [Formula: see text] Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfvénic turbulence will tend toward a nonequilibrium state in which one of the species is significantly hotter than the other, i.e., hotter ions at high [Formula: see text] and hotter electrons at low [Formula: see text] Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high [Formula: see text] and a tendency for the ion heating to be mediated by nonlinear phase mixing ("entropy cascade") when [Formula: see text] and by linear phase mixing (Landau damping) when [Formula: see text].

Dual Phase-space Cascades in 3D Hybrid-Vlasov–Maxwell Turbulence

Abstract To explain energy dissipation via turbulence in collisionless, magnetized plasmas, the existence of a dual real- and velocity-space cascade of ion-entropy fluctuations below the ion gyroradius has been proposed. Such a dual cascade, predicted by the gyrokinetic theory, has previously been observed in gyrokinetic simulations of two-dimensional, electrostatic turbulence. For the first time, we show evidence for a dual phase-space cascade of ion-entropy fluctuations in a three-dimensional simulation of hybrid-kinetic, electromagnetic turbulence. Some of the scalings observed in the energy spectra are consistent with a generalized theory for the cascade that accounts for the spectral anisotropy of critically balanced, intermittent, sub-ion-Larmor-scale fluctuations. The observed velocity-space cascade is also anisotropic with respect to the magnetic-field direction, with linear phase mixing along magnetic-field lines proceeding mainly at spatial scales above the ion gyroradius and nonlinear phase mixing across magnetic-field lines proceeding at perpendicular scales below the ion gyroradius. Such phase-space anisotropy could be sought in heliospheric and magnetospheric data of solar-wind turbulence and has far-reaching implications for the dissipation of turbulence in weakly collisional astrophysical plasmas.

Numerical investigation of kinetic turbulence in relativistic pair plasmas – I. Turbulence statistics

We describe results from particle-in-cell simulations of driven turbulence in collisionless, magnetized, relativistic pair plasma. This physical regime provides a simple setting for investigating the basic properties of kinetic turbulence and is relevant for high-energy astrophysical systems such as pulsar wind nebulae and astrophysical jets. In this paper, we investigate the statistics of turbulent fluctuations in simulations on lattices of up to $1024^3$ cells and containing up to $2 \times 10^{11}$ particles. Due to the absence of a cooling mechanism in our simulations, turbulent energy dissipation reduces the magnetization parameter to order unity within a few dynamical times, causing turbulent motions to become sub-relativistic. In the developed stage, our results agree with predictions from magnetohydrodynamic turbulence phenomenology at inertial-range scales, including a power-law magnetic energy spectrum with index near $-5/3$, scale-dependent anisotropy of fluctuations described by critical balance, log-normal distributions for particle density and internal energy density (related by a $4/3$ adiabatic index, as predicted for an ultra-relativistic ideal gas), and the presence of intermittency. We also present possible signatures of a kinetic cascade by measuring power-law spectra for the magnetic, electric, and density fluctuations at sub-Larmor scales.

Fully Kinetic versus Reduced-kinetic Modeling of Collisionless Plasma Turbulence

Abstract We report the results of a direct comparison between different kinetic models of collisionless plasma turbulence in two spatial dimensions. The models considered include a first-principles fully kinetic (FK) description, two widely used reduced models (gyrokinetic (GK) and hybrid-kinetic (HK) with fluid electrons), and a novel reduced gyrokinetic approach (KREHM). Two different ion beta ( ) regimes are considered: 0.1 and 0.5. For , good agreement between the GK and FK models is found at scales ranging from the ion to the electron gyroradius, thus providing firm evidence for a kinetic Alfvén cascade scenario. In the same range, the HK model produces shallower spectral slopes, presumably due to the lack of electron Landau damping. For , a detailed analysis of spectral ratios reveals a slight disagreement between the GK and FK descriptions at kinetic scales, even though kinetic Alfvén fluctuations likely still play a significant role. The discrepancy can be traced back to scales above the ion gyroradius, where the FK and HK results seem to suggest the presence of fast magnetosonic and ion Bernstein modes in both plasma beta regimes, but with a more notable deviation from GK in the low-beta case. The identified practical limits and strengths of reduced-kinetic approximations, compared here against the FK model on a case-by-case basis, may provide valuable insight into the main kinetic effects at play in turbulent collisionless plasmas, such as the solar wind.

Energy transfer channels and turbulence cascade in Vlasov-Maxwell turbulence.

Analysis of the Vlasov-Maxwell equations from the perspective of turbulence cascade clarifies the role of electromagnetic work, and reveals the importance of the pressure-strain relation in generating internal energy. Particle-in-cell simulation demonstrates the relative importance of the several energy exchange terms, indicating that the traceless pressure-strain interaction "Pi-D" is of particular importance for both electrons and protons. The Pi-D interaction and the second tensor invariants of the strain are highly localized in similar spatial regions, indicating that energy transfer occurs preferentially in coherent structures. The collisionless turbulence cascade may be fruitfully explored by study of these energy transfer channels, in addition to examining transfer across spatial scales.

A self-consistent analytical model for the upstream magnetic-field and ion-beam properties in Weibel-mediated collisionless shocks

A theoretical and numerical analysis is carried out for turbulent collisionless shocks mediated by the ion-Weibel instability during high-velocity plasma collisions. We develop a simple model based on the coalescence dynamics of the ion current filaments, which predicts the spatio-temporal evolution of the magnetic fluctuations formed in the upstream plasma region. From comparison with particle-in-cell simulations, our model is shown to correctly capture the magnetic-field and ion-beam properties during the early-time shock propagation.

Features of collisionless turbulence in the intracluster medium from simulated Faraday rotation maps – II. The effects of instabilities feedback

Statistical analysis of Faraday Rotation Measure (RM) maps of the intracluster medium (ICM) of galaxy clusters provides a unique tool to evaluate some spatial features of the magnetic fields there. Its combination with numerical simulations of magnetohydrodynamic (MHD) turbulence allows the diagnosis of the ICM turbulence. Being the ICM plasma weakly collisional, the thermal velocity distribution of the particles naturally develops anisotropies as a consequence of the large scale motions and the conservation of the magnetic moment of the charged particles. A previous study (Paper I) analyzed the impact of large scale thermal anisotropy on the statistics of RM maps synthesized from simulations of turbulence; these simulations employed a collisionless MHD model which considered a tensor pressure with uniform anisotropy. In the present work, we extend that analysis to a collisionless MHD model in which the thermal anisotropy develops according to the conservation of the magnetic moment of the thermal particles. We also consider the effect of anisotropy relaxation caused by the micro-scale mirror and firehose instabilities. We show that if the relaxation rate is fast enough to keep the anisotropy limited by the threshold values of the instabilities, the dispersion and power spectrum of the RM maps are indistinguishable from those obtained from collisional MHD. Otherwise, there is a reduction in the dispersion and steepening of the power spectrum of the RM maps (compared to the collisional case). Considering the first scenario, the use of collisional MHD simulations for modeling the RM statistics in the ICM becomes better justified.

''DOUBLE-HUMPED EFFECT'' IN THE TURBULENT COLLISION MAGNETIZED PLASMA

Statistical moments of the spatial power spectrum of multiple scattered ordinary and extraordinary waves in the turbulent collision magnetized plasma with aligned anisotropic electron density irregularities are investigated using modify smooth perturbation method taking into account diffraction effects. Correlation function and variances of the phase fluctuations are obtained for arbitrary correlation function of the electron density fluctuations. Double-humped Effect is investigated analytically and numerically using the anisotropic Gaussian spectral function of electron density irregularities for the polar ionospheric F-region applying the experimental data. Investigation of the anisotropy of the F layer irregularities is of great interest in ionospheric physics. It is well known that the irregularities are elongated in the direction of the geomagnetic field of lines, but especially at high latitudes they are also found to be anisotropic in the plane perpendicular to the external magnetic field vector. The anisotropy is usually investigated by correlation analysis of radio signals from satellites, observed by space receiver on the ground. The fluctuations in amplitude and phase (scintillations) of radio waves passing through the ionosphere are caused by spatial irregularities in the electron density. The spatial fluctuations in phase cause fluctuations of the angle of arrival at the observation points. Broadening of the spatial power spectrum (SPS) of scattered electromagnetic (EM) waves in the turbulent collision magnetized plasma for both power-law and anisotropic Gaussian correlation functions of electron density fluctuations was analyzed in (1) using the complex ray (-optics) approximation. Double-humped Effect, the features of the SPS, spectral width and shift of its maximum of multiple scattered EM waves in the turbulent collisionless magnetized plasma were considered in (2, 3). The influence of the collision frequency between plasma particles on the statistical characteristics of scattered EM waves in the turbulent magnetized plasma with both electron density and external magnetic field fluctuations was investigated in (4). The present paper reports the results of an analysis of the SPS, which is related to fluctuations of the radio refractive index in the F region. Analytical expressions of the correlation function of phase fluctuations of scattered both ordinary and extraordinary waves are obtained for the arbitrary correlation functions of electron density fluctuation using modify smooth perturbation method taking into account the diffraction effects. The Double-humped Effect in the collision magnetized plasma with elongated electron density irregularities is considered for the first time. Formation of a gap in the SPS of scattered radiation is analyzed numerically for the polar ionospheric F -region using the anisotropic Gaussian spectral function of electron density fluctuations. This spectrum contains angle of aligned plasma irregularities to the direction of an external magnetic field and anisotropy factor. The numerical calculation is computed based on experimental data. Finally, paper concludes the obtained results and their significance.