We solve the linearised Vlasov-Fokker-Planck (VFP) equation to show that heat flow or an electrical current in a magnetized collisional plasma is unstable to the growth of a circularly polarised transverse perturbation to a zeroth order uniform magnetic field. The Braginskii (1965) transport equations exhibit the same instability in the appropriate limit. This is relevant to laser-produced plasmas, inertial fusion energy (IFE) and to dense cold interstellar plasmas.
In modern inertial fusion experiments there is a complex interplay between non-locality and magnetisation that can greatly influence transport. In this work we use a matrix recursion method to include higher-order corrections beyond the diffusion approximation usually used for magnetised plasmas. Working in the linear regime, we show this can account for arbitrary orders of the distribution function expansion in Knudsen non-locality parameter $kλ_{ei}$. Transport coefficients, such as thermal conductivity, deviate significantly from the magnetised diffusive approximation. In particular we show…
The problem of the linear microtearing mode in a slab magnetised plasma, and its connection to kinetic reconnecting modes, is addressed. Electrons are described using a novel hybrid fluid-kinetic model that captures electron heating, ions are gyrokinetic. Magnetic reconnection can occur as a result of either electron conductivity and inertia, depending on which one predominates. We eschew the use of an energy dependent collision frequency in the collisional operator model, unlike previous works. A model of the electron conductivity that matches the weakly collisional regime to the exact Landau…
Design of experiments characterising heat conduction in magnetised, weakly collisional plasma
University of Oxford（牛津大学）；Rutherford Appleton Laboratory（卢瑟福阿普尔顿实验室）；AWE（英国原子能管理局）；University of Chicago（芝加哥大学）；Gettysburg College（盖提斯堡学院）；Queen’s University Belfast（贝尔法斯特女王大学）；University of California Berkeley（加州大学伯克利分校）；University of Rochester（罗切斯特大学）
The eruption of multiple flux tubes in a magnetised plasma atmosphere is proposed as a mechanism for explosive release of energy in plasmas. Linearly stable isolated flux tubes are shown to be metastable in a box model magnetised atmosphere in which ends of the field lines are embedded in conducting walls. The energy released by destabilising such field lines can be a significant fraction of the gravitational energy stored in the system. This energy can be released in a fast dynamical time.
The stability of a collisionless, magnetised plasma to local convective disturbances is examined, with a focus on kinetic and finite-Larmor-radius effects. Specific application is made to the outskirts of galaxy clusters, which contain hot and tenuous plasma whose temperature increases in the direction of gravity. At long wavelengths (the "drift-kinetic" limit), we obtain the kinetic version of the magnetothermal instability (MTI) and its Alfvénic counterpart (Alfvénic MTI), which were previously discovered and analysed using a magnetofluid (i.e. Braginskii) description. At sub-ion-Larmor scal…
Observational evidence in space and astrophysical plasmas with long collisional mean free path suggests that more massive charged particles may be preferentially heated. One possible mechanism for this is the turbulent cascade of energy from injection to dissipation scales, where the energy is converted to heat. Here we consider a simple system consisting of a magnetized plasma slab of electrons and a single ion species with a cross-field density gradient. We show that such a system is subject to an electron drift wave instability, known as the universal instability, which is stabilized only w…
Cluster plasmas are magnetised already at very low magnetic field strength. Low collisionality implies that conservation of the first adiabatic invariant results in an anisotropic viscous stress (Braginskii viscosity) or, equivalently, anisotropic plasma pressure. This triggers firehose and mirror instabilities, which have growth rates proportional to the wavenumber down to scales of the order of ion Larmor radius. This means that MHD equations with Braginskii viscosity are not well posed and fully kinetic description is necessary. In this paper, we review the basic picture of small-scale dyna…
In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI satura…
We investigate the low-frequency wave mode associated with heavy particles and its instability in a collisional complex plasma with drifting ions. The effect of the ion drift on the sound velocity of this mode is discussed. The general condition of the instability is derived for subthermal ion drifts, taking into account strong coupling of the particle component. As a general tendency, strong coupling effects reduce the sound velocity and facilitate the occurrence of the ion drift instability. A wide parameter range is considered from the weakly collisional to strongly collisional regimes for …
Magnetic reconnection and associated heating of ions and electrons in strongly magnetised, weakly collisional plasmas are studied by means of gyrokinetic simulations. It is shown that an appreciable amount of the released magnetic energy is dissipated to yield (irreversible) electron and ion heating via phase mixing. Electron heating is mostly localized to the magnetic island, not the current sheet, and occurs after the dynamical reconnection stage. Ion heating is comparable to electron heating only in high-beta plasmas, and results from both parallel phase mixing and perpendicular phase mixin…
The collisional drift wave instability is reexamined taking into account the ion response in the direction parallel to the magnetic field lines, which appears due to friction with electrons and which can not be omitted in view of the momentum conservation. A modified instability threshold is obtained. In plasmas with dominant electron collisions with neutrals, the instability threshold is shifted towards higher frequencies, compared to the case of dominant electron collisions with ions. The difference between the two cases vanishes when the ion sound response is negligible, i.e., when the inst…
The low-frequency instability of a cylindrical poorly magnetized plasma with an inward-directed radial electric field is studied changing the gas pressure and the ion cyclotron frequency. The unstable frequency always decreases when the gas pressure is increased indicating collisional effects. At a fixed pressure, the unstable frequency increases with the magnetic field when the B-field is low and decreases at larger magnetic field strength. We find that the transition between these two regimes is obtained when the ion cyclotron frequency equals the ion-neutrals collision frequency. This is in…
The Buneman instability occurring when an electron population is drifting with respect to the ions is analyzed in the quantum linear and nonlinear regimes. The one-dimensional low-frequency and collisional model of Shokri and Niknam [Phys. Plasmas, v. 12, p. 062110 (2005)] is revisited introducing the Bohm potential term in the momentum equation. The linear regime is investigated analytically, and quantum effects result in a reduction of the instability. The nonlinear regime is then assessed both numerically and analytically, and pure quantum density oscillations are found to appear during the…
The collisional drift wave instability in a straight magnetic field configuration is studied within a full-F gyro-fluid model, which relaxes the Oberbeck-Boussinesq (OB) approximation. Accordingly, we focus our study on steep background density gradients. In this regime we report on corrections by factors of order one to the eigenvalue analysis of former OB approximated approaches as well as on spatially localised eigenfunctions, that contrast strongly with their OB approximated equivalent. Remarkably, non-modal phenomena arise for large density inhomogeneities and for all collisionalities. As…
In the present paper, we use a coarse-graining approach to investigate the nonlinear redistribution of free energy in both position and scale space for weakly collisional magnetised plasma turbulence. For this purpose, we use high-resolution numerical simulations of gyrokinetic (GK) turbulence that span the proton-electron range of scales, in a straight magnetic guide field geometry. Accounting for the averaged effect of the particles' fast gyro-motion on the slow plasma fluctuations, the GK approximation captures the dominant energy redistribution mechanisms in strongly magnetised plasma turb…
Rayleigh-Taylor (RT) instabilities are prevalent in many physical regimes ranging from astrophysical to laboratory plasmas and have primarily been studied using fluid models, the majority of which have been ideal fluid models. This work is the first of its kind to present a 5-dimensional (2 spatial dimensions, 3 velocity space dimensions) simulation using the continuum-kinetic model to study the effect of the collisional mean-free-path and transport on the instability growth. The continuum-kinetic model provides noise-free access to the full particle distribution function permitting a detailed…
I theoretically found eigenmodes and growth rates of relativistic current filamentation instability in collisional regimes, deriving a generalized dispersion relation from self-consistent beam-Maxwell equations. For symmetrically counterstreaming, fully relativistic electron currents, the collisional coupling between electrons and ions creates the unstable modes of growing oscillation and wave, which stand out for long-wavelength perturbations. In the stronger collisional regime, the growing oscillatory mode tends to be dominant for all wavelengths. In the collisionless limit, those modes vani…
Linear gyro-kinetic simulations of the classical tearing mode in three-dimensional toroidal geometry were performed using the global gyro kinetic turbulence code, GKW . The results were benchmarked against a cylindrical ideal MHD and analytical theory calculations. The stability, growth rate and frequency of the mode were investigated by varying the current profile, collisionality and the pressure gradients. Both collision-less and semi-collisional tearing modes were found with a smooth transition between the two. A residual, finite, rotation frequency of the mode even in the absense of a pres…
It is likely that nearly all central galactic massive and supermassive black holes are nonradiative: their accretion luminosities are orders of magnitude below what can be explained by efficient black hole accretion within their ambient environments. These objects, of which Sagittarius A* is the best-known example, are also dilute (mildly collisional to highly collisionless) and optically thin. In order for accretion to occur, magnetohydrodynamic instabilities must develop that not only transport angular momentum, but also gravitational energy generated through matter infall, outwards. A class…
Weakly collisional plasmas are subject to nonlinear relaxation processes, which can operate at rates much faster than the particle collision frequencies. This causes the plasma to respond like a magnetised fluid despite having long particle mean-free-paths. In this Letter the effective collisional mechanisms are modelled in the plasma kinetic equation to produce density, pressure and magnetic field responses to compare with spacecraft measurements of the solar wind compressive fluctuations at 1 AU. This enables a measurement of the effective mean-free-path of the solar wind protons, found to b…
For plasma velocity space instabilities driven by particle distributions significantly deviated from a Maxwellian, weak collisions can damp the instabilities by an amount that is significantly beyond the collisional rate itself. This is attributed to the dual role of collisions that tend to relax the plasma distribution toward a Maxwellian and to suppress the linearly perturbed distribution function. The former effect can dominate in cases where the unstable non-Maxwellian distribution is driven by collisionless transport on a time scale much shorter than that of collisions, and the growth rat…
The friction in plasmas consisting of two species with different temperatures is discussed together with the consequent energy transfer. It is shown that the friction between the two species has no effect on the ion acoustic mode in a quasi-neutral plasma. Using the Poisson equation instead of the quasi-neutrality reveals the possibility for an instability driven by the collisional energy transfer. However, the different starting temperatures of the two species imply an evolving equilibrium. It is shown that the relaxation time of the equilibrium electron-ion plasma is, in fact, always shorter…
A perpendicular ion drift is investigated as a mechanism for the generation of magnetic field structures in a highly collisional dusty plasma. The basic dissipation mechanism is assumed to be the dust-neutrals momentum exchange, so that plasmas with a small ionization fraction are natural candidates for experiments. The model reduces to a nonlinear partial differential equation for the vector potential. The conditions for linear instability are determined. The stationary states are periodic arrangements for the magnetic field, described by a Lienard equation. The fully depleted (ion-dust) case…
Slow dynamical changes in magnetic-field strength and invariance of the particles' magnetic moments generate ubiquitous pressure anisotropies in weakly collisional, magnetized astrophysical plasmas. This renders them unstable to fast, small-scale mirror and firehose instabilities, which are capable of exerting feedback on the macroscale dynamics of the system. By way of a new asymptotic theory of the early nonlinear evolution of the mirror instability in a plasma subject to slow shearing or compression, we show that the instability does not saturate quasilinearly at a steady, low-amplitude lev…
We investigate analytically and numerically the semi-collisional regime of the plasmoid instability, defined by the inequality $δ_{SP} \gg ρ_s \gg δ_{in}$, where $δ_{SP}$ is the width of a Sweet-Parker current sheet, $ρ_S$ is the ion sound Larmor radius, and $δ_{in}$ is width of boundary layer that arises in the plasmoid instability analysis. Theoretically, this regime is predicted to exist if the Lundquist number $S$ and the length of the current sheet $L$ are such that $(L/ρ_S)^{14/9} < S <(L/ρ_S)^2$ (for a sinusoidal-like magnetic configuration; for a Harris-type sheet the lower bound is re…
In this work we consider magnetic reconnection in thin current sheets with both resistive and electron inertia effects. When the current sheet is produced by a primary instability of the internal kink type, the analysis of secondary instabilities indicates that reconnection proceeds on a time scale much shorter than the primary instability characteristic time. In the case of a sawtooth crash, non-collisional physics becomes important above a value of the Lundquist number which scales like S ~ (R/d_e)^{12/5}, in terms of the tokamak major radius R and of the electron skin depth d_e. This value …
Symmetric electron-positron plasmas in inhomogeneous magnetic fields are intrinsically subject to interchange instability and transport. Scaling relations for the propagation velocity of density blob perturbations relevant to transport in isothermal magnetically confined electron-positron plasmas are deduced, including damping effects when Debye lengths are large compared to Larmor radii. The relations are verified by nonlinear full-F gyrofluid computations. Results are in favour of sufficient magnetic confinement for planned electron-positron plasma experiments. The model is generalised to ot…
A new quasi-neutral model describing the Weibel instability of a high-current relativistic beam propagating through a resistive plasma is developed. It treats beam electrons as kinetic particles, and ambient plasma as a non-relativistic fluid. For a finite-temperature beam, a new class of negative energy magneto-sound waves is identified, which can possess negative energy. Their growth due to collisional dissipation in the cold return current destabilizes the beam-plasma system even for high beam temperatures. We perform detailed two- and three-dimensional particle-in-cell (PIC) simulations of…
Generation of relativistic electron (RE) beams during ultraintense laser pulse interaction with plasma targets is studied by collisional particle-in-cell (PIC) simulations. Strong magnetic field with transverse scale length of several local plasma skin depths, associated with RE currents propagation in the target, is generated by filamentation instability (FI) in collisional plasmas, inducing a great enhancement of the divergence of REs compared to that of collisionless cases. Such effect is increased with laser intensity and target charge state, suggesting that the RE divergence might be impr…
A self-consistent model is presented for performing steady-state fully kinetic Particle-in-Cell simulations of magnetised plasma plumes. An energy-based electron reflection prevents the numerical pump instability associated with a typical open-outflow boundary, and is shown to be sufficiently general that both the plume kinetics and plasma potential demonstrate domain independence (within 4%). This is upheld by non-stationary Robin-type boundary conditions on the Poisson's equation, coupled to a capacitive circuit that allows physical evolution of the downstream potential drop in the transient…
The thin-shell instability has been named as one process, which can generate entangled structures in astrophysical plasma on collisional (fluid) scales. It is driven by a spatially varying imbalance between the ram pressure of the inflowing upstream plasma and the downstream's thermal pressure at a non-planar shock. Here we show by means of a particle-in-cell (PIC) simulation that an analogue process can destabilize a thin shell formed by two interpenetrating, unmagnetized and collisionless plasma clouds. The amplitude of the shell's spatial modulation grows and saturates after about ten inver…
In this study, the physics of sheath formation in a collisional two-electron temperature plasma in the presence of an oblique external magnetic field has been investigated. At first, a comparative study among the fluid electron model, Boltzmann electron model and the nonextensive electron model has been carried out and a suitable range of nonextensive parameter q has been predicted. In the latter part, a collisional two-electron temperature plasma is considered. Both the hot and cold electron densities are described using the non-extensive distribution whereas cold ions are described by the fl…
Kinetic instabilities in weakly collisional, high beta plasmas are investigated using two-dimensional hybrid expanding box simulations with Coulomb collisions modeled through the Langevin equation (corresponding to the Fokker-Planck one). The expansion drives a parallel or perpendicular temperature anisotropy (depending on the orientation of the ambient magnetic field). For the chosen parameters the Coulomb collisions are important with respect to the driver but are not strong enough to keep the system stable with respect to instabilities driven by the proton temperature anisotropy. In the cas…
Within the resistive magnetohydrodynamic model, high-Lundquist number reconnection layers are unstable to the plasmoid instability, leading to a turbulent evolution where the reconnection rate can be independent of the underlying resistivity. However, the physical relevance of these results remains questionable for many applications. First, the reconnection electric field is often well above the runaway limit, implying that collisional resistivity is invalid. Furthermore, both theory and simulations suggest that plasmoid formation may rapidly induce a transition to kinetic scales, due to the f…
Temporal evolution of the inhomogeneous energy density driven instability (IEDDI) is examined in presence of a nonuniform transverse dc electric field in collisional magnetized plasma cylinder. Using experimentally known parameters relevant to IEDDI, we have estimated the growth rate for $ν$=1, 2 and 3 nonlocal eigenmodes.
We show that, under Braginskii magneto-hydrodynamics, anti-parallel gradients in average ion charge state and electron temperature can be unstable to the growth of self-generated magnetic fields. The instability is analogous to the field-generating thermomagnetic instability, although it is driven by the collisional thermal force magnetic source term rather than the Biermann battery term. The gradient in ion charge state causes a gradient in collisionality, which couples with temperature perturbations to create a self-generated magnetic field. This magnetic field deflects the electron heat flu…
Astrophysical and high-energy-density laboratory plasmas often have large-amplitude, sub-Larmor-scale electromagnetic fluctuations excited by various kinetic-streaming or anisotropy-driven instabilities. The Weibel (or the filamentation) instability is particularly important because it can rapidly generate strong magnetic fields, even in the absence of seed fields. Particles propagating in collisionless plasmas with such small-scale magnetic fields undergo stochastic deflections similar to Coulomb collisions, with the magnetic pitch-angle diffusion coefficient representing the effective "colli…
Studies have shown that in sheared $\mathbf{E}\times\mathbf{B}$ flows in an inhomogeneous ionospheric plasma, the gradient drift (GDI) or the Kelvin-Helmholtz (KHI) instability may grow. This work examines the conditions that cause one of these instabilities to dominate over the other using a novel model to study localized ionospheric instabilities. The effect of collisions with neutral particles plays an important role in the instability development. It is found that the KHI is dominant in low collisionality regimes, the GDI is dominant in high collisionality regimes, and there exists an inte…
The tertiary instability is believed to be important for governing magnetised plasma turbulence under conditions of strong zonal flow generation, near marginal stability. In this work, we investigate its role for a collisionless strongly driven fluid model, self-consistently derived as a limit of gyrokinetics. It is found that a region of absolute stability above the linear threshold exists, beyond which significant nonlinear transport rapidly develops. While within this range a complex pattern of transient zonal evolution is observed before a stable profile is found, the Dimits transition its…
Instabilities of ion-acoustic waves in a dusty plasma with electron-drift, collisional, and dust charge fluctuations effects, have been investigated. The regimes are clearly marked out where the theory is applicable. The critical electron-drift velocity required to drive the instability is predicted. It is also shown that electron thermal conductivity and charged grains concentration enhance the growth of the ion-acoustic mode whereas ion-viscosity, ion-thermal conductivity, and dust charge fluctuations have a stabilizing effect.
We report a first principles study of the coupled evolution of energetic ions, background majority ions, electrons and electromagnetic fields in magnetised plasma during the linear phase of the lower hybrid drift instability. A particle-in-cell code, with one spatial and three velocity space co-ordinates, is used to analyse the evolving distribution of a drifting ring-beam population of energetic protons in physical space and gyrophase angle. This analysis is carried out for plasma parameters that approximate to edge conditions in large tokamaks, in a scenario that is motivated by observations…
It is shown that the transport in low temperature, collisional, bounded plasma is enhanced by instabilities at high magnetic field. While the magnetic field confines the electrons in a stable plasma, the instability completely destroys the confinement such that the transport becomes independent of the magnetic field in the highly magnetized limit. An analytical expression of the instability-enhanced collision frequency is proposed, based on a magnetic field independent edge-to-center density ratio.
We analyze the role of collisional effects on the coupling between ion-acoustic waves and neutrino flavor oscillations, discussing its relevance for plasma instabilities in extreme plasma environments like in type II supernovae, where intense neutrino bursts exist. Electrons (leptons) are coupled to the electron-neutrino fluid through the weak Fermi force, but the electron-neutrinos are allowed to convert to other neutrino flavors and vice-versa. Due to the typically slow frequency of neutrino flavor oscillations, many orders smaller than e.g. the plasma frequency, an effective energy transfer…
The transport of heat and particles in the relatively collisional edge regions of magnetically confined plasmas is a scientifically challenging and technologically important problem. Understanding and predicting this transport requires the self-consistent evolution of plasma fluctuations, global profiles and flows, but the numerical tools capable of doing this in realistic (diverted) geometry are only now being developed. Here a 5-field reduced 2-fluid plasma model for the study of instabilities and turbulence in magnetised plasmas is presented, built on the BOUT++ framework. This cold ion mod…
The initial state recurrence in numerical simulations of the Vlasov-Poisson system is a well-known phenomenon. Here we study the effect on recurrence of artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456-1459 (1958)]. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through a Eulerian col…
Wave-Energy Partition Governs Weak Collisional Damping in Cold Plasmas
School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学技术学院）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论部）
This paper develops a unified linear theory of local cross-field plasma instabilities, such as the Farley-Buneman, electron thermal, and ion thermal instabilities, in collisional plasmas with fully or partially unmagnetized multi-species ions. Collisional lasma instabilities in low-ionized, highly dissipative, weakly magnetized plasmas play an important role in the lower Earth's ionosphere and may be of importance in other planet ionospheres, star atmospheres, cometary tails, molecular clouds, accretion disks, etc. In the solar chromosphere, macroscopic effects of collisional plasma instabilit…
Magnetic reconnection, breaking and reorganization of magnetic field topology, is a fundamental process for rapid release of magnetic energy into plasma particles that occurs pervasively throughout the universe. In most natural circumstances, the plasma properties on either side of the reconnection layer are asymmetric, in particular for the collision rates that are associated with a combination of density and temperature and critically determine the reconnection mechanism. To date, all laboratory experiments on magnetic reconnections have been limited to purely collisional or collisionless re…
In the outskirts of the intracluster medium (ICM) in galaxy clusters, the temperature decreases with radius. Due to the weakly collisional nature of the plasma, these regions are susceptible to the magneto-thermal instability (MTI), which can sustain turbulence and provide turbulent pressure support in the ICM. This instability arises due to heat conduction directed along the magnetic field, with a heat conductivity which is normally assumed to be given by the Spitzer value. Recent numerical studies of the ion mirror and the electron whistler instability using particle-in-cell codes have shown…
