Tangled magnetic fields, often coexisting with an ordered mean field, have a major impact on turbulence and momentum transport in many plasmas, including those found in the solar tachocline and magnetic confinement devices. We present a novel mean field theory of potential vorticity mixing in $β$-plane magnetohydrodynamic (MHD) and drift wave turbulence. Our results show that mean-square stochastic fields strongly reduce Reynolds stress coherence. This decoherence of potential vorticity flux due to stochastic field scattering leads to suppression of momentum transport and zonal flow formation. A simple calculation suggests that the breaking of the shear-eddy tilting feedback loop by stochastic fields is the key underlying physics mechanism. A dimensionless parameter that quantifies the increment in power threshold is identified and used to assess the impact of stochastic field on the L-H transition. We discuss a model of stochastic fields as a resisto-elastic network.
Exact solutions of a magnetized plasma in a vorticity containing shear flow for constant temperature are presented. This is followed by the modification of these solutions by thermomagnetic currents in the presence of temperature gradients. It is shown that solutions which are unstable for a subsonic flow, are stable if the flow is supersonic. The results are applied to the problem of vorticity shear flow stabilization of a linear z-pinch discharge.
Multi species turbulence in inhomogeneous magnetised plasmas is found to exhibit symmetry breaking in the dynamical alignment of a third species with the fluctuating electron density and vorticity with respect to the magnetic field direction and the species' relative background gradients. The possibility of truly chiral aggregation of charged molecules in magnetized space plasma turbulence is discussed.
We present experimental data providing evidence for the formation of transient ($\sim 20~μ$s) plasmas that are simultaneously weakly magnetized (i.e., Hall magnetization parameter $ωτ> 1$) and dominated by thermal pressure (i.e., ratio of thermal-to-magnetic pressure $β> 1$). Particle collisional mean free paths are an appreciable fraction of the overall system size. These plasmas are formed via the head-on merging of two plasmas launched by magnetized coaxial guns. The ratio $λ_{gun}=μ_0 I_{gun}/ψ_{gun}$ of gun current $I_{gun}$ to applied magnetic flux $ψ_{gun}$ is an experimental knob for e…
The coherent vortex extraction method, a wavelet technique for extracting coherent vortices out of turbulent flows, is applied to simulations of resistive drift-wave turbulence in magnetized plasma (Hasegawa-Wakatani system). The aim is to retain only the essential degrees of freedom, responsible for the transport. It is shown that the radial density flux is carried by these coherent modes. In the quasi-hydrodynamic regime, coherent vortices exhibit depletion of the polarization-drift nonlinearity and vorticity strongly dominates strain, in contrast to the quasiadiabatic regime.
A novel plasma equilibrium in the high-$β$, Hall regime that produces centrally-peaked, high Mach number Couette flow is described. Flow is driven using a weak, uniform magnetic field and large, cross field currents. Large magnetic field amplification (factor 20) due to the Hall effect is observed when electrons are flowing radially inward, and near perfect field expulsion is observed when the flow is reversed. A dynamic equilibrium is reached between the amplified (removed) field and extended density gradients.
The thermal stability of a weakly magnetized, rotating, stratified, optically thin plasma is studied by means of linear-perturbation analysis. We derive dispersion relations and criteria for stability against axisymmetric perturbations that generalize previous results on either non-rotating or unmagnetized fluids. The implications for the hot atmospheres of galaxies and galaxy clusters are discussed.
Analysis of driven dust vortex flow is presented in a weakly magnetized plasma. The 2D hydrodynamic model is applied to the confined dust cloud in a non-uniform magnetic field in order to recover the dust vortex flow driven in a conservative force field setup, in absence of any non-conservative fields or dust charge variation. Although the time independent electric and magnetic fields included in the analysis provide conservative forcing mechanisms, when the a drift based mechanism, recently observed in a dusty plasma experiment by [M. Puttscher and A. Melzer, Physics of Plasmas, 21,123704(201…
A novel method aimed at a kinetic moments closure for a magnetized plasma with arbitrary collisionality is proposed. The intended first application is to a tokamak edge and scrape-off-layer plasma. The velocity distribution function for each species is expanded in 8 Gaussian Radial Basis Functions (GRBFs) which are essentially shifted Maxwellians at eight representative 3D-velocity points of drift. The vector of 8 fluid moments (for particle density, 3 particle fluxes, total energy density, and 3 energy fluxes) has an 8x8 analytic linear matrix relation to the vector of 8 GRBF density weights …
We consider a plasma described by means of a two-dimensional fluid model across a constant but non-uniform magnetic field $\mathbf{B} = B(x,y) \mathbf{\hat{z}}$. The dynamical evolution of the density and the vorticity takes into account the interchange instability and magnetic field inhomogeneities. First, in order to described the Finite Larmor Radius effects we apply the gyromap to build a Hamiltonian model with ion temperature from a cold-ion model. Second, we show that the gyromap is justified using Braginskii's closure for the stress tensor as well as an apt ordering on the fluctuating q…
We study the effect of magnetic field on the viscosity of charged particles in the weakly ionized and magnetized plasma with the power-law q-distributions by using the generalized Boltzmann equation of transport in nonextensive statistics. We derive six viscosity coefficients of electrons and ions in the complex plasma, including the magnetic field introduced four viscosity coefficients, where the q-parameter and magnetic field both play significant roles. By numerical analyses, we show that these viscosity coefficients depend strongly on the magnetic field and q-parameters of the weakly ioniz…
By using the generalized Boltzmann equation of transport and the first-order approximation of Chapman-Enskog expansion on the kappa-distribution function, we study the thermal conductivity and Dufour effects in the weakly ionized and magnetized plasma. We show that in the kappa-distributed plasma, the thermal conductivity and Dufour coefficient are significantly different from those in the Maxell-distributed plasma, and the transverse thermal conductivity and Dufour coefficient in the kappa-distributed plasma are generally greater than those in the Maxwell-distributed plasma, and the Righi-Led…
An expression for the internal energy of a fluid element in a weakly coupled, magnetized, anisotropic plasma is derived from first principles. The result is a function of entropy, particle density and magnetic field, and as such plays the role of a thermodynamic potential: it determines in principle all thermodynamic properties of the fluid element. In particular it provides equations of state for the magnetized plasma. The derivation uses familiar fluid equations, a few elements of kinetic theory, the MHD version of Faraday's law, and certain familiar stability and regularity conditions.
The saturation mechanism of the Weibel instability is investigated theoretically by considering the evolution of currents in numerous cylindrical beams that are generated in the initial stage of the instability. Based on a physical model of the beams, it is shown that the magnetic field strength attains a maximum value when the currents in the beams evolve into the Alfven current and that there exist two saturation regimes. The theoretical prediction of the magnetic field strength at saturation is in good agreement with the results of two-dimensional particle-in-cell simulations for a wide ran…
Nonlinear propagation of purely stationary large amplitude electromagnetic (EM) solitary waves in a magnetized electron-positron (EP) plasma is studied using a fully relativistic two-fluid hydrodynamic model which accounts for physical regimes of both weakly relativistic $(P\ll nmc^2)$ and ultrarelativistic $(P\gg nmc^2)$ random thermal energies. Here, $P$ is the thermal pressure, $n$ the number density and $m$ the mass of a particle, and $c$ is the speed of light in vacuum. Previous theory in the literature [Phys. Plasmas \textbf{11}, 3078 (2004)] is advanced and generalized by the relativist…
We present results of 2D3V particle-in-cell simulations of non-relativistic plasma collisions with absent or parallel large-scale magnetic field for parameters applicable to the conditions at young supernova remnants. We study the collision of plasma slabs of different density, leading to two different shocks and a contact discontinuity. Electron dynamics play an important role in the development of the system. While non-relativistic shocks in both unmagnetized and magnetized plasmas can be mediated by Weibel-type instabilities, the efficiency of shock-formation processes is higher when a larg…
A sufficient condition for maser instability in a weakly magnetized relativistic plasma with an isotropic particle distribution function is given. The maser growth rates and polarizations are computed starting from the exact dielectric permittivity tensor of a magnetized plasma. For very weak magnetic fields, our results confirm the approximate validity of the 'standard maser theory', which is based on the Einstein coefficients method, with one significant exception. For inclined propagation and realistic (small but finite) field, the growth rates of the two (nearly circular) polarizations dif…
A first-principle study of diffusion in a strongly coupled one-component plasma in a magnetic field B is presented. As in a weakly coupled plasma, the diffusion coefficient perpendicular to the field exhibits a Bohm-like 1/B-behavior in the strong-field limit, but its overall scaling is substantially different. The diffusion coefficient parallel to the field is strongly affected by the field as well and also approaches a 1/B scaling, in striking contrast to earlier predictions.
When turbulent structures split more frequently before they decay, persistent turbulence forms in neutral fluid shear flows. Whether this concept can be extended to linear magnetized plasmas is investigated here and compared to the behavior of the pipe flow. With increasing control parameter the dynamics in the magnetized plasmas is known to undergo several changes from a quasiperiodic to a phase locked to a weakly turbulent regime. When the phase-locked regime breaks down, the splitting time approaches the decreasing lifetime reflecting self-sustained turbulence, as known from the pipe flow.
We report on 3D-3V particle-in-cell simulations of fast-ion energy-loss rates in cold, weakly-magnetized, weakly-coupled plasma where the electron gyroradius, $ρ_{e}$, is comparable to or less than the Debye length, $λ_{De}$, and the fast-ion velocity exceeds the electron thermal velocity, a regime in which the electron response may be impeded. These simulations use explicit algorithms, spatially resolve $ρ_{e}$ and $λ_{De}$, and temporally resolve the electron cyclotron and plasma frequencies. For mono-energetic dilute fast ions with isotropic velocity distributions, these scaling studies of …
It is demonstrated that targets with a broken rotational symmetry may facilitate generation of a strong axial (poloidal) magnetic field. An intense laser beam irradiating such a target creates intense electron currents carrying vorticity and producing strong spontaneous magnetic fields. Combined with a laser electron acceleration, such targets may be used for generation and guiding of magnetized, collimated particle or plasma beams.
Previous studies on the beam-driven plasma emission process were done mainly for unmagnetized plasmas. Here we present fully-kinetic electromagnetic particle-in-cell simulations to investigate such process in weakly-magnetized plasmas of the solar corona conditions. The primary mode excited is the beam-Langmuir (BL) mode via the classical bump-on-tail instability. Other modes include the whistler (W) mode excited by the electron cyclotron resonance instability, the generalized Langmuir (GL) waves that include a superluminal Z-mode component with smaller wave number $k$ and a thermal Langmuir c…
We study the linear stability of weakly magnetized differentially rotating plasmas in both collisionless kinetic theory and Braginskii's theory of collisional, magnetized plasmas. We focus on the very weakly magnetized limit that is important for understanding how astrophysical magnetic fields originate and are amplified at high redshift. We show that the single instability of fluid theory - the magnetorotational instability mediated by magnetic tension - is replaced by two distinct instabilities, one associated with ions and one with electrons. Each of these has a different way of tapping int…
The friction force on a test particle traveling through a plasma that is both strongly coupled and strongly magnetized is studied using molecular dynamics simulations. In addition to the usual stopping power component aligned antiparallel to the velocity, a transverse component that is perpendicular to both the velocity and Lorentz force is observed. This component, which was recently discovered in weakly coupled plasmas, is found to increase in both absolute and relative magnitude in the strongly coupled regime. Strong coupling is also observed to induce a third component of the friction forc…
We consider a recently derived kinetic model for weakly relativistic quantum plasmas. We find that that the effects of spin-orbit interaction and Thomas precession may alter the linear dispersion relation for a magnetized plasma in case of high plasma densities and/or strong magnetic fields. Furthermore, the ponderomotive force induced by an electromagnetic pulse is studied for an unmagnetized plasma. It turns out that for this case the spin-orbit interaction always give a significant contribution to the quantum part of the ponderomotive force.
Magnetized plasmas are well known to exhibit a rich spectrum of collective modes. Here, we focus on the density modes in dense or cold plasmas, where strong coupling effects alter the mode spectrum known from traditional weakly coupled plasmas. In particular, we study the dynamic structure factor (DSF) of the magnetized one-component plasma with molecular dynamics simulations. Extending our previous results [H.~Kählert and M.~Bonitz, Phys. Rev. Research \textbf{2022}, 4, 013197], it is shown that Bernstein modes can be observed in the weakly magnetized regime, where they are found below the up…
We determine the growth rate of linear instabilities resulting from long-wavelength transverse perturbations applied to periodic nonlinear wave solutions to the Schamel-Korteweg-de Vries-Zakharov-Kuznetsov (SKdVZK) equation which governs weakly nonlinear waves in a strongly magnetized cold-ion plasma whose electron distribution is given by two Maxwellians at slightly different temperatures. To obtain the growth rate it is necessary to evaluate non-trivial integrals whose number is kept to minimum by using recursion relations. It is shown that a key instance of one such relation cannot be used …
We consider wakefield generation in plasmas by electromagnetic pulses propagating perpendicular to a strong magnetic field, in the regime where the electron cyclotron frequency is equal to or larger than the plasma frequency. PIC-simulations reveal that for moderate magnetic field strengths previous results are re-produced, and the wakefield wavenumber spectrum has a clear peak at the inverse skin depth. However, when the cyclotron frequency is significantly larger than the plasma frequency, the wakefield spectrum becomes broad-band, and simultaneously the loss rate of the driving pulse is muc…
In weakly collisional astrophysical plasmas, such as the intracluster medium of galaxy clusters, the amplification of cosmic magnetic fields by chaotic fluid motions is hampered by the adiabatic production of magnetic-field-aligned pressure anisotropy. This anisotropy drives a viscous stress parallel to the field that inhibits the plasma's ability to stretch magnetic-field lines. I demonstrate through the use of kinetic simulations that in high-$β$ plasmas, kinetic ion-Larmor scale instabilities sever the adiabatic link between the thermal and magnetic pressures, reducing this viscous stress a…
Results from a numerical study of fluctuation dynamo in a collisionless, weakly magnetized plasma are presented. The key difference between this dynamo and its magnetohydrodynamic (MHD) counterpart is the adiabatic production of magnetic-field-aligned pressure anisotropy by the amplification of a weak seed field. This in turn drives kinetic instabilities on the ion-Larmor scale---namely, firehose and mirror---which sever the adiabatic link between the thermal and magnetic pressures, thereby allowing the dynamo to proceed. After an initial phase of rapid growth driven by these instabilities, th…
In non-collisional magnetized astrophysical plasmas, vortices can form as it is the case of the Venus plasma wake where Lundin et al. (2013) identified a large vortex through the integration of data of many orbits from the Venus Express (VEX) spacecraft. On the one hand, our purpose is to develop a theoretical foundation in order to explain the occurrence and formation of vortices in non-collisional astrophysical plasmas. On the other hand, to apply the latter in order to study the vorticity in the wakes of Venus and Mars. We introduce two theorems and two corollaries, which may be applicable …
Magnetothermodynamics (MTD) is the study of compression and expansion of magnetized plasma with an eye towards identifying equations of state for magneto-inertial fusion experiments. We present recent results from SSX experiments on the thermodynamics of compressed magnetized plasmas. In these experiments, we generate twisted flux ropes of magnetized, relaxed plasma accelerated from one end of a $1.5~m$ long copper flux conserver, and observe their compression in a closed conducting boundary installed at the other end. Plasma parameters are measured during compression. The instances of ion hea…
Using the dielectric theory for a weakly coupled plasma we investigate the stopping power of the ion in a temperature anisotropic magnetized electron plasma. The analysis is based on the assumption that the energy variation of the ion is much less than its kinetic energy. The obtained general expression for stopping power is analyzed for weak and strong magnetic fields (i.e., for the electron cyclotron frequency less than and greater than the plasma frequency), and for low and high ion velocities. It is found that the friction coefficient contains, in addition to the usual velocity independent…
A two-dimensional particle-in-cell simulation is performed to investigate weakly magnetized perpendicular shocks with a magnetization parameter of 6 x 10^-5, which is equivalent to a high Alfvén Mach number M_A of ~130. It is shown that current filaments form in the foot region of the shock due to the ion-beam--Weibel instability (or the ion filamentation instability) and that they generate a strong magnetic field there. In the downstream region, these current filaments also generate a tangled magnetic field that is typically 15 times stronger than the upstream magnetic field. The thermal ener…
We report the results of numerical simulations for a model of a one component plasma (a system of N point electrons with mutual Coulomb interactions) in a uniform stationary magnetic field. We take N up to 512, with periodic boundary conditions, and macroscopic parameters corresponding to the weak coupling regime, with a coupling parameter Γ=1/64. We find that a transition from order to chaos takes place when the density is increased or the field decreased so that the ratio ω_p/ω_c between plasma and cyclotron frequencies becomes of order 1 (or equivalently the ratio r_L/λ_D between Larmor rad…
Perpendicular relativistic ($γ_0=10$) shocks in magnetized pair plasmas are investigated using two dimensional Particle-in-Cell simulations. A systematic survey, from unmagnetized to strongly magnetized shocks, is presented accurately capturing the transition from Weibel-mediated to magnetic-reflection-shaped shocks. This transition is found to occur for upstream flow magnetizations $10^{-3}<σ<10^{-2}$ at which a strong perpendicular net current is observed in the precursor, driving the so-called current-filamentation instability. The global structure of the shock and shock formation time are …
Electron plasmas confined by an external magnetic field exhibit variations in a two-dimensional plane orthogonal to the confining magnetic field. A nonlinear fluid simulation code to investigate the properties of 2-D electron plasma wave turbulence in a nonuniform magnetoplasma has been developed. It is found that the presence of the density gradient convection by mean electric fields considerably influence the characteristic nonlinear interaction processes, such as the energy cascades and the cross-field electron transport. The initial random turbulent state evolves towards an intermittent st…
Scaling laws for the transport and heating of trace heavy ions in low-frequency, magnetized plasma turbulence are derived and compared with direct numerical simulations. The predicted dependences of turbulent fluxes and heating on ion charge and mass number are found to agree with numerical results for both stationary and differentially rotating plasmas. Heavy ion momentum transport is found to increase with mass, and heavy ions are found to be preferentially heated, implying a mass-dependent ion temperature for very weakly collisional plasmas and for partially-ionized heavy ions in strongly r…
We propose that pressure anisotropy causes weakly collisional turbulent plasmas to self-organize so as to resist changes in magnetic-field strength. We term this effect "magneto-immutability" by analogy with incompressibility (resistance to changes in pressure). The effect is important when the pressure anisotropy becomes comparable to the magnetic pressure, suggesting that in collisionless, weakly magnetized (high-$β$) plasmas its dynamical relevance is similar to that of incompressibility. Simulations of magnetized turbulence using the weakly collisional Braginskii model show that magneto-im…
Progress in the theory of anomalous diffusion in weakly turbulent cold magnetized plasmas is explained. Several proposed models advanced in the literature are discussed. Emphasis is put on a new proposed mechanism for anomalous diffusion transport mechanism based on the coupled action of conductive walls (excluding electrodes) bounding the plasma drain current (edge diffusion) together with the magnetic field flux "cutting" the area traced by the charged particles in their orbital motion. The same reasoning is shown to apply to the plasma core anomalous diffusion. The proposed mechanism is exp…
Magnetized plasma jets are generally modeled as magnetic flux tubes filled with flowing plasma governed by magnetohydrodynamics (MHD). We outline here a more fundamental approach based on flux tubes of canonical vorticity, where canonical vorticity is defined as the circulation of the species canonical momentum. This approach extends the concept of magnetic flux tube evolution to include the effects of finite particle momentum and enables visualization of the topology of plasma jets in regimes beyond MHD. A flared, current-carrying magnetic flux tube in an ion-electron plasma with finite ion m…
We employ magnetized plasma turbulence, described by a gyrokinetic formalism in an interval ranging from the end of the fluid scales to the electron gyroradius, to introduce the first study of kinetic intermittency, in which nonlinear structures formed directly in the distribution functions are analyzed by accounting for velocity space correlations generated by linear (Landau resonance) and nonlinear phase mixing. Electron structures are found to be strongly intermittent and dominated by linear phase mixing, while nonlinear phase mixing dominates the weakly intermittent ions. This is the first…
The question of how nonlinear interactions redistribute the energy of fluctuations across available degrees of freedom is of fundamental importance in the study of turbulence and transport in magnetized weakly collisional plasmas, ranging from space settings to fusion devices. In this letter, we present a theory for the dual cascade found in such plasmas, which predicts a range of new behavior that distinguishes this cascade from that of neutral fluid turbulence. These phenomena are explained in terms of the constrained nature of spectral transfer in nonlinear gyrokinetics. Accompanying this t…
In weakly collisional and collisionless magnetized plasmas, the pressure-strain interaction describes the rate of conversion between bulk flow and thermal energy density. In this study, we derive an analytical expression for the pressure-strain interaction in a coordinate system with an axis aligned with the local magnetic field. The result is eight groups of terms corresponding to different physical mechanisms that can contribute to the pressure-strain interaction. We provide a physical description of each term. The results are immediately of interest to weakly collisional and collisionless m…
Magnetic reconnection in strongly magnetized (low-beta), weakly collisional plasmas is investigated using a novel fluid-kinetic model [Zocco & Schekochihin, Phys. Plasmas 18, 102309 (2011)] which retains non-isothermal electron kinetics. It is shown that electron heating via Landau damping (linear phase mixing) is the dominant dissipation mechanism. In time, electron heating occurs after the peak of the reconnection rate; in space, it is concentrated along the separatrices of the magnetic island. For sufficiently large systems, the peak reconnection rate is $cE_{max}\approx 0.2v_AB_{y,0}$, whe…
The sheath formation in a weakly magnetized collisionless electronegative plasma consisting of electrons, negative and positive ions has been numerically investigated using the hydrodynamic equations. The electrons and negative ions are assumed to follow Boltzmann relation. A sheath formation criterion has been analytically derived. The paper focuses on studying the sheath structure by varying the electronegativity. It has been observed that the presence of negative ions has a substantial effect on the sheath structure. The observations made in the present work have profound significance on pr…
Intermittency of heating in weakly collisional plasma turbulence is an active subject of research, with significant potential impact on understanding of the solar wind, solar corona and astrophysical plasmas. Recent studies suggest a role of vorticity in plasma heating. In magnetohydrodynamics small scale vorticity is generated near current sheets and this effect persists in kinetic plasma, as demonstrated here with hybrid and fully kinetic Particle-In-Cell (PIC) simulations. Furthermore, vorticity enhances local kinetic effects, with a generalized resonance condition selecting sign-dependent …
