Finite Larmor Radius Corrections Research Articles

Effects of finite Larmor radius corrections and finite electron inertia on transverse Jean’s gravitational instability of radiative plasma with Hall current for star formation in ISM

We learn the consequences of finite ion Larmor radius (FLR) corrections, finite electron inertia, Hall current and radiative heat-loss function on the Jean’s-gravitational instability of an infinite homogeneous, viscous plasma integrating the impacts of finite electrical resistivity, thermal conductivity and permeability. A general dispersion relation is derived by means of the normal mode analysis method with the assistance of linearized perturbation equations of the problem. We find that the original Jeans criterion of gravitational instability is modified into the radiative instability criterion by the inclusion of thermal conductivity and radiative heat-loss function. The finite electrical resistivity eliminates the impact of the magnetic field and the viscosity of the medium eliminates the impact of FLR from radiative instability. The Hall parameter has no impact on the transverse mode of propagation. Numerical calculations demonstrate the stabilizing impact of temperature-dependent heat-loss function, FLR corrections and the destabilizing impact of density-dependent heat-loss function, finite electron inertia on the Jean’s-gravitational instability.

Firehose instability in heat-conducting solar wind plasmas including FLR corrections and electrical resistivity

The effects of finite Larmor radius (FLR) corrections and heat-flux vector are studied on the pressure anisotropy-driven firehose instability in finitely conducting solar wind plasmas described by the double-adiabatic Chew, Goldberger and Low (CGL) fluid theory. The fluid description of collisionless plasmas is governed through modified adiabatic equations due to the heat-flux vector and finite ion Larmor radius corrections. The analytical dispersion relation of the firehose instability has been derived using the normal mode analysis and discussed in the solar wind plasmas. In the transverse mode, the dispersion relation of the Alfvénic mode is modified due to electrical resistivity and FLR corrections. In the longitudinal mode, the effects of the heat-flux parameter and electrical resistivity are observed separately. The dispersion relation of the firehose mode is modified due to the combined effects of FLR corrections and electrical resistivity. The graphical illustrations show that finite electrical resistivity and ion Larmor frequency destabilize the growth rate of the firehose instability. The results are useful for analyzing the solar mission data to study the firehose instability in the solar wind plasmas.

Gyrofluid simulations of turbulence and reconnection in space plasmas

A Hamiltonian two-field gyrofluid model is used to investigate the dynamics of an electron-ion collisionless plasma subject to a strong ambient magnetic field, within a spectral range extending from the magnetohydrodynamic (MHD) scales to the electron skin depth. This model isolates Alfvén, Kinetic Alfvén and Inertial Kinetic Alfvén waves that play a central role in space plasmas, and extends standard reduced fluid models to broader ranges of the plasma parameters. Recent numerical results are reviewed, including (i) the reconnection-mediated MHD turbulence developing from the collision of counter-propagating Alfvén wave packets, (ii) the specific features of the cascade dynamics in strongly imbalanced turbulence, including a possible link between the existence of a spectral transition range and the presence of co-propagating wave interactions at sub-ion scales, for which new simulations are reported, (iii) the influence of the ion-to-electron temperature ratio in two-dimensional collisionless magnetic reconnection. The role of electron finite Larmor radius corrections is pointed out and the extension of the present model to a four-field gyrofluid model is discussed. Such an extended model accurately describes electron finite Larmor radius effects at small or moderate values of the electron beta parameter, and also retains the coupling to slow magnetosonic waves.

Modeling of the Polytropic Index and Temperature Anisotropy in the Solar Wind

The polytropic index is a fundamental physical parameter related to the thermodynamic processes present in space and astrophysical plasmas. This paper investigates the theoretical relationship between the polytropic index and the temperature anisotropy for flow parameters relevant to space plasmas. The derivation is based on the Chew–Goldberger–Low double-adiabatic equations of state and the finite Larmor radius correction. On the basis of this, we present the polytropic index relation, taking into account the temperature anisotropy, flow speed, and magnetic field of the plasma. This relation was further analyzed for the limit of the quasi-parallel and quasi-transversal cases. The quasi-transversal limit gives a polytropic index as a function of the anisotropic temperature γ = 1 + 2[2T ⊥ − T ∥]/[2T ⊥ + T ∥]. Using this result, we analyze the polytropic index for the bulk proton parameters derived from Ulysses spacecraft data spanning the interval from 1992 January 1 to 2009 June 30, and we find an average polytropic index of γ ∼ 1.43. This value is close to that of recently published results. However, unlike previous statistical studies, this research computes the polytropic index without relying on power-law fitting, and its variation is now associated with the anisotropic temperature.

Shear Alfvén waves within magnetic islands

We calculate Alfvén eigenmodes within a magnetic island (MiAE) which have been conjectured over a decade ago. Starting from a cylindrical plasma equilibrium, we calculate the complete metric of the island interior assuming an iota profile with a constant shear for Wendelstein 7-X parameters. Then, we solve the resulting Magneto-Hydrodynamic equations inside the island optionally considering Finite Larmor Radius corrections. We find various eigenmodes in the lowest gaps for n = 0. The eigenmode with the lowest frequency shows a weakly non-linear dependence on the island width which deviates considerably from an earlier estimate.

Influence of ion-to-electron temperature ratio on tearing instability and resulting subion-scale turbulence in a low- β e collisionless plasma

A two-field gyrofluid model including ion finite Larmor radius (FLR) corrections, magnetic fluctuations along the ambient field, and electron inertia is used to study two-dimensional reconnection in a low βe collisionless plasma, in a plane perpendicular to the ambient field. Both moderate and large values of the ion-to-electron temperature ratio τ are considered. The linear growth rate of the tearing instability is computed for various values of τ, confirming the convergence to reduced electron magnetohydrodynamics predictions in the large τ limit. Comparisons with analytical estimates in several limit cases are also presented. The nonlinear dynamics leads to a fully developed turbulent regime that appears to be sensitive to the value of the parameter τ. For τ = 100, strong large-scale velocity shears trigger Kelvin–Helmholtz instability, leading to the propagation of the turbulence through the separatrices, together with the formation of eddies of size of the order of the electron skin depth. In the τ = 1 regime, the vortices are significantly smaller and their accurate description requires that electron FLR effects be taken into account.

A mixed Fourier-variational approach to solve differential or integro-differential wave equations for magnetised plasmas

The All ORders Spectral Algorithm (AORSA) wave equation solver by Jaeger (Jaeger et al 2001 Phys. Plasmas 8 1573) solves the integro-differential wave equation relevant for the radio frequency (RF) domain and for fusion-relevant conditions in tokamaks or stellarators, retaining all finite Larmor radius corrections by substituting the continuous Fourier integrals by a sum over a discrete set of modes. Its strength is also its weakness: the simplicity of the method results in significant computational effort, a full matrix needing to be inverted to solve the associated linear system. Based on the notion that modes are gradually more independent if their eigenvalues differ, the present paper proposes a straightforward numerical method to partly alleviate this need, allowing to substitute the full system matrix by a banded one. The adopted method can be applied to a wide variety of equations. A few 1D examples—of relevance for solving the wave equation in the RF domain of frequencies—are provided: the tunneling equation is used to illustrate the potential of the method, and the all-FLR wave equation (retaining all Finite Larmor Radius corrections in the dielectric response) adopted by Jaeger is solved comparing the solutions found to those based on simpler models (a cold plasma and a ‘tepid plasma’ - i.e. a kinetic model truncated at zero order in Larmor radius—description).

Effects of electron inertia and finite-Larmor radius correction on Jeans instability of quantum plasma with the impact of cosmic pressure

We present a theoretical investigation of the Jeans instability in quantum plasma, taking into consideration cosmic ray (CR) pressure and diffusion effects using a generalized magneto-hydrodynamic (MHD) model. Our analysis incorporates finite electron inertia, finite electrical resistivity, and finite Larmor radius (FLR) correction. By applying the normal mode technique, we derive a unique form of a generalized dispersion relation that describes the behavior of the system. We further discuss this dispersion relation under different limiting cases. Interestingly, we find that all considered parameters have distinct impacts on the growth rate of the system in various scenarios. Additionally, our exploration reveals that both CR-driven acoustic speed as well as quantum parameter influence the conditions for Jeans instability while the remaining parameters do not have any impact on it. Consequently, when combined with the quantum parameter, electron inertia and FLR correction act as stabilizing agents to suppress instability. This research sheds light on the intricate processes involved in structure formation in the universe, highlighting the significance of considering quantum corrections, electron inertia, and FLR to accurately model the dynamics and stability of cosmic plasma systems.

Wave modes and instabilities in gravitating magnetized polytropic quantum plasmas including viscosity tensor and FLR corrections

ABSTRACT The present analytical study extends the problems of pressure anisotropy-driven instabilities and gravitational instability in space plasmas to mixed quantum polytropic gas in the interior of dense stars accounting for the effects of viscosity, finite Larmor radius (FLR) and self-gravitational effects. The generalized polytrope pressure laws are considered as adiabatic equations in which the pressure components depend upon the plasma density, magnitude of the magnetic field, and the polytrope indices. The modified properties of waves and instabilities in gravitating quantum plasmas have been analysed using the quantum magnetohydrodynamic (QMHD) fluid description in the magnetohydrodynamic (MHD) and Chew–Goldberger–Low (CGL) limits. In the parallel propagation, the Jeans instability modified by quantum diffraction parameters and firehose mode modified by FLR parameter is obtained separately. The Jeans instability condition depends upon the quantum diffraction term and polytrope index β, and it remains unaffected due to viscosity and ion Larmor frequency. The growth rate of the Jeans instability decreases due to viscosity and quantum diffraction parameters, while the growth rate of the firehose instability increases due to FLR corrections. In the transverse mode, a similar nature is observed in the growth rates; however, the instability region decreases significantly due to polytrope indices and different dispersion properties of MHD and CGL viscous quantum plasmas. The analytical results have been applied in dense degenerate stars to measure the characteristic parameters and understand the MHD wave propagation, pressure anisotropy-driven, and gravitationally driven instabilities.

Rayleigh–Taylor stability of quantum magnetohydrodynamic plasma with electron inertia and resistivity

Abstract The analytical observation of the simultaneous impacts of electrical resistivity, finite Larmor radius (FLR) correction, and electron inertia on the magnetohydrodynamic Rayleigh–Taylor unstable mode of incompressible rotating quantum plasma is carried out. The perturbation formulations of the problem are derived by applying the QMHD model to obtain the dispersion equation for the stratified quantum hydrodynamic fluid plasma. The dispersion equation is analyzed graphically and numerically for the various cases. It is obtained that the simultaneous impacts of rotation, resistivity, FLR correction, electron inertia, and quantum correction modify the Rayleigh–Taylor (RT) unstable mode of the stratified magnetized fluid plasma. The graphical studies show that the rotational effect destabilizes or stabilizes the Rayleigh–Taylor (RT) instability of the magnetized quantum plasma, with or without the impacts of electrical resistivity and electron inertia. This result may be useful for studying the magnetic reconnection process and its applications, viz., supernova explosions, neutron stars, white dwarfs, etc.

Effect of Finite Ion Larmor Radius (FLR) Corrections on Thermal Instability of Rotating Radiative Porous Astrophysical Plasma in Interstellar Medium (ISM)

Infinite homogeneous plasma’s thermal instability has been studied in relation to finite ion Larmor radius (FLR) corrections, rotation, and porosity, as well as the impacts of radiative heat-loss function and thermal conductivity. With the aid of a normal mode analysis framework and the necessary difficulty-appropriate linearized perturbation equations, a universal dispersion relation is investigated. For the propagation of transverse waves, this dispersion relationship further condenses for rotation axes parallel to and at right angles to the magnetic field. It is proven that the presence of rotation, porosity, thermal conductivity, and radiative heat-loss function altered the thermal instability criterion. To show how different parameters affect the rate at which the thermal instability grows, numerical calculations have been carried out. We discover that rotation, FLR corrections, and medium porosity stabilised the growth rate of the thermal system in the transverse mode of propagation. The conclusion of this research states that the rotation, porosity, and FLR corrections have an impact on the configuration of dense molecular clouds and star formation.

Kelvin–Helmholtz stability of rotating magnetoplasma with electron inertia

Abstract In this theoretical exploration, the stabilizing or destabilizing impacts of the rotation, electron inertia, and electrical resistivity on the Kelvin–Helmholtz stability in two-superimposed incompressible magnetized plasma fluids incorporating finite ion Larmor radius (FLR) correction and suspended dust particulates are studied. The linearized perturbation equations for the Kelvin–Helmholtz instability problems are determined based on the magnetohydrodynamic (MHD) model. The general dispersion equation is derived by using appropriate boundary conditions. By the numerical estimation, the finite ion Larmor radius does not have any significant role in the Kelvin–Helmholtz instability of the magnetoplasma medium. The graphical estimates reveal the destabilization impact of the resistivity and electron inertia on the Kelvin–Helmholtz hydrodynamic plasma fluid system. In this paper, graphical representations have also analyzed the effect of rotation on the Kelvin–Helmholtz stability growth rate with the variation of electron inertia and resistivity. This current analysis provides pertinent information about the significant involvement of this considered system in space and astrophysical structures.

Long-wavelength closures for collisional and neutral interaction terms in gyro-fluid models

A collisional gyro-fluid model is presented. The goal of the model is edge and scrape-off layer turbulence. The emphasize in the model derivation heavily lies on ”implementability” with today’s numerical methods. This translates to an avoidance of infinite sums, strongly coupled equations in time and intricate elliptic operator functions. The resulting model contains the four moments density, parallel momentum, perpendicular pressure and parallel energy and is closed by a polarisation equation and parallel Ampere law. The central ingredient is a collisional long-wavelength closure that relies on a drift-fluid gyro-fluid correspondence principle. In this way the extensive literature on fluid collisions can be incorporated into the model including sources, plasma-neutral interactions and scattering collisions. Even though this disregards the characteristic finite Larmor radius terms in the collisional terms the resulting model is at least as accurate as the corresponding drift-fluid model in these terms. Furthermore, the model does enjoy the benefits of an underlying variational principle in an energy-momentum theorem and an inherent symmetry in moment equations with regards to multiple ion species. Consistent particle drifts as well as finite Larmor radius corrections and high amplitude effects in the advection and polarization terms are further characteristics of the model. Extensions and improvements like short-wavelength expressions, a trans-collisional closure scheme for the low-collisionality regime or zeroth order potential must be added at a later stage.

Dissipation of hydromagnetic waves in the viscous polytropic zone of the solar wind including FLR corrections, ohmic diffusion, and the Hall effect

ABSTRACT In the polytropic zone of the solar wind, we have used the generalized polytrope pressure laws to investigate the dissipation of hydromagnetic waves and pressure-anisotropy-driven fluid instabilities in magnetized viscous plasmas, including finite Larmor radius (FLR) corrections and non-ideal magnetohydrodynamic (MHD) effects. The modified dispersion properties have been analysed in the MHD and Chew–Goldberger–Low (CGL) limits for typical conditions of the solar wind and corona. The theoretical results are found to be in good agreement with the observational data, which shows that the MHD and CGL waves are dissipated due to viscous and ohmic diffusion. The FLR and Hall parameters show destabilizing and stabilizing influences, respectively, for the strong magnetic fields in the solar corona, and reversed effects in the case of weak magnetic fields in the solar wind. In the solar corona, the CGL wave dissipation achieves the required damping rate in the minimum time than the dissipation of the MHD waves. The damping time is mainly associated with the considered parameters and was found to be larger for the MHD wave dissipation than the CGL wave dissipation. The theoretical results successfully demonstrate the role of the considered parameters on the reverse and forward shock waves and instabilities as observed in the solar wind parameters versus heliolatitude graph using Ulysses observations for r = 5.41 au. The results are helpful to explore the possibilities of MHD waves and pressure-anisotropy-driven fluid instabilities in the polytropic zone of the solar wind that will probably be observed by the Parker Solar Probe (PSP) mission.

Effect of rotation and FLR corrections with radiative heat-loss functions on transverse thermal instability of astrophysical porous plasma in interstellar medium (ISM)

The effect of rotation, finite ion Larmor radius (FLR) corrections and porosity on the thermal instability of infinite homogeneous plasma has been explored taking the effects of radiative heat-loss function and thermal conductivity. The general dispersion relation is derived by means of the normal mode analysis scheme with the help of appropriate linearized perturbation equations of the problem. This dispersion relations is further reduces for rotation axis parallel and perpendicular to the magnetic field for transverse wave propagation. It is found that the presence of rotation, FLR corrections and porosity amend the fundamental thermal criterion of instability. Numerical computations have been executed. Our result demonstrates that the rotation, porosity and FLR corrections affect the dens molecular clouds configuration and star formation.

Direct kinetic Alfvén wave energy cascade in the presence of imbalance

A two-field Hamiltonian gyrofluid model for kinetic Alfvén waves retaining ion finite Larmor radius corrections and parallel magnetic field fluctuations is used to study direct turbulent cascades from the magnetohydrodynamic to the sub-ion scales. For moderate energy imbalance and weak enough magnetic fluctuations, the spectrum of the transverse magnetic field and that of the most energetic wave display a steep transition zone near the ion scale, while the parallel transfer (and thus the parallel dissipation) remains weak. In this regime, the perpendicular flux of generalized cross-helicity displays a significant decay past the ion scale, while the perpendicular energy flux remains almost constant. A phenomenological model suggests that the interactions between co-propagative waves present at the sub-ion scales can play a central role in the development of a transition zone in the presence of a helicity barrier.

Critical comparison of collisionless fluid models: Nonlinear simulations of parallel firehose instability

Two different fluid models for collisionless plasmas are compared. One is based on the classical Chew–Goldberger–Low (CGL) model that includes a finite Larmor radius correction and the Landau closure for the longitudinal mode. Another one takes into account the effect of cyclotron resonance in addition to Landau resonance and is referred to as the cyclotron resonance closure (CRC) model [T. Jikei and T. Amano, Phys. Plasmas 28, 042105 (2021)]. While the linear property of the parallel firehose instability is better described by the CGL model, the electromagnetic ion cyclotron instability driven unstable by the cyclotron resonance is reproduced only by the CRC model. Nonlinear simulation results for the parallel firehose instability performed with the two models are also discussed. Although the linear and quasilinear isotropization phases are consistent with theory in both models, long-term behaviors may be substantially different. The final state obtained by the CRC model may be reasonably understood in terms of the marginal stability condition. In contrast, the lack of cyclotron damping in the CGL model makes it rather difficult to predict the long-term behavior with simple physical arguments. This suggests that incorporating collisionless damping both for longitudinal and transverse modes is crucial for a nonlinear fluid simulation model of collisionless plasmas.

Gravitational instability in radiative molecular clouds including cosmic ray diffusion and ion Larmor radius corrections

ABSTRACT The effects of cosmic ray (CR) diffusion and finite Larmor radius (FLR) corrections have been studied on the linear gravitational instability of thermally conducting plasmas typically in the H ii regions of molecular clouds. The hydrodynamic fluid–fluid approach is considered for interacting CRs with gravitating, magnetized, and thermally conducting gas in molecular clouds. The magnetohydrodynamic fluid model is formulated considering CR pressure gradients, CR diffusion, and radiative and FLR effects in terms of particle Larmor radius. The dispersion relation of the gravitational instability is analytically derived using the normal mode analysis, and the effects of CRs and FLR corrections have been discussed in longitudinal and transverse modes. It is observed that in the absence of CRs, the FLR effects (magnetic viscosity) reduce the growth rate for wavenumber smaller than a critical value, and above it gets increased. However, the growth rate is strongly suppressed in the presence of combined CRs and FLR effects. The individual behaviour of FLR effects is observed to destabilize the growth rate of the gravitational instability in the presence of CR effects. The CR pressure decreases the growth rates of the gravitational and thermal instabilities, whereas parallel CR diffusion enhances the growth rate of the gravitational instability. The Jeans length of the gravitating gas cloud gets increased due to an increase in the CR-to-gas pressure ratio. It is found that the gravitational collapse of the system is supported by high-energy (above knee) CR particles with the Larmor radii comparable to the cloud size. The present results have been applied to understand the role of CRs and FLR corrections on the gravitational collapse in the H ii regions of molecular clouds.

ICRF modelling in 2D and 3D magnetic configurations using a hot plasma model

The generation of energetic trapped ions is important for experiments investigating their confinement in 3D magnetic fields, for plasma heating, for studies into unwanted drive of instabilities, and improved transport regimes. An effective way to generate such energetic ions is with ion cyclotron resonance heating. SCENIC is a tool built to self consistently model the magnetic equilibrium, the radio frequency wave, and the minority distribution function in steady state. In this paper the impact of higher order finite Larmor radius corrections in the dielectric tensor will be described. The RF electric field and the power deposition in the new hot model are compared against the previously used warm model for several JET plasmas. Considerable differences are found in some of the scenarios. The new version of the wave code LEMan also supports the direct use of particle-in-cell marker data to compute the dielectric tensor. An expression for the dielectric tensor is derived, and it is applied to a test case in JET. The power deposition profile agrees very well with that of a Maxwellian reference case, which is promising for future applications. Moreover, a full SCENIC run shows a significantly enhanced fast ion tail. In a demonstration of the novel features of LEMan, it is also applied to minority heating in the intrinsically 3D plasma of W7-X.

Study of stability and rotation of a chain of saturated, freely-rotating magnetic islands in tokamaks

The non-linear dynamics of a chain of stationary, saturated magnetic islands is studied by solving a four-field system of equations that include non-ideal effects, lowest order finite Larmor radius corrections and neoclassical terms. The magnetic island rotation velocity is calculated self-consistently with the fields profiles. The solutions for the island rotation velocity and for the ion polarization current are determined as a function of the characteristic parameters of the system and the results are discussed. The results of the calculations show that island rotation velocity and the ion polarization current depend in a non-trivial way on the parameters characterizing the system, and some clear patterns emerge only in particular cases. An analysis of magnetic island rotation velocity is performed on experiments in COMPASS tokamak. Measured island rotation velocity is compared with the calculated ion and electron flow velocities, for different hypotheses on the toroidal rotation of the plasma. The comparison shows that the island rotation velocity is consistent with the ion flow velocity, under the hypothesis of slow toroidal rotation and low collisionality. Theoretical calculation of the island rotation velocity according to the model here developed suggests that the islands rotate weakly in the ion direction, in the hypothesis of slow toroidal rotation and high collisionality. The impossibility of directly measuring the plasma rotation velocity makes it difficult to distinguish between these different regimes.