Finite Ion Larmor Radius Research Articles

Hybrid-Vlasov Modelling of Ion Velocity Distribution Functions Associated with the Kelvin–Helmholtz Instability with a Density and Temperature Asymmetry

The Kelvin–Helmholtz instability (KHI), characterized by vortices forming at a perturbed velocity shear layer, is a prominent candidate mechanism for mass, momentum, and energy transport across boundaries with velocity shear in various space plasma environments. It is of particular interest at the flanks of Earth’s magnetopause, which separates the plasma of the magnetosphere from the adjacent shocked solar wind flow in the magnetosheath. In the present study, we use local hybrid-Vlasov simulations to investigate the ion velocity distribution functions (VDFs) associated with KHI in a magnetopause-like, transverse velocity shear layer setting (magnetic field perpendicular to the shear plane). We look for signatures of ion finite Larmor radius (FLR) effects, which could be utilized in spacecraft measurements to recognize when such effects are active, influencing KHI evolution and driving plasma mixing. We show that when a density/temperature asymmetry exists across the shear layer, FLR effects produce a heat flux along the vortex edges. With a magnitude (≳0.1 mW m−2) that is a significant fraction of the total magnetosheath energy flux, the heat flux provides a distinct signature that could be measured with a single spacecraft. During the late nonlinear stage of KHI, mixed non-Maxwellian ion VDFs are additionally found within the vortices. Our results are also valid in the presence of a small magnetic shear across the magnetopause.

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.

Simulating energetic ions and enhanced fusion rates from ion-cyclotron resonance heating with a full-wave/Fokker–Planck model

Reproducing fast-ion enhanced fusion rates from ion-cyclotron resonance heating (ICRH) in tokamaks requires the self-consistent coupling of a full-wave solver and a Fokker–Planck solver, which evolves multiple simultaneously resonant ion species. We introduce a new self-consistent model that iterates the TORIC full-wave solver with the CQL3D Fokker–Planck solver using the integrated plasma simulator (IPS). This model evolves the bounce-averaged ion distribution functions in both parallel and perpendicular velocity-space with a quasilinear radio frequency (RF) diffusion operator valid in the ion finite Larmor radius (FLR) limit and the RF electric fields with the resultant non-Maxwellian FLR dielectric tensor. This produces non-Maxwellian ICRH simulations that are fully self-consistent, fast, and interoperable with integrated modeling frameworks, such as TRANSP/GACODE/IPS-FASTRAN. We demonstrate our model's capabilities by validating it against experimental data in Alcator C-Mod. We then perform the first RF heating simulations of SPARC using self-consistent non-Maxwellian ion distributions to investigate the potential to enhance fusion rates using ion cyclotron resonance heating generated fast ions.

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.

MAS: a versatile Landau-fluid eigenvalue code for plasma stability analysis in general geometry

We have developed a new global eigenvalue code, multiscale analysis for plasma stabilities (MAS), for studying plasma problems with wave toroidal mode number (n) and frequency (ω) in a broad range of interest in general tokamak geometry, based on a five-field Landau-fluid description of thermal plasmas. Beyond keeping the necessary plasma fluid response, we further retain the important kinetic effects including diamagnetic drift, ion finite Larmor radius, finite parallel electric field (), ion and electron Landau resonances in a self-consistent and non-perturbative manner without sacrificing the attractive efficiency in computation. The physical capabilities of the code are evaluated and examined in terms of both theory and simulation. In theory, the comprehensive Landau-fluid model implemented in MAS can be reduced to the well-known ideal magnetohydrodynamic (MHD) model, electrostatic ion-fluid model, and drift-kinetic model in various limits, which clearly delineates the physics validity regime. In simulation, MAS has been well benchmarked with theory and other gyrokinetic and kinetic-MHD hybrid codes in a manner of adopting the unified physical and numerical framework, which covers the kinetic Alfvén wave, ion sound wave, low-n kink, high-n ion temperature gradient mode and kinetic ballooning mode. Moreover, MAS is successfully applied to model the Alfvén eigenmode (AE) activities in DIII-D discharge #159243, which faithfully captures the frequency sweeping of reversed shear AE, the tunneling damping of toroidal AE, as well as the polarization characteristics of kinetic beta-induced AE and beta-induced Alfvén-acoustic eigenmode being consistent with former gyrokinetic theory and simulation. With respect to the key progress contributed to the community, MAS has the advantage of combining rich physics ingredients, realistic global geometry and high computation efficiency together for plasma stability analysis in the linear regime.

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.

A gyro-fluid model of global geodesic acoustic modes supported by finite ion Larmor radius

A theory of global geodesic acoustic modes with short wavelengths based on the framework of an electrostatic gyro-fluid has been developed, in which the more thorough sorts of finite-ion-Larmor-radius effects are encompassed than in the two-fluid model (Wang et al 2021 Nucl. Fusion 61 106024), while the radial differential equation of the eigenmodes still comes up in a compact and analytically tractable form. By solving the corresponding boundary value problem numerically with typical equilibrium profiles, a multitude of global geodesic acoustic modes with quantized eigen-frequencies have been found. In particular, as the consequence of the plasma model improvement, we have obtained multiple edge-localized global geodesic acoustic modes with the features resembling those observed experimentally.

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.

Gyrofluid analysis of electron β e effects on collisionless reconnection

The linear and nonlinear evolutions of the tearing instability in a collisionless plasma with a strong guide field are analysed on the basis of a two-field Hamiltonian gyrofluid model. The model is valid for a low ion temperature and a finite $\beta _e$ . The finite $\beta _e$ effect implies a magnetic perturbation along the guide field direction, and electron finite Larmor radius effects. A Hamiltonian derivation of the model is presented. A new dispersion relation of the tearing instability is derived for the case $\beta _e=0$ and tested against numerical simulations. For $\beta _e \ll 1$ the equilibrium electron temperature is seen to enhance the linear growth rate, whereas we observe a stabilizing role when electron finite Larmor radius effects become more relevant. In the nonlinear phase, stall phases and faster than exponential phases are observed, similarly to what occurs in the presence of ion finite Larmor radius effects. Energy transfers are analysed and the conservation laws associated with the Casimir invariants of the model are also discussed. Numerical simulations seem to indicate that finite $\beta _e$ effects do not produce qualitative modifications in the structures of the Lagrangian invariants associated with Casimirs of the model.

Finite-Larmor-radius-induced global geodesic acoustic modes—a two-fluid model

A linear theory of ion finite-Larmor-radius (FLR)-induced global geodesic acoustic modes (GAMs) based on the electrostatic two-fluid model is developed, in which modest ion FLR effects are encompassed through polarization drifts. The radial differential equation obtained for the eigenmode is a type of generalized Schrödinger equation, in which the eigenfrequency is mixed with the potential term in a complex manner. By numerically solving this equation as a genuine boundary value problem, it is found that for typical equilibrium profiles, a series of global GAMs exist, with relatively higher frequencies that intersect with the GAM continuum. Those with frequencies in the intermediate range are forbidden by the singularity of the local dispersion function. When we restrict the poloidal θ harmonics up to m = ±1, we successfully interpret the bound-state profiles of global GAMs discovered in the simulation performed by Miyato et al (2006 Plasma Phys. Control. Fusion 48 A335). We also point out the limitation of their model.

Gyrokinetic theory of low-frequency electromagnetic waves in finite-β anisotropic plasmas

We present a gyrokinetic theory for the electromagnetic waves and instabilities with frequencies much lower than the ion cyclotron frequency in finite-β anisotropic uniform plasmas. Here, β is the ratio between plasma and magnetic pressures. Kinetic effects due to both the finite Larmor radii and wave-particle resonances are fully kept in the analysis. Corresponding linear dispersion relation and wave polarizations, valid for general β value and perpendicular wavelength, are then specifically derived for a bi-Maxwellian plasma. Analytic expressions for the criteria of kinetic firehose and mirror instabilities are also given. The mode frequency, stability, and wave polarization of a broad spectrum of normal modes are then investigated numerically in a systematic study over a set of parameters. Our study clearly demonstrates that, due to the finite ion Larmor radius effect, the ion-sound wave, mirror mode, and shear Alfvén wave are intrinsically coupled.

Influence of FLR correction on Jeans instability in rotating radiative QMHD fluid model

ABSTRACT The descriptive exploration of Jeans instability under the QMHD fluid model for magnetized radiative plasma, preserving the consequences of rotation and finite ion Larmor radius. The problem of equations is formulated by using the quantum magnetohydrodynamic fluid model. The general dispersion relations were achieved using a standard mode analysis by formulating a linearized equation set and the dispersion relations are explained in the transverse and parallel propagations of the magnetic field. Those latter particular situations are discussed in the light of the axis of rotation in the longitudinal and transverse magnetic field. From the numerical calculation, we observe that Jean's criteria are changed due to the existence of FLR corrections, the feature of radiation, quantum correction, and magnetic field. From the graphical presentation, we find that the effect of FLR correction with rotation, quantum correction, and the magnetic field is a more stabilizing impact on comparing the system than the simple gaseous plasma medium. The result demonstrates that the system's growth rate is affected by FLR, rotation, magnetic field, and quantum correction.

Two-fluid and finite Larmor radius effects on high-beta tokamak equilibria with flow in reduced magnetohydrodynamics

High-beta tokamak equilibria with flow comparable to the poloidal Alfvén velocity in the reduced magnetohydrodynamics (MHD) model with two-fluid and ion finite Larmor radius (FLR) effects are investigated. The reduced form of Grad-Shafranov equation for equilibrium with flow, two-fluid and FLR effects is analytically solved for simple profiles. The dependence of the Shafranov shift for the magnetic axis and the equilibrium limits on the poloidal beta and the poloidal Alfvén Mach number are modified by the two-fluid and FLR effects. In the presence of the diamagnetic drift due to the two-fluid effect, the equilibrium depends on the sign of the E × B drift velocity. The FLR effect suppresses the large modification due to the two-fluid effect. By constructing magnetic flux coordinates and a local equilibrium model from the analytic solution, the effects of the non-circular property of the magnetic flux surfaces in the poloidal cross-section on the components of the curvature vector is examined in detail. The analytic solution is also used for the benchmark of the numerical code. The numerical solutions with non-uniform pressure, density and temperature profiles show similar behavior to analytic solution.

Propagation of shear Alfvén waves in a two-ion plasma and application as a diagnostic for the ion density ratio

In this paper, we propose an efficient diagnostic technique for determining spatially resolved measurements of the ion density ratio in a magnetized two-ion species plasma. Shear Alfvén waves were injected into a mixed helium–neon plasma using a magnetic loop antenna, for frequencies spanning the ion cyclotron regime. Two distinct propagation bands are observed, bounded by $\omega < \varOmega _\textrm {Ne}$ and $\omega _{ii} < \omega < \varOmega _\textrm {He}$ , where $\omega _{ii}$ is the ion–ion hybrid cutoff frequency and $\varOmega _\textrm {He}$ and $\varOmega _\textrm {Ne}$ are the helium and neon cyclotron frequencies, respectively. A theoretical analysis of the cutoff frequency was performed and shows it to be largely unaffected by kinetic electron effects and collisionality, although it can deviate significantly from $\omega _{{ii}}$ in the presence of warm ions due to ion finite Larmor radius effects. A new diagnostic technique and accompanying algorithm was developed in which the measured parallel wavenumber $k_\parallel$ is numerically fit to the predicted inertial Alfvén wave dispersion in order to resolve the local ion density ratio. A major advantage of this algorithm is that it only requires a measurement of $k_\parallel$ and the background magnetic field in order to be employed. This diagnostic was tested on the Large Plasma Device at UCLA and was successful in yielding radially localized measurements of the ion density ratio.

Jeans instability of finitely conducting radiative rotating plasma with FLR corrections flowing through porous medium

The effect of radiative heat-loss functions, rotation, porosity, finite electrical resistivity and finite ion Larmor radius (FLR) corrections, on the gravitational instability of infinite homogeneous plasma, has been explored integrating the consequences of radiative heat-loss function and thermal conductivity. The general dispersion relation is obtained by means of the normal mode analysis method with the help of appropriate linearized perturbation equations of the problem. The general dispersion relation is further reduced for rotation axis parallel and perpendicular to the magnetic field. We locate that the presence of radiative heat-loss function and thermal conductivity amend the fundamental Jeans criterion of gravitational instability into radiative instability criterion. Numerical computations have been executed to show the effect of various parameters on the growth rate of the Jeans-gravitational instability. We find that rotation, FLR corrections and medium porosity stabilize the growth rate of the system in both the longitudinal mode and transverse mode of propagation. Our result demonstrates that the rotation, porosity and FLR corrections affect the dense molecular cloud configuration and star formation.

Temperature Gradient, Toroidal and Ion FLR Effects on Drift-Tearing Modes**Supported by the National MCF Energy R&D Program (Grant Nos. 2018YFE0304100, 2018YFE0311300, and 2017YFE0301300), the National Natural Science Foundation of China (Grant Nos. 11675256, 11675257, 11835016, and 11705275), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB16010300), the Key Research Program of Frontier Science of Chinese Academy

The influences of the temperature gradient and toroidal effects on drift-tearing modes have been studied using the Gyrokinetic Toroidal code. After the thermal force term is introduced into the parallel electron force balance equation, the equilibrium temperature gradient can cause a significant increase in the growth rate of the drift-tearing mode and a broadening of the mode structure. The simulation results show that the toroidal effects increase the growth rate of the drift-tearing mode, and the contours of the perturbation field “squeeze” toward the stronger field side in the poloidal section. Finally, the hybrid model for fluid electrons and kinetic ions has been studied briefly, and the dispersion relation of the drift-tearing mode under the influence of ion finite Larmor radius effects is obtained. Compared with the dispersion relation under the fluid model, a stabilizing effect of the ion finite Larmor radius is observed.

Electric potential barriers in the magnetic nozzle.

Magnetic nozzles are convergent-divergent applied magnetic fields which are commonly used in electric propulsion, manufacturing, and material processing industries. This paper studies the previously overlooked physics in confining the thermalized ions injected from a near-uniform inlet in the magnetic nozzle. Through fully kinetic planar-3V particle-in-cell (PIC) modeling and simulation, an electric potential barrier is found on the periphery of the nozzle throat, which serves to confine the thermalized ions by the electric force. With the initial thermal energy as driving force and insufficient magnetic confinement, the ions overshoot the most divergent magnetic line, which results in the accumulation of positive space charges around the throat. The accumulated charges would create an ion-confining potential barrier with limited extent. Apart from the finite-electron Larmor radius (FELR) effect, two more factors are put forward to account for the limited extent of the potential barrier: the depletion of ion thermal energy and the short-circuiting effect. The influences of inlet temperature ratio of ions to electrons and magnetic inductive strength B_{0} are quantitively investigated using the PIC code. The results indicate that the potential barrier serves as a medium to transfer the gas dynamic thrust to the magnetic nozzle while providing constrain to the ions, like the solid wall in a de Laval nozzle. In high-B_{0} regime, the finite-ion Larmor radius (FILR) effect becomes dominant rather than the FELR effect in the plasma confinement of magnetic nozzles.