Finite Larmor Radius Effects Research Articles

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.

On Thermal Convection of a Plasma in Porous Medium

The effect of finite Larmor radius of the ions on thermal convection of a plasma is investigated. The case with vertical magnetic field is discussed. Following linear stability theory and normal mode analysis method, the dispersion relation is obtained. It is found that the presence of finite Larmor radius and magnetic field introduces oscillatory modes in the system which were, otherwise, non-existent in their absence. When the instability sets in as stationary convection, finite Larmor radius is found to have a stabilizing effect. Medium permeability has a destabilizing (or stabilizing) effect and the magnetic field has a stabilizing (or destabilizing) effect under certain conditions in the presence of finite Larmor radius effect whereas in the absence of finite Larmor radius effect, the medium permeability and the magnetic field have destabilizing and stabilizing effects, respectively. The sufficient conditions for the non-existence of overstability are also obtained.

Formation of solitons and shocks in toroidal ion temperature gradient mode in the presence ofnon‐Maxwellianelectrons

AbstractLinear and nonlinear phenomena are investigated in toroidal ion temperature gradient (TITG)‐driven pure drift mode. The model includes inhomogeneity in background magnetic field, ion temperature, and density. Finite Larmor radius effect is incorporated to understand the effect of low‐frequency wave on ion dynamics. Electrons are assumed to follow nonthermal distribution, that is, kappa and Cairns distributions. Dispersion relation is obtained to analyse the linear behaviour of the TITG mode in the presence of non‐Maxwellian electron distribution. In the nonlinear regime, exact solutions (soliton and shocks) are obtained (in dispersive and dissipative medium respectively) by using functional variable method to solve the nonlinear partial differential equation obtained for the system under consideration. Graphical illustrations are used to exhibit the characteristics of linear and nonlinear structures and their dependence on different physical parameters. It is observed that for TITG‐driven pure drift mode, rarefactive solitons are formed for both thermal and nonthermal electron distributions. It is also observed that variation of electrons from standard thermal distribution affects the propagation characteristics of linear and nonlinear structures in TITG‐driven modes. Results of our investigations will be helpful to understand the low‐frequency waves in inhomogeneous plasmas in the presence of nonthermal electron distributions which are frequently observed by satellite missions and are also observed in laboratory plasmas.

Analytical Assessment of Kelvin‐Helmholtz Instability Growth at Ganymede's Upstream Magnetopause

AbstractGanymede is the only Solar System moon that generates a permanent magnetic field. Dynamics within the Ganymedean magnetosphere is thought to be driven by energy‐transfer interactions on its upstream magnetopause. Previously in Kaweeyanun et al. (2020), https://doi.org/10.1029/2019GL086228 we created a steady‐state analytical model of Ganymede's magnetopause and predicted global‐scale magnetic reconnection to occur frequently throughout the surface. This paper subsequently provides the first assessment of Kelvin‐Helmholtz (K‐H) instability growth on the magnetopause. Using the same analytical model, we find that linear K‐H waves are expected on both Ganymedean magnetopause flanks. Once formed, the waves propagate downstream at roughly half the speed of the external Jovian plasma flow. The Ganymedean K‐H instability growth is asymmetric between magnetopause flanks due to the finite Larmor radius effect arising from large gyroradii of Jovian plasma ions. A small but notable enhancement is expected on the sub‐Jovian flank according to the physical understanding of bulk plasma and local ion flows alongside comparisons to the well‐observed magnetopause of Mercury. Further evaluation shows that nonlinear K‐H vortices should be strongly suppressed by concurring global‐scale magnetic reconnection at Ganymede. Reconnection is therefore the dominant cross‐magnetopause energy‐transfer mechanism and driver of global‐scale plasma convection within Ganymede's magnetosphere.

Importance of gyrokinetic exact Fokker-Planck collisions in fusion plasma turbulence.

Gyrokinetic simulations of turbulence are fundamental to understanding and predicting particle and energy loss in magnetic fusion devices. Previous works have used model collision operators with approximate field-particle terms of unknown accuracy and/or have neglected collisional finite Larmor radius effects. This work moves beyond models to demonstrate important corrections using a gyrokinetic Fokker-Planck collision operator with the exact field-particle terms, in realistic simulations of turbulence in magnetically confined fusion plasmas. The exact operator shows significant corrections for temperature-gradient-driven trapped electron mode turbulence and zonal flow damping, and for microtearing modes in a Joint European Torus pedestal under ITER-like wall conditions. Analysis of the corrections using parameter scans motivates an accurate model which closely reproduces the exact results while reducing computational demands.

Key impact of phase dynamics and diamagnetic drive on Reynolds stress in magnetic fusion plasmas

Reynolds stress is a key facet of turbulence self-organization. In the magnetized plasmas of controlled fusion devices, the zonal flows that are driven by the averaged Reynolds stress modify the confinement performance. We address this problem with full-f gyrokinetic simulations of ion temperature gradient-driven turbulence. From the detailed analysis of the three-dimensional electric potential and transverse pressure fields, we show that the diamagnetic contribution to the Reynolds stress—stemming from finite Larmor radius effects—exceeds the electrostatic contribution by a factor of about two. Both contributions are in phase, indicating that pressure does not behave as a passive scalar. In addition, the Reynolds stress induced by the electric drift velocity is found to be mainly governed by the gradient of the phase of the electric potential modes rather than by their magnitude. By decoupling Reynolds stress drive and turbulence intensity, this property indicates that a careful analysis of phase dynamics is crucial in the interpretation of experiments and simulations.

Impact of shaping on microstability in high-performance tokamak plasmas

We have used the local-δf gyrokinetic code GS2 to perform studies of the effect of flux-surface shaping on two highly-shaped, low- and high-β JT-60SA-relevant equilibria, including a successful benchmark with the GKV code. We find that for a high-performance plasma, i.e. one with high plasma beta and steep pressure gradients, the turbulent outwards radial fluxes may be reduced by minimizing the elongation. We explain the results as a competition between the local magnetic shear and finite-Larmor-radius (FLR) stabilization. Electromagnetic studies indicate that kinetic ballooning modes are stabilized by increased shaping due to an increased sensitivity to FLR effects, relative to the ion-temperature-gradient instability. Nevertheless, at high enough β, increased elongation degrades the local magnetic shear stabilization that enables access to the region of ballooning second-stability.

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.

Impact of electron temperature anisotropy on the collisionless tearing mode instability in the presence of a strong guide field

We derive and analyze a dispersion relation for the growth rate of collisionless tearing modes, driven by electron inertia and accounting for equilibrium electron temperature anisotropy in a strong guide field regime. For this purpose, a new gyrofluid model is derived and subsequently simplified to make the derivation of the dispersion relation treatable analytically. The main simplifying assumptions consist in assuming cold ions, neglecting electron finite Larmor radius effects, decoupling ion gyrocenter fluctuations, and considering β⊥e≪1, with β⊥e indicating the ratio between the perpendicular electron thermal pressure and the magnetic pressure exerted by the guide field. This simplified version of the gyrofluid model is shown to possess a noncanonical Hamiltonian structure. The dispersion relation is obtained by applying the theory of asymptotic matching and does not predict an enhancement of the growth rate as the ratio Θe between perpendicular and parallel equilibrium electron temperatures increases. This indicates a significant difference with respect to the case of absent or moderate guide field. For an equilibrium magnetic shear length of the order of the perpendicular sonic Larmor radius and at a fixed β⊥e, we obtain that the tearing mode in the strong guide field regime gets actually weakly damped, as Θe increases. In the isotropic limit Θe=1, the dispersion relation reduces to a previously known formula. The analytical predictions are tested against numerical simulations, showing a very good quantitative agreement. We also provide a detailed discussion of the range of validity of the derived dispersion relation and of the compatibility among the different adopted assumptions.

Turbulent transport of fast ions in tokamak plasmas in the presence of resonant magnetic perturbations

The effects of resonant magnetic perturbations on the turbulent transport of fast ions in tokamak devices are investigated using a theoretical transport model of test-particle type. The direct numerical simulation method is used to compute, via the transport model, the diffusion coefficients. The numerical results are in good agreement with other, analytically derived, estimations. It is found that finite Larmor radius effects algebraically decrease the transport, while the amplitude of magnetic perturbations has an opposite effect. In the presence of stochastic dynamics, the asymmetric toroidal magnetic field induces a small, radial, outward pinch. A synergistic mechanism of non-linear coupling between the effects of turbulence and those of magnetic perturbations enhances the radial diffusion. General scaling laws are proposed for the transport coefficients.

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.

Solving the all-FLR ICRH integro-differential wave equation as a high-order differential equation for studying combined ICRH-NBI heating

A fast and intuitive method is proposed to solve the integro-differential wave equation relevant for modelling ion cyclotron resonance heating (ICRH) at any cyclotron harmonic, for arbitrary ion distributions and retaining all finite Larmor radius effects. The method is inspired on recent work of Budé who proposed to fit the dielectric tensor in k-space by a higher order polynomial, allowing to derive a suitable differential operator that conveniently mimics the integro-differential operator in a sufficiently large -range to describe all physically relevant wave modes in -space. Eliminating a drawback of the Budé method by going back to first principles yields a wave equation dielectric response operator that guarantees a positive definite power absorption for populations in thermal equilibrium—as physically expected—and that can directly be used in the Fokker–Planck equation. The method is exploited for 1D application but retaining the toroidal curvature. Analytical expressions of the components of the dielectric tensor are available for Maxwellian distributions as well as bi-Maxwellians with a finite parallel drift. Numerical integration of the velocity space integrals allows to account for arbitrary distributions. A number of examples relevant for high performance tokamak plasma operation and exploiting simultaneous ICRH and neutral beam injection heating are given to illustrate the method’s potential.

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.

Vorticity generation by finite Larmor radius effects from heat source and sink

We investigate the finite Larmor radius (FLR) effects that are associated with an external heat source or a sink in the full-f formulation of plasma dynamics. Specifically, we show that a gyrocenter or an additional vorticity source due to the FLR effect should be replenished in full-f turbulence simulations. A quantitative energetics analysis in particle phase space demonstrates that an additional vorticity source is required to satisfy the total energy conservation. A physics picture is presented to elucidate the mechanism of the vorticity source generation from the FLR effects of a heat source or a sink, which reproduces the main result obtained from the quantitative analysis. The additional vorticity source is expected to considerably enhance the generation of the radial electric field and subsequent E×B flow shear in the off-axis heating case.

Toroidal and slab ETG instability dominance in the linear spectrum of JET-ILW pedestals

Local linear gyrokinetic simulations show that electron temperature gradient (ETG) instabilities are the fastest growing modes for in the steep gradient region for a JET pedestal discharge (92174) where the electron temperature gradient is steeper than the ion temperature gradient. Here, ky is the wavenumber in the direction perpendicular to both the magnetic field and the radial direction, and ρi is the ion gyroradius. At , the fastest growing mode is often a novel type of toroidal ETG instability. This toroidal ETG mode is driven at scales as large as and at a sufficiently large radial wavenumber that electron finite Larmor radius effects become important; that is, , where Kx is the effective radial wavenumber. Here, ρe is the electron gyroradius, R0 is the major radius of the last closed flux surface, and 1/LTe is an inverse length proportional to the logarithmic gradient of the equilibrium electron temperature. The fastest growing toroidal ETG modes are often driven far away from the outboard midplane. In this equilibrium, ion temperature gradient instability is subdominant at all scales and kinetic ballooning modes are shown to be suppressed by shear. ETG modes are very resilient to shear. Heuristic quasilinear arguments suggest that the novel toroidal ETG instability is important for transport.

Generalized slab universal instability and its appearance in pair plasma

A generalized linear dispersion relation of electromagnetic slab universal modes is derived, taking into account arbitrary ion charge state, electron finite Larmor radius (FLR) effects, and Debye shielding effects. As a consequence, it provides more accurate predictions and is applicable to a wider range of plasmas. We find that electron FLR effects have a weakly stabilizing effect on the slab universal instability in electron–ion plasma, while Debye shielding strongly stabilizes this instability when λD approaches ρi (λD is the Debye length and ρi is the ion gyroradius). In particular, we examine the stability criterion for this instability in electron–positron pair plasmas and find that the instability persists in this simplest plasma system as long as the pair plasma number density exceeds the critical value nc=B2/(8πmec2).

Coupled MHD – Hybrid Simulations of Space Plasmas

Heliospheric plasmas require multi-scale and multi-physics considerations. On one hand, MHD codes are widely used for global simulations of the solar-terrestrial environments, but do not provide the most elaborate physical description of space plasmas. Hybrid codes, on the other hand, capture important physical processes, such as electric currents and effects of finite Larmor radius, but they can be used locally only, since the limitations in available computational resources do not allow for their use throughout a global computational domain. In the present work, we present a new coupled scheme which allows to switch blocks in the block-adaptive grids from fluid MHD to hybrid simulations, without modifying the self-consistent computation of the electromagnetic fields acting on fluids (in MHD simulation) or charged ion macroparticles (in hybrid simulation). In this way, the hybrid scheme can refine the description in specified regions of interest without compromising the efficiency of the global MHD code.

Progress in modelling fast-ion D-alpha spectra and neutral particle analyzer fluxes using FIDASIM

FIDASIM is a code that models signals produced by charge-exchange reactions between neutrals and ions (both fast and thermal) in magnetically confined plasmas. With the ion distribution function as input, the code predicts the efflux to a neutral particle analyzer diagnostic and the photon radiance of Balmer-alpha light to a fast-ion D diagnostic, in addition to many other related quantities. A new, parallelized version of the Monte Carlo code FIDASIM has been developed in Fortran90 that is substantially faster than the original interactive data language version. Modified algorithms include more accurate treatments of the time dependent collisional-radiative equations that describe neutral energy levels, of the cloud of ‘halo’ neutrals that surround the injected neutral beam, and of finite Larmor radius effects. Enhanced physics capabilities include modelling ‘passive’ signals from cold edge neutrals, the ability to treat general three-dimensional magnetic confinement configurations, and calculations of diagnostic-specific weight functions that enable tomographic reconstructions of the fast-ion distribution function. Neutral beam attenuation, beam emission, and fast-ion birth profiles are also modelled. The new algorithms have been successfully validated against experimental data and new features have been tested through benchmarks between two independently developed versions of the code.

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.

The physics of a small-scale tearing mode in collisionless slab plasmas

Microtearing modes have been widely reported as a tearing parity electron temperature gradient driven plasma instability, which leads to fine scale tearing of the magnetic flux surfaces thereby resulting in reconnection of magnetic field lines and formation of magnetic islands. In slab geometry it has previously been shown that the drive mechanism requires a finite collision frequency. However, we find in linear gyrokinetic simulations that a collisionless fine-scale tearing parity instability exists even at low and zero collision frequency. Detailed studies reveal that these slab modes are also driven by electron temperature gradient but are sensitive to electron finite Larmor radius effects, and have a radial wavenumber much smaller than the binormal wavenumber, which is comparable to the ion Larmor radius. Furthermore, they exist even in the electrostatic limit and electromagnetic effects actually have a stabilising influence on this collisionless tearing mode. An analytic model shows that this collisionless small scale tearing mode is consistent with a tearing parity slab electron temperature gradient (ETG) mode, which can be more unstable than the twisting parity ETG mode that is often studied. This small-scale tearing parity mode can lead to magnetic islands, which, in turn, can influence turbulent transport in magnetised plasmas.