Finite Ion Larmor Radius Effects Research Articles

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.

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.

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.

Gyrofluid modeling of magnetosphere in feedback instability

Feedback instability occurs in a coupling system of the magnetosphere and the ionosphere, and is a theoretical model explaining spontaneous development of the quiet aurora. In this study, we extend a model of the magnetosphere in the feedback instability to the gyrofluid model. This extension makes it possible to properly discuss kinetic effects, such as the finite Larmor radius effect, the Landau damping, and the mirror force, on the feedback instability in a framework of a fluid model. The derived model is applied to linear stability analysis of the low-frequency feedback instability in the absence of the mirror force. An analytical expression of the parallel electron momentum diffusion coefficient associated with the electron Landau damping is obtained by considering a Landau-fluid closure model. It is found that high-wavenumber modes are strongly affected by the finite ion Larmor radius effect and the electron Landau damping. In particular, a stabilizing effect of the electron Landau damping is dominant and stronger for high-parallel-wavenumber modes. This result indicates that the lowest-parallel-wavenumber mode primarily grows during the spontaneous development of the quiet aurora.

Theoretical Prediction of Asymmetric Instability of Drift Kinetic Alfven Waves in Anisotropic Plasmas

AbstractThe asymmetric instability of drift kinetic Alfvén waves (DKAWs) is analyzed to study the interplay between the density inhomogeneity and the temperature anisotropy, including the wave‐particle interaction and finite ion Larmor radius effects. The asymmetric behavior arises due to the opposite diamagnetic drifts of electrons and ions and quantifies the contribution of electron drift waves and ion drift waves in altering the dispersion characteristic of DKAWs. It is shown that the coupling of drift waves with kinetic Alfvén waves leads to the generation of three different frequency (i.e., higher, intermediate, and lower) modes of DKAWs. The comparison of their propagation characteristics and stability mechanisms applicable to a wide range of plasma parameters is provided. The analytical dispersion relation can be used as an improved theoretical tool for identifying the existence of DKAWs and their source region in the multisatellite observations, especially near the reconnection X‐line.

A reduced Landau-gyrofluid model for magnetic reconnection driven by electron inertia

An electromagnetic reduced gyrofluid model for collisionless plasmas, accounting for electron inertia, finite ion Larmor radius effects and Landau-fluid closures for the electron fluid is derived by means of an asymptotic expansion from a parent gyrofluid model. In the absence of terms accounting for Landau damping, the model is shown to possess a non-canonical Hamiltonian structure. The corresponding Casimir invariants are derived and use is made thereof, in order to obtain a set of normal field variables, in terms of which the Poisson bracket and the model equations take a remarkably simple form. The inclusion of perpendicular temperature fluctuations generalizes previous Hamiltonian reduced fluid models and, in particular, the presence of ion perpendicular gyrofluid temperature fluctuations reflects into the presence of two new Lagrangian invariants governing the ion dynamics. The model is applied, in the cold-ion limit, to investigate numerically a magnetic reconnection problem. The Landau damping terms are shown to reduce, by decreasing the electron temperature fluctuations, the linear reconnection rate and to delay the nonlinear island growth. The saturated island width, on the other hand, is independent of Landau damping. The fraction of magnetic energy converted into perpendicular kinetic energy also appears to be unaffected by the Landau damping terms, which, on the other hand, dissipate parallel kinetic energy as well as free energy due to density and electron temperature fluctuations.

Extended MHD modeling of tearing-driven magnetic relaxation

Discrete relaxation events in reversed-field pinch relevant configurations are investigated numerically with nonlinear extended magnetohydrodynamic (MHD) modeling, including the Hall term in Ohm's law and first-order ion finite Larmor radius effects. Results show variability among relaxation events, where the Hall dynamo effect may help or impede the MHD dynamo effect in relaxing the parallel current density profile. The competitive behavior arises from multi-helicity conditions where the dominant magnetic fluctuation is relatively small. The resulting changes in parallel current density and parallel flow are aligned in the core, consistent with experimental observations. The analysis of simulation results also confirms that the force density from fluctuation-induced Reynolds stress arises subsequent to the drive from the fluctuation-induced Lorentz force density. Transport of the momentum density is found to be dominated by the fluctuation-induced Maxwell stress over most of the cross section with viscous and gyroviscous contributions being large in the edge region. The findings resolve a discrepancy with respect to the relative orientation of current density and flow relaxation, which had not been realized or investigated in King et al. [Phys. Plasmas 19, 055905 (2012)], where only the magnitude of flow relaxation is actually consistent with experimental results.

Radially localized kinetic beta induced Alfven eigenmodes in tokamak plasmas

We have studied the kinetic beta induced Alfven eigenmodes (KBAEs) by developing a fast global eigenvalue solving code. Even and odd parity KBAEs radially localized at the rational surface are found with the presence of the kinetic effects, namely, the finite ion Larmor radius effects. The KBAE mode structures become broader in the presence of the parallel equilibrium current. The KBAE frequency increases with the increase in the plasma β and the ion Larmor radius (ρi). Damping of the KBAE increases with the finite Larmor radius and decreases with the plasma beta and mode with a higher radial mode number has a stronger damping. Numerical results reveal that frequency and kinetic damping of KBAEs are independent of the tokamak size, and that kinetic damping in the core region is significantly smaller by an order of magnitude compared to that in the radially outward region of tokamak.

On plasma edge ideal MHD stability/instability condition in Mercier stable magnetic hill configurations

The stability of peeling modes in zero net current stellarator plasma is studied in high poloidal mode number m 1 approximation. The vacuum region solution is taken into account. Under these conditions in Mercier stable magnetic hill plasmas internal peeling modes are stable. External peeling modes can be unstable, but several limitations on them are found. It is shown that an analytically derived pressure gradient threshold is in reasonable agreement with the experimental observations and numerical calculations. The threshold decreases with increasing poloidal mode number m. It is shown, however, that higher modes may be stabilized due to finite ion Larmor radius effects. For the sake of definiteness, we have investigated peeling mode behavior in Mercier unstable plasma. It is shown that both external and internal peeling modes can be unstable in this regime. However, external and internal peeling modes in this case are definitely different.

The influence of temperature dynamics and dynamic finite ion Larmor radius effects on seeded high amplitude plasma blobs

Thermal effects on the perpendicular convection of seeded pressure blobs in the scrape-off layer of magnetised fusion plasmas are investigated. Our numerical study is based on a four field full-F gyrofluid model, which entails the consistent description of high fluctuation amplitudes and dynamic finite Larmor radius effects. We find that the maximal radial blob velocity increases with the square root of the initial pressure perturbation and that a finite Larmor radius contributes to highly compact blob structures that propagate in the poloidal direction. An extensive parameter study reveals that a smooth transition to this compact blob regime occurs when the finite Larmor radius effect strength, defined by the ratio of the magnetic field aligned component of the ion diamagnetic to the vorticity, exceeds unity. The maximal radial blob velocities agree excellently with the inertial velocity scaling law over more than an order of magnitude. We show that the finite Larmor radius effect strength affects the poloidal and total particle transport and present an empirical scaling law for the poloidal and total blob velocities. Distinctions to the blob behaviour in the isothermal limit with constant finite Larmor radius effects are highlighted.

Effect of Hall Current and Finite Larmor Radius Corrections on Thermal Instability of Radiative Plasma for Star Formation in Interstellar Medium (ISM)

The effects of finite ion Larmor radius (FLR) corrections, Hall current and radiative heat-loss function on the thermal instability of an infinite homogeneous, viscous plasma incorporating the effects of finite electrical resistivity, thermal conductivity and permeability for star formation in interstellar medium have been investigated. A general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. The wave propagation is discussed for longitudinal and transverse directions to the external magnetic field and the conditions of modified thermal instabilities and stabilities are discussed in different cases. We find that the thermal instability criterion gets modified into radiative instability criterion. The finite electrical resistivity removes the effect of magnetic field and the viscosity of the medium removes the effect of FLR from the condition of radiative instability. The Hall parameter affects only the longitudinal mode of propagation and it has no effect on the transverse mode of propagation. Numerical calculation shows stabilizing effect of viscosity, heat-loss function and FLR corrections, and destabilizing effect of finite resistivity and permeability on the thermal instability. The outcome of the problem discussed the formation of star in the interstellar medium.

Spontaneous excitation of convective cells by kinetic Alfvén waves

Spontaneous excitation of convective cells by kinetic Alfvén waves in a uniform plasma is investigated analytically employing the nonlinear gyrokinetic equations. Self-consistent theoretical analysis demonstrates the novel results that excitation via modulational instability can only occur when the finite ion Larmor radius effects are properly included, and, furthermore, both the electrostatic and magnetostatic convective cells are excited simultaneously. Theoretical predictions are verified with direct numerical simulations; showing excellent agreement in the modulational growth rate and field structures. Significant implications of the present results to the cross-field transport in space and fusion plasmas are also briefly discussed.

Larmor electric field observed at the Earth's magnetopause by Polar satellite

We present, for the first time, observational evidence of a kinetic electric field near the X-line associated with asymmetric reconnection at the Earth's dayside magnetopause using Polar observations. On March 29, 2003, Polar satellite detected an asymmetric collisionless reconnection event. This event shows a unipolar Hall electric field signature and a simple deviation from the guide field during the magnetopause crossing, with the absence of an ion plasma jet outflow indicating that the magnetopause crossing was near the X-line. As expected from particle-in-cell simulations by Malakit et al. (Phys. Rev. Lett. 111, 135001 (2013)), an earthward pointing normal electric field appears in the magnetospheric side of the ion diffusion region. The electric field satisfies two necessary conditions for the existence of the finite ion Larmor radius effect: (1) the ion Larmor radius (rg2) is larger than the distance between the stagnation point and the edge of the ion diffusion region in the strong magnetic field side (δS2) and (2) the spatial extent of the kinetic electric field (δEL) is of the order of the ion Larmor radius. Furthermore, it is shown that the peak value of the Larmor electric field is comparable to the predicted value. The observation of the Larmor electric field can be valuable in other analyses to show that the crossing occurred near the X-line.

Ion finite Larmor radius effects on the interchange instability in an open system

A particle simulation of an interchange instability was performed by taking into account the ion finite Larmor radius (FLR) effects. It is found that the interchange instability with large FLR grows in two phases, that is, linearly growing phase and the nonlinear phase subsequent to the linear phase, where the instability grows exponentially in both phases. The linear growth rates observed in the simulation agree well with the theoretical calculation. The effects of FLR are usually taken in the fluid simulation through the gyroviscosity, the effects of which are verified in the particle simulation with large FLR regime. The gyroviscous cancellation phenomenon observed in the particle simulation causes the drifts in the direction of ion diamagnetic drifts.

Comparison of kinetic and extended magnetohydrodynamics computational models for the linear ion temperature gradient instability in slab geometry

We perform linear stability studies of the ion temperature gradient (ITG) instability in unsheared slab geometry using kinetic and extended magnetohydrodynamics (MHD) models, in the regime k∥/k⊥≪1. The ITG is a parallel (to B) sound wave that may be destabilized by finite ion Larmor radius (FLR) effects in the presence of a gradient in the equilibrium ion temperature. The ITG is stable in both ideal and resistive MHD; for a given temperature scale length LTi0, instability requires that either k⊥ρi or ρi/LTi0 be sufficiently large. Kinetic models capture FLR effects to all orders in either parameter. In the extended MHD model, these effects are captured only to lowest order by means of the Braginskii ion gyro-viscous stress tensor and the ion diamagnetic heat flux. We present the linear electrostatic dispersion relations for the ITG for both kinetic Vlasov and extended MHD (two-fluid) models in the local approximation. In the low frequency fluid regime, these reduce to the same cubic equation for the complex eigenvalue ω=ωr+iγ. An explicit solution is derived for the growth rate and real frequency in this regime. These are found to depend on a single non-dimensional parameter. We also compute the eigenvalues and the eigenfunctions with the extended MHD code NIMROD, and a hybrid kinetic δf code that assumes six-dimensional Vlasov ions and isothermal fluid electrons, as functions of k⊥ρi and ρi/LTi0 using a spatially dependent equilibrium. These solutions are compared with each other, and with the predictions of the local kinetic and fluid dispersion relations. Kinetic and fluid calculations agree well at and near the marginal stability point, but diverge as k⊥ρi or ρi/LTi0 increases. There is good qualitative agreement between the models for the shape of the unstable global eigenfunction for LTi0/ρi=30 and 20. The results quantify how far fluid calculations can be extended accurately into the kinetic regime. We conclude that for the linear ITG problem in slab geometry with unsheared magnetic field when k∥/k⊥≪1, the extended MHD model may be a reliable physical model for this problem when ρi/LTi0<10−2 and k⊥ρi<0.2.

On the mirror instability in the presence of electron temperature anisotropy

Computation of the mirror instability growth rate in an ion-electron bi-Maxwellian plasma is revisited, starting from the low-frequency kinetic theory. The role of the electron finite Larmor radius (FLR) effects on the instability quenching is shown to possibly be dominant, even near threshold where the smallest unstable scales significantly exceed the electron gyroscale. Validation of the results by comparison with predictions of the fully kinetic whamp software is also presented. The influence of the electron temperatures on the ion FLR effects very near threshold, where the electron kinetic effects are negligible, is also pointed out.

Experimental investigation of geodesic acoustic mode spatial structure, intermittency, and interaction with turbulence in the DIII-D tokamak

Geodesic acoustic modes (GAMs) and zonal flows are nonlinearly driven, axisymmetric (m=0andn=0) E×B flows, which are thought to play an important role in establishing the saturated level of turbulence in tokamaks. Results are presented showing the GAM’s observed spatial scales, temporal scales, and nonlinear interaction characteristics, which may have implications for the assumptions underpinning turbulence models towards the tokamak edge (r/a>rsim0.75). Measurements in the DIII-D tokamak [Luxon, Nucl. Fusion 42, 614 (2002)] have been made with multichannel Doppler backscattering systems at toroidal locations separated by 180∘; analysis reveals that the GAM is highly coherent between the toroidally separated systems (γ>0.8) and that measurements are consistent with the expected m=0andn=0 structure. Observations show that the GAM in L-mode plasmas with ~2.5-4.5 MW auxiliary heating occurs as a radially coherent eigenmode, rather than as a continuum of frequencies as occurs in lower temperature discharges; this is consistent with theoretical expectations when finite ion Larmor radius effects are included. The intermittency of the GAM has been quantified, revealing that its autocorrelation time is fairly short, ranging from about 4 to about 15 GAM periods in cases examined, a difference that is accompanied by a modification to the probability distribution function of the E×B velocity at the GAM frequency. Conditionally-averaged bispectral analysis shows the strength of the nonlinear interaction of the GAM with broadband turbulence can vary with the magnitude of the GAM. Data also indicate a wavenumber dependence to the GAM’s interaction with turbulence.

Stabilization of magnetic curvature-driven Rayleigh–Taylor instabilities

AbstractThe finite ion Larmor radius (FLR) stabilization of the magnetic curvature-driven Rayleigh–Taylor (MCD RT) instability in a low beta plasma with nonzero ion temperature gradient is investigated. Finite electron temperature effects and ion temperature perturbations are incorporated. A new set of nonlinear equations for flute waves with arbitrary wavelengths as compared with the ion Larmor radius in a plasma with curved magnetic field lines is derived. Particular attention is paid to the waves with spatial scales of the order of the ion Larmor radius. In the linear limit, a Fourier transform of these equations yields an improved dispersion relation for flute waves. The dependence of the MCD RT instability growth rate on the equilibrium plasma parameters and the wavelengths is studied. The condition for which the instability cannot be stabilized by the FLR effects is found.