Finite Larmor Radius Effects Research Articles

The impact of a hot sodium ion population on the growth of the Kelvin‐Helmholtz instability in Mercury's magnetotail

AbstractObservations of Mercury's local plasma environment by MErcury Surface, Space ENvironment, GEochemistry, and Ranging have revealed that the planet hosts a strongly asymmetric magnetosphere as a result of an off‐axis dipolar or quadrupolar internal field and significant finite Larmor radius effects at the boundary layer between magnetospheric and solar wind plasma environments. One important asymmetry appears in the growth and evolution of Kelvin‐Helmholtz (K‐H) waves at the dawn and dusk flanks of the magnetopause. Linear analysis and global hybrid simulations support a dusk‐dawn asymmetry in the growth rate caused by finite Larmor radius effects, and indeed, K‐H waves have been almost exclusively observed at the dusk magnetopause during northward interplanetary magnetic field. Observations of these K‐H waves at sodium gyroscales invite investigation into the impact of the hot planetary sodium ion population, itself distributed preferentially on the dusk flank, on the growth of the K‐H instability and associated plasma transport. We present local two‐dimensional hybrid simulations of the dusk and dawn boundary layers, with varying magnetospheric sodium ion number density, and examine the associated changes in the growth rates of the K‐H instability, K‐H wave spectra, and cross‐boundary particle transport. We show that gyroresonance between growing K‐H vortices and sodium ion gyration introduces a strong spectral peak at sodium gyroscales at the dusk magnetopause, that an increase in sodium ion number density increases dawn‐dusk asymmetry of K‐H growth rates, and that cross‐boundary particle transport decreases with sodium number density at the dawn flank.

Electromagnetic drift waves dispersion for arbitrarily collisional plasmas

The impacts of the electromagnetic effects on resistive and collisionless drift waves are studied. A local linear analysis on an electromagnetic drift-kinetic equation with Bhatnagar-Gross-Krook-like collision operator demonstrates that the model is valid for describing linear growth rates of drift wave instabilities in a wide range of plasma parameters showing convergence to reference models for limiting cases. The wave-particle interactions drive collisionless drift-Alfvén wave instability in low collisionality and high beta plasma regime. The Landau resonance effects not only excite collisionless drift wave modes but also suppress high frequency electron inertia modes observed from an electromagnetic fluid model in collisionless and low beta regime. Considering ion temperature effects, it is found that the impact of finite Larmor radius effects significantly reduces the growth rate of the drift-Alfvén wave instability with synergistic effects of high beta stabilization and Landau resonance.

Large‐scale jets in the magnetosheath and plasma penetration across the magnetopause: THEMIS observations

AbstractTime History of Events and Macroscale Interactions during Substorms multipoint observation of the plasma and magnetic fields, conducted simultaneously in the dayside magnetosheath and magnetosphere, were used to collect 646 large‐scale magnetosheath plasma jets interacting with the magnetopause. The jets were identified as dense and fast streams of the magnetosheath plasma whose energy density is higher than that of the upstream solar wind. The jet interaction with the magnetopause was revealed from sudden inward motion of the magnetopause and an enhancement in the geomagnetic field. The penetration was determined as appearance of the magnetosheath plasma against the background of the hot magnetospheric particle population. We found that almost 60% of the jets penetrated through the magnetopause. Vast majority of the penetrating jets was characterized by high velocities V > 220 km/s and kinetic βk > 1 that corresponded to a combination of finite Larmor radius effect with a mechanism of impulsive penetration. The average plasma flux in the penetrating jets was found to be 1.5 times larger than the average plasma flux of the solar wind. The average rate of jet‐related penetration of the magnetosheath plasma into the dayside magnetosphere was estimated to be ~1029 particles/d. The rate varies highly with time and can achieve values of 1.5 × 1029 particles/h that is comparable with estimates of the total amount of plasma entering the dayside magnetosphere.

Finite Larmor radius effects on the (m = 2, n = 1) cylindrical tearing mode

New field solvers are developed in the gyrokinetic code GEM [Chen and Parker, J. Comput. Phys. 220, 839 (2007)] to simulate low-n modes. A novel discretization is developed for the ion polarization term in the gyrokinetic vorticity equation. An eigenmode analysis with finite Larmor radius effects is developed to study the linear resistive tearing mode. The mode growth rate is shown to scale with resistivity as γ ∼ η1∕3, the same as the semi-collisional regime in previous kinetic treatments [Drake and Lee, Phys. Fluids 20, 1341 (1977)]. Tearing mode simulations with gyrokinetic ions are verified with the eigenmode calculation.

Formation of large-scale structures with sharp density gradient through Rayleigh-Taylor growth in a two-dimensional slab under the two-fluid and finite Larmor radius effects

Two-fluid and the finite Larmor effects on linear and nonlinear growth of the Rayleigh-Taylor instability in a two-dimensional slab are studied numerically with special attention to high-wave-number dynamics and nonlinear structure formation at a low β-value. The two effects stabilize the unstable high wave number modes for a certain range of the β-value. In nonlinear simulations, the absence of the high wave number modes in the linear stage leads to the formation of the density field structure much larger than that in the single-fluid magnetohydrodynamic simulation, together with a sharp density gradient as well as a large velocity difference. The formation of the sharp velocity difference leads to a subsequent Kelvin-Helmholtz-type instability only when both the two-fluid and finite Larmor radius terms are incorporated, whereas it is not observed otherwise. It is shown that the emergence of the secondary instability can modify the outline of the turbulent structures associated with the primary Rayleigh-Taylor instability.

The linear tearing instability in three dimensional, toroidal gyro-kinetic simulations

Linear gyro-kinetic simulations of the classical tearing mode in three-dimensional toroidal geometry were performed using the global gyro-kinetic turbulence code, GKW. The results were benchmarked against a cylindrical ideal MHD and analytical theory calculations. The stability, growth rate, and frequency of the mode were investigated by varying the current profile, collisionality, and the pressure gradients. Both collisionless and semi-collisional tearing modes were found with a smooth transition between the two. A residual, finite, rotation frequency of the mode even in the absence of a pressure gradient is observed, which is attributed to toroidal finite Larmor-radius effects. When a pressure gradient is present at low collisionality, the mode rotates at the expected electron diamagnetic frequency. However, the island rotation reverses direction at high collisionality. The growth rate is found to follow a η1∕7 scaling with collisional resistivity in the semi-collisional regime, closely following the semi-collisional scaling found by Fitzpatrick. The stability of the mode closely follows the stability analysis as performed by Hastie et al. using the same current and safety factor profiles but for cylindrical geometry, however, here a modification due to toroidal coupling and pressure effects is seen.

Development of semi-Lagrangian gyrokinetic code for full-f turbulence simulation in general tokamak geometry

In this work, we report the development of a new gyrokinetic code for full-f simulation of electrostatic turbulence in general tokamak geometry. Backward semi-Lagrangian scheme is employed for noise-free simulation of the gyrokinetic Vlasov equation with finite Larmor radius effects. Grid systems and numerical interpolations are implemented to deal with arbitrary equilibrium information given in a GEQDSK format file. In particular, we introduce an adaptive interpolation technique for fluctuating quantities, which have elongated structures along equilibrium magnetic fields. This field-aligned interpolation can reduce the required number of grid points to represent the fluctuating quantities. Also, it is shown that the new interpolation allows us to choose bigger time sizes with better simulation accuracy. Several benchmark simulation results are presented for comparison with previously known cases. It is demonstrated that the new code can reproduce the well known results of zonal flow and linear ITG instabilities in concentric circular equilibrium. It is also shown that the code can capture the effects of plasma shaping on the zonal flow and ITG instabilities, and the stabilization effects of the shaping result in significant up-shifts of the threshold of ion temperature gradient for ITG in nonlinear simulation.

Statistical investigation of Kelvin‐Helmholtz waves at the magnetopause of Mercury

AbstractA large study of Kelvin‐Helmholtz (KH) waves at the magnetopause of Mercury covering 907 days of data from the MErcury Surface Space ENvironment GEochemistry Ranging spacecraft have resulted in 146 encounters of not only nonlinear KH waves but also linear surface waves, including the first observations of KH waves at the dawnside magnetopause. Most of the waves are in the nonlinear phase (90%) occur at the duskside magnetopause (93%), under northward magnetosheath magnetic field conditions (89%) and during greater magnetosheath Bz (23 nT) values than in general. The average period and amplitude is 30 ± 14 s and 14 ± 10 nT, respectively. Unlike duskside events, dawnside waves do not appear at the magnetopause flank (<6 magnetic local time). This is in agreement with previous observations and modeling results and possibly explained by finite Larmor radius effects and/or a lack of a large‐scale laminar flow at the dawnside magnetopause boundary.

Hot magnetospheric O+ and cold ion behavior in magnetopause reconnection: Cluster observations

AbstractIn reconnection, the presence of heavy ions like O+ increases the ion mass density reducing the fluid's Alfvén speed. In addition, it may modify the reconnection structure, which can also change the reconnection rate. However, because O+ ions have a larger Larmor radii than H+ ions at the same velocity, they may not be fully entrained in the reconnection flow and may have kinetic effects other than just increasing the mass density. In this study, for the first time, the ion velocity distribution functions of H+ and O+ from one magnetopause reconnection event with a strong guide field are analyzed to determine in detail the behavior of the different ion populations. We show that the hot magnetospheric O+ ions, along with the hot magnetospheric H+ ions almost fully participate in the reconnection exhaust flows. Finite Larmor radius effects are also apparent and control how far the ions extend on the magnetosheath side. Ion signatures consistent with heating after being picked up in the reconnection exhaust flow are observed in the H+ and O+ distribution functions. The dynamics of the cold magnetospheric ions depends on where they enter the reconnection region. If they enter the reconnection region at the downstream separatrix, they will be taken away by the magnetic field in an adiabatic way as analyzed by Drake et al. (2009a); if they enter close to the diffusion region, they behave as pick‐up ions.

Full kinetic simulations of plasma flow interactions with meso- and microscale magnetic dipoles

We examined the plasma flow response to meso- and microscale magnetic dipoles by performing three-dimensional full particle-in-cell simulations. We particularly focused on the formation of a magnetosphere and its dependence on the intensity of the magnetic moment. The size of a magnetic dipole immersed in a plasma flow can be characterized by a distance L from the dipole center to the position where the pressure of the local magnetic field becomes equal to the dynamic pressure of the plasma flow under the magnetohydrodynamics (MHD) approximation. In this study, we are interested in a magnetic dipole whose L is smaller than the Larmor radius of ions riL calculated with the unperturbed dipole field at the distance L from the center. In the simulation results, we confirmed the clear formation of a magnetosphere consisting of a magnetopause and a tail region in the density profile, although the spatial scale is much smaller than the MHD scale. One of the important findings in this study is that the spatial profiles of the plasma density as well as the current flows are remarkably affected by the finite Larmor radius effect of the plasma flow, which is different from the Earth's magnetosphere. The magnetopause found in the upstream region is located at a position much closer to the dipole center than L. In the equatorial plane, we also found an asymmetric density profile with respect to the plasma flow direction, which is caused by plasma gyration in the dipole field region. The ion current layers are created in the inner region of the dipole field, and the electron current also flows in the region beyond the ion current layer because ions with a large inertia can closely approach the dipole center. Unlike the ring current structure of the Earth's magnetosphere, the current layers in the microscale dipole fields are not circularly closed around the dipole center. Since the major current is caused by the particle gyrations, the current is independently determined to be in the direction of the electron and ion gyrations, which are the same in both the upstream and downstream regions. The present analysis on the formation of a magnetosphere in the regime of a microscale magnetic dipole is significant for understanding the solar wind response to the crustal magnetic anomalies on the Moon surface, such as were recently observed by spacecraft.

Ion and electron heating during magnetic reconnection in weakly collisional plasmas

Magnetic reconnection and associated heating of ions and electrons in strongly magnetized, weakly collisional plasmas are studied by means of gyrokinetic simulations. It is shown that an appreciable amount of the released magnetic energy is dissipated to yield (irreversible) electron and ion heating via phase mixing. Electron heating is mostly localized to the magnetic island, not the current sheet, and occurs after the dynamical reconnection stage. Ion heating is comparable to electron heating only in high-β plasmas, and results from both parallel and perpendicular phase mixing due to finite Larmor radius (FLR) effects; in space, ion heating is mostly localized to the interior of a secondary island (plasmoid) that arises from the instability of the current sheet.

Numerical evaluation of heat flux and surface temperature on a misaligned JET divertor W lamella during ELMs

A series of experiments has been performed on JET to investigate the dynamics of transient melting due to edge localized modes (ELMs). The experiment employs a deliberately misaligned lamella in one module of the JET bulk tungsten outer divertor, allowing the combination of stationary power flux and ELMs to transiently melt the misaligned edge. During the design of the experiment a number of calculations were performed using 2D particle-in-cell simulations and a heat transfer code to investigate the influence on the deposited power flux of finite Larmor radius effects associated with the energetic ELM ions. This has been performed using parameter scans inside a range of pedestal temperatures and densities to scope different experimentally expected ELM energies. On the one hand, we observe optimistic results, with smoothing of the heat flux due to the Larmor gyration on the protruding side of the lamella which sees the direct parallel flux—the deposited power tends to be lower than the nominal value expected from geometric magnetic field line impact over a distance smaller than 2 Larmor radii, a finding which is always valid during ELMs for such a geometry. On the other hand, the fraction of the flux not reaching the directly wetted side is transferred and spread to the top surface of the lamella. The hottest point of the lamella (corner side/top) does not always benefit from the gain from the Larmor smoothing effect because of an enhanced power deposition from the second contribution.

Intrinsic instabilities in X-point geometry: A tool to understand and predict the Scrape Off Layer transport in standard and advanced divertors

Intrinsic Scrape Off Layer (SOL) instabilities are studied using flute approximation and incorporating the appropriate sheath boundary conditions at the target. The linear growth rate and the structure of the modes are obtained. The associated diffusion is estimated using a γ/k⊥2 approach for the fastest growing modes. The model used includes curvature and sheath drives, finite Larmor radius effects and partial line tying at the target. The magnetic geometry is obtained using current carrying wires, representing the plasma current and the divertor coils, and naturally generates X-point geometry and magnetic shear effects. The calculation is performed for ITER relevant parameters and scans in SOL width and distance from the separatrix are presented. In addition to a standard Lower Single Null, Super-X and Snowflake configurations are examined in order to assess the importance of the geometry on the stability of the boundary plasma.

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.

Analytic dispersion relation of energetic particle driven geodesic acoustic modes and simulations with NEMORB

Recent progress regarding the excitation of energetic-particle driven geodesic acoustic modes (EGAMs) in particle-in-cell simulations is presented in this paper. The exact dispersion relation with adiabatic electrons is derived and solved. The origin of the so-called EGAM is briefly analysed and we show that its nature changes, at least, with the safety factor. A simple expression for the GAM frequency modified in the presence of a small concentration of energetic particles is given in the fluid limit. We show that gyrokinetic simulations with Nemorb in the presence of adiabatic electrons are able to reproduce the analytic predictions. Also, different energy channels are analysed by means of dedicated energy diagnostics characterizing the wave-particle interaction. Finite Larmor radius and finite orbit width effects are studied regarding the excitation of geodesic acoustic modes, showing that these effects are likely to be negligible for sufficiently high concentration of energetic particles, but significant when approaching the threshold of excitation.

Area-preserving maps models of gyroaveraged E×B chaotic transport

Discrete maps have been extensively used to model 2-dimensional chaotic transport in plasmas and fluids. Here we focus on area-preserving maps describing finite Larmor radius (FLR) effects on E × B chaotic transport in magnetized plasmas with zonal flows perturbed by electrostatic drift waves. FLR effects are included by gyro-averaging the Hamiltonians of the maps which, depending on the zonal flow profile, can have monotonic or non-monotonic frequencies. In the limit of zero Larmor radius, the monotonic frequency map reduces to the standard Chirikov-Taylor map, and in the case of non-monotonic frequency, the map reduces to the standard nontwist map. We show that in both cases FLR leads to chaos suppression, changes in the stability of fixed points, and robustness of transport barriers. FLR effects are also responsible for changes in the phase space topology and zonal flow bifurcations. Dynamical systems methods based on the counting of recurrences times are used to quantify the dependence on the Larmor radius of the threshold for the destruction of transport barriers.

Radial convection of finite ion temperature, high amplitude plasma blobs

We present results from simulations of seeded blob convection in the scrape-off-layer of magnetically confined fusion plasmas. We consistently incorporate high fluctuation amplitude levels and finite Larmor radius (FLR) effects using a fully nonlinear global gyrofluid model. This is in line with conditions found in tokamak scrape-off-layers (SOL) regions. Varying the ion temperature, the initial blob width, and the initial amplitude, we found an FLR dominated regime where the blob behavior is significantly different from what is predicted by cold-ion models. The transition to this regime is very well described by the ratio of the ion gyroradius to the characteristic gradient scale length of the blob. We compare the global gyrofluid model with a partly linearized local model. For low ion temperatures, we find that simulations of the global model show more coherent blobs with an increased cross-field transport compared to blobs simulated with the local model. The maximal blob amplitude is significantly higher in the global simulations than in the local ones. When the ion temperature is comparable to the electron temperature, global blob simulations show a reduced blob coherence and a decreased cross-field transport in comparison with local blob simulations.

Electromagnetic nonlinear gyrokinetics with polarization drift

A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.

Energetic-particle-induced electromagnetic geodesic acoustic mode in tokamak plasmas

Energetic-particle-induced kinetic electromagnetic geodesic acoustic modes (EKEGAMs) are numerically studied in low β (=plasma pressure/magnetic pressure) tokamak plasmas. The parallel component of the perturbed vector potential is considered along with the electrostatic potential perturbation. The effects of finite Larmor radius and finite orbit width of the bulk and energetic ions as well as electron parallel dynamics are all taken into account in the dispersion relation. Systematic harmonic and ordering analysis are performed for frequency and growth rate spectra of the EKEGAMs, assuming (kρi)∼q−3∼β≪1, where q, k, and ρi are the safety factor, radial component of the EKEGAMs wave vector, and the Larmor radius of the ions, respectively. It is found that there exist critical βh/βi values, which depend, in particular, on pitch angle of energetic ions and safety factor, for the mode to be driven unstable. The EKEGAMs may also be unstable for pitch angle λ0B<0.4 in certain parameter regions. Finite β effect of the bulk ions is shown to have damping effect on the EKEGAMs. Modes with higher radial wave vectors have higher growth rates. The damping from electron dynamics is found decreasing with decrease of the temperature ratio Te/Ti. The modes are easily to be driven unstable in low safety factor q region and high temperature ratio Th/Ti region. The harmonic features of the EKEGAMs are discussed as well.

Diamagnetic drift effects on the low-n magnetohydrodynamic modes at the high mode pedestal with plasma rotation

The diamagnetic drift effects on the low-n magnetohydrodynamic instabilities at the high-mode (H-mode) pedestal are investigated in this paper with the inclusion of bootstrap current for equilibrium and rotation effects for stability, where n is the toroidal mode number. The AEGIS (Adaptive EiGenfunction Independent Solutions) code [L. J. Zheng and M. T. Kotschenreuther, J. Comp. Phys. 211 (2006)] is extended to include the diamagnetic drift effects. This can be viewed as the lowest order approximation of the finite Larmor radius effects in consideration of the pressure gradient steepness at the pedestal. The H-mode discharges at Jointed European Torus is reconstructed numerically using the VMEC code [P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)], with bootstrap current taken into account. Generally speaking, the diamagnetic drift effects are stabilizing. Our results show that the effectiveness of diamagnetic stabilization depends sensitively on the safe factor value (qs) at the safety-factor reversal or plateau region. The diamagnetic stabilization are weaker, when qs is larger than an integer; while stronger, when qs is smaller or less larger than an integer. We also find that the diamagnetic drift effects also depend sensitively on the rotation direction. The diamagnetic stabilization in the co-rotation case is stronger than in the counter rotation case with respect to the ion diamagnetic drift direction.