Finite Larmor Radius Effects Research Articles

Electron Dynamics Within the Electron Diffusion Region of Asymmetric Reconnection

AbstractWe investigate the agyrotropic nature of electron distribution functions and their substructure to illuminate electron dynamics in a previously reported electron diffusion region (EDR) event. In particular, agyrotropy is examined as a function of energy to reveal detailed finite Larmor radius effects for the first time. It is shown that the previously reported ∼66 eV agyrotropic “crescent” population that has been accelerated as a result of reconnection is evanescent in nature because it mixes with a denser, gyrotopic background. Meanwhile, accelerated agyrotropic populations at 250 and 500 eV are more prominent because the background plasma at those energies is more tenuous. Agyrotropy at 250 and 500 eV is also more persistent than at 66 eV because of finite Larmor radius effects; agyrotropy is observed 2.5 ion inertial lengths from the EDR at 500 eV, but only in close proximity to the EDR at 66 eV. We also observe linearly polarized electrostatic waves leading up to and within the EDR. They have wave normal angles near 90°, and their occurrence and intensity correlate with agyrotropy. Within the EDR, they modulate the flux of 500 eV electrons travelling along the current layer. The net electric field intensifies the reconnection current, resulting in a flow of energy from the fields into the plasma.

Marginal stability, characteristic frequencies, and growth rates of gradient drift modes in partially magnetized plasmas with finite electron temperature

The detailed analysis of stability of azimuthal oscillations in partially magnetized plasmas with crossed electric and magnetic fields is presented. The instabilities are driven by the transverse electron current which, in general, is due to a combination of E×B and electron diamagnetic drifts. Marginal stability boundary is determined for a wide range of the equilibrium plasma parameters. It is shown that in some regimes near the instability threshold, only the low-frequency long-wavelength oscillations are unstable, while the short-wavelength high-frequency modes are stabilized by the finite Larmor radius effects. Without such stabilization, the high-frequency modes have much larger growth rates and dominate. A new regime of the instability driven exclusively by the magnetic field gradient is identified. Such instability takes place in the region of the weak electric field and for relatively large gradients of plasma density (ρs/ln>1, where ρs is the ion-sound Larmor radius and ln is the scale length of plasma density inhomogeneity).

Effects of finite electron temperature on gradient drift instabilities in partially magnetized plasmas

The gradient-drift instabilities of partially magnetized plasmas in plasma devices with crossed electric and magnetic fields are investigated in the framework of the two-fluid model with finite electron temperature in an inhomogeneous magnetic field. The finite electron Larmor radius (FLR) effects are also included via the gyroviscosity tensor taking into account the magnetic field gradient. This model correctly describes the electron dynamics for k⊥ρe>1 in the sense of Padé approximants (here, k⊥ and ρe are the wavenumber perpendicular to the magnetic field and the electron Larmor radius, respectively). The local dispersion relation for electrostatic plasma perturbations with the frequency in the range between the ion and electron cyclotron frequencies and propagating strictly perpendicular to the magnetic field is derived. The dispersion relation includes the effects of the equilibrium E×B electron current, finite ion velocity, electron inertia, electron FLR, magnetic field gradients, and Debye length effects. The necessary and sufficient condition of stability is derived, and the stability boundary is found. It is shown that, in general, the electron inertia and FLR effects stabilize the short-wavelength perturbations. In some cases, such effects completely suppress the high-frequency short-wavelength modes so that only the long-wavelength low-frequency (with respect to the lower-hybrid frequency) modes remain unstable.

Current flow instability and nonlinear structures in dissipative two-fluid plasmas

The current flow in two-fluid plasma is inherently unstable if plasma components (e.g., electrons and ions) are in different collisionality regimes. A typical example is a partially magnetized E×B plasma discharge supported by the energy released from the dissipation of the current in the direction of the applied electric field (perpendicular to the magnetic field). Ions are not magnetized so they respond to the fluctuations of the electric field ballistically on the inertial time scale. In contrast, the electron current in the direction of the applied electric field is dissipatively supported either by classical collisions or anomalous processes. The instability occurs due to a positive feedback between the electron and ion current coupled by the quasi-neutrality condition. The theory of this instability is further developed taking into account the electron inertia, finite Larmor radius and nonlinear effects. It is shown that this instability results in highly nonlinear quasi-coherent structures resembling breathing mode oscillations in Hall thrusters.

Global Structure and Sodium Ion Dynamics in Mercury's Magnetosphere With the Offset Dipole

AbstractWe conducted global magnetohydrodynamics (MHD) simulation of Mercury's magnetosphere with the dipole offset, which was revealed by MESSENGER (Mercury Surface, Space Environment, Geochemistry, and Ranging) observations, in order to investigate its global structure under northward interplanetary magnetic field conditions. Sodium ion dynamics originating from the Mercury's exosphere is also investigated based on statistical trajectory tracing in the electric and magnetic fields obtained from the MHD simulations. The results reveal a north‐south asymmetry characterized by open field lines around the southern polar region and northward deflection of the plasma sheet in the far tail. The asymmetry of magnetic field structure near the planet drastically affects trajectories of sodium ion and thus their pressure distributions and precipitation pattern onto the planet. Weaker magnetic field strength in the southern hemisphere than in the north increases ion loss by precipitation onto the planetary surface in the southern hemisphere. The “sodium ring,” which is formed by high‐energy sodium ions drifting around the planet, is also found in the vicinity of the planet. The sodium ring is almost circular under nominal solar wind conditions. The ring becomes partial under high solar wind density, because dayside magnetosphere is so compressed that there is no space for the sodium ions to drift around. In both cases, the sodium ring is formed by sodium ions that are picked up, accelerated in the magnetosheath just outside the magnetopause, and reentered into the magnetosphere due to combined effects of finite Larmor radius and convection electric field in the dawnside magnetosphere.

Hamiltonian closures in fluid models for plasmas

This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac’s theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and connections with previously discussed fluid models are pointed out.

Pushforward transformation of gyrokinetic moments under electromagnetic fluctuations

Pushforward transformation is one of the two important transformations in modern nonlinear gyrokinetic theory. In this work, a gyrokinetic system under electromagnetic fluctuations has been derived using a purely pushforward transformation, where the finite Larmor radius (FLR) effect is fully retained. From the perspective of polarization and magnetization, clear physical pictures of macroscopic equilibrium flow are presented, and the generation of macroscopic perturbed flow is discussed with the incorporation of the full FLR effect using the systematical analysis of the gyrocenter gyroradius and the decoupling of particle velocity.

Global Alfvén eigenmodes in the H-1 heliac

Recent upgrades in H-1 power supplies have enabled the operation of the H-1 experiment at higher heating powers than previously attainable. A heating power scan in mixed hydrogen/helium plasmas reveals a change in mode activity with increasing heating power. At low power ( kW) modes with beta-induced Alfvén eigenmode frequency scaling are observed. At higher power modes consistent with an analysis of nonconventional global Alfvén eigenmodes (GAEs) are observed, the subject of this work. We have computed the mode continuum, and identified GAE structures using the ideal MHD solver CKA and the gyrokinetic code EUTERPE. An analytic model for ICRH-heated minority ions is used to estimate the fast ion temperature from the hydrogen species. Linear growth rate scans using a local flux surface stability calculation, LGRO, are performed. These studies demonstrate drive from the radial spatial gradient of circulating particles whose speed is significantly less than the Alfvén speed, and are resonant with the mode through harmonics of the Fourier decomposition of the strongly shaped heliac magnetic field. They reveal drive is possible with a small hot energetic tail of the hydrogen species, for which . Local linear growth rate scans are also complemented with global calculations from CKA and EUTERPE. These qualitatively confirm the findings from the LGRO study, and show that the inclusion of finite Larmor radius effects can reduce the growth rate by a factor of up to ten, and increases the marginal stability fast ion temperature by a factor of two. Finally, a study of damping of the global mode with the thermal plasma is conducted, computing continuum damping , and the damping arising from finite Larmor radius and parallel electric fields (via resistivity). We find that continuum damping is of order 0.1% for the configuration studied. A similar calculation in the cylindrical plasma model produces a frequency 35% higher and a damping 30% of the three-dimensional result: this confirms the importance of strong magnetic shaping to the frequency and damping. The inclusion of resistivity lifts the damping to . Such large damping is consistent with experimental observations that in absence of drive the mode decays rapidly (∼0.1 ms).

Numerical simulation on the multiple dipolarization fronts in the magnetotail

Using an extended MHD model including the Hall effect and finite Larmor radius effect, we reproduce multiple dipolarization fronts (DFs) associated with the interchange instability in the braking region of bursty bulk flow in the plasma sheet. Our simulations reveal that the multiple DFs produced by the interchange instability are “growing” type DFs because the maximum plasma flow speeds are behind the fronts. Both the earthward and tailward moving DFs can be produced by interchange instability in the near-Earth region. The Hall electric field is the dominant electric field component in the dip region and the DF layer. The convective and the electron pressure gradient electric field components are smaller. The sharp Bz changes in both the dip region and DF layer correspond to the oppositely directed currents that are primarily associated with electrons. The ion diamagnetic current due to the strong ion pressure gradient causes an intense downward current in the dip region, which can produce the dip ahead of the front. The energy dissipations in the dip region and DF layer are dominated by ions through the work done by the Lorentz force. Our simulation results indicate that the magnetic energy can be converted to plasmas on the DF layer, and vice versa in the dip region.

Effect of rotation on structure formation of degenerate anisotropic white dwarfs

In the present work, the effect of rotation and finite Larmor radius (FLR) correction of ions on gravitational instability in the context of anisotropic white dwarf situation is investigated. The propagation dynamics of the various modes has been discussed using general dispersion relation which is obtained by quantum magnetohydrodynamic and Chew-Goldberger-Low (CGL) set of equations. The properties of dispersion relation are discussed for four different cases. The Alfven mode is modified with rotation and FLR correction while the gravitational mode remains unaffected by both the parameter for the case when rotation and wave vector both are parallel to magnetic field. Moreover, rotation (when longitudinal to magnetic field) becomes effective on gravitational mode in the perpendicular direction of propagation, as it modifies the condition of gravitational instability. The obtained analytical results are also discussed numerically. The implication of the present work is described for dense white dwarfs where the electrons are in a degenerate state with a strong magnetic field. The estimated value of Jeans length and Jeans mass are $L_{J1} = 5.5 \times 10^{7}~\mbox{m}$ and $M_{J1} = 3.5~M_{ \odot }$ respectively for rotating anisotropic plasma which corresponds to super Chandrashekhar white dwarfs while for non-rotating degenerate magnetized plasma, the Jeans length is $L_{J1}' = 4.7 \times 10^{7}~\mbox{m}$ and Jeans mass is $M_{J1}' = 2.1~M_{ \odot }$ . The presence of rotation effectively increases the critical mass of white dwarf.

Drift-wave stability in the field-reversed configuration

Gyrokinetic simulations of C-2-like field-reversed configuration (FRC) find that electrostatic drift-waves are locally stable in the core. The stabilization mechanisms include finite Larmor radius effects, magnetic well (negative grad-B), and fast electron short circuit effects. In the scrape-off layer (SOL), collisionless electrostatic drift-waves in the ion-to-electron-scale are destabilized by electron temperature gradients due to the resonance with locally barely trapped electrons. Collisions can suppress this instability, but a collisional drift-wave instability still exists at realistic pressure gradients. Simulation results are in qualitative agreement with C-2 FRC experiments. In particular, the lack of ion-scale instability in the core is not inconsistent with experimental measurements of a fluctuation spectrum showing a depression at ion-scales. The pressure gradient thresholds for the SOL instability from simulations are also consistent with the critical gradient behavior observed in experiments.

Equilibrium potential well due to finite Larmor radius effects at the tokamak edge

We present a novel mechanism for producing an equilibrium potential well near the edge of a tokamak. Briefly, because of the difference in gyroradii between electrons and ions, an equilibrium electrostatic potential is generated in the presence of spatial inhomogeneity of the background plasma, which, in turn, produces a well associated with the radial electric field, Er, as observed at the edge of many tokamak experiments. We will show that this theoretically predicted Er field, which can be regarded as producing a long radial wavelength zonal flow, agrees well with recent experimental measurements. The relationship between the equilibrium configuration used in this study and that of the Woltjer-Taylor state will be discussed.

Effects of a static inhomogeneous magnetic field acting on a laser-produced carbon plasma plume

We present time- and space-resolved observations of the dynamics of a laser-produced carbon plasma, propagating in a sub-Tesla inhomogeneous magnetic field, with both, axial and radial field gradients. An Nd:YAG laser pulse, 340 mJ, 3.5 ns, at 1.06 μm, with a fluence of 7 J/cm2, is used to generate the plasma from a solid graphite target, in vacuum. The magnetic field is produced using two coaxial sets of two NeFeB ring magnets, parallel to the laser target surface. The diagnostics include plasma imaging with 50 ns time resolution, spatially resolved optical emission spectroscopy and Faraday cup. Based on our observations, evidence of radial and axial plasma confinement due to magnetic field gradients is presented. Formation of C2 molecules, previously observed in the presence of a low pressure neutral gas background, and enhanced on-axis ion flux, are ascribed to finite Larmor radius effects and reduced radial transport due to the presence of the magnetic field.

Molecular cloud formation via thermal instability of finite resistive viscous radiating plasma with finite Larmor radius corrections

The effect of radiative heat-loss function and finite ion Larmor radius (FLR) corrections on the thermal instability of infinite homogeneous viscous plasma has been investigated incorporating the effects of thermal conductivity and finite electrical resistivity for the formation of a molecular cloud. The general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. Furthermore the wave propagation along and perpendicular to the direction of external magnetic field has been discussed. Stability of the medium is discussed by applying Routh Hurwitz’s criterion and it is found that thermal instability criterion determines the stability of the medium. We find that the presence of radiative heat-loss function and thermal conductivity modify the fundamental criterion of thermal instability into radiatively driven thermal instability criterion. In longitudinal direction FLR corrections, viscosity, magnetic field and finite resistivity have no effect on thermal instability criterion. The presence of radiative heat-loss function and thermal conductivity modify the fundamental thermal instability criterion into radiatively driven thermal instability criterion. Also the FLR corrections modify the growth rate of the Alfven mode. For transverse wave propagation FLR corrections, radiative heat-loss function, magnetic field and thermal conductivity modify the thermal instability criterion. From the curves it is clear that heat-loss function, FLR corrections and viscosity have stabilizing effect, while finite resistivity has destabilizing effect on the thermal modes. Our results show that the FLR corrections and radiative heat-loss functions affect the evolution of interstellar molecular clouds and star formation.

Stabilizing effect of resistivity towards ELM-free H-mode discharge in lithium-conditioned NSTX

Linear stability analysis of the national spherical torus experiment (NSTX) Li-conditioned ELM-free H-mode equilibria is carried out in the context of the extended magneto-hydrodynamic (MHD) model in NIMROD. The purpose is to investigate the physical cause behind edge localized mode (ELM) suppression in experiment after the Li-coating of the divertor and the first wall of the NSTX tokamak. Besides ideal MHD modeling, including finite-Larmor radius effect and two-fluid Hall and electron diamagnetic drift contributions, a non-ideal resistivity model is employed, taking into account the increase of Zeff after Li-conditioning in ELM-free H-mode. Unlike an earlier conclusion from an eigenvalue code analysis of these equilibria, NIMROD results find that after reduced recycling from divertor plates, profile modification is necessary but insufficient to explain the mechanism behind complete ELMs suppression in ideal two-fluid MHD. After considering the higher plasma resistivity due to higher Zeff, the complete stabilization could be explained. A thorough analysis of both pre-lithium ELMy and with-lithium ELM-free cases using ideal and non-ideal MHD models is presented, after accurately including a vacuum-like cold halo region in NIMROD to investigate ELMs.

Population Mixing in Asymmetric Magnetic Reconnection with a Guide Field.

We investigate how population mixing leads to structured electron distribution functions in asymmetric guide-field magnetic reconnection based on particle-in-cell simulations. The change of magnetic connectivity patches populations from different inflow regions to form multicomponent distributions in the exhaust, illustrating the direct consequence of the breaking and rejoining of magnetic flux tubes. Finite Larmor radius (FLR) effects of electrons accelerated by the perpendicular electric fields result in crescent-type nongyrotropic distributions. A new type of nongyrotropy is found to be caused by the combined effects of the FLR and velocity dispersion of electrons accelerated by the parallel electric field. The patching together of populations and the effects of acceleration and the FLR form the first steps of mixing in the exhaust and separatrix regions.

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.

Geodesic acoustic modes with poloidal mode couplings ad infinitum

Geodesic acoustic modes (GAMs) are studied including all poloidal mode (m) couplings within a drift reduced Braginskii framework. An exact analytical formula for GAM frequency is given within the toroidal Hasegawa Mima model with the full finite larmor radius effect and poloidal mode couplings ad infinitum using a scalar continued fraction formulation, which results from reduction of the semi-infinite chain of interactions that is obtained from the nearest neighbor coupling pattern due to geodesic curvature. This pattern can be described by a semi-infinite chain model of the GAM with the mode-mode coupling matrix elements proportional to the radial wave number kr. In the more general case of multi-field description of the GAM, the infinite chain can be reduced to a renormalized bi-nodal chain with a matrix continued fraction formulation. The convergence study of the linear GAM dispersion with respect to kr and the m-spectra confirms that the coupling beyond m = 1 is sustained only when kr ≠ 0 and the higher m couplings become important with increasing kr and increasing ion to electron temperature ratio τi.

A Finite-Orbit-Width Fokker-Planck solver for modeling of energetic particle interactions with waves, with application to Helicons in ITER

The bounce-average (BA) finite-difference Fokker-Planck (FP) code CQL3D [1,2] now includes the essential physics to describe the RF heating of Finite-Orbit-Width (FOW) ions in tokamaks. The FP equation is reformulated in terms of Constants-Of-Motion coordinates, which we select to be particle speed, pitch angle, and major radius on the equatorial plane thus obtaining the distribution function directly at this location. Full-orbit, low collisionality neoclassical radial transport emerges from averaging the local friction and diffusion coefficients along guiding center orbits. Similarly, the BA of local quasilinear RF diffusion terms gives rise to additional radial transport. The local RF electric field components needed for the BA operator are usually obtained by a ray-tracing code, such as GENRAY, or in conjunction with full-wave codes. As a new, practical application, the CQL3D-FOW version is used for simulation of alpha-particle heating by high-harmonic waves in ITER. Coupling of high harmonic or helicon fast waves power to electrons is a promising current drive (CD) scenario for high beta plasmas. However, the efficiency of current drive can be diminished by parasitic channeling of RF power into fast ions, such as alphas, through finite Larmor-radius effects. We investigate possibilities to reduce the fast ion heating in CD scenarios.

On all-FLR order numerical modelling of RF wave propagation and damping

Determining the fate of waves in hot magnetized plasmas in magnetic confinement fusion machines close to arbitrary cyclotron harmonics retaining finite Larmor radius effects requires solving the relevant integro-differential wave equation for waves of arbitrary wavelength. Anticipating exploitation in as realistic geometry as possible this requires massive computer resources. Work is ongoing to attempt reducing the required CPU memory and time. As Morlet wavelets are localised in x-space as well as k-space, they potentially offer a means to solve the relevant wave equation at reduced CPU requirement cost. Encouraging first results are obtained.