Gyrokinetic Landau collision operator in conservative form.

The effects of finite Larmor radius (FLR) corrections and heat-flux vector are studied on the pressure anisotropy-driven firehose instability in finitely conducting solar wind plasmas described by the double-adiabatic Chew, Goldberger and Low (CGL) fluid theory. The fluid description of collisionless plasmas is governed through modified adiabatic equations due to the heat-flux vector and finite ion Larmor radius corrections. The analytical dispersion relation of the firehose instability has been derived using the normal mode analysis and discussed in the solar wind plasmas. In the transverse mode, the dispersion relation of the Alfvénic mode is modified due to electrical resistivity and FLR corrections. In the longitudinal mode, the effects of the heat-flux parameter and electrical resistivity are observed separately. The dispersion relation of the firehose mode is modified due to the combined effects of FLR corrections and electrical resistivity. The graphical illustrations show that finite electrical resistivity and ion Larmor frequency destabilize the growth rate of the firehose instability. The results are useful for analyzing the solar mission data to study the firehose instability in the solar wind plasmas.

Dynamics of planetary ions in the induced magnetospheres of Venus and Mars

The steady state of dipolar magnetic field expansion is examined by injecting a plasma jet from the center of the dipolar magnetic field (magnetic inflation). An effective magnetic inflation is essential for the realization of a magneto plasma sail (MPS), which produces a propulsive force by the interaction between the solar wind and an artificial dipolar magnetic field that is inflated by the plasma jet injected from the spacecraft. During the process of magnetic inflation, the finite Larmor radius effect is of practical significance since rL/LB is considerably greater than unity in a region far from the center of the dipolar magnetic field. The simulation result obtained using the ideal magnetohydrodynamics (MHD) model is overestimated, namely, it shows that the inflated magnetic field decays according to |B| ∝ r -2.0 since the magnetic field is frozen into the plasma jet. In comparison with the MHD result, the results obtained using the hybrid particle-in-cell code are more accurate. These results show that the inflated magnetic field decays according to |B| ∝ r -2.3 under the condition βin = 1 since the finite ion Larmor radius effect decreases the flow of magnetic flux with respect to the flow of plasma jet.

Low-frequency electrostatic turbulence in low-\ensuremath{\mathrm{B}} plasmas is studied in two spatial dimensions by direct numerical simulations. In this limit the guiding center velocity in the direction perpendicular to a homogeneous magnetic field is in a first approximation the E\ifmmode\times\else\texttimes\fi{}${\mathrm{B}}_{0}$/${\mathrm{B}}_{0}^{2}$ velocity. The electron Larmor radius can safely be set to zero for most relevant conditions, but the ion dynamics are noticeably influenced by their finite Larmor radius. In the present study we use a fluid model where these effects are included by a simple filtering operation. The equilibrium spectra are investigated and compared with known analytical results. Particular attention is given to the finite Larmor radius effect for the turbulent diffusion of charged particles across magnetic field lines. The integral time scale and the micro time scale associated with the velocity correlations for the turbulent flow are discussed with attention to their dependence on the finite Larmor radius corrections. Finally, the numerical code is generalized to a hybrid model, which incorporates many ion species with different Larmor radii simultaneously present in the flow.

This study investigates the impact of various impurity species on peeling-ballooning (PB) modes and microturbulence in tokamak plasmas through the extension of traditional twofluid and gyro-Landau-fluid (GLF) models. By incorporating finite Larmor radius (FLR) effects, the analysis provides a comprehensive understanding of impurity-driven impact and its interaction with plasma turbulence. Depending on charge state and local plasma conditions, heavy impurities may exhibit gyro-radii larger than those of main ions, which are captured in the extended GLF model presented. Following the presentation of modified two-fluid equations incorporating impurity effects, we systematically analyze the distinctions between impurity and main ion dynamics and their resultant feedback mechanisms on plasma behavior. Derivation of the linear dispersion relation enables quantification of impurity-mediated modifications to: plasma vorticity, diamagnetic drift and gyroviscous effects, electron Hall physics, and FLR effects. BOUT++ -based linear simulations corroborate this formalism, demonstrating systematic stabilization of peeling-ballooning (PB) modes upon impurity seeding. And then operational implications for practical impurity control strategies in tokamak devices are proposed. The results underscore the necessity of impurity management to maintain stability and optimize plasma confinement, with specific focus on how FLR effects contribute to transport dynamics. This work paves the way for enhanced modeling and simulation efforts, supporting the development of strategies to control impurity-induced turbulence and improve overall reactor performance.

A numerical simulation is performed to study the effect of a viscous dissipation term on the generation of shear flow at a plasma edge in the guiding center approximation. The guiding center model includes the effects of finite Larmor radius corrections and polarization drift. The numerical code applies the method of fractional steps to the fluid guiding center equations. We attempt to discriminate between the smoothing of the microstructure by a small viscous dissipation term to control numerical instabilities, and the modification of the macroscopic physical results introduced by this small viscous dissipation term. The finite Larmor radius effect allows for a charge separation to exist, which can be further accentuated by the polarization drift. A difference in the viscous term between electrons and ions can add to the charge separation effect at the plasma edge, which can modify the physical results. The numerical calculation is effected using a slab model, periodic in one direction and finite in the other direction, with an inhomogeneous density of guiding centers to simulate a plasma edge. The evolution of the system shows the potential evolving to a shape characterized by the longest wavelength associated with the transverse dimension of the system, an evolution characteristic of an inverse cascade. We present an analysis of the effect of different values of the viscous term on the time evolution of this guiding center system, and on the formation and existence of a charge separation and an electric field at the edge of a plasma and the associated shear in the E × B flow.

Thermosolutal-convective instability of a composite plasma in a stellar atmosphere is considered to include the effects, separately, due to finite Larmor radius (FLR) and Hall currents in the presence of a uniform horizontal magnetic field. The sufficient conditions for the existence of monotonic instability are derived and are found to hold good both in the presence, separately, of FLR and Hall current effects.

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.

Generalized Bessel functions and Kapteyn series

Preliminary simulations of finite Larmor radius (FLR) effects on m = 1 tearing instabilities in a reverse field pinch (RFP) plasma are presented. δ f particle-in-cell (PIC) simulations were performed by extending a hybrid drift kinetic-MHD model to include the full Lorentz equations of motion to take into account finite Larmor radius (FLR) effects. The simulations show that for an idealized phase space distribution, sufficiently energetic ions stabilize the tearing mode. These simulations show good agreement with analytic theory and demonstrate the FLR physics capability of the hybrid kinetic-MHD model.

Transport of test particles in two-dimensional weak turbulence with waves propagating along the poloidal direction is studied using a reduced model. Finite Larmor radius (FLR) effects are included by gyroaveraging over one particle orbit. For low wave amplitudes the motion is mostly regular with particles trapped in the potential wells. As the amplitude increases the trajectories become chaotic and the Larmor radius modifies the orbits. For a thermal distribution of Finite Larmor radii the particle distribution function (PDF) is Gaussian for small $\unicode[STIX]{x1D70C}_{th}$ (thermal gyroradius) but becomes non-Gaussian for large $\unicode[STIX]{x1D70C}_{th}$. However, the time scaling of transport is diffusive, as characterized by a linear dependence of the variance of the PDF with time. An explanation for this behaviour is presented that provides an expression for an effective diffusion coefficient and reproduces the numerical results for large wave amplitudes which implies generalized chaos. When a shear flow is added in the direction of wave propagation, a modified model is obtained that produces free-streaming particle trajectories in addition to trapped ones; these contribute to ballistic transport for low wave amplitude but produce super-ballistic transport in the chaotic regime. As in the previous case, the PDF is Gaussian for low $\unicode[STIX]{x1D70C}_{th}$ becoming non-Gaussian as it increases. The perpendicular transport presents the same behaviour as in the case with no flow but the diffusion is faster in the presence of the flow.

Turbulence in plasmas is modeled by fluctuating electric fields that determine particle motion through the E × B drift velocity which can lead to chaotic behavior. When applied to an ensemble of plasma particles in the chaotic regime their transport is studied: the anomalous plasma transport. The fluctuations are modeled by a spectrum of traveling waves with a wide frequency span which converts the equations of motion into an iterative mapping. The statistical properties of transport are derived. When the waves amplitude is small the particle orbits are regular, but as it is increased the behavior becomes increasingly chaotic. The effect of finite Larmor radius and the presence of a background plasma flow is also studied. We show that when a thermal population of particles is considered, the transport becomes non-local, as evidenced by a non-Gaussian particle distribution function (PDF). We have analyzed two different kinds of sheared flows: (1) a monotonic velocity shear and (2) a non-monotonic shear. The presence of transport barriers associated with the sheared velocity is also studied. We also present the application of the same techniques to study the transport of energetic particles that are born with a monoenergetic distribution.

The Rayleigh-Taylor instability of a compressible plasma in the presence of a horizontal magnetic field is investigated, taking into account the effects of finite Larmor radius. Only transverse perturbations are considered. The problem is shown to be characterized by a variational principle. Using it, the dispersion relation is obtained for a plasma layer of finite thickness and having an exponentially varying density. It is found that the finite Larmor radius effects can thoroughly stabilize unstable configurations. For configurations which are not completely stabilized, the compressibility stabilizes some of the disturbances which are unstable for an incompressible plasma.

The stability of an infinitely conducting plasma of variable density has been investigated taking into account the finiteness of the ion Larmor radius. The perturbations propagating along the ambient magnetic field are considered. It is established that, in general,n2 is necessarily real, wheren is the growth rate of disturbance, thus ruling out the possibility of overstability or damped oscillations. The solution is shown to be characterized by a variational principle, which provides the basis for obtaining an approximate solution of the problem. Two density distributions are considered: (i) a continuously stratified plasma layer and (ii) two semi-infinitely extending plasmas of constant densities separated by a horizontal interface. In both cases it has been shown that for the said disturbances the stability criterion remains unaffected by the inclusion of finite Larmor radius effects, though the amplified motion is strongly inhibited due to their inclusion.

A dispersion relation has been derived which shows the combined stabilizing effects of convective damping (outgoing boundary condition), average curvature and finite Larmor radius (FLR) on ballooning modes. It has been found that, in contrast to the MHD case, the convective damping influences the stability threshold when FLR effects are included. The highest allowed shear as a function of mode number for free passage to the second stability region has been calculated analytically.