Showing papers in "Journal of Plasma Physics in 2015"

A kinetic model of plasma turbulence

Abstract: A Hybrid Vlasov–Maxwell (HVM) model is presented and recent results about the link between kinetic effects and turbulence are reviewed. Using five-dimensional (2D in space and 3D in the velocity space) simulations of plasma turbulence, it is found that kinetic effects (or non-fluid effects) manifest through the deformation of the proton velocity distribution function (DF), with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. The direction of the proper temperature anisotropy, calculated in the main reference frame of the distribution itself, has a finite probability of being along or across the ambient magnetic field, in general agreement with the classical definition of anisotropy T ⊥/T ∥ (where subscripts refer to the magnetic field direction). Adopting the latter conventional definition, by varying the global plasma beta (β) and fluctuation level, simulations explore distinct regions of the space given by T ⊥/T ∥ and β∥, recovering solar wind observations. Moreover, as in the solar wind, HVM simulations suggest that proton anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. The role of alpha particles is reviewed using multi-ion kinetic simulations, revealing a similarity between proton and helium non-Maxwellian effects. The techniques presented here are applied to 1D spacecraft-like analysis, establishing a link between non-fluid phenomena and solar wind magnetic discontinuities. Finally, the dimensionality of turbulence is investigated, for the first time, via 6D HVM simulations (3D in both spaces). These preliminary results provide support for several previously reported studies based on 2.5D simulations, confirming several basic conclusions. This connection between kinetic features and turbulence open a new path on the study of processes such as heating, particle acceleration, and temperature-anisotropy, commonly observed in space plasmas.

Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas

Abstract: A theoretical framework for low-frequency electromagnetic (drift-)kinetic turbulence in a collisionless, multi-species plasma is presented. The result generalises reduced magnetohydrodynamics (RMHD) and kinetic RMHD (Schekochihin et al., Astrophys. J. Suppl. Ser., vol. 182, 2009, pp. 310–377) to the case where the mean distribution function of the plasma is pressure-anisotropic and different ion species are allowed to drift with respect to each other – a situation routinely encountered in the solar wind and presumably ubiquitous in hot dilute astrophysical plasmas such as the intracluster medium. Two main objectives are achieved. First, in a non-Maxwellian plasma, the relationships between fluctuating fields (e.g. the Alfven ratio) are order-unity modified compared to the more commonly considered Maxwellian case, and so a quantitative theory is developed to support quantitative measurements now possible in the solar wind. Beyond these order-unity corrections, the main physical feature of low-frequency plasma turbulence survives the generalisation to non-Maxwellian distributions: Alfvenic and compressive fluctuations are energetically decoupled, with the latter passively advected by the former; the Alfvenic cascade is fluid, satisfying RMHD equations (with the Alfven speed modified by pressure anisotropy and species drifts), whereas the compressive cascade is kinetic and subject to collisionless damping (and for a bi-Maxwellian plasma splits into three independent collisionless cascades). Secondly, the organising principle of this turbulence is elucidated in the form of a conservation law for the appropriately generalised kinetic free energy. It is shown that non-Maxwellian features in the distribution function reduce the rate of phase mixing and the efficacy of magnetic stresses, and that these changes influence the partitioning of free energy amongst the various cascade channels. As the firehose or mirror instability thresholds are approached, the dynamics of the plasma are modified so as to reduce the energetic cost of bending magnetic-field lines or of compressing/rarefying them. Finally, it is shown that this theory can be derived as a long-wavelength limit of non-Maxwellian slab gyrokinetics.

Monte Carlo particle-in-cell methods for the simulation of the Vlasov–Maxwell gyrokinetic equations

Abstract: The particle-in-cell (PIC) algorithm is the most popular method for the discretisation of the general 6D Vlasov–Maxwell problem and it is widely used also for the simulation of the 5D gyrokinetic equations. The method consists of coupling a particle-based algorithm for the Vlasov equation with a grid-based method for the computation of the self-consistent electromagnetic fields. In this review we derive a Monte Carlo PIC finite-element model starting from a gyrokinetic discrete Lagrangian. The variations of the Lagrangian are used to obtain the time-continuous equations of motion for the particles and the finite-element approximation of the field equations. The Noether theorem for the semi-discretised system implies a certain number of conservation properties for the final set of equations. Moreover, the PIC method can be interpreted as a probabilistic Monte Carlo like method, consisting of calculating integrals of the continuous distribution function using a finite set of discrete markers. The nonlinear interactions along with numerical errors introduce random effects after some time. Therefore, the same tools for error analysis and error reduction used in Monte Carlo numerical methods can be applied to PIC simulations.

The Wisconsin Plasma Astrophysics Laboratory

Abstract: The Wisconsin Plasma Astrophysics Laboratory (WiPAL) is a flexible user facility designed to study a range of astrophysically relevant plasma processes as well as novel geometries that mimic astrophysical systems. A multi-cusp magnetic bucket constructed from strong samarium cobalt permanent magnets now confines a , fully ionized, magnetic-field-free plasma in a spherical geometry. Plasma parameters of to and to provide an ideal testbed for a range of astrophysical experiments, including self-exciting dynamos, collisionless magnetic reconnection, jet stability, stellar winds and more. This article describes the capabilities of WiPAL, along with several experiments, in both operating and planning stages, that illustrate the range of possibilities for future users.

Novel aspects of direct laser acceleration of relativistic electrons

Abstract: We examine the impact of several factors on electron acceleration by a laser pulse and the resulting electron energy gain. Specifically, we consider the role played by: (1) static longitudinal electric field, (2) static transverse electric field, (3) electron injection into the laser pulse, and (4) static longitudinal magnetic field. It is shown that all of these factors lead, under certain conditions, to a considerable electron energy gain from the laser pulse. In contrast with other mechanisms such as wakefield acceleration, the static electric fields in this case do not directly transfer substantial energy to the electron. Instead, they reduce the longitudinal dephasing between the electron and the laser beam, which then allows the electron to gain extra energy from the beam. The mechanisms discussed here are relevant to experiments with under-dense gas jets, as well as to experiments with solid-density targets involving an extended pre-plasma.

Ion and electron heating during magnetic reconnection in weakly collisional plasmas

Abstract: 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.

BOUT++: Recent and current developments

Abstract: BOUT++ is a 3D nonlinear finite-difference plasma simulation code, capable of solving quite general systems of Partial Differential Equations (PDEs), but targeted particularly on studies of the edge region of tokamak plasmas. BOUT++ is publicly available, and has been adopted by a growing number of researchers worldwide. Here we present improvements which have been made to the code since its original release, both in terms of structure and its capabilities. Some recent applications of these methods are reviewed, and areas of active development are discussed. We also present algorithms and tools which have been developed to enable creation of inputs from analytic expressions and experimental data, and for processing and visualisation of output results. This includes a new tool Hypnotoad for the creation of meshes from experimental equilibria. Algorithms have been implemented in BOUT++ to solve a range of linear algebraic problems encountered in the simulation of reduced Magnetohydrodynamics (MHD) and gyro-fluid models: A preconditioning scheme is presented which enables the plasma potential to be calculated efficiently using iterative methods supplied by the PETSc library (the Portable, Extensible Toolkit for Scientific Computation) (Balay et al. 2014), without invoking the Boussinesq approximation. Scaling studies are also performed of a linear solver used as part of physics-based preconditioning to accelerate the convergence of implicit time-integration schemes.

Landau fluid closures with nonlinear large-scale finite Larmor radius corrections for collisionless plasmas

Abstract: With the aim to develop a tool for simulating turbulence in collisionless magnetized plasmas, fluid models retaining low-frequency kinetic effects such as Landau damping and finite Larmor radius (FLR) corrections are discussed. It turns out that, in the absence of ion-cyclotron resonance, the dispersion and damping of kinetic Alfven waves at scales as small as a fraction of the ion Larmor radius are accurately reproduced when using fluid estimates of the non-gyrotropic moments, at leading-order within a large-scale asymptotics. Differently, evaluations based on the low-frequency linear kinetic theory are necessary in regimes of large temperature anisotropies, and in particular in the presence of the mirror instability. Combining both descriptions leads to a new Landau fluid model retaining large-scale FLR nonlinearities, while reproducing the linear dynamics of low-frequency modes at the sub-ionic scales.

Fluctuation-dissipation relations for a plasma-kinetic Langevin equation

Abstract: A linearised kinetic equation describing electrostatic perturbations of a Maxwellian equilibrium in a weakly collisional plasma forced by a random source is considered. The problem is treated as a kinetic analogue of the Langevin equation and the corresponding fluctuation-dissipation relations are derived. The kinetic fluctuation-dissipation relation reduces to the standard “fluid” one in the regime where the Landau damping rate is small and the system has no real frequency; in this case the simplest possible Landau-fluid closure of the kinetic equation coincides with the standard Langevin equation. Phase mixing of density fluctuations and emergence of fine scales in velocity space is diagnosed as a constant flux of free energy in Hermite space; the fluctuation-dissipation relations for the perturbations of the distribution function are derived, in the form of a universal expression for the Hermite spectrum of the free energy. Finite-collisionality effects are included. This work is aimed at establishing the simplest fluctuation-dissipation relations for a kinetic plasma, clarifying the connection between Landau and Hermite-space formalisms, and setting a benchmark case for a study of phase mixing in turbulent plasmas.

The Inherently Three-Dimensional Nature of Magnetized Plasma Turbulence

Abstract: It is often asserted or implicitly assumed, without justification, that the results of two-dimensional investigations of plasma turbulence are applicable to the three-dimensional plasma environments of interest. A projection method is applied to derive two scalar equations that govern the nonlinear evolution of the Alfvenic and pseudo-Alfvenic components of ideal incompressible magnetohydrodynamic (MHD) plasma turbulence. The mathematical form of these equations makes clear the inherently three-dimensional nature of plasma turbulence, enabling an analysis of the nonlinear properties of two-dimensional limits often used to study plasma turbulence. In the anisotropic limit, k⊥ ≫ k∥, that naturally arises in magnetized plasma systems, the perpendicular 2D limit retains the dominant nonlinearities that are mediated only by the Alfvenic fluctuations but lacks the wave physics associated with the linear term that is necessary to capture the anisotropic cascade of turbulent energy. In the in-plane 2D limit, the nonlinear energy transfer is controlled instead by the pseudo-Alfven waves, with the Alfven waves relegated to a passive role. In the oblique 2D limit, an unavoidable azimuthal dependence connecting the wavevector components will likely cause artificial azimuthal asymmetries in the resulting turbulent dynamics. Therefore, none of these 2D limits is sufficient to capture fully the rich three-dimensional nonlinear dynamics critical to the evolution of plasma turbulence.

Turbulent dissipation challenge: a community-driven effort

Abstract: Many naturally occurring and man-made plasmas are collisionless and turbulent. It is not yet well understood how the energy in fields and fluid motions is transferred into the thermal degrees of freedom of constituent particles in such systems. The debate at present primarily concerns proton heating. Multiple possible heating mechanisms have been proposed over the past few decades, including cyclotron damping, Landau damping, heating at intermittent structures and stochastic heating. Recently, a community-driven effort was proposed (Parashar & Salem, 2013, arXiv:1303.0204) to bring the community together and understand the relative contributions of these processes under given conditions. In this paper, we propose the first step of this challenge: a set of problems and diagnostics for benchmarking and comparing different types of 2.5D simulations. These comparisons will provide insights into the strengths and limitations of different types of numerical simulations and will help guide subsequent stages of the challenge.

Superdiffusive transport in laboratory and astrophysical plasmas

Abstract: In the last few years it has been demonstrated, both by data analysis and by numerical simulations, that the transport of energetic particles in the presence of magnetic turbulence can be superdiffusive rather than normal diffusive (Gaussian). The term ‘superdiffusive’ refers to the mean square displacement of particle positions growing superlinearly with time, as compared to the normal linear growth. The so-called anomalous transport, which in general comprises both subdiffusion and superdiffusion, has gained growing attention during the last two decades in many fields including laboratory plasma physics, and recently in astrophysics and space physics. Here we show a number of examples, both from laboratory and from astrophysical plasmas, where superdiffusive transport has been identified, with a focus on what could be the main influence of superdiffusion on fundamental processes like diffusive shock acceleration and heliospheric energetic particle propagation. For laboratory plasmas, superdiffusion appears to be due to the presence of electrostatic turbulence which creates long-range correlations and convoluted structures in perpendicular transport: this corresponds to a similar phenomenon in the propagation of solar energetic particles (SEPs) which leads to SEP dropouts. For the propagation of energetic particles accelerated at interplanetary shocks in the solar wind, parallel superdiffusion seems to be prevailing; this is based on a pitch-angle scattering process different from that envisaged by quasi-linear theory, and this emphasizes the importance of nonlinear interactions and trapping effects. In the case of supernova remnant shocks, parallel superdiffusion is possible at quasi-parallel shocks, as occurring in the interplanetary space, and perpendicular superdiffusion is possible at quasi-perpendicular shocks, as corresponding to Richardson diffusion: therefore, cosmic ray acceleration at supernova remnant shocks should be formulated in terms of superdiffusion. The possible relations among anomalous transport in laboratory, heliospheric, and astrophysical plasmas will be indicated.

Fourier–Hermite spectral representation for the Vlasov–Poisson system in the weakly collisional limit

Abstract: We study Landau damping in the 1+1D Vlasov–Poisson system using a Fourier–Hermite spectral representation. We describe the propagation of free energy in Fourier–Hermite phase space using forwards and backwards propagating Hermite modes recently developed for gyrokinetic theory. We derive a free energy equation that relates the change in the electric field to the net Hermite flux out of the zeroth Hermite mode. In linear Landau damping, decay in the electric field corresponds to forward propagating Hermite modes; in nonlinear damping, the initial decay is followed by a growth phase characterized by the generation of backwards propagating Hermite modes by the nonlinear term. The free energy content of the backwards propagating modes increases exponentially until balancing that of the forward propagating modes. Thereafter there is no systematic net Hermite flux, so the electric field cannot decay and the nonlinearity effectively suppresses Landau damping. These simulations are performed using the fully-spectral 5D gyrokinetics code SpectroGK, modified to solve the 1+1D Vlasov–Poisson system. This captures Landau damping via Hou–Li filtering in velocity space. Therefore the code is applicable even in regimes where phase mixing and filamentation are dominant.

Wavelet transforms and their applications to MHD and plasma turbulence: a review

Abstract: Wavelet analysis and compression tools are reviewed and different applications for the study of MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics based on the wavelet coefficients. We then show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising. Finally some multiscale numerical simulation schemes using wavelets are described. Several examples for analysing, compressing and computing one-, two- and three-dimensional turbulent MHD or plasma flows are presented.

Positron clouds within thunderstorms

Abstract: We report the observation of two isolated clouds of positrons inside an active thunderstorm. These observations were made by the Airborne Detector for Energetic Lightning Emissions (ADELE), an array of six gamma-ray detectors, which flew on a Gulfstream V jet aircraft through the top of an active thunderstorm in August 2009. ADELE recorded two 511 keV gamma-ray count rate enhancements, 35 s apart, each lasting approximately 0.2 s. The enhancements, which were approximately a factor of 12 above background, were both accompanied by electrical activity as measured by a flat-plate antenna on the underside of the aircraft. The energy spectra were consistent with a source mostly composed of positron annihilation gamma rays, with a prominent 511 keV line clearly visible in the data. Model fits to the data suggest that the aircraft was briefly immersed in clouds of positrons, more than a kilometre across. It is not clear how the positron clouds were created within the thunderstorm, but it is possible they were caused by the presence of the aircraft in the electrified environment.

Separatrices : The crux of reconnection

Abstract: Magnetic reconnection is one of the key processes in astrophysical and laboratory plasmas: it is the opposite of a dynamo. Looking at energy, a dynamo transforms kinetic energy in magnetic energy while reconnection takes magnetic energy and returns it to its kinetic form. Most plasma processes at their core involve first storing magnetic energy accumulated over time and then releasing it suddenly. We focus here on this release. A key concept in analysing reconnection is that of the separatrix, a surface (line in 2D) that separates the fresh unperturbed plasma embedded in magnetic field lines not yet reconnected with the hotter exhaust embedded in reconnected field lines. In kinetic physics, the separatrices become a layer where many key processes develop. We present here new results relative to the processes at the separatrices that regulate the plasma flow, the energization of the species, the electromagnetic fields and the instabilities developing at the separatrices.

The magnetized dusty plasma experiment (MDPX)

Abstract: The magnetized dusty plasma experiment (MDPX) is a newly commissioned plasma device that started operations in late spring, 2014. The research activities of this device are focused on the study of the physics, highly magnetized plasmas, and magnetized dusty plasmas. The design of the MDPX device is centered on two main components: an open bore, superconducting magnet that is designed to produce, in a steady state, both uniform magnetic fields up to 4 Tesla and non-uniform magnetic fields with gradients of 1–2 T m−1 and a flexible, removable, octagonal vacuum chamber that provides substantial probe and optical access to the plasma. This paper will provide a review of the design criteria for the MDPX device, a description of the research objectives, and brief discussion of the research opportunities offered by this multi-institution, multi-user project.

Quasi-static free-boundary equilibrium of toroidal plasma with CEDRES++: Computational methods and applications

Abstract: We present a comprehensive survey of the various computational methods in CEDRES++ for finding equilibria of toroidal plasma. Our focus is on free-boundary plasma equilib-ria, where either poloidal field coil currents or the temporal evolution of voltages in poloidal field circuit systems are given data. Centered around a piecewise linear finite element representation of the poloidal flux map, our approach allows in large parts the use of established numerical schemes. The coupling of a finite element method and a boundary element method gives consistent numerical solutions for equilibrium problems in unbounded domains. We formulate a new Newton method for the discretized non-linear problem to tackle the various non-linearities, including the free plasma boundary. The Newton method guarantees fast convergence and is the main building block for the inverse equilibrium problems that we can handle in CEDRES++ as well. The inverse problems aim at finding either poloidal field coil currents that ensure a desired shape and position of the plasma or at finding the evolution of the voltages in the poloidal field circuit systems that ensure a prescribed evolution of the plasma shape and position. We provide equilibrium simulations for the tokamaks ITER and WEST to illustrate the performance of CEDRES++ and its application areas.

Overview of laser-driven generation of electron–positron beams

Abstract: Electron–positron (e–p) plasmas are widely thought to be emitted, in the form of ultra-relativistic winds or collimated jets, by some of the most energetic or powerful objects in the Universe, such as black-holes, pulsars, and quasars. These phenomena represent an unmatched astrophysical laboratory to test physics at its limit and, given their immense distance from Earth (some even farther than several billion light years), they also provide a unique window on the very early stages of our Universe. However, due to such gigantic distances, their properties are only inferred from the indirect interpretation of their radiative signatures and from matching numerical models: their generation mechanism and dynamics still pose complicated enigmas to the scientific community. Small-scale reproductions in the laboratory would represent a fundamental step towards a deeper understanding of this exotic state of matter. Here we present recent experimental results concerning the laser-driven production of ultra-relativistic e–p beams. In particular, we focus on the possibility of generating beams that present charge neutrality and that allow for collective effects in their dynamics, necessary ingredients for the testing pair-plasma physics in the laboratory. A brief discussion of the analytical and numerical modelling of the dynamics of these plasmas is also presented in order to provide a summary of the novel plasma physics that can be accessed with these objects. Finally, general considerations on the scalability of laboratory plasmas up to astrophysical scenarios are given.

Superbanana and superbanana plateau transport in finite aspect ratio tokamaks with broken symmetry

Abstract: Superbanana and superbanana plateau transport processes are critical to plasma confinement in tokamaks with broken symmetry. The transport is caused by the superbanana resonance, which occurs at a pitch angle that makes the toroidal drift speed vanish, i.e. the tips of the superbananas. The physics consequences of the resonance on the symmetry breaking induced toroidal momentum damping and on the energetic alpha particle transport have been demonstrated using large aspect ratio expansion. Here, the existing theory for the superbanana and superbanana plateau transport is extended for finite aspect ratio tokamaks with broken symmetry. The effects of finite plasma β, and magnetic field shear are naturally included. Here, β is the ratio of the thermal plasma pressure to the magnetic field pressure. The explicit expressions for the transport fluxes in these regimes in terms of the equilibrium quantities are presented. It is shown that the main effects are to modify the resonance function G(k) and the expression for the pitch angle parameter k in the existing theory.

Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics

Abstract: Ideal magnetohydrodynamics (IMHD) is strongly constrained by an infinite number of microscopic constraints expressing mass, entropy and magnetic flux conservation in each infinitesimal fluid element, the latter preventing magnetic reconnection. By contrast, in the Taylor relaxation model for formation of macroscopically self-organized plasma equilibrium states, all these constraints are relaxed save for the global magnetic fluxes and helicity. A Lagrangian variational principle is presented that leads to a new, fully dynamical, relaxed magnetohydrodynamics (RxMHD), such that all static solutions are Taylor states but also allows state with flow. By postulating that some long-lived macroscopic current sheets can act as barriers to relaxation, separating the plasma into multiple relaxation regions, a further generalization, multi-region relaxed magnetohydrodynamics (MRxMHD) is developed.

Parametric decay of parallel and oblique Alfvén waves in the expanding solar wind

Abstract: The long-term evolution of large-amplitude Alfven waves propagating in the solar wind is investigated by performing two-dimensional MHD simulations within the expanding box model. The linear and nonlinear phases of the parametric decay instability are studied for both circularly polarized waves in parallel propagation and for arc-polarized waves in oblique propagation. The non-monochromatic case is also considered. In the oblique case, the direct excitation of daughter modes transverse to the local background field is found for the first time in an expanding environment, and this transverse cascade seems to be favored for monochromatic mother waves. The expansion effect reduces the instability growth rate, and it can even suppress its onset for the lowest frequency modes considered here, possibly explaining the persistence of these outgoing waves in the solar wind.

A tutorial introduction to the statistical theory of turbulent plasmas, a half-century after Kadomtsev’s Plasma Turbulence and the resonance-broadening theory of Dupree and Weinstock

Abstract: In honour of the 50th anniversary of the influential review/monograph on plasma turbulence by B. B. Kadomtsev as well as the seminal works of T. H. Dupree and J. Weinstock on resonance-broadening theory, an introductory tutorial is given about some highlights of the statistical–dynamical description of turbulent plasmas and fluids, including the ideas of nonlinear incoherent noise, coherent damping, and self-consistent dielectric response. The statistical closure problem is introduced. Incoherent noise and coherent damping are illustrated with a solvable model of passive advection. Self-consistency introduces turbulent polarization effects that are described by the dielectric function$${\mathcal{D}}$$. Dupree’s method of using$${\mathcal{D}}$$to estimate the saturation level of turbulence is described; then it is explained why a more complete theory that includes nonlinear noise is required. The general theory is best formulated in terms of Dyson equations for the covariance$C$and an infinitesimal response function$R$, which subsumes$${\mathcal{D}}$$. An important example is the direct-interaction approximation (DIA). It is shown how to use Novikov’s theorem to develop an$$\boldsymbol{x}$$-space approach to the DIA that is complementary to the original$$\boldsymbol{k}$$-space approach of Kraichnan. A dielectric function is defined for arbitrary quadratically nonlinear systems, including the Navier–Stokes equation, and an algorithm for determining the form of$${\mathcal{D}}$$in the DIA is sketched. The independent insights of Kadomtsev and Kraichnan about the problem of the DIA with random Galilean invariance are described. The mixing-length formula for drift-wave saturation is discussed in the context of closures that include nonlinear noise (shielded by$${\mathcal{D}}$$). The role of$R$in the calculation of the symmetry-breaking (zonostrophic) instability of homogeneous turbulence to the generation of inhomogeneous mean flows is addressed. The second-order cumulant expansion and the stochastic structural stability theory are also discussed in that context. Various historical research threads are mentioned and representative entry points to the literature are given. In addition, some outstanding conceptual issues are enumerated.

Proton temperature-anisotropy-driven instabilities in weakly collisional plasmas: Hybrid simulations

Abstract: Kinetic instabilities in weakly collisional, high beta plasmas are investigated using two-dimensional hybrid expanding box simulations with Coulomb collisions modeled through the Langevin equation (corresponding to the Fokker-Planck one). The expansion drives a parallel or perpendicular temperature anisotropy (depending on the orientation of the ambient magnetic field). For the chosen parameters the Coulomb collisions are important with respect to the driver but are not strong enough to keep the system stable with respect to instabilities driven by the proton temperature anisotropy. In the case of the parallel temperature anisotropy the dominant oblique fire hose instability efficiently reduces the anisotropy in a quasilinear manner. In the case of the perpendicular temperature anisotropy the dominant mirror instability generates coherent compressive structures which scatter protons and reduce the temperature anisotropy. For both the cases the instabilities generate temporarily enough wave energy so that the corresponding (anomalous) transport coefficients dominate over the collisional ones and their properties are similar to those in collisionless plasmas.

Plasma turbulence, suprathermal ion dynamics and code validation on the basic plasma physics device TORPEX

Abstract: The TORPEX basic plasma physics device at the Center for Plasma Physics Research (CRPP) in Lausanne, Switzerland is described. In TORPEX, simple magnetized toroidal configurations, a paradigm for the tokamak scrape-off layer (SOL), as well as more complex magnetic geometries of direct relevance for fusion are produced. Plasmas of different gases are created and sustained by microwaves in the electron-cyclotron (EC) frequency range. Full diagnostic access allows for a complete characterization of plasma fluctuations and wave fields throughout the entire plasma volume, opening new avenues to validate numerical codes. We detail recent advances in the understanding of basic aspects of plasma turbulence, including its development from linearly unstable electrostatic modes, the formation of filamentary structures, or blobs, and its influence on the transport of energy, plasma bulk and suprathermal ions. We present a methodology for the validation of plasma turbulence codes, which focuses on quantitative assessment of the agreement between numerical simulations and TORPEX experimental data.

Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

Abstract: Gyrokinetic simulations of electromagnetic turbulence in magnetically confined torus plasmas including tokamak and heliotron/stellarator are reviewed. Numerical simulation of turbulence in finite beta plasmas is an important task for predicting the performance of fusion reactors and a great challenge in computational science due to multiple spatio-temporal scales related to electromagnetic ion and electron dynamics. The simulation becomes further challenging in non-axisymmetric plasmas. In finite beta plasmas, magnetic perturbation appears and influences some key mechanisms of turbulent transport, which include linear instability and zonal flow production. Linear analysis shows that the ion-temperature gradient (ITG) instability, which is essentially an electrostatic instability, is unstable at low beta and its growth rate is reduced by magnetic field line bending at finite beta. On the other hand, the kinetic ballooning mode (KBM), which is an electromagnetic instability, is destabilized at high beta. In addition, trapped electron modes (TEMs), electron temperature gradient (ETG) modes, and micro-tearing modes (MTMs) can be destabilized. These instabilities are classified into two categories: ballooning parity and tearing parity modes. These parities are mixed by nonlinear interactions, so that, for instance, the ITG mode excites tearing parity modes. In the nonlinear evolution, the zonal flow shear acts to regulate the ITG driven turbulence at low beta. On the other hand, at finite beta, interplay between the turbulence and zonal flows becomes complicated because the production of zonal flow is influenced by the finite beta effects. When the zonal flows are too weak, turbulence continues to grow beyond a physically relevant level of saturation in finite-beta tokamaks. Nonlinear mode coupling to stable modes can play a role in the saturation of finite beta ITG mode and KBM. Since there is a quadratic conserved quantity, evaluating nonlinear transfer of the conserved quantity from unstable modes to stable modes is useful for understanding the saturation mechanism of turbulence.

Generalized self-similarity of intermittent plasma turbulence in space and laboratory plasmas

Abstract: Statistical characteristics of plasma fluctuations in the solar wind (SW), the Earth’s magnetosphere and fusion devices are reviewed. The turbulence in all these media has a complicated multiscale structure and exhibits a generalized self-similarity in an extended scale range. The anomalous transport of mass and momentum is intermittent and is carried by sporadic plasma flux bursts with non-Gaussian statistics, long-range correlation and multifractality. Intermittent turbulent transport is characterized by superdiffusion with power law , . The structure functions in all these plasma environments are well fitted by the log-Poisson model of turbulence. Intermittent plasma turbulence displays universal properties and consists of quasi-1-D singular dissipative structures.

Dust ion acoustic rogue waves in superthermal warm ion plasma

Abstract: The properties of dust ion acoustic rogue waves (DIARWs) in an unmagnetized collisionless plasma system composed of charged dust grains, superthermal electrons and warm ions as a fluid are studied. The multiple scale perturbation method is used to derive a nonlinear Schrodinger equation (NLSE) for DIARWs. From the coefficients of nonlinearity and dispersion, we have determined the critical wave number threshold kcr at which modulational instability sets in. This critical wave number depends on the various plasma parameters, viz. superthermality of electrons, ion temperature and dust concentration. Within the modulational instability region, a random perturbation of amplitude grows and thus, creates DIARWs. It is found that DIARWs are significantly affected by electron superthermality (via κ), ion temperature (via σ) and dust concentration (via f). In view of the crucial importance of DIARWs in space environments, our results may be useful in understanding the basic features of DIARWs that may occur in space plasmas.

Nonlinear collisionless damping of Weibel turbulence in relativistic blast waves

Abstract: The Weibel/filamentation instability is known to play a key role in the physics of weakly magnetized collisionless shock waves. From the point of view of high energy astrophysics, this instability also plays a crucial role because its development in the shock precursor populates the downstream with a small-scale magneto-static turbulence which shapes the acceleration and radiative processes of suprathermal particles. The present work discusses the physics of the dissipation of this Weibel-generated turbulence downstream of relativistic collisionless shock waves. It calculates explicitly the first-order nonlinear terms associated to the diffusive nature of the particle trajectories. These corrections are found to systematically increase the damping rate, assuming that the scattering length remains larger than the coherence length of the magnetic fluctuations. The relevance of such corrections is discussed in a broader astrophysical perspective, in particular regarding the physics of the external relativistic shock wave of a gamma-ray burst.

Validating modeling assumptions of alpha particles in electrostatic turbulence

Abstract: To rigorously model fast ions in fusion plasmas, a non-Maxwellian equilibrium distribution must be used. In this work, the response of high-energy alpha particles to electrostatic turbulence has been analyzed for several different tokamak parameters. Our results are consistent with known scalings and experimental evidence that alpha particles are generally well confined: on the order of several seconds. It is also confirmed that the effect of alphas on the turbulence is negligible at realistically low concentrations, consistent with linear theory. It is demonstrated that the usual practice of using a high-temperature Maxwellian, while previously shown to give an adequate order-of-magnitude estimate of the diffusion coefficient, gives incorrect estimates for the radial alpha particle flux, and a method of correcting it in general is provided. Furthermore, we see that the timescales associated with collisions and transport compete at moderate energies, calling into question the assumption that alpha particles remain confined to a flux surface that is used in the derivation of the slowing-down distribution.