N. H. Bian

Radial interchange motions of plasma filaments

Radial convection of isolated filamentary structures due to interchange motions in magnetized plasmas is investigated. Following a basic discussion of vorticity generation, ballooning, and the role of sheaths, a two-field interchange model is studied by means of numerical simulations on a biperiodic domain perpendicular to the magnetic field. It is demonstrated that a blob-like plasma structure develops dipolar vorticity and electrostatic potential fields, resulting in rapid radial acceleration and formation of a steep front and a trailing wake. While the dynamical evolution strongly depends on the amount of collisional diffusion and viscosity, the structure travels a radial distance many times its initial size in all parameter regimes in the absence of sheath dissipation. In the ideal limit, there is an inertial scaling for the maximum radial velocity of isolated filaments. This velocity scales as the acoustic speed times the square root of the structure size relative to the length scale of the magnetic field. The plasma filament eventually decelerates due to mixing and collisional dissipation. Finally, the role of sheath dissipation is investigated. When included in the simulations, it significantly reduces the radial velocity of isolated filaments. The results are discussed in the context of convective transport in scrape-off layer plasmas, comprising both blob-like structures in low confinement modes and edge localized mode filaments in unstable high confinement regimes.

Mechanism and scaling for convection of isolated structures in nonuniformly magnetized plasmas

Large-scale radial advection of isolated structures in nonuniformly magnetized plasmas is investigated. The underlying mechanism considered is due to the nonlinear evolution of interchange motions, without any presumption of plasma sheaths. Theoretical arguments supported by numerical simulations reveal an inertial scaling for the radial velocity of isolated structures in the ideal limit. This velocity increases as the square root of the structure size relative to the length scale of the magnetic field. The magnitude of the radial advection velocity, as well as the dynamical evolution of the structures, compares favorably with recent experimental measurements of radially propagating blob structures in the scrape-off layer of magnetically confined plasmas.

ACCELERATION, MAGNETIC FLUCTUATIONS, AND CROSS-FIELD TRANSPORT OF ENERGETIC ELECTRONS IN A SOLAR FLARE LOOP

Plasma turbulence is thought to be associated with various physical processes involved in solar flares, including magnetic reconnection, particle acceleration, and transport. Using RHESSI observations and the X-ray visibility analysis, we determine the spatial and spectral distributions of energetic electrons for a flare (GOES M3.7 class, 2002 April 14, 23:55 UT), which was previously found to be consistent with a reconnection scenario. It is demonstrated that because of the high density plasma in the loop, electrons have to be continuously accelerated about the loop apex of length ~2 × 109 cm and width ~7 × 108 cm. Energy-dependent transport of tens of keV electrons is observed to occur both along and across the guiding magnetic field of the loop. We show that the cross-field transport is consistent with the presence of magnetic turbulence in the loop, where electrons are accelerated, and estimate the magnitude of the field line diffusion coefficient for different phases of the flare. The energy density of magnetic fluctuations is calculated for given magnetic field correlation lengths and is larger than the energy density of the non-thermal electrons. The level of magnetic fluctuations peaks when the largest number of electrons is accelerated and is below detectability or absent at the decay phase. These hard X-ray observations provide the first observational evidence that magnetic turbulence governs the evolution of energetic electrons in a dense flaring loop and is suggestive of their turbulent acceleration.

Particle acceleration and transport in reconnecting twisted loops in a stratified atmosphere

Context. Twisted coronal loops should be ubiquitous in the solar corona. Twisted magnetic fields contain excess magnetic energy, which can be released during magnetic reconnection, causing solar flares. Aims. The aim of this work is to investigate magnetic reconnection, and particle acceleration and transport in kink-unstable twisted coronal loops, with a focus on the effects of resistivity, loop geometry and atmospheric stratification. Another aim is to perform forward-modelling of bremsstrahlung emission and determine the structure of hard X-ray sources. Methods. We use a combination of magnetohydrodynamic (MHD) and test-particle methods. First, the evolution of the kinking coronal loop is considered using resistive MHD model, incorporating atmospheric stratification and loop curvature. Then, the obtained electric and magnetic fields and density distributions are used to calculate electron and proton trajectories using a guiding-centre approximation, taking into account Coulomb collisions. Results. It is shown that electric fields in twisted coronal loops can effectively accelerate protons and electrons to energies up to 10 MeV. High-energy particles have hard, nearly power-law energy spectra. The volume occupied by high-energy particles demonstrates radial expansion, which results in the expansion of the visible hard X-ray loop and a gradual increase in hard X-ray footpoint area. Synthesised hard X-ray emission reveals strong footpoint sources and the extended coronal source, whose intensity strongly depends on the coronal loop density.

Parallel electric field generation by Alfvén wave turbulence

Aims. This work aims to investigate the spectral structure of the parallel electric field generated by strong anisotropic and balanced Alfvenic turbulence in relation with the problem of electron acceleration from the thermal population in solar flare plasma conditions. Methods. We consider anisotropic Alfvenic fluctuations in the presence of a strong background magnetic field. Exploiting this anisotropy, a set of reduced equations governing non-linear, two-fluid plasma dynamics is derived. The low-β limit of this model is used to follow the turbulent cascade of the energy resulting from the non-linear interaction between kinetic Alfven waves, from the large magnetohydrodynamics (MHD) scales with k⊥ρs � 1 down to the small “kinetic” scales with k⊥ρs � 1, ρs being the ion sound gyroradius. Results. Scaling relations are obtained for the magnitude of the turbulent electromagnetic fluctuations, as a function of k⊥ and k� , showing that the electric field develops a component parallel to the magnetic field at large MHD scales. Conclusions. The spectrum we derive for the parallel electric field fluctuations can be effectively used to model stochastic resonant acceleration and heating of electrons by Alfven waves in solar flare plasma conditions

TURBULENT PITCH-ANGLE SCATTERING AND DIFFUSIVE TRANSPORT OF HARD X-RAY-PRODUCING ELECTRONS IN FLARING CORONAL LOOPS

Recent observations from RHESSI have revealed that the number of non-thermal electrons in the coronal part of a flaring loop can exceed the number of electrons required to explain the hard X-ray-emitting footpoints of the same flaring loop. Such sources cannot, therefore, be interpreted on the basis of the standard collisional transport model, in which electrons stream along the loop while losing their energy through collisions with the ambient plasma; additional physical processes, to either trap or scatter the energetic electrons, are required. Motivated by this and other observations that suggest that high-energy electrons are confined to the coronal region of the source, we consider turbulent pitch-angle scattering of fast electrons off low-frequency magnetic fluctuations as a confinement mechanism, modeled as a spatial diffusion parallel to the mean magnetic field. In general, turbulent scattering leads to a reduction of the collisional stopping distance of non-thermal electrons along the loop, and hence to an enhancement of the coronal hard X-ray source relative to the footpoints. The variation of source size L with electron energy E becomes weaker than the quadratic behavior pertinent to collisional transport, with the slope of L(E) depending directly on the mean free path λ associated with the non-collisional scattering mechanism. Comparing the predictions of the model with observations, we find that λ ~ (108-109) cm for ~30 keV, less than the length of a typical flaring loop and smaller than, or comparable to, the size of the electron acceleration region.

Effect of Collisions and Magnetic Convergence on Electron Acceleration and Transport in Reconnecting Twisted Solar Flare Loops

We study a model of particle acceleration coupled with an MHD model of magnetic reconnection in unstable twisted coronal loops. The kink instability leads to the formation of helical currents with strong parallel electric fields resulting in electron acceleration. The motion of electrons in the electric and magnetic fields of the reconnecting loop is investigated using a test-particle approach taking into account collisional scattering. We discuss the effects of Coulomb collisions and magnetic convergence near loop footpoints on the spatial distribution and energy spectra of high-energy electron populations and possible implications on the hard X-ray emission in solar flares.

Wave-particle interactions in non-uniform plasma and the interpretation of hard X-ray spectra in solar flares

Context. High-energy electrons accelerated during solar flares are abundant in the solar corona and in interplanetary space. Commonly, the number and energy of non-thermal electrons at the Sun is estimated through hard X-ray (HXR) spectral observations (e.g. RHESSI) and a single-particle collisional approximation. Aims. We aim to investigate the role of the spectrally evolving Langmuir turbulence on the population of energetic electrons in the solar corona. Methods. We numerically simulated the relaxation of a power-law non-thermal electron population in a collisional inhomogeneous plasma, including wave-particle and wave-wave interactions. Results. The numerical simulations show that the long-time evolution of electron population above 20 keV deviates substantially from the collisional approximation when wave-particle interactions in non-uniform plasma are taken into account. The evolution of the Langmuir wave spectrum towards smaller wavenumbers, caused by large-scale density fluctuations and wave-wave interactions, leads to an effective acceleration of electrons. Furthermore, the time-integrated spectrum of non-thermal electrons, which is normally observed with HXR above 20 keV, is noticeably increased because of acceleration of non-thermal electrons through Langmuir waves. Conclusions. The results show that the observed HXR spectrum, when interpreted in terms of collisional relaxation, can lead to an overestimated number and energy of energetic electrons accelerated in the corona.

Two-dimensional convection and interchange motions in fluids and magnetized plasmas

In this contribution some recent investigations of two-dimensional thermal convection relevant to ordinary fluids as well as magnetized plasmas are reviewed. An introductory discussion is given of the physical mechanism for baroclinic vorticity generation and convective motions in stratified fluids, emphasizing its relation to interchange motions of non-uniformly magnetized plasmas. This is followed by a review of the theories for the onset of convection and quasi-linear saturation in driven-dissipative systems. Non-linear numerical simulations which result in stationary convective states reveal the process of laminar scalar gradient expulsion, leading to the formation of temperature plumes and vorticity sheets. These dissipative structures are demonstrated to result in temperature profile consistency and power law transport scaling far from the threshold. The last part of this paper deals with the generation of differential rotation by fluctuating motions through tilting of the convective structures. The role of kinetic energy transfer and shearing due to differential advection is pointed out. Numerical simulations for strongly driven systems reveal turbulent states with a bursty behaviour of the fluctuation level which is associated with relaxation oscillations in the kinetic energy of the azimuthally mean flows. This leads to a state of large-scale intermittency manifested by exponential tails in the single-point probability distribution function of the dependent variables. The global bursting is interpreted in terms of a predator–prey regulation from the point of view of energetics. Finally, a discussion is given of the relevance of these phenomena to a variety of magnetized plasma experiments.

Particle acceleration in a model of a turbulent reconnecting plasma: a fractional diffusion approach

High-energy charged particles are produced during solar flares. These may be accelerated by the strong electric fields associated with the magnetic reconnection process which is the source of energy release in flares. A simple model of random acceleration of charged particles due to fragmented electric fields is considered for the case of a turbulent reconnecting plasma in which the fluctuating electric field is highly localized and its magnitude distributed according to power laws. The statistical properties of the acceleration process are expressed in terms of a fractional diffusion equation in velocity space, whose solution displays a power-law tail related only to the statistics of the electric field.