arXiv subjects

Loukas Vlahos

Publications and source records attributed to Loukas Vlahos.

At least 37 records · Page 2Linked to original sources

arXiv2017

Synergy of stochastic and systematic energization of plasmas during turbulent reconnection

The important characteristic of turbulent reconnection is that it combines large scale magnetic disturbances $(δB/B \sim 1)$ with randomly distributed Unstable Current Sheets (UCSs). Many well known non linear MHD structures (strong turbulence, current sheet(s), shock(s)) lead asymptotically to the state of turbulent reconnection. We analyze in this article, for the first time, the energization of electrons and ions in a {\bf large scale} environment that {\bf combines} large amplitude disturbances propagating with sub-Alfvénic speed with UCSs. The magnetic disturbances interact stochastically (second order Fermi) with the charged particles and they play a crucial role in the heating of the particles, while the UCS interact systematically (first order Fermi) and play a crucial role in the formation of the high energy tail. The synergy of stochastic and systematic acceleration provided by the mixture of magnetic disturbances and UCSs influences the energetics of the thermal and non-thermal particles, the power law index, and the time the particles remain inside the energy release volume. We show that this synergy can explain the observed very fast and impulsive particle acceleration and the slightly delayed formation of a super-hot particle population.

astro-ph.HE↗

arXiv2017

Particle Acceleration and Fractional Transport in Turbulent Reconnection

We consider a large scale environment of turbulent reconnection that is fragmented into a number of randomly distributed Unstable Current Sheets (UCS), and we statistically analyze the acceleration of particles within this environment. We address two important cases of acceleration mechanisms when the particles interact with the UCS: (a) electric field acceleration, and (b) acceleration through reflection at contracting islands. Electrons and ions are accelerated very efficiently, attaining an energy distribution of power-law shape with an index $1-2$, depending on the acceleration mechanism. The transport coefficients in energy space are estimated from the test-particle simulation data, and we show that the classical Fokker-Planck (FP) equation fails to reproduce the simulation results when the transport coefficients are inserted into it and it is solved numerically. The cause for this failure is that the particles perform Levy flights in energy space, the distributions of energy increments exhibit power-law tails. We then use the fractional transport equation (FTE) derived by Isliker et al., 2017, whose parameters and the order of the fractional derivatives are inferred from the simulation data, and, solving the FTE numerically, we show that the FTE successfully reproduces the kinetic energy distribution of the test-particles. We discuss in detail the analysis of the simulation data and the criteria that allow judging the appropriateness of either an FTE or a classical FP equation as a transport model.

astro-ph.HE↗

arXiv2017

Fractional Transport in Strongly Turbulent Plasmas

We analyze statistically the energization of particles in a large scale environment of strong turbulence that is fragmented into a large number of distributed current filaments. The turbulent environment is generated through strongly perturbed, 3D, resistive MHD simulations, and it emerges naturally from the nonlinear evolution, without a specific reconnection geometry being set up. Based on test-particle simulations, we estimate the transport coefficients in energy space for use in the classical Fokker-Planck (FP) equation, and we show that the latter fails to reproduce the simulation results. The reason is that transport in energy space is highly anomalous (strange), the particles perform Levy flights, and the energy distributions show extended power-law tails. Newly then, we motivate the use and derive the specific form of a fractional transport equation (FTE), we determine its parameters and the order of the fractional derivatives from the simulation data, and we show that the FTE is able to reproduce the high energy part of the simulation data very well. The procedure for determining the FTE parameters also makes clear that it is the analysis of the simulation data that allows to make the decision whether a classical FP or a FTE is appropriate.

physics.plasm-ph↗

arXiv2016

Stochastic Fermi Energization of Coronal Plasma during explosive magnetic energy release

The aim of this study is to analyze the interaction of charged particles (ions and electrons) with randomly formed particle scatterers (e.g.\ large scale local "magnetic fluctuations" or "coherent magnetic irregularities"), using the set up proposed initially by \cite{Fermi49}. These scatterers are formed by the explosive magnetic energy release and propagate with the Alfvén speed along the irregular magnetic fields. They are large scale local fluctuations ($δB/B \approx 1$), randomly distributed inside the unstable magnetic topology and will here be called {\bf Alfvénic Scatterers (AS)}. We constructed a 3D grid on which a small fraction of randomly chosen grid points are acting as AS. In particular, we study how a large number of test particles evolve inside a collection of AS, analyzing the evolution of their energy distribution and their escape time distribution. We use a well established method to estimate the transport coefficients directly from the trajectories of the particles. Using the estimated transport coefficients and solving the Fokker-Planck (FP) equation numerically, we can recover the energy distribution of the particles. We have shown that the Stochastic Fermi Energization (SFE) of mildly relativistic and relativistic plasma can heat and accelerate the tail of the ambient particle distribution as predicted by \citet{Parker58} and \citet{Ramaty79}. The temperature of the hot plasma and the tail of the energetic particles depend on the mean free path ($λ_{\rm sc}$) of the particles between the scatterers inside the energization volume.

astro-ph.HE↗

arXiv2016

Limits of applicability of the quasilinear approximation to the electrostatic wave-plasma interaction

The limitation of the Quasilinear Theory (QLT) to describe the diffusion of electrons and ions in velocity space when interacting with a spectrum of large amplitude electrostatic Langmuir, Upper and Lower hybrid waves, is analyzed. We analytically and numerically estimate the threshold for the amplitude of the waves above which the QLT breaks down, using a test particle code. The evolution of the velocity distribution, the velocity-space diffusion coefficients, the driven current, and the heating of the particles are investigated, for the interaction with small and large amplitude electrostatic waves, i.e. in both regimes, there where QLT is valid and there where it clearly breaks down.

physics.plasm-ph↗

arXiv2016

Particle Acceleration and Heating by Turbulent Reconnection

Turbulent flows in the solar wind, large scale current sheets, multiple current sheets, and shock waves lead to the formation of environments in which a dense network of current sheets is established and sustains "turbulent reconnection". We constructed a 2D grid on which a number of randomly chosen grid points are acting as scatterers (i.e. magnetic clouds or current sheets). Our goal is to examine how test particles respond inside this large scale collection of scatterers. We study the energy gain of individual particles, the evolution of their energy distribution and their escape time distribution. We have developed a new method to estimate the transport coefficients from the dynamics of the interaction of the particles with the scatterers. Replacing the "magnetic clouds" with current sheets, we have proven that the energization processes can be more efficient depending on the strength of the effective electric fields inside the current sheets and their statistical properties. Using the estimated transport coefficients and solving the Fokker-Planck (FP) equation we can recover the energy distribution of the particles only for the sstochastic Fermi process. We have shown that the evolution of the particles inside a turbulent reconnecting volume is not a solution of the FP equation, since the interaction of the particles with the current sheets is "anomalous", in contrast to the case of the second order Fermi process.

astro-ph.SR↗

arXiv2016

Complexity Methods Applied to Turbulence in Plasma Astrophysics

In this review many of the well known tools for the analysis of Complex systems are used in order to study the global coupling of the turbulent convection zone with the solar atmosphere where the magnetic energy is dissipated explosively. Several well documented observations are not easy to interpret with the use of Magnetohydrodynamic (MHD) and/or Kinetic numerical codes. Such observations are: (1) The size distribution of the Active Regions (AR) on the solar surface, (2) The fractal and multi fractal characteristics of the observed magnetograms, (3) The Self-Organised characteristics of the explosive magnetic energy release and (4) the very efficient acceleration of particles during the flaring periods in the solar corona. We review briefly the work published the last twenty five years on the above issues and propose solutions by using methods borrowed from the analysis of complex systems. The scenario which emerged is as follows: (a) The fully developed turbulence in the convection zone generates and transports magnetic flux tubes to the solar surface. Using probabilistic percolation models we were able to reproduce the size distribution and the fractal properties of the emerged and randomly moving magnetic flux tubes. (b) Using a Non Linear Force Free (NLFF) magnetic extrapolation numerical code we can explore how the emerged magnetic flux tubes interact nonlinearly and form thin and Unstable Current Sheets (UCS) inside the coronal part of the AR. (c) The fragmentation of the UCS and the redistribution of the magnetic field locally, when the local current exceeds a Critical threshold, is a key process which drives avalanches and forms coherent structures. This local reorganization of the magnetic field, enhances the energy dissipation and influences the global evolution of the complex magnetic topology.

astro-ph.SR↗

arXiv2013

Self-consistent modeling of the dynamic evolution of magnetic island growth in the presence of stabilizing ECCD

The most promising technique for the control of neoclassical tearing modes in tokamak experiments is the compensation of the missing bootstrap current with electron-cyclotron current drive. In this frame, the dynamics of magnetic islands has been studied extensively in terms of the modified Rutherford equation, including the presence of current drive, either analytically described or computed by numerical methods. In this article, a self-consistent model for the dynamic evolution of the magnetic island and the driven current is derived, which takes into account the island's magnetic topology and its effect on the current drive. The model combines the modified Rutherford equation with a ray-tracing approach to electron-cyclotron wave propagation and absorption. Numerical results exhibit a decrease in the time required for complete stabilization with respect to the conventional computation (not taking into account the island geometry), which increases with increasing initial island size and radial misalignment of the deposition.

physics.plasm-ph↗

arXiv2011

Recent Advances in Understanding Particle Acceleration Processes in Solar Flares

We review basic theoretical concepts in particle acceleration, with particular emphasis on processes likely to occur in regions of magnetic reconnection. Several new developments are discussed, including detailed studies of reconnection in three-dimensional magnetic field configurations (e.g., current sheets, collapsing traps, separatrix regions) and stochastic acceleration in a turbulent environment. Fluid, test-particle, and particle-in-cell approaches are used and results compared. While these studies show considerable promise in accounting for the various observational manifestations of solar flares, they are limited by a number of factors, mostly relating to available computational power. Not the least of these issues is the need to explicitly incorporate the electrodynamic feedback of the accelerated particles themselves on the environment in which they are accelerated. A brief prognosis for future advancement is offered.

astro-ph.SR↗

arXiv2010

A self-organized criticality model for ion temperature gradient (ITG) mode driven turbulence in confined plasma

A new Self-Organized Criticality (SOC) model is introduced in the form of a Cellular Automaton (CA) for ion temperature gradient (ITG) mode driven turbulence in fusion plasmas. Main characteristics of the model are that it is constructed in terms of the actual physical variable, the ion temperature, and that the temporal evolution of the CA, which necessarily is in the form of rules, mimics actual physical processes as they are considered to be active in the system, i.e. a heating process and a local diffusive process that sets on if a threshold in the normalized ion temperature gradient R/L_T is exceeded. The model reaches the SOC state and yields ion temperature profiles of exponential shape, which exhibit very high stiffness, in that they basically are independent of the loading pattern applied. This implies that there is anomalous heat transport present in the system, despite the fact that diffusion at the local level is imposed to be of a normal kind. The distributions of the heat fluxes in the system and of the heat out-fluxes are of power-law shape. The basic properties of the model are in good qualitative agreement with experimental results.

physics.plasm-ph↗

arXiv2008

Gravito-magnetic instabilities in anisotropically expanding fluids

Gravitational instabilities in a magnetized Friedman - Robertson - Walker (FRW) Universe, in which the magnetic field was assumed to be too weak to destroy the isotropy of the model, are known and have been studied in the past. Accordingly, it became evident that the external magnetic field disfavors the perturbations' growth, suppressing the corresponding rate by an amount proportional to its strength. However, the spatial isotropy of the FRW Universe is not compatible with the presence of large-scale magnetic fields. Therefore, in this article we use the general-relativistic (GR) version of the (linearized) perturbed magnetohydrodynamic equations with and without resistivity, to discuss a generalized Jeans criterion and the potential formation of density condensations within a class of homogeneous and anisotropically expanding, self-gravitating, magnetized fluids in curved space-time. We find that, for a wide variety of anisotropic cosmological models, gravito-magnetic instabilities can lead to sub-horizonal, magnetized condensations. In the non-resistive case, the power spectrum of the unstable cosmological perturbations suggests that most of the power is concentrated on large scales (small k), very close to the horizon. On the other hand, in a resistive medium, the critical wave-numbers so obtained, exhibit a delicate dependence on resistivity, resulting in the reduction of the corresponding Jeans lengths to smaller scales (well bellow the horizon) than the non-resistive ones, while increasing the range of cosmological models which admit such an instability.

astro-ph↗

arXiv2008

Imprints of cosmic strings on the cosmological gravitational wave background

The equation which governs the temporal evolution of a gravitational wave (GW) in curved space-time can be treated as the Schrodinger equation for a particle moving in the presence of an effective potential. When GWs propagate in an expanding Universe with constant effective potential, there is a critical value (k_c) of the comoving wave-number which discriminates the metric perturbations into oscillating (k > k_c) and non-oscillating (k < k_c) modes. As a consequence, if the non-oscillatory modes are outside the horizon they do not freeze out. The effective potential is reduced to a non-vanishing constant in a cosmological model which is driven by a two-component fluid, consisting of radiation (dominant) and cosmic strings (sub-dominant). It is known that the cosmological evolution gradually results in the scaling of a cosmic-string network and, therefore, after some time (\Dl \ta) the Universe becomes radiation-dominated. The evolution of the non-oscillatory GW modes during \Dl \ta (while they were outside the horizon), results in the distortion of the GW power spectrum from what it is anticipated in a pure radiation-model, at present-time frequencies in the range 10^{-16} Hz < f < 10^5 Hz.

gr-qc↗

arXiv2008

Normal and Anomalous Diffusion: A Tutorial

The purpose of this tutorial is to introduce the main concepts behind normal and anomalous diffusion. Starting from simple, but well known experiments, a series of mathematical modeling tools are introduced, and the relation between them is made clear. First, we show how Brownian motion can be understood in terms of a simple random walk model. Normal diffusion is then treated (i) through formalizing the random walk model and deriving a classical diffusion equation, (ii) by using Fick's law that leads again to the same diffusion equation, and (iii) by using a stochastic differential equation for the particle dynamics (the Langevin equation), which allows to determine the mean square displacement of particles. (iv) We discuss normal diffusion from the point of view of probability theory, applying the Central Limit Theorem to the random walk problem, and (v) we introduce the more general Fokker-Planck equation for diffusion that includes also advection. We turn then to anomalous diffusion, discussing first its formal characteristics, and proceeding to Continuous Time Random Walk (CTRW) as a model for anomalous diffusion. It is shown how CTRW can be treated formally, the importance of probability distributions of the Levy type is explained, and we discuss the relation of CTRW to fractional diffusion equations and show how the latter can be derived from the CTRW equations. Last, we demonstrate how a general diffusion equation can be derived for Hamiltonian systems, and we conclude this tutorial with a few recent applications of the above theories in laboratory and astrophysical plasmas.

nlin.CD↗

arXiv2008

Solar and Stellar Active Regions:Cosmic laboratories for the study of Complexity

Solar active regions are driven dissipative dynamical systems. The turbulent convection zone forces new magnetic flux tubes to rise above the photosphere and shuffles the magnetic fields which are already above the photosphere. The driven 3D active region responds to the driver with the formation of Thin Current Sheets in all scales and releases impulsively energy, when special thresholds are met, on the form of nano-, micro-, flares and large scale coronal mass ejections. It has been documented that active regions form self similar structures with area Probability Distribution Functions (PDF's) following power laws and with fractal dimensions ranging from $1.2-1.7$. The energy release on the other hand follows a specific energy distribution law $f(E_T)\sim E_T^{-a}$, where $a \sim 1.6-1.8$ and $E_T$ is the total energy released. A possible explanation for the statistical properties of the magnetogrms and the energy release by the active region is that the magnetic field formation follows rules analogous to \textbf{percolating models}, and the 3D magnetic fields above the photosphere reach a \textbf{Self Organized Critical (SOC) state}. The implications of these findings on the acceleration of energetic particles during impulsive phenomena will briefly be outlined.

astro-ph↗

arXiv2006

Stochastic Acceleration in Turbulent Electric Fields Generated by 3-D Reconnection

Electron and proton acceleration in three-dimensional electric and magnetic fields is studied through test particle simulations. The fields are obtained by a three-dimensional magnetohydrodynamic simulation of magnetic reconnection in slab geometry. The nonlinear evolution of the system is characterized by the growth of many unstable modes and the initial current sheet is fragmented with formation of small scale structures. We inject at random points inside the evolving current sheet a Maxwellian distribution of particles. In relatively short time (less than a millisecond) the particles develop a power law tail. The acceleration is extremely efficient and the electrons absorb a large percentage of the available energy in a small fraction of the characteristic time of the MHD simulation, suggesting that resistive MHD codes, used extensively in the current literature, are unable to represent the full extent of particle acceleration in 3D reconnection.

astro-ph↗

arXiv2006

Gyrokinetic electron acceleration in the force-free corona with anomalous resistivity

We numerically explore electron acceleration and coronal heating by dissipative electric fields. Electrons are traced in linear force-free magnetic fields extrapolated from SOHO/MDI magnetograms, endowed with anomalous resistivity ($η$) in localized dissipation regions where the magnetic twist $\nabla \times \bhat$ exceeds a given threshold. Associated with $η> 0$ is a parallel electric field ${\bf E} = η{\bf j}$ which can accelerate runaway electrons. In order to gain observational predictions we inject electrons inside the dissipation regions and follow them for several seconds in real time. Precipitating electrons which leave the simulation system at height $z$ = 0 are associated with hard X rays, and electrons which escape at height $z$ $\sim$ 3$\cdot 10^4$ km are associated with normal-drifting type IIIs at the local plasma frequency. A third, trapped, population is related to gyrosynchrotron emission. Time profiles and spectra of all three emissions are calculated, and their dependence on the geometric model parameters and on $η$ is explored. It is found that precipitation generally preceeds escape by fractions of a second, and that the electrons perform many visits to the dissipation regions before leaving the simulation system. The electrons impacting $z$ = 0 reach higher energies than the escaping ones, and non-Maxwellian tails are observed at energies above the largest potential drop across a single dissipation region. Impact maps at $z$ = 0 show a tendency of the electrons to arrive at the borders of sunspots of one polarity. Although the magnetograms used here belong to non-flaring times, so that the simulations refer to nanoflares and `quiescent' coronal heating, it is conjectured that the same process, on a larger scale, is responsible for solar flares.

astro-ph↗

arXiv2005

The Effect of Coherent Structures on Stochastic Acceleration in MHD Turbulence

We investigate the influence of coherent structures on particle acceleration in the strongly turbulent solar corona. By randomizing the Fourier phases of a pseudo-spectral simulation of isotropic MHD turbulence (Re $\sim 300$), and tracing collisionless test protons in both the exact-MHD and phase-randomized fields, it is found that the phase correlations enhance the acceleration efficiency during the first adiabatic stage of the acceleration process. The underlying physical mechanism is identified as the dynamical MHD alignment of the magnetic field with the electric current, which favours parallel (resistive) electric fields responsible for initial injection. Conversely, the alignment of the magnetic field with the bulk velocity weakens the acceleration by convective electric fields $- \bfu \times \bfb$ at a non-adiabatic stage of the acceleration process. We point out that non-physical parallel electric fields in random-phase turbulence proxies lead to artificial acceleration, and that the dynamical MHD alignment can be taken into account on the level of the joint two-point function of the magnetic and electric fields, and is therefore amenable to Fokker-Planck descriptions of stochastic acceleration.

astro-ph↗

arXiv2005

Statistical Properties of Dissipative MHD Accelerators

We use exact orbit integration to investigate particle acceleration in a Gauss field proxy of magnetohydrodynamic (MHD) turbulence. Regions where the electric current exceeds a critical threshold are declared to be `dissipative' and endowed with super-Dreicer electric field ${\bf E}_Ω= η{\bf j}$. In this environment, test particles (electrons) are traced and their acceleration to relativistic energies is studied. As a main result we find that acceleration mostly takes place within the dissipation regions, and that the momentum increments have heavy (non-Gaussian) tails, while the waiting times between the dissipation regions are approximately exponentially distributed with intensity proportional to the particle velocity. No correlation between the momentum increment and the momentum itself is found. Our numerical results suggest an acceleration scenario with ballistic transport between independent `black box' accelerators.

astro-ph↗