Loukas Vlahos

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.

Local re-acceleration and a modified thick target model of solar flare electrons

Context. The collisional thick target model (CTTM) of solar hard X-ray (HXR) bursts has become an almost “standard model” of flare impulsive phase energy transport and radiation. However, it faces various problems in the light of recent data, particularly the high electron beam density and anisotropy it involves. Aims. We consider how photon yield per electron can be increased, and hence fast electron beam intensity requirements reduced, by local re-acceleration of fast electrons throughout the HXR source itself, after injection. Methods. We show parametrically that, if net re-acceleration rates due to e.g. waves or local current sheet electric (E) fields are a significant fraction of collisional loss rates, electron lifetimes, and hence the net radiative HXR output per electron can be substantially increased over the CTTM values. In this local re-acceleration thick target model (LRTTM) fast electron number requirements and anisotropy are thus reduced. One specific possible scenario involving such re-acceleration is discussed, viz, a current sheet cascade (CSC) in a randomly stressed magnetic loop. Results. Combined MHD and test particle simulations show that local E fields in CSCs can efficiently accelerate electrons in the corona and and re-accelerate them after injection into the chromosphere. In this HXR source scenario, rapid synchronisation and variability of impulsive footpoint emissions can still occur since primary electron acceleration is in the high Alfven speed corona with fast re-acceleration in chromospheric CSCs. It is also consistent with the energy-dependent time-of-flight delays in HXR features. Conclusions. Including electron re-acceleration in the HXR source allows an LRTTM modification of the CTTM in which beam density and anisotropy are much reduced, and alleviates theoretical problems with the CTTM, while making it more compatible with radio and interplanetary electron numbers. The LRTTM is, however, different in some respects such as spatial distribution of atmospheric heating by fast electrons.

Particle acceleration in stochastic current sheets in stressed coronal active regions

Aims. To perform numerical experiments of particle acceleration in the complex magnetic and electric field environment of the stressed solar corona. Methods. The magnetic and electric fields are obtained from a 3-D MHD experiment that resembles a coronal loop with photospheric regions at both footpoints. Photospheric footpoint motion leads to the formation of a hierarchy of stochastic current sheets. Particles (protons and electrons) are traced within these current sheets starting from a thermal distribution using a relativistic test particle code. Results. In the corona the particles are subject to acceleration as well as deceleration, and a considerable portion of them leave the domain having received a net energy gain. Particles are accelerated to high energies in a very short time (both species can reach energies up to 100 GeV within 5 × 10 −2 s for electrons and 5 × 10 −1 s for protons). The final energy distribution shows that while one quarter of the particles retain their thermal distribution, the rest have been accelerated, forming a two-part power law. Accelerated particles are either trapped within electric field regions of opposite polarities, or escape the domain mainly through the footpoints. The particle dynamics are followed in detail and it is shown how this dynamic affects the time evolution of the system and the energy distribution. The scaling of these results with time and length scale is examined and the Bremstrahlung signature of X-ray photons resulting from escaping particles hitting the chromosphere is calculated and found to have a main power law part with an index γ = −1.8, steeper than observed. Possible resolutions of this discrepency are discussed.

Stochastic acceleration in turbulent electric fields generated by 3D 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 a 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 are unable to represent the full extent of particle acceleration.

Turbulence, Magnetic Reconnection in Turbulent Fluids and Energetic Particle Acceleration

Turbulence is ubiquitous in astrophysics. It radically changes many astrophysical phenomena, in particular, the propagation and acceleration of cosmic rays. We present the modern understanding of compressible magnetohydrodynamic (MHD) turbulence, in particular its decomposition into Alfvén, slow and fast modes, discuss the density structure of turbulent subsonic and supersonic media, as well as other relevant regimes of astrophysical turbulence. All this information is essential for understanding the energetic particle acceleration that we discuss further in the review. For instance, we show how fast and slow modes accelerate energetic particles through the second order Fermi acceleration, while density fluctuations generate magnetic fields in pre-shock regions enabling the first order Fermi acceleration of high energy cosmic rays. Very importantly, however, the first order Fermi cosmic ray acceleration is also possible in sites of magnetic reconnection. In the presence of turbulence this reconnection gets fast and we present numerical evidence supporting the predictions of the Lazarian and Vishniac (Astrophys. J. 517:700–718, 1999) model of fast reconnection. The efficiency of this process suggests that magnetic reconnection can release substantial amounts of energy in short periods of time. As the particle tracing numerical simulations show that the particles can be efficiently accelerated during the reconnection, we argue that the process of magnetic reconnection may be much more important for particle acceleration than it is currently accepted. In particular, we discuss the acceleration arising from reconnection as a possible origin of the anomalous cosmic rays measured by Voyagers as well as the origin cosmic ray excess in the direction of Heliotail.

Collective plasma effects associated with the continuous injection model of solar flare particle streams

A modified continous injection model for impulsive solar flares that includes self-consistently plasma nonlinearities based on the concept of marginal stability is presented. A quasi-stationary state is established, composed of a hot truncated electron Maxwellian distribution confined by acoustic turbulence on the top of the loop and energetic electron beams precipitating in the chromosphere. It is shown that the radiation properties of the models are in accordance with observations.

PARTICLE ACCELERATION IN STRESSED CORONAL MAGNETIC FIELDS

This Letter presents an analysis of particle acceleration in a model of the complex magnetic field environment in the flaring solar corona. A slender flux tube, initially in hydrodynamic equilibrium, is stressed by random photospheric motions. A three-dimensional MHD code is used to follow the stochastic development of transient current sheets. These processes generate a highly fragmented electric field, through which particles are tracked using a relativistic test particle code. It is shown that both ions and electrons are accelerated readily to relativistic energies in times of order 10-2 s for electrons and 10-1 s for protons forming power-law distributions in energy.

Derivation of Solar Flare Cellular Automata Models from a Subset of the Magnetohydrodynamic Equations

Cellular automata (CA) models account for the power-law distributions found for solar flare hard X-ray observations, but their physics has been unclear. We examine four of these models and show that their criteria and magnetic field distribution rules can be derived by discretizing the MHD diffusion equation as obtained from a simplified Ohms law. Identifying the discrete MHD with the CA models leads to an expression for the resistivity as a function of the current on the flux tube boundary, as may be expected from current-driven instabilities. Anisotropic CA models correspond to a nonlinear resistivity η(J), while isotropic ones are associated with hyperresistivity η(2J). The discrete equations satisfy the necessary conditions for self-organized criticality (Lu): there is local conservation of a field (magnetic flux), while the nonlinear resistivity provides a rapid dissipation and relaxation mechanism. The approach justifies many features of the CA models that were originally based on intuition.

On the Self-Similarity of Unstable Magnetic Discontinuities in Solar Active Regions

We investigate the statistical properties of possible magnetic discontinuities in two solar active regions over the course of several hours. We use linear force-free extrapolations to calculate the three-dimensional magnetic structure in the active regions. Magnetic discontinuities are identified using various selection criteria. Independently of the selection criterion, we identify large numbers of magnetic discontinuities whose free magnetic energies and volumes obey well-formed power-law distribution functions. The power-law indices for the free energies are in the range [-1.6, -1.35], in remarkable agreement with the power-law indices found in the occurrence frequencies of solar flare energies. This agreement and the strong self-similarity of the volumes that are likely to host flares suggest that the observed statistics of flares may be the natural outcome of a preexisting spatial self-organization accompanying the energy fragmentation in solar active regions. We propose a dynamical picture of flare triggering consistent with recent observations by reconciling our results with the concepts of percolation theory and self-organized criticality. These concepts rely on self-organization, which is expected from the fully turbulent state of the magnetic fields in the solar atmosphere.

MHD consistent cellular automata (CA) models - II. Applications to solar flares

In Isliker et al. (2000b), an extended cellular automaton (X-CA) model for solar flares was introduced. In this model, the interpretation of the models grid-variable is specied, and the magnetic eld, the current, and an approximation to the electric eld are yielded, all in a way that is consistent with Maxwells and the MHD equations. The model also reproduces the observed distributions of total energy, peak-flux, and durations. Here, we reveal which relevant plasma physical processes are implemented by the X-CA model and in what form, and what global physical set-up is assumed by this model when it is in its natural state (self-organized criticality, SOC). The basic results are: (1) On large-scales, all variables show characteristic quasi-symmetries: the current has everywhere a preferential direction, the magnetic eld exhibits a quasi-cylindrical symmetry. (2) The global magnetic topology forms either (i) closed magnetic eld lines around and along a more or less straight neutral line for the model in its standard form, or (ii) an arcade of eld lines above the bottom plane and centered along a neutral line, if the model is slightly modied. (3) In case of the magnetic topology (ii), loading can be interpreted as if there were a plasma which flows predominantly upwards, whereas in case of the magnetic topology (i), as if there were a plasma flow expanding from the neutral line. (4) The small-scale physics in the bursting phase represent localized diusive processes, which are triggered when a quantity which is an approximately linear function of the current exceeds a threshold. (5) The interplay of loading and bursting in the X-CA model can be interpreted as follows: the local diusivity usually has a value which is eectively zero, and it turns locally to an anomalous value if the mentioned threshold is exceeded, whereby diusion dominates the quiet evolution (loading), until the critical quantity falls below the threshold again. (6) Flares (avalanches) are accompanied by the appearance of localized, intense electric elds. A typical example of the spatio-temporal evolution of the electric eld during a flare is presented. (7) In a variant on the X-CA model, the magnitude of the current is used directly in the instability criterion, instead of the approximately linear function of it. First results indicate that the SOC state persists and is only slightly modied: distributions of the released energy are still power-laws with slopes comparable to the ones of the non-modied X-CA model, and the large scale structures, a characteristic of the SOC state, remain unchanged. (8) The current-dissipation during flares is spatially fragmented into a large number of dissipative current-surfaces of varying sizes, which are spread over a considerably large volume, and which do not exhibit any kind of simple spatial organization as a whole. These current-surfaces do not grow in the course of time, they are very short-lived, but they multiply, giving rise to new dissipative current-surfaces which are spread further around. They show thus a highly dynamic temporal evolution. It follows that the X-CA model represents an implementation of the flare scenario of Parker (1993) in a rather complete way, comprising aspects from small scale physics to the global physical set-up, making though some characteristic simplications which are unavoidable in the frame-work of a CA.