arXiv subjects

Eduard P. Kontar

Publications and source records attributed to Eduard P. Kontar.

At least 91 records · Page 5Linked to original sources

arXiv2015

Stopping Frequency of Type III Solar Radio Bursts in Expanding Magnetic Flux Tubes

Understanding the properties of type III radio bursts in the solar corona and interplanetary space is one of the best ways to remotely deduce the characteristics of solar accelerated electron beams and the solar wind plasma. One feature of all type III bursts is the lowest frequency they reach (or stopping frequency). This feature reflects the distance from the Sun that an electron beam can drive the observable plasma emission mechanism. The stopping frequency has never been systematically studied before from a theoretical perspective. Using numerical kinetic simulations, we explore the different parameters that dictate how far an electron beam can travel before it stops inducing a significant level of Langmuir waves, responsible for plasma radio emission. We use the quasilinear approach to model self-consistently the resonant interaction between electrons and Langmuir waves in inhomogeneous plasma, and take into consideration the expansion of the guiding magnetic flux tube and the turbulent density of the interplanetary medium. We find that the rate of radial expansion has a significant effect on the distance an electron beam travels before enhanced leves of Langmuir waves, and hence radio waves, cease. Radial expansion of the guiding magnetic flux tube rarefies the electron stream to the extent that the density of non-thermal electrons is too low to drive Langmuir wave production. The initial conditions of the electron beam have a significant effect, where decreasing the beam density or increasing the spectral index of injected electrons would cause higher type III stopping frequencies. We also demonstrate how the intensity of large-scale density fluctuations increases the highest frequency that Langmuir waves can be driven by the beam and how the magnetic field geometry can be the cause of type III bursts only observed at high coronal frequencies.

astro-ph.SR↗

arXiv2015

Resonance broadening due to particle scattering and mode-coupling in the quasi-linear relaxation of electron beams

Of particular interest for radio and hard X-ray diagnostics of accelerated electrons during solar flares is the understanding of the basic non-linear mechanisms regulating the relaxation of electron beams propagating in turbulent plasmas. In this work, it is shown that in addition to scattering of beam electrons, scattering of the beam-generated Langmuir waves via for instance mode-coupling, can also result in broadening of the wave-particle resonance. We obtain a resonance-broadened version of weak-turbulence theory with mode-coupling to ion-sound modes. Resonance broadening is presented here as a unified framework which can quantitatively account for the reduction and possible suppression of the beam instability due to background scattering of the beam electrons themselves or due to scattering of the beam-generated Langmuir waves in fluctuating plasmas. Resonance broadening being essentially equivalent to smoothing of the electron phase-space distribution, it is used to construct an intuitive physical picture for the stability of inverted populations of fast electrons that are commonly observed \emph{in-situ} to propagate in the solar-wind.

physics.space-ph↗

arXiv2015

3D Radio and X-Ray Modeling and Data Analysis Software: Revealing Flare Complexity

We have undertaken a major enhancement of our IDL-based simulation tools developed earlier for modeling microwave and X-ray emission. The object-based architecture provides an interactive graphical user interface that allows the user to import photospheric magnetic field maps and perform magnetic field extrapolations to almost instantly generate 3D magnetic field models, to investigate the magnetic topology of these models by interactively creating magnetic field lines and associated magnetic flux tubes, to populate the flux tubes with user-defined nonuniform thermal plasma and anisotropic, nonuniform, nonthermal electron distributions; to investigate the spatial and spectral properties of radio and X-ray emission calculated from the model, and to compare the model-derived images and spectra with observational data. The application integrates shared-object libraries containing fast gyrosynchrotron emission codes developed in FORTRAN and C++, soft and hard X-ray codes developed in IDL, a FORTRAN-based potential-field extrapolation routine and an IDL-based linear force free field extrapolation routine. The interactive interface allows users to add any user-defined radiation code that adheres to our interface standards, as well as user-defined magnetic field extrapolation routines. Here we use this tool to analyze a simple single-loop flare and use the model to constrain the 3D structure of the magnetic flaring loop and 3D spatial distribution of the fast electrons inside this loop. We iteratively compute multi-frequency microwave and multi-energy X-ray images from realistic magnetic fluxtubes obtained from an extrapolation of a magnetogram taken prior to the flare, and compare them with imaging data obtained by SDO, NoRH, and RHESSI instruments. We use this event to illustrate use of the tool for general interpretation of solar flares to address disparate problems in solar physics.

astro-ph.SR↗

arXiv2014

The Formation of Kappa-Distribution Accelerated Electron Populations in Solar Flares

Driven by recent RHESSI observations of confined loop-top hard X-ray sources in solar flares, we consider stochastic acceleration of electrons in the presence of Coulomb collisions. If electron escape from the acceleration region can be neglected, the electron distribution function is determined by a balance between diffusive acceleration and collisions. Such a scenario admits a stationary solution for the electron distribution function that takes the form of a kappa distribution. We show that the evolution toward this kappa distribution involves a "wave front" propagating forwards in velocity space, so that electrons of higher energy are accelerated later; the acceleration time scales with energy according to $τ_{\rm acc} \sim E^{3/2}$. At sufficiently high energies escape from the finite-length acceleration region will eventually dominate. For such energies, the electron velocity distribution function is obtained by solving a time-dependent Fokker-Planck equation in the "leaky-box" approximation. Solutions are obtained in the limit of a small escape rate from an acceleration region that can effectively be considered a thick target.

astro-ph.SR↗

arXiv2014

On the variation of solar flare coronal x-ray source sizes with energy

Observations with {\em RHESSI} have enabled the detailed study of the structure of dense hard X-ray coronal sources in solar flares. The variation of source extent with electron energy has been discussed in the context of streaming of non-thermal particles in a one-dimensional cold-target model, and the results used to constrain both the physical extent of, and density within, the electron acceleration region. Here we extend this investigation to a more physically realistic model of electron transport that takes into account the finite temperature of the ambient plasma, the initial pitch-angle distribution of the accelerated electrons, and the effects of collisional pitch-angle scattering. The finite temperature results in the thermal diffusion of electrons, that leads to the observationally-inferred value of the acceleration region volume being an overestimate of its true value. The different directions of the electron trajectories, a consequence of both the non-zero injection pitch-angle and scattering within the target, cause the projected propagation distance parallel to the guiding magnetic field to be reduced, so that a one-dimensional interpretation can overestimate the actual density by a factor of up to $\sim 6$. The implications of these results for the determination of acceleration region properties (specific acceleration rate, filling factor, etc.) are discussed.

astro-ph.SR↗

arXiv2014

The Low-High-Low Trend of Type III Radio Burst Starting Frequencies and Solar Flare Hard X-rays

Using simultaneous X-ray and radio observations from solar flares, we investigate the link between the type III radio burst starting frequency and hard X-ray spectral index. For a proportion of events the relation derived between the starting height (frequency) of type III radio bursts and the electron beam velocity spectral index (deduced from X-rays) is used to infer the spatial properties (height and size) of the electron beam acceleration region. Both quantities can be related to the distance travelled before an electron beam becomes unstable to Langmuir waves. To obtain a list of suitable events we considered the RHESSI catalogue of X-ray flares and the Phoenix 2 catalogue of type III radio bursts. From the 200 events that showed both type III and X-ray signatures, we selected 30 events which had simultaneous emission in both wavelengths, good signal to noise in the X-ray domain and > 20 seconds duration. We find that > 50 % of the selected events show a good correlation between the starting frequencies of the groups of type III bursts and the hard X-ray spectral indices. A low-high-low trend for the starting frequency of type III bursts is frequently observed. Assuming a background electron density model and the thick target approximation for X-ray observations, this leads to a correlation between starting heights of the type III emission and the beam electron spectral index. Using this correlation we infer the altitude and vertical extents of the flare acceleration regions. We find heights from 183 Mm down to 25 Mm while the sizes range from 13 Mm to 2 Mm. These values agree with previous work that places an extended flare acceleration region high in the corona. We analyse the assumptions required and explore possible extensions to our assumed model. We discuss these results with respect to the acceleration heights and sizes derived from X-ray observations alone.

astro-ph.SR↗

arXiv2013

Electron Distribution Functions in Solar Flares from combined X-ray and EUV Observations

Simultaneous solar flare observations with SDO and RHESSI provide spatially resolved information about hot plasma and energetic particles in flares. RHESSI allows the properties of both hot (> 8 MK) thermal plasma and nonthermal electron distributions to be inferred, while SDO/AIA is more sensitive to lower temperatures. We present and implement a new method to reconstruct electron distribution functions from SDO/AIA data. The combined analysis of RHESSI and AIA data allows the electron distribution function to be inferred over the broad energy range from ~0.1 keV up to a few tens of keV. The analysis of two well observed flares suggests that the distributions in general agree to within a factor of three when the RHESSI values are extrapolated into the intermediate range 1-3 keV, with AIA systematically predicting lower electron distributions. Possible instrumental and numerical effects, as well as potential physical origins for this discrepancy are discussed. The inferred electron distribution functions in general show one or two nearly Maxwellian components at energies below ~ 15 keV and a non-thermal tail above.

astro-ph.SR↗

arXiv2013

Probing Dynamics of Electron Acceleration with Radio and X-ray Spectroscopy, Imaging, and Timing in the 2002 Apr 11 Solar Flare

Based on detailed analysis of radio and X-ray observations of a flare on 2002 April 11 augmented by realistic 3D modeling, we have identified a radio emission component produced directly at the flare acceleration region. This acceleration region radio component has distinctly different (i) spectrum, (ii) light curves, (iii) spatial location, and, thus, (iv) physical parameters from those of the separately identified, trapped or precipitating electron components. To derive evolution of physical parameters of the radio sources we apply forward fitting of the radio spectrum time sequence with the gyrosynchrotron source function with 5 to 6 free parameters. At the stage when the contribution from the acceleration region dominates the radio spectrum, the X-ray- and radio- derived electron energy spectral indices agree well with each other. During this time the maximum energy of the accelerated electron spectrum displays a monotonic increase with time from ~ 300 keV to ~ 2 MeV over roughly one minute duration indicative of an acceleration process in the form of growth of the power-law tail; the fast electron residence time in the acceleration region is about 2 - 4 s, which is much longer than the time of flight and so requires a strong diffusion mode there to inhibit free-streaming propagation. The acceleration region has a relatively strong magnetic field, B ~ 120 G, and a low thermal density, less than 2x10^9 cm^-3. These acceleration region properties are consistent with a stochastic acceleration mechanism.

astro-ph.SR↗

arXiv2013

Implications for electron acceleration and transport from non-thermal electron rates at looptop and footpoint sources in solar flares

The interrelation of hard X-ray (HXR) emitting sources and the underlying physics of electron acceleration and transport presents one of the major questions in high-energy solar flare physics. Spatially resolved observations of solar flares often demonstrate the presence of well-separated sources of bremsstrahlung emission, so-called coronal and footpoint sources. Using spatially resolved X-ray observations by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and recently improved imaging techniques, we investigate in detail the spatially resolved electron distributions in a few well-observed solar flares. The selected flares can be interpreted as having a standard geometry with chromospheric HXR footpoint sources related to thick-target X-ray emission and the coronal sources characterised by a combination of thermal and thin-target bremsstrahlung. Using imaging spectroscopy techniques, we deduce the characteristic electron rates and spectral indices required to explain the coronal and footpoint X-ray sources. We found that, during the impulsive phase, the electron rate at the looptop is several times (a factor of 1.7-8) higher than at the footpoints. The results suggest that a sufficient number of electrons accelerated in the looptop explain the precipitation into the footpoints and imply that electrons accumulate in the looptop. We discuss these results in terms of magnetic trapping, pitch-angle scattering, and injection properties. Our conclusion is that the accelerated electrons must be subject to magnetic trapping and/or pitch-angle scattering, keeping a fraction of the population trapped inside the coronal loops. These findings put strong constraints on the particle transport in the coronal source and provide quantitative limits on deka-keV electron trapping/scattering in the coronal source.

astro-ph.SR↗

arXiv2013

Temporal variations of X-ray solar flare loops: length, corpulence, position, temperature, plasma pressure and spectra

The spatial and spectral properties of three solar flare coronal X-ray loops are studied before, during and after the peak X-ray emission. Using observations from the Ramaty High Energy Solar Spectroscopic Imager (RHESSI), we deduce the temporal changes in emitting X-ray length, corpulence, volume, position, number density and thermal pressure. We observe a decrease in the loop length, width and volume before the X-ray peak, and an increasing number density and thermal pressure. After the X-ray peak, volume increases and loop corpulence grows due to an increasing width. The volume variations are more pronounced than the position variations, often known as magnetic line contraction. We believe this is the first dedicated study of the temporal evolution of X-ray loop lengths and widths. Collectively, the observations also show for the first time three temporal phases given by peaks in temperature, X-ray emission and thermal pressure, with minimum volume coinciding with the X-ray peak. Although the volume of the flaring plasma decreases before the peak in X-ray emission, the relationship between temperature and volume does not support simple compressive heating in a collapsing magnetic trap model. Within a low beta plasma, shrinking loop widths perpendicular to the guiding field can be explained by squeezing the magnetic field threading the region. Plasma heating leads to chromospheric evaporation and growing number density, producing increasing thermal pressure and decreasing loop lengths as electrons interact at shorter distances and we believe after the X-ray peak, the increasing loop corpulence.

astro-ph.SR↗

arXiv2012

Density fluctuations and the acceleration of electrons by beam-generated Langmuir waves in the solar corona

Non-thermal electron populations are observed throughout the heliosphere. The relaxation of an electron beam is known to produce Langmuir waves which, in turn, may substantially modify the electron distribution function. As the Langmuir waves are refracted by background density gradients and as the solar and heliospheric plasma density is naturally perturbed with various levels of inhomogeneity, the interaction of Langmuir waves with non-thermal electrons in inhomogeneous plasmas is an important topic. We investigate the role played by ambient density fluctuations on the beam-plasma relaxation, focusing on the effect of acceleration of beam electrons. The scattering of Langmuir waves off turbulent density fluctuations is modeled as a wavenumber diffusion process which is implemented in numerical simulations of the one-dimensional quasilinear kinetic equations describing the beam relaxation. The results show that a substantial number of beam electrons are accelerated when the diffusive time scale in wavenumber space τ_D is of the order of the quasilinear time scale τ_ql, while when τ_D << τ_ql, the beam relaxation is suppressed. Plasma inhomogeneities are therefore an important means of energy redistribution for waves and hence electrons, and so must be taken into account when interpreting, for example, hard X-ray or Type III emission from flare-accelerated electrons.

astro-ph.SR↗

arXiv2012

RHESSI and SDO/AIA observations of the chromospheric and coronal plasma parameters during a solar flare

X-ray and EUV observations are an important diagnostic of various plasma parameters of the solar atmosphere during solar flares. Soft X-ray and EUV observations often show coronal sources near the top of flaring loops, while hard X-ray emission is mostly observed from chromospheric footpoints. Combining RHESSI with simultaneous SDO/AIA observations, it is possible for the first time to determine the density, temperature, and emission profile of the solar atmosphere over a wide range of heights during a flare, using two independent methods. Here we analyze a near limb event during the first of three hard X-ray peaks. The emission measure, temperature, and density of the coronal source is found using soft X-ray RHESSI images while the chromospheric density is determined using RHESSI visibility analysis of the hard X-ray footpoints. A regularized inversion technique is applied to AIA images of the flare to find the differential emission measure (DEM). Using DEM maps we determine the emission and temperature structure of the loop, as well as the density, and compare it with RHESSI results. The soft X-ray and hard X-ray sources are spatially coincident with the top and bottom of the EUV loop, but the bulk of the EUV emission originates from a region without co-spatial RHESSI emission. The temperature analysis along the loop indicates that the hottest plasma is found near the coronal loop top source. The EUV observations suggest that the density in the loop legs increases with increasing height while the temperature remains constant within uncertainties.

astro-ph.SR↗

arXiv2012

Evolution of the Solar Flare Energetic Electrons in the Inhomogeneous Inner Heliosphere

Solar flare accelerated electrons escaping into the interplanetary space and seen as type III solar radio bursts are often detected near the Earth. Using numerical simulations we consider the evolution of energetic electron spectrum in the inner heliosphere and near the Earth. The role of Langmuir wave generation, heliospheric plasma density fluctuations, and expansion of magnetic field lines on the electron peak flux and fluence spectra is studied to predict the electron properties as could be observed by Solar Orbiter and Solar Probe Plus. Considering various energy loss mechanisms we show that the substantial part of the initial energetic electron energy is lost via wave-plasma processes due to plasma inhomogeneity. For the parameters adopted, the results show that the electron spectra changes mostly at the distances before $\sim20 R_\odot$. Further into the heliosphere, the electron flux spectra of electrons forms a broken power-law relatively similar to what is observed at 1 AU.

astro-ph.SR↗

arXiv2012

Determination of the Acceleration Region Size in a Loop-structured Solar Flare

In order to study the acceleration and propagation of bremsstrahlung-producing electrons in solar flares, we analyze the evolution of the flare loop size with respect to energy at a variety of times. A GOES M3.7 loop-structured flare starting around 23:55 on 2002 April 14 is studied in detail using \textit{Ramaty High Energy Solar Spectroscopic Imager} (\textit{RHESSI}) observations. We construct photon and mean-electron-flux maps in 2-keV energy bins by processing observationally-deduced photon and electron visibilities, respectively, through several image-processing methods: a visibility-based forward-fit (FWD) algorithm, a maximum entropy (MEM) procedure and the uv-smooth (UVS) approach. We estimate the sizes of elongated flares (i.e., the length and width of flaring loops) by calculating the second normalized moments of the intensity in any given map. Employing a collisional model with an extended acceleration region, we fit the loop lengths as a function of energy in both the photon and electron domains. The resulting fitting parameters allow us to estimate the extent of the acceleration region which is between $\sim 13 \rm{arcsec}$ and $\sim 19 \rm{arcsec}$. Both forward-fit and uv-smooth algorithms provide substantially similar results with a systematically better fit in the electron domain.The consistency of the estimates from these methods provides strong support that the model can reliably determine geometric parameters of the acceleration region. The acceleration region is estimated to be a substantial fraction ($\sim 1/2$) of the loop extent, indicating that this dense flaring loop incorporates both acceleration and transport of electrons, with concurrent thick-target bremsstrahlung emission.

astro-ph.SR↗

arXiv2012

A Classification Scheme For Turbulent Acceleration Processes In Solar Flares

We establish a classification scheme for stochastic acceleration models involving low-frequency plasma turbulence in a strongly magnetized plasma. This classification takes into account both the properties of the accelerating electromagnetic field, and the nature of the transport of charged particles in the acceleration region. We group the acceleration processes as either resonant, non-resonant or resonant-broadened, depending on whether the particle motion is free-streaming along the magnetic field, diffusive or a combination of the two. Stochastic acceleration by moving magnetic mirrors and adiabatic compressions are addressed as illustrative examples. We obtain expressions for the momentum-dependent diffusion coefficient $D(p)$, both for general forms of the accelerating force and for the situation when the electromagnetic force is wave-like, with a specified dispersion relation $ω=ω(k)$. Finally, for models considered, we calculate the energy-dependent acceleration time, a quantity that can be directly compared with observations of the time profile of the radiation field produced by the accelerated particles, such as during solar flares.

astro-ph.SR↗

arXiv2012

Numerical simulations of chromospheric hard X-ray source sizes in solar flares

X-ray observations are a powerful diagnostic tool for transport, acceleration, and heating of electrons in solar flares. Height and size measurements of X-ray footpoints sources can be used to determine the chromospheric density and constrain the parameters of magnetic field convergence and electron pitch-angle evolution. We investigate the influence of the chromospheric density, magnetic mirroring and collisional pitch-angle scattering on the size of X-ray sources. The time-independent Fokker-Planck equation for electron transport is solved numerically and analytically to find the electron distribution as a function of height above the photosphere. From this distribution, the expected X-ray flux as a function of height, its peak height and full width at half maximum are calculated and compared with RHESSI observations. A purely instrumental explanation for the observed source size was ruled out by using simulated RHESSI images. We find that magnetic mirroring and collisional pitch-angle scattering tend to change the electron flux such that electrons are stopped higher in the atmosphere compared with the simple case with collisional energy loss only. However, the resulting X-ray flux is dominated by the density structure in the chromosphere and only marginal increases in source width are found. Very high loop densities (>10^{11} cm^{-3}) could explain the observed sizes at higher energies, but are unrealistic and would result in no footpoint emission below about 40 keV, contrary to observations. We conclude that within a monolithic density model the vertical sizes are given mostly by the density scale-height and are predicted smaller than the RHESSI results show.

astro-ph.SR↗

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↗

arXiv2011

Implications of X-ray Observations for Electron Acceleration and Propagation in Solar Flares

High-energy X-rays and gamma-rays from solar flares were discovered just over fifty years ago. Since that time, the standard for the interpretation of spatially integrated flare X-ray spectra at energies above several tens of keV has been the collisional thick-target model. After the launch of the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) in early 2002, X-ray spectra and images have been of sufficient quality to allow a greater focus on the energetic electrons responsible for the X-ray emission, including their origin and their interactions with the flare plasma and magnetic field. The result has been new insights into the flaring process, as well as more quantitative models for both electron acceleration and propagation, and for the flare environment with which the electrons interact. In this article we review our current understanding of electron acceleration, energy loss, and propagation in flares. Implications of these new results for the collisional thick-target model, for general flare models, and for future flare studies are discussed.

astro-ph.SR↗