Parallel electric field amplification by phase-mixing of Alfven waves

Previous numerical studies have identified "phase mixing" of low-frequency Alfven waves as a mean of parallel electric field amplification and acceleration of electrons in a collisionless plasma. Theoretical explanations are given of how this produces an amplification of the parallel electric field, and as a consequence, also leads to enhanced collisionless damping of the wave by energy transfer to the electrons. Our results are based on the properties of the Alfven waves in a warm plasma which are obtained from drift-kinetic theory, in particular, the rate of their electron Landau damping. Phase mixing in a collisionless low-$\beta$ plasma proceeds in a manner very similar to the visco-resistive case, except for the fact that electron Landau damping is the primary energy dissipation channel. The time and length scales involved are evaluated. We also focus on the evolution of the parallel electric field and calculate its maximum value in the course of its amplification

Multi-thermal dynamics and energetics of a coronal mass ejection in the low solar atmosphere

The aim of this work is to determine the multi-thermal characteristics and plasma energetics of an eruptive plasmoid and occulted flare observed by Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA). We study an event from 03-Nov-2010 (peaking at 12:20UT in GOES soft X-rays) of a coronal mass ejection and occulted flare which demonstrates the morphology of a classic erupting flux rope. The high spatial, and time resolution, and six coronal channels, of the SDO/AIA images allows the dynamics of the multi-thermal emission during the initial phases of eruption to be studied in detail. The Differential Emission Measure (DEM) is calculated, using an optimised version of a regularized inversion method (Hannah & Kontar 2012), for each pixel across the six channels at different times, resulting in emission measure maps and movies in a variety of temperature ranges. We find that the core of the erupting plasmoid is hot (8-11, 11-14MK) with a similarly hot filamentary "stem" structure connecting it to the lower atmosphere, which could be interpreted as the current sheet in the flux rope model, though is wider than these models suggest. The velocity of the leading edge of the eruption is 597-664 km s$^{-1}$ in the temperature range $\ge$3-4MK and between 1029-1246 km s$^{-1}$ for $\le$2-3MK. We estimate the density (in 11-14 MK) of the erupting core and stem during the impulsive phase to be about $3\times10^9$ cm$^{-3}$, $6\times10^9$ cm$^{-3}$, $9\times10^8$ cm$^{-3}$ in the plasmoid core, stem and surrounding envelope of material. This gives thermal energy estimates of $5\times10^{29}$ erg, $1\times10^{29}$ erg and $2\times10^{30}$ erg. The kinetic energy for the core and envelope is slightly smaller. The thermal energy of the core and current sheet grows during the eruption, suggesting continuous influx of energy presumably via reconnection.Comment: Submitted to A&A: in revisio

The influence of albedo on the size of hard X-ray flare sources

Context: Hard X-rays from solar flares are an important diagnostic of particle acceleration and transport in the solar atmosphere. Any observed X-ray flux from on-disc sources is composed of direct emission plus Compton backscattered photons (albedo). This affects both the observed spectra and images as well as the physical quantities derived from them such as the spatial and spectral distributions of accelerated electrons or characteristics of the solar atmosphere. Aims: We propose a new indirect method to measure albedo and to infer the directivity of X-rays in imaging using RHESSI data. Methods: Visibility forward fitting is used to determine the size of a disc event observed by RHESSI as a function of energy. This is compared to the sizes of simulated sources from a Monte Carlo simulation code of photon transport in the chromosphere for different degrees of downward directivity and true source sizes to find limits on the true source size and the directivity. Results: The observed full width half maximum of the source varies in size between 7.4 arcsec and 9.1 arcsec with the maximum between 30 and 40 keV. Such behaviour is expected in the presence of albedo and is found in the simulations. A source size smaller than 6 arcsec is improbable for modest directivities and the true source size is likely to be around 7 arcsec for small directivities. Conclusions: While it is difficult to image the albedo patch directly, the effect of backscattered photons on the observed source size can be estimated. The increase in source size caused by albedo has to be accounted for when computing physical quantities that include the size as a parameter such as flare energetics. At the same time, the study of the albedo signature provides vital information about the directivity of X-rays and related electrons.Comment: 8 pages, 6 figures, A&A (accepted

Hard X-ray footpoint sizes and positions as diagnostics of flare accelerated energetic electrons in the low solar atmosphere

The hard X-ray (HXR) emission in solar flares comes almost exclusively from a very small part of the flaring region, the footpoints of magnetic loops. Using RHESSI observations of solar flare footpoints, we determine the radial positions and sizes of footpoints as a function of energy in six near-limb events to investigate the transport of flare accelerated electrons and the properties of the chromosphere. HXR visibility forward fitting allows to find the positions/heights and the sizes of HXR footpoints along and perpendicular to the magnetic field of the flaring loop at different energies in the HXR range. We show that in half of the analyzed events, a clear trend of decreasing height of the sources with energy is found. Assuming collisional thick-target transport, HXR sources are located between 600 and 1200 km above the photosphere for photon energies between 120 and 25 keV respectively. In the other events, the position as a function of energy is constant within the uncertainties. The vertical sizes (along the path of electron propagation) range from 1.3 to 8 arcseconds which is up to a factor 4 larger than predicted by the thick-target model even in events where the positions/heights of HXR sources are consistent with the collisional thick-target model. Magnetic mirroring, collisional pitch angle scattering and X-ray albedo are discussed as potential explanations of the findings.Comment: 10 pages, 8 figures, accepted for publication in Ap

Solar Physics with the Square Kilometre Array

The Square Kilometre Array (SKA) will be the largest radio telescope ever built, aiming to provide collecting area larger than 1 km$^2$. The SKA will have two independent instruments, SKA-LOW comprising of dipoles organized as aperture arrays in Australia and SKA-MID comprising of dishes in South Africa. Currently the phase-1 of SKA, referred to as SKA1, is in its late design stage and construction is expected to start in 2020. Both SKA1-LOW (frequency range of 50-350 MHz) and SKA1-MID Bands 1, 2, and 5 (frequency ranges of 350-1050, 950-1760, and 4600-15300 MHz, respectively) are important for solar observations. In this paper we present SKA's unique capabilities in terms of spatial, spectral, and temporal resolution, as well as sensitivity and show that they have the potential to provide major new insights in solar physics topics of capital importance including (i) the structure and evolution of the solar corona, (ii) coronal heating, (iii) solar flare dynamics including particle acceleration and transport, (iv) the dynamics and structure of coronal mass ejections, and (v) the solar aspects of space weather. Observations of the Sun jointly with the new generation of ground-based and space-borne instruments promise unprecedented discoveries.Comment: Accepted for publication in Advances in Space Researc

Dynamics of electron beams in the solar corona plasma with density fluctuations

The problem of beam propagation in a plasma with small scale and low intensity inhomogeneities is investigated. It is shown that the electron beam propagates in a plasma as a beam-plasma structure and is a source of Langmuir waves. The plasma inhomogeneity changes the spatial distribution of the waves. The spatial distribution of the waves is fully determined by the distribution of plasma inhomogeneities. The possible applications to the theory of radio emission associated with electron beams are discussed

LOFAR observations of fine spectral structure dynamics in type IIIb radio bursts

Solar radio emission features a large number of fine structures demonstrating great variability in frequency and time. We present spatially resolved spectral radio observations of type IIIb bursts in the $30-80$ MHz range made by the Low Frequency Array (LOFAR). The bursts show well-defined fine frequency structuring called "stria" bursts. The spatial characteristics of the stria sources are determined by the propagation effects of radio waves; their movement and expansion speeds are in the range of 0.1-0.6c. Analysis of the dynamic spectra reveals that both the spectral bandwidth and the frequency drift rate of the striae increase with an increase of their central frequency; the striae bandwidths are in the range of ~20-100 kHz and the striae drift rates vary from zero to ~0.3 MHz s^-1. The observed spectral characteristics of the stria bursts are consistent with the model involving modulation of the type III burst emission mechanism by small-amplitude fluctuations of the plasma density along the electron beam path. We estimate that the relative amplitude of the density fluctuations is of dn/n~10^-3, their characteristic length scale is less than 1000 km, and the characteristic propagation speed is in the range of 400-800 km/s. These parameters indicate that the observed fine spectral structures could be produced by propagating magnetohydrodynamic waves

Positions and sizes of X-ray solar flare sources

<p><b>Aims:</b> The positions and source sizes of X-ray sources taking into account Compton backscattering (albedo) are investigated.</p> <p><b>Methods:</b> Using a Monte Carlo simulation of X-ray photon transport including photo-electric absorption and Compton scattering, we calculate the apparent source sizes and positions of X-ray sources at the solar disk for various source sizes, spectral indices and directivities of the primary source.</p> <p><b>Results:</b> We show that the albedo effect can alter the true source positions and substantially increase the measured source sizes. The source positions are shifted by up to ~0.5” radially towards the disk centre and 5 arcsec source sizes can be two times larger even for an isotropic source (minimum albedo effect) at 1 Mm above the photosphere. The X-ray sources therefore should have minimum observed sizes, and thus their FWHM source size (2.35 times second-moment) will be as large as ~7” in the 20-50 keV range for a disk-centered point source at a height of 1 Mm (~1.4”) above the photosphere. The source size and position change is greater for flatter primary X-ray spectra, a stronger downward anisotropy, for sources closer to the solar disk centre, and between the energies of 30 and 50 keV.</p> <p><b>Conclusions:</b> Albedo should be taken into account when X-ray footpoint positions, footpoint motions or source sizes from e.g. RHESSI or Yohkoh data are interpreted, and we suggest that footpoint sources should be larger in X-rays than in either optical or EUV ranges.</p&gt

Chromospheric magnetic field and density structure measurements using hard X-rays in a flaring coronal loop

<p><b>Aims:</b> A novel method of using hard X-rays as a diagnostic for chromospheric density and magnetic structures is developed to infer sub-arcsecond vertical variation of magnetic flux tube size and neutral gas density.</p> <p><b>Methods:</b> Using Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) X-ray data and the newly developed X-ray visibilities forward fitting technique we find the FWHM and centroid positions of hard X-ray sources with sub-arcsecond resolution (~0.2'') for a solar limb flare. We show that the height variations of the chromospheric density and the magnetic flux densities can be found with an unprecedented vertical resolution of ~150 km by mapping 18-250 keV X-ray emission of energetic electrons propagating in the loop at chromospheric heights of 400-1500 km.</p> <p><b>Results:</b> Our observations suggest that the density of the neutral gas is in good agreement with hydrostatic models with a scale height of around 140 30 km. FWHM sizes of the X-ray sources decrease with energy suggesting the expansion (fanning out) of magnetic flux tubes in the chromosphere with height. The magnetic scale height B(z)(dB/dz)-1 is found to be of the order of 300 km and a strong horizontal magnetic field is associated with noticeable flux tube expansion at a height of ~900 km.</p&gt