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Solar flare electron acceleration is an extremely efficient process, but the method of acceleration is not well constrained. Two of the essential diagnostics: electron anisotropy (velocity angle to the guiding magnetic field) and the high energy cutoff (highest energy electrons produced by the acceleration conditions: mechanism, spatial extent, time), are important quantities that can help to constrain electron acceleration at the Sun but both are poorly determined. Here, using electron and X-ray transport simulations that account for both collisional and non-collisional transport processes such as turbulent scattering, and X-ray albedo, we show that X-ray polarization can be used to constrain the anisotropy of the accelerated electron distribution and the most energetic accelerated electrons together. Moreover, we show that prospective missions, e.g. CubeSat missions without imaging information, can be used alongside such simulations to determine these parameters. We conclude that a fuller understanding of flare acceleration processes will come from missions capable of both X-ray flux and polarization spectral measurements together. Although imaging polarimetry is highly desired, we demonstrate that spectro-polarimeters without imaging can also provide strong constraints on electron anisotropy and the high energy cutoff., Comment: Accepted for publication in Astronomy & Astrophysics August 2020

Observations of solar flares at sub-THz frequencies (mm and sub-mm wavelengths) over the last two decades often show a spectral component rising with frequency. Unlike a typical gyrosynchrotron spectrum decreasing with frequency, or a weak thermal component from hot coronal plasma, the observations can demonstrate a high flux level (up to ~10^4 s.f.u. at 0.4 THz) and fast variability on sub-second time scales. Although, many models has been put forward to explain the puzzling observations, none of them have clear observational support. Here we propose a scenario to explain the intriguing sub-THz observations. We show that the model, based on free-free emission from the plasma of flare ribbons at temperatures 10^4-10^6 K, is consistent with all existing observations of frequency-rising sub-THz flare emission. The model provides a temperature diagnostic of the flaring chromosphere and suggests fast heating and cooling of the dense transition region plasma., Comment: 6 pages, 3 figures, 2 tables, A&A, accepted

The imaging spectroscopy capabilities of the Reuven Ramaty high energy solar spectroscopic imager (RHESSI) enable the examination of the accelerated electron distribution throughout a solar flare region. In particular, it has been revealed that the energisation of these particles takes place over a region of finite size, sometimes resolved by RHESSI observations. In this paper, we present, for the first time, a spatially distributed acceleration model and investigate the role of inhomogeneous acceleration on the observed X-ray emission properties. We have modelled transport explicitly examining scatter-free and diffusive transport within the acceleration region and compare with the analytic leaky-box solution. The results show the importance of including this spatial variation when modelling electron acceleration in solar flares. The presence of an inhomogeneous, extended acceleration region produces a spectral index that is, in most cases, different from the simple leaky-box prediction. In particular, it results in a generally softer spectral index than predicted by the leaky-box solution, for both scatter-free and diffusive transport, and thus should be taken into account when modelling stochastic acceleration in solar flares., Comment: 10 pages, submitted to Astronomy and Astrophysics Journal

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., Comment: 11 pages, 8 figures, accepted in Astronomy and Astrophysics

We analyse the RHESSI photon spectra of four flares that exhibit significant deviations from power laws - i.e. changes in the "local" Hard X-ray spectral index. These spectra are characterised by two regions of constant power law index connected by a region of changing spectral index - the "knee". We develop theoretical and numerical methods of describing such knees in terms of variable photon spectral indices and we study the results of their inversions for source mean thin target and collisional thick target injection electron spectra. We show that a particularly sharp knee can produce unphysical negative values in the electron spectra, and we derive inequalities that can be used to test for this without the need for an inversion to be performed. Such unphysical features would indicate that source model assumptions were being violated, particularly strongly for the collisional thick target model which assumes a specific form for electron energy loss. For all four flares considered here we find that the knees do not correspond to unphysical electron spectra. In the three flares that have downward knees we conclude that the knee can be explained in terms of transport eects through a region of non-uniform ionisation. In the other flare, which has an upward knee, we conclude that it is most likely a feature of the accelerated spectrum.

Context. During a solar flare, a large percentage of the magnetic energy released goes into the kinetic energy of non-thermal particles,\ud with X-ray observations providing a direct connection to keV flare-accelerated electrons. However, the electron angular distribution,\ud a prime diagnostic tool of the acceleration mechanism and transport, is poorly known.\ud Aims. During the next solar maximum, two upcoming space-borne X-ray missions, STIX on board Solar Orbiter and MiSolFA,\ud will perform stereoscopic X-ray observations of solar flares at two different locations: STIX at 0.28 AU (at perihelion) and up to\ud inclinations of ∼ 25◦\ud , and MiSolFA in a low-Earth orbit. The combined observations from these cross-calibrated detectors will allow\ud us to infer the electron anisotropy of individual flares confidently for the first time.\ud Methods. We simulated both instrumental and physical effects for STIX and MiSolFA including thermal shielding, background and\ud X-ray Compton backscattering (albedo effect) in the solar photosphere. We predict the expected number of observable flares available\ud for stereoscopic measurements during the next solar maximum. We also discuss the range of useful spacecraft observation angles for\ud the challenging case of close-to-isotropic flare anisotropy.\ud Results. The simulated results show that STIX and MiSolFA will be capable of detecting low levels of flare anisotropy, for M1-class\ud or stronger flares, even with a relatively small spacecraft angular separation of 20–30◦\ud . Both instruments will directly measure the\ud flare X-ray anisotropy of about 40 M- and X-class solar flares during the next solar maximum.\ud Conclusions. Near-future stereoscopic observations with Solar Orbiter/STIX and MiSolFA will help distinguishing between competing\ud flare-acceleration mechanisms, and provide essential constraints regarding collisional and non-collisional transport processes\ud occurring in the flaring atmosphere for individual solar flares.

Magnetic reconnection and particle acceleration due to the kink instability in twisted coronal loops can be a viable scenario for confined solar flares. Detailed investigation of this phenomenon requires reliable methods for observational detection of magnetic twist in solar flares, which may not be possible solely through extreme UV and soft X-ray thermal emission. Polarisation of microwave emission in flaring loops can be used as one of the detection criteria. The aim of this study is to investigate the effect of magnetic twist in flaring coronal loops on the polarisation of gyro-synchrotron microwave (GSMW) emission, and determine whether it could provide a means for magnetic twist detection. We use time-dependent magnetohydrodynamic and test-particle models developed using LARE3D and GCA codes to investigate twisted coronal loops relaxing following the kink-instability. Synthetic GSMW emission maps (I and V Stokes components) are calculated using GX simulator. It is found that flaring twisted coronal loops produce GSMW radiation with a gradient of circular polarisation across the loop. However, these patterns may be visible only for a relatively short period of time due to fast magnetic reconfiguration after the instability. Their visibility also depends on the orientation and position of the loop on solar disk. Typically, it would be difficult to see these characteristic polarisation pattern in a twisted loop seen from the top (close to the centre of the solar disk), but easier in a twisted loop seen from the side (i.e. observed very close to the limb)., Accepted for publication in Astronomy & Astrophysics

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., 8 pages, 7 figures

Observation of coronal EUV spectral lines sensitive to different temperatures offers an opportunity to evaluate the thermal structure and flows in flaring atmospheres. This can be used to estimate the partitioning between the thermal and kinetic energies. Our aim is to model large-scale (50-10000km) velocity distributions in order to interpret non-thermal broadening of different spectral EUV lines. The developed models allow us to understand the origin of the observed spectral line shifts and broadening, and link these features to particular physical effects in flaring atmospheres. We use ideal MHD to derive twisted magnetic fluxtube configurations in a stratified atmosphere. The evolution of these fluxtubes is followed using resistive MHD, with anomalous resistivity depending on the local density and temperature. The model also takes into account the thermal conduction and radiative losses. The model allows us to evaluate average velocities and velocity dispersions, which would be interpreted as `non-thermal' velocities in observations, at different temperatures for different parts of the models. Our models show qualitative and quantitative agreement with observations. The line-of-sight (LOS) velocity dispersions demonstrate substantial correlation with the temperature, increasing from about 20-30 km/s around 1 MK to about 200-400 km/s near 10-20 MK. The average LOS velocities also correlate with velocity dispersions, although they demonstrate a very strong scattering, compared to observations. We also note that near foot-points the velocity dispersions across the magnetic field are systematically lower than those along the field. We conclude, that the correlation between the flow velocities, velocity dispersions and temperatures are likely to indicate that the same heating mechanism is responsible for heating the plasma, its turbulisation and expansion/evaporation., Comment: Accepted to Astronomy & Astrophysics

Energetic electrons produced during solar flares are known to be responsible for generating solar type III radio bursts. The radio emission is a byproduct of Langmuir wave generation via beam-plasma interaction and nonlinear wave-wave and wave-particle interaction processes. In addition to type III radio bursts, electrons traveling downwards toward the chromosphere lead to the hard X-ray emission via electron-ion collisions. Recently, the role of Langmuir waves on the X-ray-producing electrons has been identified as important, because Langmuir waves may alter the electron distribution, thereby affecting the X-ray profile. Both Coulomb collisions and wave-particle interactions lead electrons to scattering and energy exchange that necessitates considering the two-dimensional (2D) problem in velocity space. The present paper investigates the influence of binary collisions on the beam-plasma instability development in 2D in order to elucidate the nonlinear dynamics of Langmuir waves and binary collisions. The significance of the present findings in the context of solar physics is discussed.

Aims. Type III radio bursts are intense radio emissions triggered by beams of energetic electrons often associated with solar flares. These exciter beams propagate outwards from the Sun along an open magnetic field line in the corona and in the interplanetary (IP) medium.\ud Methods. We performed a statistical survey of 29 simple and isolated IP type III bursts observed by STEREO/Waves instruments between January 2013 and September 2014. We investigated their time-frequency profiles in order to derive the speed and acceleration of exciter electron beams.\ud Results. We show these beams noticeably decelerate in the IP medium. Obtained speeds range from ~0.02c up to ~0.35c depending on initial assumptions. It corresponds to electron energies between tens of eV and hundreds of keV, and in order to explain the characteristic energies or speeds of type III electrons (~0.1c) observed simultaneously with Langmuir waves at 1 au, the emission of type III bursts near the peak should be predominately at double plasma frequency. Derived properties of electron beams can be used as input parameters for computer simulations of interactions between the beam and the plasma in the IP medium.

Non-thermal electrons accelerated in the solar corona can produce intense coherent radio emission, known as solar type III radio bursts. This intense radio emission is often observed from hundreds of MHz in the corona down to the tens of kHz range in interplanetary space. It involves a chain of physical processes from the generation of Langmuir waves to nonlinear processes of wave-wave interaction. We develop a self-consistent model to calculate radio emission from a non-thermal electron population over large frequency range, including the effects of electron transport, Langmuir wave-electron interaction, the evolution of Langmuir waves due to non-linear wave-wave interactions, Langmuir wave conversion into electromagnetic emission, and finally escape of the electromagnetic waves. For the first time we simulate escaping radio emission over a broad frequency range from 500~MHz down to a few MHz and infer key properties of the radio emission observed: the onset (starting) frequency, {identification as fundamental or harmonic emission}, peak flux density, instantaneous frequency bandwidth, and timescales for rise and decay. Comparing with the observations, these large scale simulations enable us to identify the processes governing the key type III solar radio burst characteristics.

We investigate the effects of acceleration during non-linear electron-beam relaxation in magnetized plasma in the case of electron transport in solar flares. The evolution of electron distribution functions is computed using a three-dimensional particle-in-cell electromagnetic code. Analytical estimations under simplified assumptions are made to provide comparisons. We show that, during the non-linear evolution of the beam-plasma system, the accelerated electron population appears. We found that, although the electron beam loses its energy efficiently to the thermal plasma, a noticeable part of the electron population is accelerated. For model cases with initially monoenergetic beams in uniform plasma, we found that the amount of energy in the accelerated electrons above the injected beam-electron energy varies depending the plasma conditions and could be around 10-30% of the initial beam energy. This type of acceleration could be important for the interpretation of non-thermal electron populations in solar flares. Its neglect could lead to the over-estimation of accelerated electron numbers. The results emphasize that collective plasma effects should not be treated simply as an additional energy-loss mechanism, when hard X-ray emission in solar flares is interpreted, notably in the case of RHESSI data., 9 pages, 8 figures, accepted to Astronomy and Astrophysics

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., 8 pages, 6 figures, A&A (accepted)

{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.} {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-$\beta$ 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 $k_{\perp}\rho_{s}\ll 1$ down to the small "kinetic" scales with $k_{\perp}\rho_{s} \gg 1$, $\rho_{s}$ being the ion sound gyroradius.} {Scaling relations are obtained for the magnitude of the turbulent electromagnetic fluctuations, as a function of $k_{\perp}$ and $k_{\parallel}$, showing that the electric field develops a component parallel to the magnetic field at large MHD scales.} {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}

We investigate the positions and source sizes of X-ray solar flare sources taking into account Compton backscattering (albedo). 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. We show that the albedo effect will alter the true source positions and substantially increase the measured source sizes. The source positions are shifted up to $\sim 0.5"$ radially towards the disk centre and 5 arcsecond source sizes can be two times larger even for an isotropic source (minimum albedo effect) at 1 Mm above the photosphere. X-ray sources therefore should have minimum observed sizes, thus FWHM source size (2.35 times second-moment) will be as large as $\sim 7"$ in the 20-50 keV range for a disk-centered point source at a height of 1 Mm ($\sim 1.4"$) above the photosphere. The source size and position change is the largest for flatter primary X-ray spectra, stronger downward anisotropy, for sources closer to the solar disk centre, and between the energies of 30 and 50 keV. 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 suggest that footpoint sources should be larger in X-rays than in optical or EUV ranges., Comment: 4 pages, 2 figures, submitted to Astronomy and Astrophysics Letters