The Sun frequently accelerates near-relativistic electron beams that travel out through the solar corona and interplanetary space. Interacting with their plasma environment, these beams produce type III radio bursts, the brightest astrophysical radio
sources seen from the Earth. The formation and motion of type III fine frequency structures is a puzzle but is commonly believed to be related to plasma turbulence in the solar corona and solar wind. Combining a theoretical framework with kinetic simulations and high-resolution radio type III observations using the Low Frequency Array, we quantitatively show that the fine structures are caused by the moving intense clumps of Langmuir waves in a turbulent medium. Our results show how type III fine structure can be used to remotely analyse the intensity and spectrum of compressive density fluctuations, and can infer ambient temperatures in astrophysical plasma, both significantly expanding the current diagnostic potential of solar radio emission.
Drift-pair bursts are an unusual type of solar low-frequency radio emission, which appear in the dynamic spectra as two parallel drifting bright stripes separated in time. Recent imaging spectroscopy observations allowed for the quantitative characte
rization of the drifting pairs in terms of source size, position, and evolution. Here, the drift-pair parameters are qualitatively analyzed and compared with the newly-developed Monte Carlo ray-tracing technique simulating radio-wave propagation in the inhomogeneous anisotropic turbulent solar corona. The results suggest that the drift-pair bursts can be formed due to a combination of the refraction and scattering processes, with the trailing component being the result of turbulent reflection (turbulent radio echo). The formation of drift-pair bursts requires an anisotropic scattering with the level of plasma density fluctuations comparable to that in type III bursts, but with a stronger anisotropy at the inner turbulence scale. The anisotropic radio-wave scattering model can quantitatively reproduce the key properties of drift-pair bursts: the apparent source size and its increase with time at a given frequency, the parallel motion of the source centroid positions, and the delay between the burst components. The trailing component is found to be virtually co-spatial and following the main component. The simulations suggest that the drift-pair bursts are likely to be observed closer to the disk center and below 100 MHz due to the effects of free-free absorption and scattering. The exciter of drift-pairs is consistent with propagating packets of whistlers, allowing for a fascinating way to diagnose the plasma turbulence and the radio emission mechanism.
The observed properties (i.e., source size, source position, time duration, decay time) of solar radio emission produced through plasma processes near the local plasma frequency, and hence the interpretation of solar radio bursts, are strongly influe
nced by propagation effects in the inhomogeneous turbulent solar corona. In this work, a 3D stochastic description of the propagation process is presented, based on the Fokker-Planck and Langevin equations of radio-wave transport in a medium containing anisotropic electron density fluctuations. Using a numerical treatment based on this model, we investigate the characteristic source sizes and burst decay times for Type III solar radio bursts. Comparison of the simulations with the observations of solar radio bursts shows that predominantly perpendicular density fluctuations in the solar corona are required, with an anisotropy factor $sim 0.3$ for sources observed at around 30~MHz. The simulations also demonstrate that the photons are isotropized near the region of primary emission, but the waves are then focused by large-scale refraction, leading to plasma radio emission directivity that is characterized by a half-width-half-maximum of about 40~degrees near 30~MHz. The results are applicable to various solar radio bursts produced via plasma emission.
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 inhomog
eneity 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.
Dynamics of an spatially limited electron beam in the inhomogeneous solar corona plasma is considered in the framework of weak turbulence theory when the temperature of the beam significantly exceeds that of surrounding plasma. The numerical solution
of kinetic equations manifests that generally the beam accompanied by Langmuir waves propagates as a beam-plasma structure with a decreasing velocity. Unlike the uniform plasma case the structure propagates with the energy losses in the form of Langmuir waves. The results obtained are compared with the results of observations of type III bursts. It is shown that the deceleration of type III sources can be explained by the corona inhomogeneity. The frequency drift rates of the type III sources are found in a good agreement with the numerical results of beam dynamics.
The dynamics of a hot electron cloud in the solar corona-like plasma based on the numerical solution of kinetic equations of weak turbulence theory is considered. Different finite difference schemes are examined to fit the exact analytical solutions
of quasilinear equations in hydrodynamic limit (gas-dynamic solution). It is shown that the scheme suggested demonstrates correct asymptotic behavior and can be employed to solve initial value problems for an arbitrary initial electron distribution function.
We present observations of electron energization in magnetic reconnection outflows during the pre-impulsive phase of solar flare SOL2012-07-19T05:58. During a time-interval of about 20 minutes, starting 40 minutes before the onset of the impulsive ph
ase, two X-ray sources were observed in the corona, one above the presumed reconnection region and one below. For both of these sources, the mean electron distribution function as a function of time is determined over an energy range from 0.1~keV up to several tens of keV, for the first time. This is done by simultaneous forward fitting of X-ray and EUV data. Imaging spectroscopy with RHESSI provides information on the high-energy tail of the electron distribution in these sources while EUV images from SDO/AIA are used to constrain the low specific electron energies. The measured electron distribution spectrum in the magnetic reconnection outflows is consistent with a time-evolving kappa-distribution with $kappa =3.5-5.5$. The spectral evolution suggests that electrons are accelerated to progressively higher energies in the source above the reconnection region, while in the source below, the spectral shape does not change but an overall increase of the emission measure is observed, suggesting density increase due to evaporation. The main mechanisms by which energy is transported away from the source regions are conduction and free-streaming electrons. The latter dominates by more than one order of magnitude and is comparable to typical non-thermal energies during the hard X-ray peak of solar flares, suggesting efficient acceleration even during this early phase of the event.
Solar flare hard X-ray spectroscopy serves as a key diagnostic of the accelerated electron spectrum. However, the standard approach using the collisional cold thick-target model poorly constrains the lower-energy part of the accelerated electron spec
trum, and hence the overall energetics of the accelerated electrons are typically constrained only to within one or two orders of magnitude. Here we develop and apply a physically self-consistent warm-target approach which involves the use of both hard X-ray spectroscopy and imaging data. The approach allows an accurate determination of the electron distribution low-energy cutoff, and hence the electron acceleration rate and the contribution of accelerated electrons to the total energy released, by constraining the coronal plasma parameters. Using a solar flare observed in X-rays by the {em RHESSI} spacecraft, we demonstrate that using the standard cold-target methodology, the low-energy cutoff (and hence the energy content in electrons) is essentially undetermined. However, the warm-target methodology can determine the low-energy electron cutoff with $sim$7% uncertainty at the $3sigma$ level and hence permits an accurate quantitative study of the importance of accelerated electrons in solar flare energetics.
A component of space weather, electron beams are routinely accelerated in the solar atmosphere and propagate through interplanetary space. Electron beams interact with Langmuir waves resulting in type III radio bursts. Electron beams expand along the
trajectory, and using kinetic simulations, we explore the expansion as the electrons propagate away from the Sun. Specifically, we investigate the front, peak and back of the electron beam in space from derived radio brightness temperatures of fundamental type III emission. The front of the electron beams travelled at speeds from 0.2c--0.7c, significantly faster than the back of the beam that travelled between 0.12c--0.35c. The difference in speed between the front and the back elongates the electron beams in time. The rate of beam elongation has a 0.98 correlation coefficient with the peak velocity; in-line with predictions from type III observations. The inferred speeds of electron beams initially increase close to the acceleration region and then decrease through the solar corona. Larger starting densities and harder initial spectral indices result in longer and faster type III sources. Faster electron beams have higher beam energy densities, produce type IIIs with higher peak brightness temperatures and shorter FWHM durations. Higher background plasma temperatures also increase speeds, particularly at the back of the beam. We show how our predictions of electron beam evolution influences type III bandwidth and drift-rates. Our radial predictions of electron beam speed and expansion can be tested by the upcoming in situ electron beam measurements made by Solar Orbiter and Parker Solar Probe.
Observational detection of quasi-periodic drifting fine structures in a type III radio burst associated with a solar flare SOL2015-04-16T11:22, with Low Frequency Array, is presented. Although similar modulations of the type III emission have been ob
served before and were associated with the plasma density fluctuations, the origin of those fluctuations was unknown. Analysis of the striae of the intensity variation in the dynamic spectrum allowed us to reveal two quasi-oscillatory components. The shorter component has the apparent wavelength of $sim2$ Mm, phase speed of $sim657$ km s$^{-1}$, which gives the oscillation period of $sim3$ s, and the relative amplitude of $sim0.35$%. The longer component has the wavelength of $sim12$ Mm, and relative amplitude of $sim5.1$%. The short frequency range of the detection does not allow us to estimate its phase speed. However, the properties of the shorter oscillatory component allowed us to interpret it as a fast magnetoacoustic wave guided by a plasma non-uniformity along the magnetic field outwards from the Sun. The assumption that the intensity of the radio emission is proportional to the amount of plasma in the emitting volume allowed us to show that the superposition of the plasma density modulation by a fast wave and a longer-wavelength oscillation of an unspecified nature could readily reproduce the fine structure of the observed dynamic spectrum. The observed parameters of the fast wave give the absolute value of the magnetic field in the emitting plasma of $sim1.1$ G which is consistent with the radial magnetic field model.
