arXiv subjects

Natasha L. S. Jeffrey

Publications and source records attributed to Natasha L. S. Jeffrey.

At least 19 recordsLinked to original sources

arXiv2026

A new methodology for inferring the plasma conditions in solar flare energetic electron source regions from in situ electron energy spectra

The conditions within solar flares that lead to efficient electron acceleration are not well constrained. It is not clear whether the populations accelerated out into the heliosphere and inward into the chromosphere originate in the same regions. By analysing the energy distributions of heliospheric populations, modelling suggests that it should be possible to see evidence of their originating region(s), including the presence of hot, dense flare plasma. By creating and utilising a novel in situ spectral analysis package called INSPEX we have performed this analysis for flare electrons observed in situ on 09/10/2021, constructing both peak flux and fluence spectra from combined Solar Orbiter in situ electron measurements. We compare how differing methodologies for combining the datasets influence the spectral shapes and the retrieved parameters over an energy range of 0.5-80 keV. We fit different functions to the multi-component form of the energy spectra, testing combinations of thermal and/or power law components, comparing the fit statistics. We find that the spectra can be fitted with two distinct thermal curves at energies below 20 keV, corresponding to typical corona/active region and flaring material temperatures, varying between 1.4 - 4.1 MK and 12.5 - 23.1 MK depending on the rebinning window and peak flux extraction method. This study showcases how INSPEX can provide a novel and user-friendly methodology for studying electron spectra with different instrumentation, allowing investigation of multiple spectral types and signatures of acceleration and transport. This first application provides a benchmark case for the analysis of similar flares.

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arXiv2026

Multi-wavelength observations of substructures in solar flare ribbons

Solar flare ribbons are extensive brightenings in the chromosphere during flares, often showing fine scale structuring that reflects the underlying energy release. Using high cadence imaging from the Swedish 1-m Solar Telescope/CRISP during an X1.5-class limb flare on 10 June 2014, we identify and track 232 coherent, thread-like substructures, which we term for the first time ``riblets''. From a statistical analysis, riblets have well defined lifetimes and plane-of-sky speeds (typically 5-15 s and 50-150 km/s respectively), establishing them as distinct ribbon substructures. From analysis of their temporal distributions, their distance-time (X-T) evolution uniquely reveal approximately linear and non-linear (accelerating/decelerating) classes, a discrepancy that may be influenced by projection geometry. From analysis of their spatial distributions, we find no clear correspondence between the properties of adjacent riblets, suggesting that local atmospheric conditions (fine-scale thermodynamic and/or magnetic structuring) govern their kinematics more than spatial variations in electron-beam energy flux. From analysis of their spectral distributions, clusters of riblets do show temporal and spatial coincidence with hard X-ray emission signatures, consistent with episodic electron-beam injection into the chromosphere. Using Fermi/GBM spectroscopy, we derive thick-target parameters suitable for flare simulations, with representative values $δ_{\rm low}\approx 5.93$, $E_{\rm c}\approx 24.7$ keV, and an implied beam energy flux $\mathcal{F}_{\rm beam}\approx 1.5\times 10^{10}$ erg cm$^{-2}$ s$^{-1}$ (based on RHESSI footpoint area). Together, these results identify riblets as the fundamental building block of flare ribbons and provide quantitative constraints for forward tests of riblet formation mechanisms.

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arXiv2025

Time-dependent Turbulent Electron Acceleration and Transport in Solar Flares

Solar flares are explosive releases of magnetic energy stored in the solar corona, driven by magnetic reconnection. These events accelerate electrons, generating hard X-ray emissions and often display Quasi Periodic Pulsations (QPPs) across the energy spectra. However, the energy transfer process remains poorly constrained, with competing theories proposing different acceleration mechanisms. We investigate electron acceleration and transport in a flaring coronal loop by solving a time-dependent Fokker-Planck equation. Our model incorporates transient turbulent acceleration, simulating the effects of impulsive energy input to emulate the dynamics of time-dependent reconnection processes. We compute the density-weighted electron flux, a diagnostic directly comparable to observed X-ray emissions, across the energy and spatial domains from the corona to the chromosphere. We investigate different time-dependent functional forms of the turbulent acceleration, finding that the functional form of the acceleration source maintains its signature across energy bands (1 to 100 keV) with a response time that is energy dependent (with higher energy bands displaying a longer response time). In addition, we find that (a) for a square pulse the switch on and off response time is different; (b) for a sinusoidal input the periodicity is preserved; and (c) for a damped sinusoidal the decay rate increases with density and higher energy bands lose energy faster. This work presents a novel methodology for analyzing electron acceleration and transport in flares driven by time-dependent sources.

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arXiv2025

Tracing the Heliospheric Magnetic Field via Anisotropic Radio-Wave Scattering

Astrophysical radio sources are embedded in turbulent magnetised environments. In the 1 MHz sky, solar radio bursts are the brightest sources, produced by electrons travelling along magnetic field lines from the Sun through the heliosphere. We demonstrate that the magnetic field not only guides the emitting electrons, but also directs radio waves via anisotropic scattering from density irregularities in the magnetised plasma. Using multi-vantage-point type III solar radio burst observations and anisotropic radio wave propagation simulations, we show that the interplanetary field structure is encoded in the observed radio emission directivity, and that large-scale turbulent channelling of radio waves is present over large distances, even for relatively weak anisotropy in the embedded density fluctuations. Tracing the radio emission at many frequencies (distances), the effects of anisotropic scattering can be disentangled from the electron motion along the interplanetary magnetic field, and the emission source locations are unveiled. Our analysis suggests that magnetic field structures within turbulent media could be reconstructed using radio observations and is found consistent with the Parker field, offering a novel method for remotely diagnosing the large-scale field structure in the heliosphere and other astrophysical plasmas.

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arXiv2025

Exploring the Origin of Solar Energetic Electrons II: Investigating Turbulent Coronal Acceleration

Non-thermal particle acceleration in the solar corona is evident from both remote hard X-ray (HXR) sources in the chromosphere and direct in-situ detection in the heliosphere. Correlation of spectral indices between remote and in-situ energy spectra presents the possibility of a common source acceleration region within the corona, however the properties and location of this region are not well constrained. To investigate this we perform a parameter study for both the properties of the ambient plasma of a simulated acceleration region and the turbulent acceleration profile acting on an initially isotropic thermal electron population. We find that the independently varying the turbulent acceleration timescale $τ_{acc}$, acceleration profile standard deviation $σ$ and acceleration region length L result in in-situ spectral index variation of between 0.5 and 2.0 at 1.0 AU for < 100 keV electrons. Short timescale turbulent scattering in the flaring corona steepens the spectra by $\sim$ 0.5. It was also found that the in-situ spectral index $δ$ derived from the peak electron flux produces a spectral index $\sim$ 1.6 harder than that from a full-flare X-ray photon flux (of spectral index $γ$) simulated with the same intermediate parameters. Previous studies have indicated an approximate $δ\approx γ$ relationship for selected flares with measured in-situ electron and X-ray photon observations, suggesting that an extended source region with non-uniform plasma and/or acceleration properties may be necessary to reproduce this relationship.

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arXiv2024

First joint X-ray solar microflare observations with NuSTAR and Solar Orbiter/STIX

We present the first joint spectral and imaging analysis of hard X-ray (HXR) emission from 3 microflares observed by the Nuclear Spectroscopic Telescope ARray (NuSTAR) and Solar Orbiter/Spectrometer/Telescope for Imaging X-rays (STIX). We studied 5 joint spectra from GOES A7, B1 and B6 class microflares from active region AR12765 on 2020 June 6 and 7. As these events are very bright for NuSTAR, resulting in extremely low (<1%) livetime, we introduce a pile-up correction method. All five joint spectra were fitted with an isothermal model finding temperatures in the 9-11 MK range. Furthermore, three joint spectra required an additional non-thermal thick-target model finding non-thermal powers of $10^{25}$-$10^{26}$ erg s$^{-1}$. All the fit parameters were within the ranges expected for HXR microflares. The fit results give a relative scaling of STIX and NuSTAR mostly between 6-28% (one outlier at 52%) suggesting each instrument are well calibrated. In addition to spectral analysis, we performed joint HXR imaging of the June 6 and one of the June 7 microflares. In NuSTAR's field of view (FOV), we observed two separate non-thermal sources connected by an elongated thermal source during the June 6 microflares. In STIX's FOV (44 degrees W with respect to NuSTAR), we imaged thermal emission from the hot flare loops which when reprojected to an Earth viewpoint matches the thermal sources seen with NuSTAR and in the hotter EUV channels with the Solar Dynamic Observatory's Atmospheric Imaging Assembly.

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arXiv2024

A Modelling Investigation for Solar Flare X-ray Stereoscopy with Solar Orbiter/STIX and Earth Orbiting Missions

The Spectrometer/Telescope for Imaging X-rays (STIX) on board Solar Orbiter (SolO) provides a unique opportunity to systematically perform stereoscopic X-ray observations of solar flares with current and upcoming X-ray missions at Earth. These observations will produce the first reliable measurements of hard X-ray (HXR) directivity in decades, providing a new diagnostic of the flare-accelerated electron angular distribution and helping to constrain the processes that accelerate electrons in flares. However, such observations must be compared to modelling, taking into account electron and X-ray transport effects and realistic plasma conditions, all of which can change the properties of the measured HXR directivity. Here, we show how HXR directivity, defined as the ratio of X-ray spectra at different spacecraft viewing angles, varies with different electron and flare properties (e.g., electron angular distribution, highest energy electrons, and magnetic configuration), and how modelling can be used to extract these typically unknown properties from the data. Lastly, we present a preliminary HXR directivity analysis of two flares, observed by the Fermi Gamma-ray Burst Monitor (GBM) and SolO/STIX, demonstrating the feasibility and challenges associated with such observations, and how HXR directivity can be extracted by comparison with the modelling presented here.

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arXiv2023

Source positions of an interplanetary type III radio burst and anisotropic radio-wave scattering

Interplanetary solar radio type III bursts provide the means for remotely studying and tracking energetic electrons propagating in the interplanetary medium. Due to the lack of direct radio source imaging, several methods have been developed to determine the source positions from space-based observations. Moreover, none of the methods consider the propagation effects of anisotropic radio-wave scattering, which would strongly distort the trajectory of radio waves, delay their arrival times, and affect their apparent characteristics. We investigate the source positions and directivity of an interplanetary type III burst simultaneously observed by Parker Solar Probe, Solar Orbiter, STEREO, and Wind and compare the results of applying the intensity fit and timing methods with ray-tracing simulations of radio-wave propagation with anisotropic density fluctuations. The simulation calculates the trajectories of the rays, their time profiles at different viewing sites, and the apparent characteristics for various density fluctuation parameters. The results indicate that the observed source positions are displaced away from the locations where emission is produced, and their deduced radial distances are larger than expected from density models. This suggests that the apparent position is affected by anisotropic radio-wave scattering, which leads to an apparent position at a larger heliocentric distance from the Sun. The methods to determine the source positions may underestimate the apparent positions if they do not consider the path of radio-wave propagation and incomplete scattering at a viewing site close to the intrinsic source position.

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arXiv2023

Exploring the Origin of Solar Energetic Electrons I: Constraining the Properties of the Acceleration Region Plasma Environment

Solar flare electron acceleration is an efficient process, but its properties (mechanism, location) are not well constrained. Via hard X-ray (HXR) emission, we routinely observe energetic electrons at the Sun, and sometimes we detect energetic electrons in interplanetary space. We examine if the plasma properties of an acceleration region (size, temperature, density) can be constrained from in-situ observations, helping to locate the acceleration region in the corona, and infer the relationship between electrons observed in-situ and at the Sun. We model the transport of energetic electrons, accounting for collisional and non-collisional effects, from the corona into the heliosphere (to 1.0 AU). In the corona, electrons are transported through a hot, over-dense region. We test if the properties of this region can be extracted from electron spectra (fluence and peak flux) at different heliospheric locations. We find that cold, dense coronal regions significantly reduce the energy at which we see the peak flux and fluence for distributions measured out to 1.0 AU, the degree of which correlates with the temperature and density of plasma in the region. Where instrument energy resolution is insufficient to differentiate the corresponding peak values, the spectral ratio of [7-10) to [4-7) keV can be more readily identified and demonstrates the same relationship. If flare electrons detected in-situ are produced in, and/or transported through hot, over-dense regions close to HXR-emitting electrons, then this plasma signature should be present in their lower-energy spectra (1-20 keV), observable at varying heliospheric distances with missions such as Solar Orbiter.

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arXiv2023

The existence of hot X-ray onsets in solar flares

It is well known among the scientific community that solar flare activity often begins well before the main impulsive energy release. Our aim is to investigate the earliest phase of four distinct flares observed by Solar Orbiter/STIX and determine the relationships of the newly heated plasma to flare structure and dynamics. The analysis focuses on four events that were observed from both Earth and Solar Orbiter, which allows for a comparison of STIX observations with those of GOES/XRS and SDO/AIA. The early phases of the events were studied using STIX and GOES spectroscopic analysis to investigate the evolution of the physical parameters of the plasma, including the isothermal temperature and emission measure. Furthermore, to determine the location of the heated plasma, STIX observations were combined with AIA images. The events with clear emission prior to the impulsive phase show elevated temperatures ($> 10\,\mathrm{MK}$) from the very beginning, which indicates that energy release started before any detection by STIX. Although the temperature shows little variation during the initial phase, the emission measure increases by about two orders of magnitude, implying a series of incrementally greater energy releases. The spectral analysis of STIX and GOES from the very first time bins suggests that the emission has a multi-thermal nature, with a hot component of more than $10\,\mathrm{MK}$. This analysis confirms the existence of "hot onsets," with STIX detecting the hot onset pattern even earlier than GOES. These elevated temperatures imply that energy release actually begins well before any detection by STIX. Therefore, hot onsets may be significant in the initiation, early development, or even prediction of solar flares.

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arXiv2023

An Anisotropic Density Turbulence Model from the Sun to 1 au Derived From Radio Observations

Solar radio bursts are strongly affected by radio-wave scattering on density inhomogeneities, changing their observed time characteristics, sizes, and positions. The same turbulence causes angular broadening and scintillation of galactic and extra-galactic compact radio sources observed through the solar atmosphere. Using large-scale simulations of radio-wave transport, the characteristics of anisotropic density turbulence from $0.1 \, R_\odot$ to $1$ au are explored. For the first time, a profile of heliospheric density fluctuations is deduced that accounts for the properties of extra-solar radio sources, solar radio bursts, and in-situ density fluctuation measurements in the solar wind at $1$ au. The radial profile of the spectrum-weighted mean wavenumber of density fluctuations (a quantity proportional to the scattering rate of radio-waves) is found to have a broad maximum at around $(4-7) \, R_\odot$, where the slow solar wind becomes supersonic. The level of density fluctuations at the inner scale (which is consistent with the proton resonance scale) decreases with heliocentric distance as $\langleδ{n_i}^2 \rangle (r) \simeq 2 \times 10^7 \, (r/R_\odot-1)^{-3.7}$ cm$^{-6}$. Due to scattering, the apparent positions of solar burst sources observed at frequencies between $0.1$ and $300$ MHz are computed to be essentially cospatial and to have comparable sizes, for both fundamental and harmonic emission. Anisotropic scattering is found to account for the shortest solar radio burst decay times observed, and the required wavenumber anisotropy is $q_\parallel/q_\perp =0.25-0.4$, depending on whether fundamental or harmonic emission is involved. The deduced radio-wave scattering rate paves the way to quantify intrinsic solar radio burst characteristics.

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arXiv2023

Spectral and Imaging Diagnostics of Spatially-Extended Turbulent Electron Acceleration and Transport in Solar Flares

Solar flares are efficient particle accelerators with a large fraction of released magnetic energy (10-50%) converted into energetic particles such as hard X-ray producing electrons. This energy transfer process is not well constrained, with competing theories regarding the acceleration mechanism(s), including MHD turbulence. We perform a detailed parameter study examining how various properties of the acceleration region, including its spatial extent and the spatial distribution of turbulence, affect the observed electron properties, such as those routinely determined from X-ray imaging and spectroscopy. Here, a time-independent Fokker-Planck equation is used to describe the acceleration and transport of flare electrons through a coronal plasma of finite temperature. Motivated by recent non-thermal line broadening observations that suggested extended regions of turbulence in coronal loops, an extended turbulent acceleration region is incorporated into the model. We produce outputs for the density weighted electron flux, a quantity directly related to observed X-rays, modelled in energy and space from the corona to chromosphere. We find that by combining several spectral and imaging diagnostics (such as spectral index differences or ratios, energy or spatial-dependent flux ratios, and electron depths into the chromosphere) the acceleration properties, including the timescale and velocity dependence, can be constrained alongside the spatial properties. Our diagnostics provide a foundation for constraining the properties of acceleration in an individual flare from X-ray imaging spectroscopy alone, and can be applied to past, current and future observations including those from RHESSI and Solar Orbiter.

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arXiv2021

The Spatial and Temporal Variations of Turbulence in a Solar Flare

Magnetohydrodynamic (MHD) plasma turbulence is believed to play a vital role in the production of energetic electrons during solar flares and the non-thermal broadening of spectral lines is a key sign of this turbulence. Here, we determine how flare turbulence evolves in time and space using spectral profiles of Fe xxiv, Fe xxiii and Fe xvi, observed by Hinode/EIS. Maps of non-thermal velocity are created for times covering the X-ray rise, peak, and decay. For the first time, the creation of kinetic energy density maps reveal where energy is available for energization, suggesting that similar levels of energy may be available to heat and/or accelerate electrons in large regions of the flare. We find that turbulence is distributed throughout the entire flare; often greatest in the coronal loop tops, and decaying at different rates at different locations. For hotter ions (Fe xxiv and Fe xxiii), the non-thermal velocity decreases as the flare evolves and during/after the X-ray peak shows a clear spatial variation decreasing linearly from the loop apex towards the ribbon. For the cooler ion (Fe xvi), the non-thermal velocity remains relativity constant throughout the flare, but steeply increases in one region corresponding to the southern ribbon, peaking just prior to the peak in hard X-rays before declining. The results suggest turbulence has a more complex temporal and spatial structure than previously assumed, while newly introduced turbulent kinetic energy maps show the availability of the energy and identify important spatial inhomogeneities in the macroscopic plasma motions leading to turbulence.

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arXiv2020

Probing solar flare accelerated electron distributions with prospective X-ray polarimetry missions

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.

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arXiv2020

Sub-second time evolution of Type III solar radio burst sources at fundamental and harmonic frequencies

Recent developments in astronomical radio telescopes opened new opportunities in imaging and spectroscopy of solar radio bursts at sub-second timescales. Imaging in narrow frequency bands has revealed temporal variations in the positions and source sizes that do not fit into the standard picture of type III solar radio bursts, and require a better understanding of radio-wave transport. In this paper, we utilise 3D Monte Carlo ray-tracing simulations that account for the anisotropic density turbulence in the inhomogeneous solar corona to quantitatively explain the image dynamics at the fundamental (near plasma frequency) and harmonic (double) plasma emissions observed at \sim 32~MHz. Comparing the simulations with observations, we find that anisotropic scattering from an instantaneous emission point source can account for the observed time profiles, centroid locations, and source sizes of the fundamental component of type III radio bursts (generated where f_{pe} \approx 32~MHz). The best agreement with observations is achieved when the ratio of the perpendicular to the parallel component of the wave vector of anisotropic density turbulence is around 0.25. Harmonic emission sources observed at the same frequency (\sim 32~MHz, but generated where f_{pe} \approx 16~MHz) have apparent sizes comparable to those produced by the fundamental emission, but demonstrate a much slower temporal evolution. The simulations of radio-wave propagation make it possible to quantitatively explain the variations of apparent source sizes and positions at sub-second time-scales both for the fundamental and harmonic emissions, and can be used as a diagnostic tool for the plasma turbulence in the upper corona.

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arXiv2019

Anisotropic Radio-Wave Scattering and the Interpretation of Solar Radio Emission Observations

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 influenced 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.

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arXiv2019

Global Energetics of Solar Flares: VIII. The Low-Energy Cutoff

One of the key problems in solar flare physics is the determination of the low-energy cut-off; the value that determines the energy of nonthermal electrons and hence flare energetics. We discuss different approaches to determine the low-energy cut-off in the spectrum of accelerated electrons: (i) the total electron number model, (ii) the time-of-flight model (based on the equivalence of the time-of-flight and the collisional deflection time); (iii) the warm target model of Kontar et al.~(2015), and (iv) the model of the spectral cross-over between thermal and nonthermal components. We find that the first three models are consistent with a low-energy cutoff with a mean value of $\approx 10$ keV, while the cross-over model provides an upper limit for the low-energy cutoff with a mean value of $ \approx 21$ keV. Combining the first three models we find that the ratio of the nonthermal energy to the dissipated magnetic energy in solar flares has a mean value of $q_E=0.57\pm0.08$, which is consistent with an earlier study based on the simplified approximation of the warm target model alone ($q_E=0.51\pm0.17$). This study corroborates the self-consistency between three different low-energy cutoff models in the calculation of nonthermal flare energies.

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arXiv2019

The Role of Energy Diffusion in the Deposition of Energetic Electron Energy in Solar and Stellar Flares

During solar flares, a large fraction of the released magnetic energy is carried by energetic electrons that transfer and deposit energy in the Sun's atmosphere. Electron transport is often approximated by a cold thick-target model (CTTM), assuming that electron energy is much larger than the temperature of the ambient plasma, and electron energy evolution is modeled as a systematic loss. Using kinetic modeling of electrons, we re-evaluate the transport and deposition of flare energy. Using a full collisional warm-target model (WTM), we account for electron thermalization and for the properties of the ambient coronal plasma such as its number density, temperature and spatial extent. We show that the deposition of non-thermal electron energy in the lower atmosphere is highly dependent on the properties of the flaring coronal plasma. In general, thermalization and a reduced WTM energy loss rate leads to an increase of non-thermal energy transferred to the chromosphere, and the deposition of non-thermal energy at greater depths. The simulations show that energy is deposited in the lower atmosphere initially by high energy non-thermal electrons, and later by lower energy non-thermal electrons that partially or fully thermalize in the corona, over timescales of seconds, unaccounted for in previous studies. This delayed heating may act as a diagnostic of both the injected non-thermal electron distribution and the coronal plasma, vital for constraining flare energetics.

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