# Non-thermal Observations of a Flare Loop-top using IRIS Fe XXI: Implications
for Turbulence and Electron Acceleration

William Ashfield IV Bay Area Environmental Research Institute, NASA Research
Park, Moffett Field, CA 94035-0001, USA  Lockheed Martin Solar and
Astrophysics Laboratory, Building 203, 3251 Hanover Street, Palo Alto, CA
94304, USA  Vanessa Polito Lockheed Martin Solar and Astrophysics Laboratory,
Building 203, 3251 Hanover Street, Palo Alto, CA 94304, USA  Oregon State
University, Department of Physics, 301 Weniger Hall, Corvallis, 97331, OR, USA
Sijie Yu Center for Solar-Terrestrial Research, New Jersey Institute of
Technology, 323 M L King Jr Boulevard, Newark, NJ 07102-1982, USA  Hannah
Collier University of Applied Sciences and Arts Northwestern Switzerland,
Bahnhofstrasse 6, 5210 Windisch, Switzerland  ETH Zürich, Rämistrasse 101,
8092 Zürich Switzerland  Laura A. Hayes European Space Agency, ESTEC,
Keplerlaan 1 - 2201 AZ, Noordwijk, The Netherlands

(Accepted July 16th, 2024)

###### Abstract

The excess broadening of high-temperature spectral lines, long observed near
the tops of flare arcades, is widely considered to result from
magnetohydrodynamic (MHD) turbulence. According to different theories, plasma
turbulence is also believed to be a candidate mechanism for particle
acceleration during solar flares. However, the degree to which this broadening
is connected to the acceleration of non-thermal electrons remains largely
unexplored outside of recent work, and many observations have been limited by
limited spatial resolution and cadence. Using the Interface Region Imaging
Spectrometer (IRIS), we present spatially resolved observations of loop-top
broadenings using hot ($\approx 11$ MK) Fe xxi 1354.1 Å line emission at
$\approx 9$ s cadence during the 2022 March 30 X1.3 flare. We find non-thermal
velocities upwards of 65 km s-1 that decay linearly with time, indicating the
presence and subsequent dissipation of plasma turbulence. Moreover, the
initial Fe xxi signal was found to be co-spatial and co-temporal with
microwave emission measured by the Expanded Owens Valley Solar Array (EOVSA),
placing a population of non-thermal electrons in the same region as the loop-
top turbulence. Evidence of electron acceleration at this time is further
supported by hard X-ray measurements from the Spectrometer/Telescope for
Imaging X-rays (STIX) aboard Solar Orbiter. Using the decay of non-thermal
broadenings as a proxy for turbulent dissipation, we found the rate of energy
dissipation to be consistent with the power of non-thermal electrons deposited
into the chromosphere, suggesting a possible connection between turbulence and
electron acceleration.

††journal: ApJ

##  1 Introduction

According to the standard model of solar flares, magnetic free energy stored
in the corona is released through the reconfiguration of highly stressed field
lines via magnetic reconnection. This energy is ultimately converted to other
forms and transported throughout the solar atmosphere (Syrovatskii & Shmeleva,
1972; Craig & McClymont, 1976; Kopp & Pneuman, 1976), driving the phenomena
observed with these events. One such transport mechanism at the heart of the
standard model is the acceleration of non-thermal electrons from the
reconnection site to the lower atmosphere, which in turn allows for the
heating and ablation of chromospheric plasma upwards into newly reconnected
flare loops during the evaporation process. While indirect evidence for this
process is observed as the increases in soft X-ray (SXR) and extrema
ultraviolet (EUV) emission of flare loops Neupert (1968), direct evidence of
non-thermal electron deposition manifests in the form of hard X-ray emission
(HXR) at the location of flare footpoints in the chromosphere Brown (1971).

Although there is much evidence for non-thermal electron transport from the
corona to the lower atmosphere (Aschwanden et al., 1996; Holman et al., 2011),
the mechanism behind particle acceleration is still in question. Popular
theories regarding this process are linked to the dynamics of the reconnection
process, such as the formation of magnetic islands and plasmoids (Drake et
al., 2006), or termination shocks following the impact of reconnection
outflows at the base of the current sheet (Forbes, 1986; Chen et al., 2015).
These outflows, especially in the regions stemming from the flare arcade loop-
top (LT) and above, are also likely to generate magnetohydrodynamic (MHD)
turbulence given the large Reynolds number of coronal plasma, as has been seen
in several numerical studies (Ruan et al., 2018; Ye et al., 2020; Shen et al.,
2023a),in addition to observation (McKenzie, 2013; Cheng et al., 2018). The
cascade of energy to smaller scales in MHD turbulence can also energize
electrons on the kinetic scale, providing a stochastic transfer of energy to
electrons that would result in their acceleration (Larosa & Moore, 1993a;
Goldreich & Sridhar, 1995; Miller et al., 1997; Petrosian, 2012). Recent
microwave (MW) spectral imaging data taken with the Expanded Owens Valley
Solar Array (EOVSA; Gary et al., 2018) has brought about a paradigm shift in
high-energy flare physics, allowing for spatially and temporally resolved
measurements of non-thermal electrons and magnetic fields through
gyrosynchrotron emission of accelerated electrons in the flaring corona.
Although recent work using EOVSA has provided evidence for the acceleration
site location near the post-flare LTs (Chen et al., 2020a; Yu et al., 2020;
Fleishman et al., 2022), additional diagnostics are necessary to constrain the
acceleration mechanisms involved.

Given the high-temperature nature of flare plasma, spectroscopic observations
of ultraviolet (UV) emission lines — sensitive to such high-temperature plasma
— have shed much light on the properties of plasma dynamics during flares,
such as mass flows and electron densities (see reviews by Fletcher et al.
(2011) and Del Zanna & Mason (2018)). An observable of UV spectra that
continues to remain of particular interest to the flare community is the
degree to which measured line profiles broaden beyond their respective thermal
widths. Due to the fluctuations in the plasma velocity field, either from
large-scale bulk plasma flows or microscopic ion perturbations, the presence
of enhanced line broadening is widely believed to be a signature of MHD
turbulence (e.g. Milligan, 2011; Polito et al., 2019).

While the signatures of turbulence in solar flares remain a topic of active
research, investigations have started exploring the evolution of non-thermal
broadenings in the context of turbulent dissipation. Starting with Kontar et
al. (2017), measurements in non-thermal broadening were found to decay over
time, which was used to infer a rate of turbulent kinetic energy dissipation.
This energy was found to be consistent with the power of non-thermal elections
as measured by RHESSI, indicating a possible connection between MHD turbulence
and the coronal electron acceleration site. However, the study was limited to
values of non-thermal line width averaged over the total emission region using
the Extreme-ultraviolet Imaging Spectrometer (EIS). A follow-up study by
Stores et al. (2021) mapped the spatial distribution and evolution of non-
thermal velocities of the same event at a resolution of 4″, confirming that
turbulence as inferred from such velocities is not necessarily localized, but
can vary along the LT and loop-leg regions of a post flare arcade. The most
recent work by Shen et al. (2023a) used observations from the Interface Region
Imaging Spectrometer (IRIS; De Pontieu et al., 2014) to study the evolution of
non-thermal broadenings in the IRIS Fe xxi 1354.08 Å line and their subsequent
decay in the context of MHD turbulence. Using a three-dimensional MHD
simulation, they found turbulent bulk plasma flows in the current sheet and
flare LT regions were responsible for the non-thermal broadening of the Fe xxi
emission line. Despite this progress, the decay of non-thermal broadenings and
their subsequent connection to the acceleration site of non-thermal electrons
remains largely unexplored.

The present investigation undertakes a multi-instrument approach to study the
evolution of non-thermal signatures associated with the March 30th, 2022 X1.3
flare. Using observations with high spatial and spectral resolution measured
by IRIS, we find instances where the Fe xxi spectral line displays relatively
large non-thermal widths at the flare LT, with non-thermal velocities reaching
upwards of 65 km s-1. By tracking the evolution of these broadenings, we find
two periods of time where the non-thermal broadenings decrease linearly with
time, an evolution characteristic of MHD turbulent decay. Moreover, the
initial Fe xxi signal is co-spatial and co-temporal with gyrosynchrotron
microwave emission as measured with EOVSA. When combined with HXR measurements
taken from the Spectrometer/Telescope for Imaging X-rays (STIX) aboard Solar
Orbiter (SolO), we find this activity indicates a population of non-thermal
electrons along the loop in conjunction with electron deposition in the
chromosphere. As these non-thermal signatures exist in unison, we aim to
explore their possible relationships.

The paper is organized as follows. An overview of the flare and the
observational data used in this study is presented in Section 2, followed by
an analysis of the Fe xxi line profiles and their implications for the flare
LT dynamics presented in Section 3. Signatures of electron acceleration using
EOVSA and STIX in relation to the initial Fe xxi emission are analyzed in
Section 4. We discuss the implications of the decay of non-thermal broadenings
in terms of kinetic energy dissipation and its connection to the acceleration
site in Section 5. A brief summary of the results and conclusions is given in
Section 6.

##  2 Flare Overview

The March 30th 2022 event (SOL2022-03-30T17:23:06) was an X1.3 GOES class
eruptive flare in NOAA active region AR 12975, located on the NW quadrant of
the solar disk as viewed from Earth. From the GOES X-ray Sensor (XRS) 1-8 Å
filter light curve in Figure 1, the flare began at $\approx$17:20 UT, peaked
at 17:37:42 UT, and lasted roughly 1.5 hours. Throughout its lifetime, the
flare was well observed in EUV by Atmospheric Imaging Assembly aboard the
Solar Dynamics Observatory (SDO/AIA; Lemen et al., 2012), 4-150 keV X-rays by
SolO/STIX (Krucker et al., 2020), and 1-18 GHz MW by EOVSA (Gary et al.,
2018).

Figure 1: Light curve overview of the 2022 March 30 X1.3-class flare. GOES SXR
fluxes (blue and red lines) and normalized SJI 1330 Å counts (green) in the
top panel illustrate the evolution of the flare captured by IRIS. The two
enlarged panels on the bottom show the HXR (red) and SXR (blue) count rate
from SolO/STIX, and microwave flux densities in three frequency bands from
EOVSA, respectively. The vertical dashed lines indicate the start time of the
initial loop-top Fe xxi emission, the peak time of the second phase, and the
first pulse in the third phase, respectively, and correspond to the three
times in Figure 7.

Beginning in the impulsive phase, STIX observed high-energy signatures in
three discrete HXR emission pulsations, or phases (Collier et al., 2023).
Figure 1 shows the HXR emission count rate over the 32-76 keV energy bin at a
0.5 s cadence. Given SolO’s near-perihelion location at 0.33 AU, reference
times have been adjusted to Earth’s reference time at UT. Likewise, full-disk
integrated MW dynamic spectra taken with EOVSA show three distinct intensity
phases. The bottom panel of Figure 1 plots MW flux in three GHz bins covering
the effective broadband range of EOVSA, each correlating with the phases and
individual bursts seen in the 32-76 keV STIX channels. As gyrosynchrotron
radiation from coronal electrons dominates EOVSA MW emission, the degree to
which the MWs phases correlate with the HXR emission emphasizes its use as a
valuable diagnostic for electron acceleration.The following work focuses on
times occurring over the second and third energy phases, which coincide with
MW emissions occurring in proximity to the IRIS SG slit. A more in-depth
investigation of HXR and MW pulsations during the first phase can be found in
recent work by Collier et al. (2024).

Observations taken with IRIS (De Pontieu et al., 2014, 2021) captured most of
the flare’s evolution in the UV, with the observing run ending at 17:54:31
(see the green curve in Figure 1). Running in a sit-and-stare mode (OBSID
3660259102), the spacecraft captured slit-jaw images (SJI) at a cadence of
28.1 seconds in the 1330 Å channel. A flare line list spectral readout
including the O i window (1351.3 - 1356.46 Å) had a variable exposure time
ranging from 0.8-8.0 seconds and a cadence of 3.9-14.7 s. The spatial
resolution of the SJI and spectrograph (SG) slit was 0.166″ per pixel, with a
0.33″ wide slit. The FUV1 channel (1331.7–1358.4) was binned spectrally by two
onboard, resulting in a resolution of 26 mÅ.

The IRIS field of view (FOV) was favorably positioned over the post-flare loop
arcade during its observing run, as shown in the right panels in Figure 2.
Here, the arcade is given by images of AIA 131 Å and illustrates the
morphology of hot coronal plasma over time. Because the event was a so-called
two-ribbon flare, with the parallel ribbons roughly running in the east-west
direction, the location of the slit allowed for complete spectral measurements
of the southern ribbon and the westward edge of the northern ribbon. Moreover,
the slit position aids in the identification of the LT emission, as spectra
emanating between the two ribbons could belong to arcade plasma. The following
section explores the behavior of Fe xxi spectra in this region.

Figure 2: AIA 131 Å images in inverse logarithmic greyscale (left), along with
corresponding IRIS SJI 1330 Å images (right), showing the evolution of the
flare arcade at two times. The red boxes and dashed lines show the SJI FOV and
slit position, respectively.EUV knots correspond to the brightest (most-black)
emission along the LT, with an example highlighted by the blue arrow. The
multi-color line gives the peak Fe xxi intensity measured along the IRIS SG
slit.

##  3 Loop-top Fe XXI Emission

The IRIS Fe xxi 1354.1 Å emission line, formed at temperatures of
$\approx$11.5 MK, allows for spectrographic observations of the flaring
corona. Like many optically thin spectra, Fe xxi is frequently observed to
have a Gaussian line profile, given an isothermal Maxwellian distribution of
plasma ions (e.g. Graham & Cauzzi, 2015; Polito et al., 2019). Following an
initial verification of the line profile shapes, we perform Gaussian fits to
the Fe xxi spectra to infer plasma motion diagnostics stemming from the arcade
LT.

Prior to fitting, level 2 raster data were processed starting at 17:24:31 UT,
preceding the start of the impulsive phase, and lasting until the end of the
observation run 30 minutes later. The lower IRIS SG fiducial mark, visible as
dark bands on SG detector images, overlapped regions of interest in our
observations and was excluded by ignoring pixels 142-144 (314.4″-314.9″)
throughout our analysis to ensure no related intensity artifacts. The SG data
was further normalized by exposure time to remove any effects of variable
exposure time and cleaned via the de-spiking procedure iris_prep_despike in
SolarSoft to remove bad pixels (Freeland & Handy, 1998). Lastly, because the
Fe xxi signal was relatively weak throughout the observation, an additional
spectral binning of two was applied to the SG data to reduce noise for the
fitting process, resulting in a 52 mÅ spectral resolution.

Although LT emission is the focus of this work, we aim to fit Fe xxi spectra
along the entire SG slit, including emission from the flare ribbons. Previous
observations have shown that Fe xxi ribbon emission is blended with other
chromospheric and photospheric lines in the O i channel, including the
predominant the C i 1354.3 Å line (Polito et al., 2015, 2016). We therefore
employed the iris_auto_fit multi-Gaussian routine111Further details can be
found at https://www.pyoung.org/quick_guides/iris_auto_fit.html in SolarSoft
to account for the presence of these lines. Prior to the routine, weak signals
with wavelength-integrated intensity $\pm$0.5Å of the Fe xxi line below a
threshold of 50 DN Å s-1 were ignored from the fit. Likewise, the fit was
discarded from the results if the Gaussian amplitude, or peak intensity, was
less than twice the measured background intensity at a given time.

Figure 3: Time-distance stack plots of Fe xxi spectral line parameters and AIA
emission in three channels along the IRIS SG slit. The top three panels show
intensity (a), Doppler velocity (b), and FWHM line width (c) as inferred from
Gaussian fits to Fe xxi . Dashed and dashed-dotted lines give the northward
and southward Fe xxi emission propagation speed away from the LT,
respectively.The orange and cyan lines in (a) and (c), respectively, outline
the pixels used in Figure 4. The white dashed box (c) outlines the time and
location of the initial LT Fe xxi signal. Times of high CCD noise due to
increased cosmic ray exposure are masked in red. Overlaid contours outline the
Fe xxi intensity at [4,9,18] DN s-1.

Figure 3 shows time-distance stack plots of the resulting plasma diagnostics
inferred using Fe xxi spectral line parameters along the IRIS SG slit. The top
three panels (a-c) show peak intensity, Doppler velocity, and non-thermal line
width, respectively. Doppler velocities were calculated using the differences
between Gaussian centroid positions and the rest wavelength, taken here to be
1354.08 Å following several studies of this line (Sandlin et al., 1986; Polito
et al., 2015). Non-thermal widths were calculated using the FWHM of the
Gaussian fits, where FWHM = 2$\sqrt{2\ln 2}$ $\sigma$ for Gaussian line width
$\sigma$. By decomposing the line width into thermal, non-thermal, and
instrumental components, the FWHM can be expressed as

$\mathrm{FWHM}=\sqrt{4\ln
2\Bigg{(}\frac{\lambda_{0}}{c}\Bigg{)}^{2}\Big{(}v_{\mathrm{th}}^{2}+v_{\mathrm{nth}}^{2}\Big{)}+\mathrm{FWHM}_{\mathrm{IRIS}}^{2}},$
(1)

where $v_{\mathrm{nth}}$ is the non-thermal broadening expressed as a
velocity. The thermal velocity $v_{\mathrm{th}}$ is given by the Doppler
broadening of the line, $\sqrt{2k_{b}T_{\mathrm{Fe}}/m_{i}}$, for ion mass
$m_{i}$=56 and formation temperature $T_{\mathrm{Fe}}$. Here, we take
Log${}_{10}\,T_{\mathrm{Fe}}$[K] = 7.06, the temperature at the contribution
function maximum calculated using Chianti v10 (Del Zanna et al., 2021), which
gives a thermal width of 0.439 Å = 58.4 km s-1. Broadening due to instrumental
effects is given by $\mathrm{FWHM}_{\mathrm{IRIS}}$ = 26 mÅ. The flight time
of IRIS through the Southern Atlantic Anomaly (SAA) during the observation
run, resulting in increased cosmic ray exposure and SG noise, is highlighted
in red.

Fe xxi emission along the slit can be considered to evolve from two separate
regions: the LT and the ribbons. The southern ribbon, starting at $y\approx
295$″ , is outlined by the strong Doppler velocity blueshifts in Figure 3(b).
These large upflows, reaching speeds upwards of 130 km s-1 provide clear
evidence of chromospheric evaporation. While the northern ribbon is not as
clearly defined here, chromospheric lines in the O i detector images show its
location starting at $y\approx 317$″ and spreading northward over time (Figure
5). A more detailed ribbon analysis of this flare can be found in recent work
by Xu et al. (2023) and Wang et al. (2023a).

We identify the LT emission by the distinct increase in Fe xxi intensity at
$y\approx 311$″, which brightens almost in tandem with the ribbon emission. As
mentioned above, emission in the region between the ribbons in a two-ribbon
flare could belong to the post-flare arcade loops. This idea can be more
readily seen by the location of the Fe xxi intensity along the slit
illustrated in Figure 2, where the initial signal of the emission does not
emanate from either ribbon. Moreover, the LT Fe xxi profiles themselves
support a coronal source by lacking the blend photospheric lines that are
typical of ribbon emission. Although this notion constrains the emission to
the coronal plasma, a more rigorous definition of LT emission is provided by
comparing Fe xxi intensity to AIA 131 Å emission. As seen inFigure 2, the
morphology of AIA 131 Å is characterized by bright, localized LT structures,
commonly referred to as EUV knots. These knots have long been observed along
the arcades of post-flare loops (Widing & Cheng, 1974; Acton et al., 1992),
and while their formation mechanism remains unclear (e.g. Patsourakos et al.,
2004; Reeves et al., 2007), they are widely considered to exist at the apex of
such loops.

To study the connection between knots and Fe xxi emission in this study,
slices along AIA images in three wavelengths (94 Å,131 Å, and 193 Å) were
taken over time, with the artificial slit interpolated in space to match the
IRIS slit position at AIA observation times. We note that all AIA images used
in this work were first prepped using routines found in the aiapy Python
package (Barnes et al., 2020), filtered to select only non-saturated data, and
deconvolved using the instrumental PSF. The resulting time-distance stack
plots are shown in Figure 3(d)-(f), with the loop-top knots corresponding to
the regions of peak intensity. Notably, the knots in each channel brighten
sequentially, hinting at a cooling plasma provided the characteristic
formation temperatures of the three AIA channels — Log${}_{10}\,T$ [K] =
7.3,7.0,6.8 for AIA 193 Å, 131 Å, and 94 Å, respectively — during flares
(O’Dwyer et al., 2010). Focusing on the 131 Å channel in Figure 3(e), we found
the evolution to neatly match that of the Fe xxi peak intensity (grey
contours). While this result is not surprising given that AIA 131 Å is
dominated by Fe xxi 128.75 Å during flares (O’Dwyer et al., 2010), the
similarity between the two emission sources along the SG slit shows that the
IRIS Fe xxi emission is also capturing the evolution of the AIA LT knot,
thereby acting as a spectroscopic proxy by providing plasma diagnostics for
the AIA 131 Å channel.

Figure 4: Time series of peak intensities (top) and non-thermal velocities
(bottom) from SG slit pixels corresponding to the region [312.9″-319.9″] in
Figure 3 (a) and (c), respectively. Pixels are aligned in time according to
their respective activation time. Black curves signify the average values in
each plot. The bottom panel shows the best linear fit (red-dashed) when
$v_{\mathrm{nth}}$ is decreasing.

Several aspects of the LT dynamics inferred from Fe xxi are worth noting.
First, following a period of stationary emission, the signal begins to spread
outward along the slit at nearly constant velocities, as illustrated in Figure
3(a). This movement implies the top-down motion of hot flare plasma from the
LT towards the ribbons, and in particular, the evaporation signatures from the
southern ribbon appear to connect with the southward moving LT front much
lower down at $y\approx 302$″. Second, the entire LT structure is weakly
redshifted. Velocities between 304.1″- 319.9″range from 0.1-15.5 km s-1, with
average value of 7.8 km s-1. Lastly, the bright LT knots are preceded by a
period of non-thermal line broadening, as shown in Figure 3(c). In particular,
there exists an apparent gradient in $v_{\mathrm{nth}}$ over time, beginning
as the LT emission starts to spread along the slit. This gradient is more
clearly seen in Figure 4, where $v_{\mathrm{nth}}$ and peak intensities from
each pixel in the region [312.9″-319.9″] are aligned according to their
respective activation time (e.g. when the intensity first appears). Averaging
over these pixels, we find the gradient is well described by a linear fit,
with a decay rate of -0.092$\pm$0.006 km s-2, and has an inverse relationship
with the increase in peak intensity observed in the same period. This decay in
$v_{\mathrm{nth}}$ also complements earlier observations made by (Young et
al., 2015) regarding a two-ribbon flare, where they did not detect any
significant line broadening along the loops at the points where the IRIS
raster and AIA 131 Å knots overlapped. Comparing the widths in their Figure 12
to the non-thermal velocities in our Figure 3(c), we see that the broadening
at the peak time and location of the LT knots are comparable. Moreover, they
found the non-thermal velocities of the Fe xxi line to decrease over time,
falling from 42.8 to 26.3 km s-1 over the course of 6 minutes by taking the
median value of each 8-step raster at a cadence of 75 s. By using a sit-and-
stare observation, this work allows for a more comprehensive analysis of this
non-thermal decay.

Large values of non-thermal velocities are also seen as the LT Fe xxi emission
becomes visible. The initial signal also appears to precede the formation of
the EUV knot, which first manifests in the AIA 193 Å channel (Figure 3(d)) at
$\approx$17:37:00. As this signal is separate from the knot evolution
described above, a closer look is warranted to understand the nature of the LT
emission.

Figure 5: Examples of the dynamic binning routine. IRIS detector images of the
O i channel in inverse greyscale are shown on the left. Grey dashed lines give
the rest wavelength of Fe xxi 1354.08 Å, and blue boxes outline the applied
region. The red box outlines the selected signal, with the height and width
denoting the spatially binned pixels and the resulting FWHM of the Gaussian
fit to the binned spectra, respectively. The binned spectra (black) and
Gaussian fits (red dashed) are shown on the right, overtop the selected
individual spectra.  Figure 6: Time series of Fe xxi spectral line parameters
from the dynamic binning routine over the initial signal. Lines show peak
intensity (blue), Doppler velocity (green), and non-thermal velocity (orange).
The red dashed line shows the linear best fit to the non-thermal velocity.
Times of increased cosmic ray exposure are masked in red.

###  3.1 Initial Signal

Although the LT Fe xxi emission in Figure 3 starts at around 17:34:30, closer
inspection of O i detector images shows the Fe xxi signal appearing at
17:33:25. To fix this discrepancy, due to the signal threshold selection
criteria in the multi-Gaussian fitting routine, we performed a second fitting
routine that automatically binned the spectra in space according to the
signal-to-noise ratio (SNR) of the Fe xxi line. Two examplesof this routine,
henceforth the dynamic binning routine, can be found in Figure 5. The routine
is applied to a region in detector image space corresponding to the LT
emission along the slit (306.6″-314.2″) and spanning $\pm 0.75$ of Fe xxi line
center (blue box). Within that region, pixels with signals greater than
0.5$\sigma$ above the region are flagged to identify the Fe xxi emission
(height of the red box) and are subsequently binned to create a single
spectrum (black curve) that is then fit with a Gaussian (red dashed curve).
The FWHM of the Gaussian fit determines the width of the red box. We note that
a single Gaussian was sufficient here, as no chromospheric line blends were
detected in the Fe xxi spectra. By automatically binning the spectra in this
way, we increase the SNR without including superfluous signals and mitigate
the loss of spatial resolution.

The dynamic binning routine was applied on the SG data at each time during the
initial signal from 17:33:25-17:36:14. Figure 6 shows the time series of the
Fe xxi spectral line fit parameters. The LT emission begins with a relatively
high non-thermal velocity at 65.7 km s-1, which decreases steadily to 17.4 km
s-1 in less than three minutes. Like the line width decay preceding the EUV
knots (Figure 2), there exists an inverse trend between $v_{\mathrm{nth}}$ and
peak intensity. The non-thermal velocities here also decay linearly with time
but at a faster decay rate of -0.21$\pm$0.02 km s-2. The times of increased
cosmic ray exposure were excluded from the fit to limit the effects of
background noise on the downward trend. In comparison to other investigations
into the decay of LT non-thermal broadening in flares (e.g., Stores et al.,
2021; Shen et al., 2023a), the time scales on which we observe the decay —
either here during the initial signal or that which precedes the brightest Fe
xxi emission in Figure 4 — are much shorter, on the order of minutes compared
to several tens of minutes. The duration here also results in a rate of decay
that is nearly an order of magnitude faster than those measured by Stores et
al. (2021). Moreover, the maximum non-thermal velocities observed in this work
are also relatively lower than these other works as well, which reach values
of 100 km s-1 or more.

In addition to the Gaussian fits, the dynamic binning routine also provides a
measure of the LT emission’s size and location during the initial signal. The
size — defined by the number of pixels selected, or the height of the red box
in Figure 5 — was found to be roughly constant, with an average size of 3.1″.
The box’s center location also deviated slightly over time, traveling
northward from 310.1″to 311.1″. We note that although our routine bins this
region to increase the SNR, the signal of the LT Fe xxi emission in the O i
detector images (left panels in Figure 5) is defined by a homogeneous
structure that is well approximated by the red boxes. The initial LT emission
is therefore well-resolved in our observations, as the 3.1″ size of this
structure is well over the IRIS SG spatial resolution of 0.166″. Again, this
resolution is in contrast to previous investigations into the decay of non-
thermal broadenings in flares using Hinode/EIS (e.g. Kontar et al., 2017;
Stores et al., 2021), where the resolution, albeit sufficient to locate
different regions of excess line widths along the flare loops, could have been
affected by averaging over variations of macroscopic plasma dynamics within
these individual regions.

The broadening of spectral lines beyond their respective thermal values can
have several implications for the plasma dynamics of the emitting region. If
we assume the line broadening is due to thermal effects alone, then the large
widths in this work would indicate plasma temperatures beyond the expected
Log${}_{10}\,T_{\mathrm{Fe}}$[K] = 7.06 thermal formation temperature. For
example, the highest value of $v_{\mathrm{nth}}$ = 66 km s-1 is equivalent to
a Doppler broadened Fe xxi line formed at Log${}_{10}\,T$[K] = 7.41. However,
this assumption begs whether it is possible for Fe xxi 1354.08 Å to emit at
such high temperatures. During flares, rapid heating of tenuous coronal plasma
could lead to under-ionized conditions, as the ions in the plasma — especially
highly charged Fe — will not have time to adjust to equilibrium (i.e., non-
equilibrium ionization (NEI) Shen et al., 2013). Under-ionization shifts the
distribution of charge states, or ionization fractions, amongst different
species, giving a bias towards lower plasma temperatures that could result in
an underestimation of the actual plasma temperature. Recent work by Shen et
al. (2023b) used three-dimensional MHD simulations to study the effects of NEI
on Fe ions during flares, where they found instances of plasma emission
dominated by Fe xxi but with true temperatures of more than
Log${}_{10}\,T$[K]=7.25 — a difference of over 40%. While a scenario such as
this could help explain some of the large non-thermal broadenings observed in
this work, it is unclear whether NEI would be enough to account for such large
temperatures. For instance, the 40% temperature discrepancy in Shen et al.
(2023b) was taken behind a Petschek-type reconnection shock in the current
sheet with ambient plasma densities of $5\times 10^{8}$cm-3. As our event is
viewed on-disk, emission contributions from the current sheet are likely to be
washed out by the denser, underlying arcade plasma. Moreover, the decay in
excess line broadening, in either the initial signal or during the time
preceding the brightest LT emission, suggests that the plasma is quickly
cooling. This scenario would be more consistent with an over-ionized plasma,
in which temperatures inferred from dominant Fe species would be overestimated
with respect to their equilibrium plasma temperatures (i.e., lower than 11.5
MK in the case of Fe xxi ). The location of over-ionized plasma in the Shen et
al. (2023b) simulations at the base of the current sheet is also more
congruent with the LT emission observed in this work.

Figure 7: Spatially resolved MW spectra at various locations in the flaring
loops at three selected times. Top panels (a)-(c) show inverse greyscale AIA
1600 Å maps overlaid with 70% contours from the EOVSA MW map (3.5-18 GHz) at
17:33:22, 17:33:48, and 17:35:15 UT. Grey contours outline 75% AIA 1600 Å
flare ribbon intensity. Colored boxes in the top panels correspond to regions
selected for spectral analysis, as shown in panels (d-f), with no change in
box location between (a) and (b). The filled circles in the upper right corner
of panel (a) represent the FWHM size of the restoring beams at the respective
frequencies. Middle panels (d)-(f) display the brightness temperature (TB)
spectra at these times, color-coded to match the boxes. The colored curves in
these spectra represent the best-fit models based on homogeneous
gyrosynchrotron emissions from non-thermal electrons following a single power-
law distribution, with each curve’s color matching that of the corresponding
spectra. Open circles in the plots indicate data points excluded for the
spectral fitting. Bottom panels (g)-(i) show physical parameter ranges derived
from the best-fit homogeneous gyrosynchrotron emission model fits, including
magnetic field strength $B$, non-thermal power-law spectral index
$\delta_{\mathrm{MW}}$, and non-thermal electron density $n_{\mathrm{nth}}$.

If the LT plasma is assumed to be at the peak formation temperature of Fe xxi
, then the excess broadening must instead arise from non-thermal plasma
fluctuations, ranging from scales on the order of the emitting ion to large
scales associated with bulk mass flows. One popular mechanism proposed for
these observations during flares has been the superposition of Doppler-shifted
emission from multiple bulk plasma flows. A recent study by Polito et al.
(2019), however, used a multi-threaded 1D flare loop model to find that such a
superposition results in asymmetric line profiles not commonly observed in Fe
xxi during flares. The symmetric line profiles observed here at the resolution
of individual IRIS pixels (i.e., Figure 5) also substantiate this claim. Other
mechanisms, such as pressure broadening and optical depth effects, are
unlikely to contribute to excess broadening in optically thin UV lines
(Milligan, 2011). The most likely explanation for the excess broadening,
therefore, is the superposition of Doppler-shifted emission from unresolved
turbulence — a consensus reached by several studies (e.g. Antonucci et al.,
1984; Polito et al., 2019; Shen et al., 2023a). Moreover, the decay of
$v_{\mathrm{nth}}$ is also characteristic of MHD turbulence, where the energy
cascade from large to small scales results in the dissipation of the turbulent
energy contained in the plasma (Kontar et al., 2017; Stores et al., 2021). As
we will show in the following sections, it is possible that this energy is
being transferred into the acceleration of non-thermal electrons.

##  4 Electron Acceleration Signatures

###  4.1 Microwave Imaging Spectroscopy

Full-disk MW images of the flare were captured by EOVSA in 1-18 GHz. Each
image used 451 frequency channels distributed across 50 spectral windows with
equally-spaced bandwidths of 325 MHz, and was calibrated using standard
procedures as described in Chen et al. (2020a). Due to a calibration
discrepancy in the lowest-frequency spectral windows, images were produced
from 45 windows ranging from 3.5-18 GHz. Final images were obtained after
subtracting the background between the second and third MW phases at 17:34:50
- 17:35:00 UT. Image reconstruction was accomplished using the CLEAN algorithm
with a frequency-dependent circular beam of size
$60\arcsec/\nu_{\mathrm{GHz}}$.

Preliminary analysis of MW images during the period of initial LT Fe xxi
emission found instances where the collection of compact, multi-GHz frequency
sources overlapped the IRIS SG slit. Three images were selected for further
analysis, corresponding to the start of the initial LT Fe xxi emission, the
peak time of the second phase, and the first pulse in the third phase,
respectively, and are shown in Figure 7(a)-(c). The selected times are also
indicated in Figure 1. We see during the first two images that lower-frequency
MW sources ($\lessapprox 6$ GHz) are co-spatial with the IRIS slit. Notably,
the edge of the MW source in the lowest-frequency spectral window reaches the
region of LT Fe xxi emission as it first begins at time 17:33:22 (blue box in
panels (a) and (b)). Over time, the MW sources move southwest into and then
completely off the slit during the duration of the initial Fe xxi signal.

Beyond the spatiotemporal correlation between the MW and Fe xxi emission, we
highlight two points regarding the morphology of the MW sources. First, the
apparent southwestward movement of the MW sources along the arcade is
continuous between images (a) and (b) in Figure 7, which belong to the second
pulsation phase, while the transition between (b) and (c) is discontinuous,
following a period of decreased MW emission before the start of the third
phase. This behavior is consistent with the time-distance stack plots in
Figure 3, and indicates a spatial variance between the MW pulsations. Second,
there exists a clear spatial organization between the GHz spectral windows.
Previous investigations using EOVSA MW images — namely those from the 2017
September 10 X8.2 flare (e.g., Gary et al., 2018; Fleishman et al., 2020; Yu
et al., 2020) — have shown that different GHz spectral windows can correspond
to different regions of the flaring arcade, ranging from the lower regions of
the flare loop-legs to high in the reconnection current sheet. In our case,
the on-disk orientation complicates the interpretation of the MW sources in
relation to the flare structure (i.e., loop-legs vs current sheet). Here we
see that the higher frequency emission shows a distinct correlation with the
intense emission regions of the underlying northern ribbon, shown by the gray
75% AIA 1600 Å contours. Moving downwards in frequency, the MW sources reach
further southward, seemingly into the LT region of the arcade. A natural
interpretation of this organization follows from the standard flare model,
where MW sources are tracing out the northern half of a post-flare loop,
outlined by the higher frequencies emanating near the ribbon and the lower
frequencies originating from higher up in the corona, possibly from the LT or
cusp regions.

To assist with this interpretation, we analyzed spatially-resolved MW
brightness temperature spectra $T_{B}$ derived from different locations along
the MW sources. Figure 7 (d)-(f) shows the TB spectra (closed and open
circles) corresponding to the colored boxes in panels (a)-(c), respectively,
with box locations chosen to roughly map out our assumed orientation of the MW
sources along a post-flare arcade loop. Considering the beam size may be
larger than the boxes drawn, the error of the spectra created for each box was
estimated using the image RMS across different frequencies coupled with a
systematic error — 10% of the maximum brightness temperature (TB) of each
frequency — to accommodate the larger beam sizes at lower GHz. Each of the
eight spectra sampled is consistent with gyrosynchrotron radiation from a
population of non-thermal electrons with a power-law energy distribution (Dulk
& Marsh, 1982; Chen et al., 2020a), exhibiting both positive and negative
slopes on the lower and high-end frequencies, respectively. A forward fit to
the spectra using the homogeneous gyrosynchrotron emission model described in
Chen et al. (2020b) and Fleishman et al. (2020) was performed to derive the
physical parameters of the non-thermal emission. This routine employs the fast
gyrosynchrotron codes outlined in Fleishman & Kuznetsov (2010) and depends on
free parameters such as magnetic field strength $B$, non-thermal power-law
spectral index $\delta_{\mathrm{MW}}$, thermal $n_{\mathrm{th}}$ and non-
thermal electron densities $n_{\mathrm{nth}}$ above $E_{\mathrm{min}}$=10 keV.
The best fits to these spectra are shown by the solid lines in Figure
7(d)-(f), where data points having $T_{B}<1$[MK] or an SNR less than than 1.8
were excluded from the fit (open circles).

Trends in the inferred gyrosynchrotron fit parameters are visualized in the
bottom panels of Figure 7. Here, the error bars designate the range of
accepted values from the fitting routine spanning plus/minus the standard
deviation of each model parameter. Starting with the magnetic field strengths,
we find that $B$ is lower in Box 1 and increases sequentially to Box 3,
supporting the interpretation that Box 1 represents the LT region and and
Boxes 2 and 3 sequentially decrease in height along the flare loop. Values for
the power-law spectral index of the non-thermal electron energy distribution
$\delta_{\mathrm{MW}}$ are also consistent with those expected for
gyrosynchrotron emission Dulk & Marsh (1982). The non-thermal electron density
$n_{\mathrm{nth}}$ is also highest in the Box 1, reaching values upwards of
$10^{10}$ cm-3. Using these values and in addition to the thermal electron
density from the GS model, we found the percentage of non-thermal-to-total
electron population to be notable, with Box 1 ranging from 15-35%. This result
not only supports the interpretation of the MW sources as gyrosynchrotron
emission from non-thermal electrons, but also suggests that the LT is a site
of efficient non-thermal electron acceleration during the flare.

###  4.2 Hard X-ray Imaging Spectroscopy

Additional evidence for electron acceleration comes from HXR data collected by
the STIX instrument aboard SolO. A Fourier-imaging spectroscopy instrument,
STIX measures X-ray emission in the 4-150 keV range, and is capable of imaging
the Sun with a spatial resolution of $\approx 10$″. Figure 8(a) shows SXR
(yellow) and HXR (red) contours at [20,40,60]% peak emission integrated for 48
s over the first instance of Fe xxi LT emission from 17:33:14-17:34:06 UT in
the Earth’s time frame (but from the SolO FOV), with the images reconstructed
using the MEM_GE algorithm (Massa et al., 2020). The X-ray contours are
overlaid on the corresponding AIA 1600Å image reprojected to the SolO
observing frame, with the contours shifted manually by (-13, 45)″ to account
for inaccuracies in the STIX aspect system, as was performed in Collier et al.
(2024). We find the HXR emission correlates with the intense UV ribbon
emission at the southern ribbon, with the northern ribbon showing no
significant HXR emission. However, we note the limited dynamic range of STIX
($\sim 10:1$) may be overpowering any HXR emission in the northern ribbon. The
SolO spacecraft location with respect to Earth at the time of the event is
shown in Figure 8(b) in Heliographic Stonyhurst coordinates. At the time of
this observation, SolO was close to its perihelion with a heliocentric
distance of 0.33 AU.

Figure 8: (a) STIX X-ray images integrated from 17:33:14-17:34:06 UT from
point of view of SolO, corresponding to the initial LT Fe xxi emission period.
HXR (red) and SXR (yellow) contours at [20,40,60]% peak emission are overlaid
on the corresponding reprojected AIA 1600 Å image. Orange contours outline 75%
AIA 1600 Å flare ribbon intensity, and match those shown in Figure 7. (b) 2022
March 03 Solar Orbiter spacecraft location with respect to Earth in
Heliographic Stonyhurst coordinate orientation.

The correlation between the HXR and UV ribbon emission is consistent with the
model of electron energy transport in flares, where non-thermal electrons
accelerated in the corona impact the chromosphere, depositing their energy and
producing bremsstrahlung radiation in the form of HXRs (Brown, 1971). To study
the extent of electron deposition in the chromosphere, we performed an
analysis of the HXR spectra over the time surrounding the second high-energy
phase, also corresponding to the time of the initial LT Fe xxi signal. HXR
spectra were fit using the SolarSoft OSPEX routine using a combination of
thermal and cold thick-target non-thermal functions (f_vth and f_thick2,
respectively) at 4 s intervals over the period matching the second high-energy
phase from time 17:32:43-17:34:47 UT. The resulting non-thermal electron flux,
$F_{e}$ [$e^{-}$ s-1], low energy cutoff, $E_{c}$ [keV], and electron spectral
index, $\delta$, of the single-power, thick-target component are shown in
Figure 9. Here we see a single, steady evolution of the spectral index from
soft to hard and back throughout the second phase, which is indicative of a
single energy pulsation, or electron acceleration event (in contrast to the
many soft-hard-soft pulsations seen in the first phase (Collier et al.,
2024)). Using the best-fit parameters, we can then estimate the power of non-
thermal electrons — those with energy above $E_{c}$ — deposited in the
chromosphere, $P_{\mathrm{nth}}$, by

$P_{\mathrm{nth}}(E\geq
E_{c})=k_{E}\;F_{e}\;E_{c}\;\frac{\delta-1}{\delta-2},$ (2)

where $k_{E}$ is the energy conversion factor from keV to erg (Kontar et al.,
2019). However, the low energy cutoff measured here is poorly constrained,
which adds significant uncertainty to the power estimate. To mitigate this
error, we choose a fixed energy reference $E_{r}$=30 keV above the mean
$\bar{E_{c}}$=26 keV and calculate the non-thermal electron power, integrating
from $E_{r}$ to $\infty$. To do this, we use the f_thick2_vnorm thick-target
function in OSPEX. As a result, Equation 3 becomes

$P_{\mathrm{nth}}(E\geq E_{r})=\frac{k_{E}\;A\;E_{r}^{2}}{\delta-2},$ (3)

where $A$ is the electron flux [$e^{-}$ s-1 $\mathrm{keV}^{-1}$] at the
reference energy $E_{r}$ and the other parameters are the same as before.
While this method underestimates $P_{\mathrm{nth}}$, it provides a more
reliable estimate of the power and its time evolution. The resulting power is
shown in the bottom panel of Figure 9, where the trend in $P_{\mathrm{nth}}$
roughly tracks that of the HXR count rate. The peak of the power also
corresponds well with the start time of the initial LT Fe xxi emission (dashed
line) — a connection we explore further in the following section.

Figure 9: HXR overview of the second phase. Count rate in the STIX 32-75 keV
channel and non-thermal electron flux $F_{e}$ are plotted in the top panel.
The middle panel shows the low energy cutoff ($E_{c}$) and electron spectral
index ($\delta$). Non-thermal electron power is shown in the bottom panel, as
calculated by Equation (3) for energies over $E_{r}$=30 keV. Values for
$F_{e}$, $E_{c}$, and $\delta$ follow from best fits to the HXR spectra
integrated over 4 s second intervals. The vertical dashed lines indicate the
start time of the initial Fe xxi emission.

##  5 Turbulent energy transfer

The analysis of non-thermal signatures in this work has revealed excess line-
broadening in the Fe xxi line, gyrosynchrotron MW emission, and the deposition
of high-energy electrons into the chromosphere — all of which have been shown
to occur concurrently and in close spatial proximity. Together, these
signatures are consistent with the acceleration and transport of non-thermal
electrons in the LT plasma via a stochastic acceleration mechanism (Larosa &
Moore, 1993b; Petrosian, 2012). Here we return to the initial non-thermal
broadening decay measured in Section 3.1 to extrapolate on its significance to
turbulent dissipation and kinetic energy transfer in light of the associated
electron acceleration signatures.

Following the analysis presented in Kontar et al. (2017) and Stores et al.
(2021), a decrease in excess spectral line broadening can be used to estimate
the dissipation of turbulent kinetic energy $K$ in a plasma. Provided a
measurement of the non-thermal velocity $v_{\mathrm{nth}}$, we calculate $K$
by:

$K=\frac{3}{2}\;m_{i}\;v_{\mathrm{nth}}^{2}\;n_{p}\;V,$ (4)

where $m_{i}=1.3\,m_{p}$ is the mean ion mass given coronal abundances
(Reames, 2014), $n_{p}$ is the proton number density, and $V$ is the plasma
volume of the emitting region.

While $v_{\mathrm{nth}}$ is directly measured, assumptions must be made to
estimate $n_{p}$ and $V$ in order to calculate the dissipation of kinetic
energy. Using the size of the low-GHz MW sources as a proxy for the LT plasma
volume at the time of the initial Fe xxi signal (Figure 7(a)), we estimated
the volume of the LT plasma to be $V\approx 3\times 10^{27}$ cm3 assuming a
cylindrical source with a radius and length of 6 Mm and 25 Mm, respectively.
We note that the apparent size of the MW sources is biased by the beam size
used in their reconstruction (Figure 7(a)), likely making our rough estimate
of the coronal volume the upper limit of the actual MW source size.
Nonetheless, the size of the high-frequency MW source from the northern ribbon
footprint agrees well with the AIA 1600 Å ($\approx 5$″, or 3 Mm) emission
there, thereby adding support to our estimation technique. The coronal volume
of the SXR source ($\approx 4\times 10^{27}$ cm3 (Figure 8(a)) also agrees
with our MW source estimate when using the 50% contour level. To calculate the
proton number density, we assume $n_{p}=n_{e}$ following the approach in
Kontar et al. (2017), and then use the differential emission measure (DEM)
diagnostic to estimate the electron number density $n_{e}$ in the LT plasma.
The details of this analysis are described below.

###  5.1 DEM Density Diagnostic

To understand the evolution of electron number density over time, DEM maps
were first created using AIA images in five passbands (94, 131, 193, 211, and
335Å) over the period 17:29:00-17:53:48 UT. Due to saturation effects, all 171
Å images were excluded from the analysis. Images used for a single DEM map
were selected at 12 s intervals within the period, with each channel image
selected having the smallest time delta from a given interval. In addition to
the AIA image processing described in Section 3, each image was further
corrected for degradation and normalized by the exposure time.

DEM calculations in this work were computed using the Python
implementation222Avaliable online at https://github.com/ianan/demreg of the
regularized inversion method first described in Hannah & Kontar (2012). AIA
temperature responses used in the calculations were constructed using a
convolution between the effective AIA area taken from the SolarSoft
aia_get_response.pro routine and atomic data from CHIANTI v10 as described in
Del Zanna et al. (2011). Because we speculate the initial LT plasma is coronal
plasma heated to temperatures above 10 MK, as opposed to evaporated
chromospheric plasma, temperature responses were calculated assuming a coronal
abundance Feldman et al. (1992). Each DEM map was internally calculated in
emission measure (EM) space and constrained using the EM loci curves of each
AIA channel — a method found to be the most robust following a series of tests
of different DEM calculations. Finally, all DEM maps were background
subtracted using a DEM map calculated at the pre-flare time 16:45:00 UT
(Motorina et al., 2020). Additional details regarding the DEM method, AIA
response functions, and abundance assumptions can be found in Appendix A.

Panels (a) and (b) in Figure 10 show two EM maps calculated from the DEM
results at the start time of the initial Fe xxi signal and at the peak time of
the Fe xxi emission, respectively, over the range Log10 [K] 6.83-7.19. The
dashed lines indicate the IRIS slit position and the black boxes outline the
location of the LT Fe xxi emission. At time 17:33:24, there is relatively
little EM associated with the initial IRIS Fe xxi emission, which changes as
the flare progresses and regions of high EM shift westward over the IRIS slit.
To calculate the electron number density $n_{e}$, we use the following:

$n_{e}=\sqrt{\frac{EM}{0.83\;\ell}},$ (5)

where EM is the total emission measure integrated overall temperature bins in
a single DEM map (Log10 [K] 5.7-7.6) and $\ell$ is the LOS column depth of the
emitting plasma, assuming a fully-ionized plasma with a relative hydrogen to
free electron density ratio of 0.83 (Reeves et al., 2020; Del Zanna et al.,
2021). Here we take $\ell=12$ Mm, following our coronal volume estimate.

Figure 10: DEM-weighted emission measure (EM) maps in the Log10 [K] 6.83-7.19
range at the start time of the initial signal (a) and peak Fe xxi emission
time (b). Dashed lines indicate the IRIS slit position. Black boxes outline
the location of Fe xxi LT emission. Time-distance stack plots of the electron
number density (c) and DEM-weighted mean temperature (d) calculated using
slices in the EM maps (Equations (5) and (6), respectively). Artificial slices
made in the EM maps mimic the IRIS slit position over time. Grey and cyan
contours are of the Fe xxi intensity levels matching that in Figure 3. (e)
Time series of the DEM-weighted mean temperature (blue) and electron number
density (red), averaged over the area in the black boxes as illustrated in (a)
and (b). Vertical dashed lines indicate the start time of the initial signal.

To study the number density evolution across the IRIS slit, we calculate
$n_{e}$ across an artificial slit along the DEM maps matching the SG slit
location over time. The resulting time-distance stack plots of $n_{e}$ are
shown in Figure 10(c). In addition to $n_{e}$, we also calculate the DEM-
weighted mean temperature $\langle T\rangle$ using the following:

$\langle T\rangle=\frac{\sum_{i}DEM(T_{i})\;T_{i}\;\Delta
T}{\sum_{i}DEM(T_{i})\;\Delta T}=\frac{\sum_{i}DEM(T_{i})\;T_{i}\;\Delta
T}{EM},$ (6)

with the resulting time-distance stack plot shown in Figure 10(d). Notably,
the density begins to increase at the point $y\approx 311$″— consistent with
the location of the initial LT Fe xxi emission — and continues to increase and
spread spatially across the SG over time, reaching a peak value of
$n_{e}\approx 1.5\times 10^{11}$ cm-3 at roughly 17:39:00 UT. The region of
peak density also corresponds to the LT location of the bright EUV knots as
seen in Figure 3(d)-(f). Preceding the increase in $n_{e}$ is a rapid increase
in the LT plasma temperature, with values $\langle T\rangle$ reaching Log10
[K] $\approx 7.4$ at 17:32:00 UT. The temperature continues to remain elevated
above Log10 [K] $\approx 7.2$ across the LT region, and gradually decreasing
over time.

As a means to directly compare the values of the number density and
temperature at the site of the initial Fe xxi non-thermal broadening, we
performed a separate DEM calculation on the region corresponding to the black
boxes in Figure 10(a) and (b). Defined in a 2x2″ area centered on the IRIS SG
slit over time and $y=311.7$″, the corresponding AIA pixels were selected to
create a 3x3 pixel box, given the 0.6″ per pixel resolution of AIA, which was
then averaged over. The resulting time series of $n_{e}$ and $\langle
T\rangle$ are shown in Figure 10(e). In a consistency check, we find the
values of $n_{e}$ in the range of 0.5-1.5$\times 10^{11}$ cm-3 are in
agreement with the values of thermal electron population density derived from
EOVSA MW spectra (Figure 7). Additionally, using the EMSXR from the f_vth of
the thermal STIX source and our coronal volume estimate, we find the number
density inferred from the SXRs are in the range
$n_{e}=\sqrt{EM_{\mathrm{SXR}}/V}=[0.3-0.5]\times 10^{11}$ cm-3 during the
period of the initial Fe xxi signal, which also agrees with our DEM estimate.
We further note that the calculated densities on the order of $10^{10-11}$
cm-3 at the time of the initial Fe xxi emission suggest that any effects due
to NEI on the Fe xxi line formation would likely be small.

###  5.2 Kinetic Energy Dissipation

Following the estimate of the electron number density evolution in the LT
plasma above, the dissipation of turbulent kinetic energy in the initial Fe
xxi signal is calculated using Equation (4). Using the time series of the non-
thermal velocity $v_{\mathrm{nth}}$ inferred from the dynamic binning routine
(Figure 6) and the associated electron number density $n_{e}$ from the DEM
analysis, the resulting time series of $K$ is shown in Figure 11 (orange). The
peak kinetic energy is found to be $2.8\pm 0.8\times 10^{28}$ erg, which then
decreases to $0.6\pm 0.1\times 10^{28}$ erg over the next 100 s. As $n_{e}$ is
increasing over this period, from $0.7\times 10^{11}$ to $0.9\times
10^{11}\;\mathrm{cm}^{-3}$, the decay in $K$ is slower than the decay in
$v_{\mathrm{nth}}$ inferred in Section 3.1. Furthermore, as the total kinetic
energy calculation relies on an estimate of the plasma volume, values of
kinetic energy density ($K/V$) are also provided in Figure 11, read off the
right axis, with energy densities roughly on the order of 2-9 erg cm-3. This
reduction allows for a more direct comparison to the values derived in Stores
et al. (2021), who found kinetic energy densities nearly an order of magnitude
lower using Fe xxiv 255 Å but for an off-limb X1.2-class flare. However, this
discrepancy is likely due to the lower values of $n_{e}$ calculated in their
work ($\approx 10^{9}$ cm-3 in regions of high $K$), as similar magnitudes of
$v_{\mathrm{nth}}$ were found in both studies.

Figure 11: Time series of the turbulent kinetic energy inferred from IRIS Fe
xxi non-thermal broadening during the initial signal (orange) and the
corresponding time-integrated non-thermal power from STIX HXR emission during
the second energy phase (purple). A kinetic energy density scale is also
provided for the turbulent kinetic energy on the right axis.

To put the kinetic energy dissipation in context, we compare it to the power
imparted on the chromosphere by non-thermal electron deposition during the
second energy phase (bottom panel Figure 9). Time integrating
$P_{\mathrm{nth}}$ at each 4 s interval, the resulting energy time series is
shown in Figure 11 (purple). The non-thermal energy peaks at $2.4\pm 0.4\times
10^{28}$ erg, which is consistent with the peak of the turbulent kinetic
energy. While the cadence of the IRIS observation is higher than that of the
OSPEX time-integrated HXR fitting parameters, there is also a remarkable
agreement between the evolution of the two energy estimates starting at the
beginning of the initial Fe xxi signal and lasting until the end of the second
phase. Despite this agreement, we note that because the reference energy
$E_{r}$ is used to calculate our non-thermal electron power
$P_{\mathrm{nth}}$, which is larger than the inferred high-energy cutoffs
$E_{c}$ during this period (Figure 9), the values of $P_{\mathrm{nth}}$, and
subsequently the integrated non-thermal election energy, are likely
underestimated to a slight degree.

Assuming our coronal volume estimate is accurate, the agreement between the
two energy curves in Figure 11 suggests the dissipation of turbulent kinetic
energy in the LT plasma is enough to drive the acceleration of non-thermal
electrons into the chromosphere. Not only does this connection hint at a
causal relationship, but it also suggests that energy transfer from turbulence
to electron acceleration is quite efficient, given the virtual lack of any
time delay between the driver (turbulence) and the response (non-thermal
electron deposition). This efficiency is supported by numerical experiments of
stochastic acceleration in turbulent flare plasmas (Miller et al., 1996;
Stackhouse & Kontar, 2018), which have demonstrated sub-second timescales for
particle acceleration. However, our coronal volume estimate assumes the
kinetic energy derived from the Fe xxi non-thermal broadening is contained
within a volume representative of the MW and SXR sources. As we showed in
Section 3.1, the spatial extent of the initial Fe xxi signal along the IRIS
slit is $\approx 3.1$″— a fraction of the overall extent of the MW emission.
While the smaller size of the Fe xxi emission implies that the turbulent
kinetic energy may be overestimated, the IRIS slit may only be sampling a
small portion of the turbulent LT plasma responsible for the electron
acceleration. Nonetheless, when combined with the possibility of an
underestimated range of $P_{\mathrm{nth}}$, we cannot neglect the possibility
that the turbulent kinetic energy inferred by IRIS is less than the energy of
chromospheric electron deposition measured by STIX, suggesting turbulence is
not the sole acceleration mechanism at work. The dependency of the turbulent
kinetic energy $K$ on the coronal volume $V$ is put into context in Figure 12,
where the observed peak Fe xxi non-thermal velocity value is used to calculate
possible values of $K$ using an estimated range of coronal volumes, as well as
electron number densities $n_{e}$ found from our DEM analysis (Figure 10(e)).
The volume range is constructed such that the lower bound is a cylindrical
volume calculated using a diameter of 3.1$\arcsec$ from the IRIS observation
and the upper bound is the volume of the coronal SXR source as measured by
STIX.

Figure 12: Parameter space exploration of kinetic energy using the peak non-
thermal velocity of the IRIS Fe xxi line during the initial signal
$v_{\mathrm{nth}}$=65.7 km s-1 for a range of hypothetical number densities
$n_{e}$ and coronal volumes calculated using Equation (4). The white marker
indicates the number density at the time of peak $v_{\mathrm{nth}}$,
Log${}_{10}\,n_{e}$ [cm-3] = 10.83, and coronal volume estimate used in this
work, $V=3\times 10^{27}$ cm3.

In addition to the non-thermal energy derived from HXR emission, a comparison
can be made between the turbulent kinetic energy density and the non-thermal
energy density inferred from the EOVSA MW spectra. As detailed in Fleishman et
al. (2020), the non-thermal energy density $w_{\mathrm{nth}}$ is calculated
using the following:

$w_{\mathrm{nth}}=k_{E}\,n_{\mathrm{nth}}\,E_{\mathrm{min}}\;\frac{\delta_{\mathrm{MW}}-1}{\delta_{\mathrm{MW}}-2},$
(7)

given the best-fit parameters from the MW spectra shown in Figure 7 and a
minimum energy cutoff of $E_{\mathrm{min}}$=10 keV used in the GSFIT routine.
The resulting non-thermal energy density was found to be highest in the LT
region, increasing from 4.7$\times 10^{1}$ to 2.4$\times 10^{2}$ erg cm-3
between times 17:33:22-17:33:48 (Figure 7). This increase in
$w_{\mathrm{nth}}$ occurs concurrently with the decay in kinetic energy,
fitting the narrative of non-thermal electron activity driven by the
dissipation of turbulence. However, the MW non-thermal energy density attains
values nearly two orders of magnitude higher than the kinetic energy densities
inferred from the Fe xxi non-thermal broadening.

This second order of magnitude discrepancy between the non-thermal and kinetic
energy densities was also observed in (Fleishman et al., 2020), who attributed
the difference to the emission regions from which the MW and EUV — responsible
for the two energy estimates — emanate. In their work, which focused on the
September 10th, 2017 event, MWs were observed to stem from the cusp region
near the LTs and large values of non-thermal broadening from the Fe xxiv 255 Å
EIS line ($\approx 100$ km s-1) was primarily confined to the overlying plasma
sheet (see also Warren et al. (2018); Polito et al. (2018)), suggesting that
the cusp region contained a higher degree of non-thermal electron activity.
Although the on-disk nature of our observation hinders a direct comparison
between flare geometries, the location of the MW sources in Figure 7 in
combination with the HXR footpoint emission in Figure 8 creates a coherent
picture of a loop-like structure, where the MW sources trace out one half of
the loop from the corona (low-GHz) to the northern ribbon footpoint (high-GHz)
and the HXR emission highlights the location of the southern ribbon footprint
(This picture is also consistent with a magnetic mirroring effect, where
accelerated electrons reflect off high-$B$ regions in the northern ribbon and
precipitate into the southern ribbon, possibly explaining the opposing
asymmetry seen in the MW and HXR sources).

If we adopt the reasoning presented in Fleishman et al. (2020), then it
follows the non-thermal broadening in the Fe xxi should lie above the MW
sources, either higher up in the LT/cusp region or reaching into the current
sheet. We note that this location of Fe xxi non-thermal broadening also agrees
with simulations in Shen et al. (2023a), who found the source of large non-
thermal broadening in the IRIS Fe xxi line to be the highly turbulent plasma
located along the current sheet and LT/Cusp region. The location of the SG
slit shown in Figure 7, slightly to the right of the MW sources, further
supports the notion of vertical separation between the non-thermal signatures
measured by IRIS and EOVSA when considering the projection of the arcade on
the disk and the LOS of these observations. A schematic of this interpretation
is illustrated in Figure 13. The configuration of the drawn flare loop
orientation is further justified by that produced from a magnetic field
extrapolation (left panel) performed using the GX simulator modeling package
(Nita et al., 2023), which employed a nonlinear force-free field
reconstruction of the magnetic field from the preflare SDO/HMI magnetogram at
17:23:36 UT.

Figure 13: Left: Magnetic field extrapolation (blue lines) overplotted on AIA
1600 Å image at 17:35:26, along with IRIS FOV and SG slit (red-dashed lines).
Right: Schematic diagram showing the interpreted locations of the different
observations along the line-of-sight (LOS) as they pertain to the standard
flare model. Microwave (MW) sources are confined to the closed, reconnected
post-flare loops, which trace out the northern half of the loop-like
structure. High-frequency sources (yellow) stem from the northern ribbon,
while the low-frequency sources (blue) emanate from the LT/Cusp region. The
hard X-ray (HXR) source marks the location of the southern footprint, arising
from the precipitation of accelerated electrons. Lying above the MWs in the
LT/Cusp region, near the location where the current sheet meets the arcade, is
the Fe xxi non-thermal broadening detected along the IRIS SG slit.

Altogether, these findings indicate the co-spatiotemporal presence of non-
thermal signatures in the LT and cusp regions. We interpret the decay in non-
thermal velocity as the dissipation of turbulent energy in these regions,
which can provide the required energy necessary to accelerate electrons into
the lower solar atmosphere. Nonetheless, because the SG slit is positioned
over the flare arcade at a single location, we can only infer that stochastic
acceleration occurs at the time and place in which we observe the initial
decay in Fe xxi broadening and the associated MW and HXR signals. In other
words, our analysis only pertains to the second high-energy phase (see Figure
1), where we see the compact MW source move into the SG slit and not the
entire flare. Moreover, the decay in non-thermal velocity suggests that the
turbulence in the LT/Cusp region is dissipating and no longer being generated
— a notion potentially at odds with investigations that see persistent
reconnection outflows generating turbulence for sustained periods (Shibata et
al., 2023; Wang et al., 2023b). While it is likely that reconnection is
ongoing following the generation of the Fe xxi broadening, as evidenced by the
third high-energy phase, the movement of the MW and HXR sources westward along
the flare arcade suggests that the mechanisms responsible for their formation
(e.g. reconnection outflows, Yu et al., 2020) are discrete and localized along
the current sheet. The generation of turbulence observed in the Fe xxi line
under this assumption would not be ongoing at the location of the IRIS slit
and would therefore be allowed to decay freely. An analysis of such extended
outflows, albeit beyond the scope of the present work, would be a promising
focus for future research.

##  6 Summary and Conclusion

The X1.3 class flare on March 30th, 2022 analyzed in our study exhibited non-
thermal signatures across measurements taken by IRIS, EOVSA, and STIX. Our
findings highlight significant excess broadening of the Fe xxi 1354.08 Å
spectral line emanating from the flare arcade’s LT region, reaching values
upwards of 65 km s-1. These non-thermal velocities were also observed to decay
over time at two different periods, beginning at the onset of LT emission and
before peak line emission. We found the evolution of the latter period to
coincide with the appearance of bright EUV knots in AIA 94, 131, and 193 Å
channels, offering a new spectroscopic insight into this phenomenon.

Our observations of the LT Fe xxi emission present a unique perspective on the
dynamics of solar flares, with the high spatial resolution of IRIS and a fast
cadence of $\approx 9$ s, allowing for the direct measurement of non-thermal
broadening in a well-resolved LT structure. The rapid decay of non-thermal
broadening in the LT plasma, on the order of minutes, is significantly quicker
than the tens of minutes reported in earlier studies. Moreover, confirming the
LT emission from a well-resolved structure challenges earlier works with lower
resolution spectrometers and lower cadence where flare emissions might have
been interpreted as a superposition of flows from different macroscopic
locations along the flare arcade and LOS. This highlights the importance of
spatial resolution and cadence in understanding solar flare dynamics.

Excess broadening in the Fe xxi line was interpreted as the presence of
turbulent plasma in the LT region, with its decay indicative of energy
dissipation via a turbulent cascade. Following methodologies from Kontar et
al. (2017), we estimated the LT plasma’s peak turbulent kinetic energy to be
approximately $2.8\pm 0.8\times 10^{28}$ erg. This energy correlated well with
the time-integrated non-thermal electron power $P_{\mathrm{nth}}$ deposited in
the chromosphere, as inferred from STIX HXR measurements, which peaked at
$2.4\pm 0.4\times 10^{28}$ erg. As the temporal decay in turbulent kinetic
energy also matched that of the integrated electron power, the agreement
between the two energies suggests a relationship between the dissipation of
turbulent energy and the acceleration of non-thermal electrons, thereby
supporting stochastic acceleration theories. We note, however, that this
interpretation is contingent on two factors: first, the assumption of a
coronal volume estimate, which may overestimate the turbulent kinetic energy
as observed by IRIS; and second, the values of $P_{\mathrm{nth}}$, which are
potentially underestimated in our calculations. The

The connection between the turbulent plasma and non-thermal electron
populations was further supported by the simultaneous presence of
gyrosynchrotron MW emission from EOVSA, where the MW sources were found to be
co-spatial and co-temporal with the initial LT Fe xxi emission. Analysis of MW
spectra at different times and locations along the flare arcade indicated a
significant non-thermal electron fraction in the LT plasma, with a ratio of
non-thermal to thermal electrons ranging upwards of 35%. Although this high
percentage indicates an efficient electron acceleration mechanism at work and
also places plasma turbulence in the vicinity of these non-thermal electrons
at the flare LT, the non-thermal energy density inferred from the MW sources
was found to be substantially higher than the turbulent kinetic energy density
inferred from the Fe xxi broadening. This discrepancy, first seen in Fleishman
et al. (2020), supports the idea of a vertical variation in the non-thermal
energy density across the flare arcade, where the formation region of Fe xxi
belongs to a region of lesser non-thermal energy density, possibly higher in
the solar corona than the underlying MW emission, as summarised in our cartoon
in Fig. 13.

Together, these findings contribute to a deeper understanding of non-thermal
processes in the flare LT region, setting a foundation for future
investigations and modeling efforts. The forthcoming MUSE mission, with its
advanced EUV spectroscopic capabilities and 35 slits (Cheung et al., 2022),
promises to enhance our ability to study these processes in greater detail.

W.A. is supported by NASA contract NNG09FA40C (IRIS). VP acknowledges support
from NASA Heliophysics System Observatory Connect Grant #80NSSC20K1283,NASA
ROSES Heliophysics Guest Investigator program Grant #80NSSC20K0716, and from
NASA under contract NNG09FA40C (IRIS). S.Y. is supported by NASA grant
80NSSC20K1318 and NSF grant AST-2108853 awarded to NJIT. H.C. is supported by
the Swiss National Science Foundation Grant 200021L_189180 for STIX. L.A.H is
supported by an ESA Research Fellowship. IRIS is a NASA small explorer mission
developed and operated by LMSAL with mission operations executed at NASA Ames
Research Center and major contributions to downlink communications funded by
ESA and the Norwegian Space Center. EOVSA operation is supported by NSF grant
AST1910354 and AGS-2130832 to NJIT. Solar Orbiter is a mission of
international cooperation between ESA and NASA, operated by ESA. The STIX
instrument is an international collaboration between Switzerland, Poland,
France, Czech Republic, Germany, Austria, Ireland, and Italy. AIA and data are
provided courtesy of NASA/SDO and the AIA science team. This work has
benefited from the use of NASA’s Astrophysics Data System. CHIANTI is a
collaborative project involving researchers at the universities of Cambridge
(UK), George Mason, and Michigan (USA). This research used version 5.1.1 of
the SunPy open-source software package (The SunPy Community et al., 2020). The
authors thank the referee for suggestions that improved the manuscript.

##  Appendix A DEM Methods

Figure 14 shows the AIA temperature response functions used for the DEM
calculations in Section 5.1 (solid). These functions were calculated using the
convolution method described in Del Zanna et al. (2011) with ion abundances
calculated using the CHIANTI v10 atomic database and assuming coronal
abundances Feldman et al. (1992). We note that the response function for the
171 Å channel was not calculated, as the channel was excluded from the DEM
calculations due to saturation effects. Temperature response functions
calculated using the SolarSoft aia_get_response.pro routine are also shown in
Figure 14 (dashed) for comparison.

Figure 14: SDO AIA temperature response functions calculated using the
SolarSoft aia_get_response.pro routine (dashed) and using the method described
in Del Zanna et al. (2011).

As AIA 171 Å images were not included in our analysis, we are consequently
neglecting any emission contributions from the Fe IX 171 Å line (peak
Log${}_{10}\,T$ [K] =5.9). To ensure the validity of the DEM calculations in
the absence of the 171 Å channel, consistency checks were performed by
comparing the predicted emission from the DEM results to the input AIA data.
An example of this check is shown in Figure 15 for the pixels averaged within
the box in Figure 10(a) at time 17:33:24 for two inversion methods: the
regularized inversion method described in Hannah & Kontar (2012) and the same
method constrained by the EM loci curves of the five AIA channels, calculated
internally in EM space. While both methods were able to reproduce the observed
AIA emission well in the absence of the 171 Å channel, the EM loci-constrained
method was found to be the most robust with a reduced $\chi^{2}$ of 0.99.

Figure 15: Top Panel: DEM calculation results for the pixels averaged within
the box in Figure 10(a) at time 17:33:24, assuming a coronal abundance. The
results of the regularized inversion method are shown in red and the EM loci
constrained results are shown in blue. Bottom Panel: Standardized residuals
between the predicted emission from the DEM results and the input AIA data for
each method.

An additional consistency check was done to test our assumption of coronal
abundances, given that the ablation of chromospheric material into the corona
from evaporation is likely to occur during flares. Performing the same DEM
calculations above, but using AIA temperature response functions recalculated
with a photospheric abundance Asplund et al. (2009), we found both methods
performed considerably worse than those using a coronal abundance (Figure 16).
However, while this test agrees with our initial assumption for the use of
DEMs in this paper, we acknowledge that a more comprehensive study of the DEM
calculations using different abundances is beyond the scope of the current
work.

Figure 16: DEM calculation results and standardized residuals assuming a
photospheric abundance, plotted as in Figure 15.

## References

  * Acton et al. (1992) Acton, L. W., Feldman, U., Bruner, M. E., et al. 1992, PASJ, 44, L71
  * Antonucci et al. (1984) Antonucci, E., Gabriel, A. H., & Dennis, B. R. 1984, ApJ, 287, 917, doi: 10.1086/162749
  * Aschwanden et al. (1996) Aschwanden, M. J., Hudson, H., Kosugi, T., & Schwartz, R. A. 1996, ApJ, 464, 985, doi: 10.1086/177386
  * Asplund et al. (2009) Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481, doi: 10.1146/annurev.astro.46.060407.145222
  * Barnes et al. (2020) Barnes, W. T., m. Cheung, M. C., Bobra, M. G., et al. 2020, Journal of Open Source Software, 5, 2801, doi: 10.21105/joss.02801
  * Brown (1971) Brown, J. C. 1971, Sol. Phys., 18, 489, doi: 10.1007/BF00149070
  * Chen et al. (2015) Chen, B., Bastian, T. S., Shen, C., et al. 2015, Science, 350, 1238, doi: 10.1126/science.aac8467
  * Chen et al. (2020a) Chen, B., Yu, S., Reeves, K. K., & Gary, D. E. 2020a, ApJ, 895, L50, doi: 10.3847/2041-8213/ab901a
  * Chen et al. (2020b) Chen, B., Shen, C., Gary, D. E., et al. 2020b, Nature Astronomy, 4, 1140, doi: 10.1038/s41550-020-1147-7
  * Cheng et al. (2018) Cheng, X., Li, Y., Wan, L. F., et al. 2018, ApJ, 866, 64, doi: 10.3847/1538-4357/aadd16
  * Cheung et al. (2022) Cheung, M. C. M., Martínez-Sykora, J., Testa, P., et al. 2022, ApJ, 926, 53, doi: 10.3847/1538-4357/ac4223
  * Collier et al. (2023) Collier, H., Hayes, L. A., Battaglia, A. F., Harra, L. K., & Krucker, S. 2023, A&A, 671, A79, doi: 10.1051/0004-6361/202245293
  * Collier et al. (2024) Collier, H., Hayes, L. A., Yu, S., et al. 2024, A&A, 684, A215, doi: 10.1051/0004-6361/202348652
  * Craig & McClymont (1976) Craig, I. J. D., & McClymont, A. N. 1976, Sol. Phys., 50, 133, doi: 10.1007/BF00206198
  * De Pontieu et al. (2014) De Pontieu, B., Title, A. M., Lemen, J. R., et al. 2014, Sol. Phys., 289, 2733, doi: 10.1007/s11207-014-0485-y
  * De Pontieu et al. (2021) De Pontieu, B., Polito, V., Hansteen, V., et al. 2021, Sol. Phys., 296, 84, doi: 10.1007/s11207-021-01826-0
  * Del Zanna et al. (2021) Del Zanna, G., Dere, K. P., Young, P. R., & Landi, E. 2021, ApJ, 909, 38, doi: 10.3847/1538-4357/abd8ce
  * Del Zanna & Mason (2018) Del Zanna, G., & Mason, H. E. 2018, Living Reviews in Solar Physics, 15, 5, doi: 10.1007/s41116-018-0015-3
  * Del Zanna et al. (2011) Del Zanna, G., O’Dwyer, B., & Mason, H. E. 2011, A&A, 535, A46, doi: 10.1051/0004-6361/201117470
  * Drake et al. (2006) Drake, J. F., Swisdak, M., Che, H., & Shay, M. A. 2006, Nature, 443, 553, doi: 10.1038/nature05116
  * Dulk & Marsh (1982) Dulk, G. A., & Marsh, K. A. 1982, ApJ, 259, 350, doi: 10.1086/160171
  * Feldman et al. (1992) Feldman, U., Mandelbaum, P., Seely, J. F., Doschek, G. A., & Gursky, H. 1992, ApJS, 81, 387, doi: 10.1086/191698
  * Fleishman et al. (2020) Fleishman, G. D., Gary, D. E., Chen, B., et al. 2020, Science, 367, 278, doi: 10.1126/science.aax6874
  * Fleishman & Kuznetsov (2010) Fleishman, G. D., & Kuznetsov, A. A. 2010, ApJ, 721, 1127, doi: 10.1088/0004-637X/721/2/1127
  * Fleishman et al. (2022) Fleishman, G. D., Nita, G. M., Chen, B., Yu, S., & Gary, D. E. 2022, Nature, 606, 674, doi: 10.1038/s41586-022-04728-8
  * Fletcher et al. (2011) Fletcher, L., Dennis, B. R., Hudson, H. S., et al. 2011, Space Sci. Rev., 159, 19, doi: 10.1007/s11214-010-9701-8
  * Forbes (1986) Forbes, T. G. 1986, ApJ, 305, 553, doi: 10.1086/164268
  * Freeland & Handy (1998) Freeland, S. L., & Handy, B. N. 1998, Sol. Phys., 182, 497, doi: 10.1023/A:1005038224881
  * Gary et al. (2018) Gary, D. E., Chen, B., Dennis, B. R., et al. 2018, ApJ, 863, 83, doi: 10.3847/1538-4357/aad0ef
  * Goldreich & Sridhar (1995) Goldreich, P., & Sridhar, S. 1995, ApJ, 438, 763, doi: 10.1086/175121
  * Graham & Cauzzi (2015) Graham, D. R., & Cauzzi, G. 2015, ApJ, 807, L22, doi: 10.1088/2041-8205/807/2/L22
  * Hannah & Kontar (2012) Hannah, I. G., & Kontar, E. P. 2012, A&A, 539, A146, doi: 10.1051/0004-6361/201117576
  * Holman et al. (2011) Holman, G. D., Aschwanden, M. J., Aurass, H., et al. 2011, Space Sci. Rev., 159, 107, doi: 10.1007/s11214-010-9680-9
  * Kontar et al. (2019) Kontar, E. P., Jeffrey, N. L. S., & Emslie, A. G. 2019, ApJ, 871, 225, doi: 10.3847/1538-4357/aafad3
  * Kontar et al. (2017) Kontar, E. P., Perez, J. E., Harra, L. K., et al. 2017, Phys. Rev. Lett., 118, 155101, doi: 10.1103/PhysRevLett.118.155101
  * Kopp & Pneuman (1976) Kopp, R. A., & Pneuman, G. W. 1976, Sol. Phys., 50, 85, doi: 10.1007/BF00206193
  * Krucker et al. (2020) Krucker, S., Hurford, G. J., Grimm, O., et al. 2020, A&A, 642, A15, doi: 10.1051/0004-6361/201937362
  * Larosa & Moore (1993a) Larosa, T. N., & Moore, R. L. 1993a, ApJ, 418, 912, doi: 10.1086/173448
  * Larosa & Moore (1993b) —. 1993b, ApJ, 418, 912, doi: 10.1086/173448
  * Lemen et al. (2012) Lemen, J. R., Title, A. M., Akin, D. J., et al. 2012, 275, 17, doi: 10.1007/s11207-011-9776-8
  * Massa et al. (2020) Massa, P., Schwartz, R., Tolbert, A. K., et al. 2020, ApJ, 894, 46, doi: 10.3847/1538-4357/ab8637
  * McKenzie (2013) McKenzie, D. E. 2013, ApJ, 766, 39, doi: 10.1088/0004-637X/766/1/39
  * Miller et al. (1996) Miller, J. A., Larosa, T. N., & Moore, R. L. 1996, ApJ, 461, 445, doi: 10.1086/177072
  * Miller et al. (1997) Miller, J. A., Cargill, P. J., Emslie, A. G., et al. 1997, J. Geophys. Res., 102, 14631, doi: 10.1029/97JA00976
  * Milligan (2011) Milligan, R. O. 2011, ApJ, 740, 70, doi: 10.1088/0004-637X/740/2/70
  * Motorina et al. (2020) Motorina, G. G., Fleishman, G. D., & Kontar, E. P. 2020, ApJ, 890, 75, doi: 10.3847/1538-4357/ab67d1
  * Neupert (1968) Neupert, W. M. 1968, ApJ, 153, L59, doi: 10.1086/180220
  * Nita et al. (2023) Nita, G. M., Fleishman, G. D., Kuznetsov, A. A., et al. 2023, ApJS, 267, 6, doi: 10.3847/1538-4365/acd343
  * O’Dwyer et al. (2010) O’Dwyer, B., Del Zanna, G., Mason, H. E., Weber, M. A., & Tripathi, D. 2010, A&A, 521, A21, doi: 10.1051/0004-6361/201014872
  * Patsourakos et al. (2004) Patsourakos, S., Antiochos, S. K., & Klimchuk, J. A. 2004, ApJ, 614, 1022, doi: 10.1086/423779
  * Petrosian (2012) Petrosian, V. 2012, Space Sci. Rev., 173, 535, doi: 10.1007/s11214-012-9900-6
  * Polito et al. (2018) Polito, V., Dudík, J., Kašparová, J., et al. 2018, ApJ, 864, 63, doi: 10.3847/1538-4357/aad62d
  * Polito et al. (2016) Polito, V., Reep, J. W., Reeves, K. K., et al. 2016, ApJ, 816, 89, doi: 10.3847/0004-637X/816/2/89
  * Polito et al. (2015) Polito, V., Reeves, K. K., Del Zanna, G., Golub, L., & Mason, H. E. 2015, ApJ, 803, 84, doi: 10.1088/0004-637X/803/2/84
  * Polito et al. (2019) Polito, V., Testa, P., & De Pontieu, B. 2019, ApJ, 879, L17, doi: 10.3847/2041-8213/ab290b
  * Reames (2014) Reames, D. V. 2014, Sol. Phys., 289, 977, doi: 10.1007/s11207-013-0350-4
  * Reeves et al. (2020) Reeves, K. K., Polito, V., Chen, B., et al. 2020, ApJ, 905, 165, doi: 10.3847/1538-4357/abc4e0
  * Reeves et al. (2007) Reeves, K. K., Warren, H. P., & Forbes, T. G. 2007, ApJ, 668, 1210, doi: 10.1086/521291
  * Ruan et al. (2018) Ruan, W., Xia, C., & Keppens, R. 2018, A&A, 618, A135, doi: 10.1051/0004-6361/201833362
  * Sandlin et al. (1986) Sandlin, G. D., Bartoe, J. D. F., Brueckner, G. E., Tousey, R., & Vanhoosier, M. E. 1986, ApJS, 61, 801, doi: 10.1086/191131
  * Shen et al. (2023a) Shen, C., Polito, V., Reeves, K. K., et al. 2023a, Frontiers in Astronomy and Space Sciences, 10, 19, doi: 10.3389/fspas.2023.1096133
  * Shen et al. (2023b) Shen, C., Raymond, J. C., & Murphy, N. A. 2023b, ApJ, 943, 111, doi: 10.3847/1538-4357/aca6e7
  * Shen et al. (2013) Shen, C., Reeves, K. K., Raymond, J. C., et al. 2013, ApJ, 773, 110, doi: 10.1088/0004-637X/773/2/110
  * Shibata et al. (2023) Shibata, K., Takasao, S., & Reeves, K. K. 2023, ApJ, 943, 106, doi: 10.3847/1538-4357/acaa9c
  * Stackhouse & Kontar (2018) Stackhouse, D. J., & Kontar, E. P. 2018, A&A, 612, A64, doi: 10.1051/0004-6361/201730708
  * Stores et al. (2021) Stores, M., Jeffrey, N. L. S., & Kontar, E. P. 2021, ApJ, 923, 40, doi: 10.3847/1538-4357/ac2c65
  * Syrovatskii & Shmeleva (1972) Syrovatskii, S. I., & Shmeleva, O. P. 1972, Soviet Ast., 16, 273
  * The SunPy Community et al. (2020) The SunPy Community, Barnes, W. T., Bobra, M. G., et al. 2020, The Astrophysical Journal, 890, 68, doi: 10.3847/1538-4357/ab4f7a
  * Wang et al. (2023a) Wang, L. F., Li, Y., Li, Q., Cheng, X., & Ding, M. D. 2023a, ApJS, 268, 62, doi: 10.3847/1538-4365/acf127
  * Wang et al. (2023b) Wang, Y., Cheng, X., Ding, M., et al. 2023b, ApJ, 954, L36, doi: 10.3847/2041-8213/acf19d
  * Warren et al. (2018) Warren, H. P., Brooks, D. H., Ugarte-Urra, I., et al. 2018, ApJ, 854, 122, doi: 10.3847/1538-4357/aaa9b8
  * Widing & Cheng (1974) Widing, K. G., & Cheng, C. C. 1974, ApJ, 194, L111, doi: 10.1086/181681
  * Xu et al. (2023) Xu, Y., Kerr, G. S., Polito, V., et al. 2023, ApJ, 958, 67, doi: 10.3847/1538-4357/acf8c6
  * Ye et al. (2020) Ye, J., Cai, Q., Shen, C., et al. 2020, ApJ, 897, 64, doi: 10.3847/1538-4357/ab93b5
  * Young et al. (2015) Young, P. R., Tian, H., & Jaeggli, S. 2015, ApJ, 799, 218, doi: 10.1088/0004-637X/799/2/218
  * Yu et al. (2020) Yu, S., Chen, B., Reeves, K. K., et al. 2020, ApJ, 900, 17, doi: 10.3847/1538-4357/aba8a6