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At least 37 records · Page 2

A predicted energetic ion signature of a neutral line in the geomagnetic tail

Under certain assumptions one can predict the formation of a magnetic neutral line on theoretical grounds, generally as a result of an unstable current sheet. Neutral points also seen to form spontaneously in a wide variety of plasma simulatioons, from MHD to fully kinetic. Hence, such magnetic null regions are central to some models of magnetotail energization and magnetic substorms. Yet the observational evidence for such regions remains controversial. This paper presents a new signature of a neutral line: the field-aligned ion beam characteristic of current sheet acceleration becomes dispersed into a 'ridge' in the velocity space distribution function as a neutral line is approached. The results were obtained using single-particle simulations in a fixed magnetic field model. The origin of the ridge is shown to be due to initially earthward going ions which pass through the neutral line region. These ions come from a smaller part of the initially antiearthward flowing distribution, generating the depletion of the distribution function below the ridge.

Martin, R. F., Jr.↗

Consequences of the Breakout Model for Particle Acceleration in CMEs and Flares

The largest and most efficient particle accelerators in the solar system are the giant events consisting of a fast coronal mass ejection (CME) and an intense X-class solar flare. Both flares and CMEs can produce l0(exp 32) ergs or more in nonthermal particles. Two general processes are believed to be responsible: particle acceleration at the strong shock ahead of the CME, and reconnection-driven acceleration in the flare current sheet. Although shock acceleration is relatively well understood, the mechanism by which flare reconnection produces nonthermal particles is still an issue of great debate. We address the question of CME/flare particle acceleration in the context of the breakout model using 2.5D MHD simulations with adaptive mesh refinement (AMR). The AMR capability allows us to achieve ultra-high numerical resolution and, thereby, determine the detailed structure and dynamics of the flare reconnection region. Furthermore, we employ newly developed numerical analysis tools for identifying and characterizing magnetic nulls, so that we can quantify accurately the number and location of magnetic islands during reconnection. Our calculations show that flare reconnection is dominated by the formation of magnetic islands. In agreement with many other studies, we find that the number of islands scales with the effective Lundquist number. This result supports the recent work by Drake and co-workers that postulates particle acceleration by magnetic islands. On the other hand, our calculations also show that the flare reconnection region is populated by numerous shocks and other indicators of strong turbulence, which can also accelerate particles. We discuss the implications of our calculations for the flare particle acceleration mechanism and for observational tests of the models.

Antiochos, S. K.↗

EIT Crinkles as Evidence for the Breakout Model of Solar Eruptions

We present observations of two homologous flares in NOAA active region 8210 occurring on 1998 May 1 and May 2, using EUV data from the Extreme Ultraviolet Radiation Imaging Telescope (EIT) on the Solar and Heliospheric Observatory (SOHO), high-resolution and high-time cadence images from the soft X-ray telescope (SXT) on Yohkoh, images or fluxes from the hard X-ray telescope (HXT) on Yohkoh and the BATSE experiment on the Compton Gamma Ray Observatory (CGRO), and Ca xix soft X-ray spectra from the Bragg crystal spectrometer (BCS) on Yohkoh. Magnetograms indicate that the flares occurred in a complex magnetic topology, consisting of an emerging flux region (EFR) sandwiched between a sunspot to the west and a coronal hole to the east. In an earlier study we found that in EIT images, both flaring episodes showed the formation of a crinkle-like pattern of emission ("EIT crinkles") occurring in the coronal hole vicinity, well away from a central "core field" area near the EFR-sunspot boundary. With our expanded data set, here we find that most of the energetic activity occurs in the core region in both events, with some portions of the core brightening shortly after the onset of the EIT crinkles, and other regions of the core brightening several minutes later, coincident with a burst of hard X-rays: there are no obvious core brightenings prior to the onset of the EIT crinkles. These timings are consistent with the "breakout model" of solar eruptions, whereby the emerging flux is initially constrained by a system of overlying magnetic field lines, and is able to erupt only after an opening develops in the overlying fields as a consequence of magnetic reconnection at a magnetic null point. In our case, the EIT crinkles would be a signature of this pre-impulsive-phase magnetic reconnection, and brightening of the core only occurs after the core fields begin to escape through the newly-created opening in the overlying fields. Morphology in soft X-ray images and properties in hard X-rays differ between the two events, with complexities that preclude a simple determination of the dynamics in the core at the times of eruption. From the BCS spectra, we find that the core region expends energy at a rate of approx. 10(exp 26) erg per second during the time of the growth of the EIT crinkles; this rate is an upper limit to energy expended in the reconnections opening the overlying fields. Energy losses occur at an order-of-magnitude higher rate near the time of the peak of the events. There is little evidence of asymmetry in the spectra, consistent with the majority of the mass flows occurring normal to the line-of-sight. Both events have similar electron temperature dependencies on time.

Sterling, Alphonse C.↗

EIT Crinkles as Evidence for the Breakout Model of Solar Eruptions

We present observations of two homologous flares in NOAA Active Region 8210 occurring on 1998 May 1 and 2, using EUV data from the EUV Imaging Telescope (EIT) on board the Solar and Heliospheric Observatory, high-resolution and high-time cadence images from the soft X-ray telescope on Yohkoh, images or fluxes from the hard X-ray telescope on Yohkoh and the BATSE experiment on board the Compton Gamma Ray Observatory, and Ca(XIX) soft X-ray spectra from the Bragg crystal spectrometer (BCS) on Yohkoh. Magnetograms indicate that the flares occurred in a complex magnetic topology, consisting of an emerging flux region (EFR) sandwiched between a sunspot to the west and a coronal hole to the east. In an earlier study we found that in EIT images, both flaring episodes showed the formation of a crinkle-like pattern of emission (EIT crinkles) occurring in the coronal hole vicinity, well away from a central 'core field' area near the EFR-sunspot boundary. With our expanded data set, here we find that most of the energetic activity occurs in the core region in both events, with some portions of the core brightening shortly after the onset of the EIT crinkles, and other regions of the core brightening several minutes later, coincident with a burst of hard X-rays; there are no obvious core brightenings prior to the onset of the EIT crinkles. These timings are consistent with the 'breakout model' of solar eruptions, whereby the emerging flux is initially constrained by a system of overlying magnetic field lines, and is able to erupt only after an opening develops in the overlying fields as a consequence of magnetic reconnection at a magnetic null point. In our case, the EIT crinkles would be a signature of this pre-impulsive phase magnetic reconnection, and brightening of the core only occurs after the core fields begin to escape through the newly created opening in the overlying fields. Morphology in soft X-ray images and properties in hard X-rays differ between the two events, with complexities that preclude a simple determination of the dynamics in the core at the times of eruption. From the BCS spectra, we find that the core region expends energy at a rate of approximately 10(exp 26) ergs/s during the time of the growth of the EIT crinkles; this rate is an upper limit to energy expended in the reconnections opening the overlying fields. Energy losses occur at an order of magnitude higher rate near the time of the peak of the events. There is little evidence of asymmetry in the spectra, consistent with the majority of the mass flows occurring normal to the line of sight. Both events have similar electron temperature dependencies on time.

Sterling, Alphonse C.↗

Separator Reconnection at the Magnetopause for Predominantly Northward and Southward IMF: Techniques and Results

In this work, we demonstrate how to track magnetic separators in three-dimensional simulated magnetic fields with or without magnetic nulls, apply these techniques to enhance our understanding of reconnection at the magnetopause. We present three methods for locating magnetic separators and apply them to 3-D resistive MHD simulations of the Earth's magnetosphere using the Block-Adaptive-Tree Solar-wind Roe-type Upwind Scheme code. The techniques for finding separators and determining the reconnection rate are insensitive to interplanetary magnetic field (IMF) clock angle and can in principle be applied to any magnetospheric model. Moreover, the techniques have a number of advantages over prior separator finding techniques applied to the magnetosphere. The present work examines cases of high and low resistivity for two clock angles. We go beyond previous work examine the separator during Flux Transfer Events (FTEs). Our analysis of reconnection on the magnetopause yields a number of interesting conclusions: Reconnection occurs all along the separator even during predominately northward IMF cases. Multiple separators form in low-resistivity conditions, and in the region of an FTE the separator splits into distinct branches. Moreover, the local contribution to the reconnection rate, as determined by the local parallel electric field, drops in the vicinity of the FTE with respect to the value when there are none.

modeling↗

Direct Imaging of Magnetohydrodynamic Wave Mode Conversion Near A 3D Null Point on the Sun

Mutual conversion of various kinds of magnetohydrodynamic (MHD) waves can have profound impacts on wave propagation, energy transfer, and heating of the solar chromosphere and corona. Mode conversion occurs when an MHD wave travels through a region where the Alfvén and sound speeds are equal (e.g., a 3D magnetic null point). Here we report the direct extreme ultraviolet (EUV) imaging of mode conversion from a fast-mode to a slow-mode MHD wave near a 3D null point using Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) observations. An incident fast EUV wavefront associated with an adjacent eruptive flare propagates laterally through a neighboring pseudostreamer. Shortly after the passage of the fast EUV wave through the null point, a slow-mode wave appears near the null that propagates upward along the open structures and simultaneously downward along the separatrix encompassing the fan loops of the pseudostreamer base. These observations suggest the existence of mode conversion near 3D nulls in the solar corona, as predicted by theory and MHD simulations. Moreover, we observe decaying transverse oscillations in both the open and closed structures of the pseudostreamer, along with quasiperiodic type III radio bursts indicative of repetitive episodes of electron acceleration.

Pankaj Kumar↗

Interpreting ion-energy distributions using charge exchange emitted from deeply kinetic field-reversed-configuration plasmas

Energy resolving the atomic hydrogen outflux created within plasmas by charge exchange (CX) of hot plasma ions with cooler hydrogen neutrals is used to infer the ion energy distribution within the plasma, IED p . In high- β plasma with field nulls and ion gyro-radii comparable to the plasma size, the measured ion energy distribution (IED m ) of the CX outflux will depend on the viewing angle and position of the detector. Here, we describe the physics for this, results from a synthetic diagnostic code that contrasts the IED m to the IED p within relatively small and hot field-reversed-configuration plasmas, and how these data can show the presence of magnetic nulls and different orbit classes in the plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Statistical analysis of magnetic divertor configuration influence on H-mode transitions

DIII-D plasmas are compared for two upper divertor configurations: with the outer strike point on the small angle slot (SAS) divertor target and with the outer strike point on the horizontal divertor target (HT). Scanning the vertical distance between the magnetic null point and the divertor target over a range 0.10–0.16 m is shown to increase the threshold power, $P_\mathrm{th}$, and edge plasma power, $P_\mathrm{Loss},$ for the low-to-high confinement (L–H) and H–L transitions respectively, by up to a factor of 1.4. The X-point height scans were performed at three L-mode core plasma line average electron densities, $\bar{n}_\mathrm{e} = $ 1.2, 2.2 and 3.6 $\times 10^{19}\,\mathrm{m}^{-3}$, to investigate the density dependence of divertor magnetic configuration influence on $P_\mathrm{th}$. The X-point height, $Z_\textrm{x-pt}$, was further extended across the range 0.16–0.22 m with the more open HT divertor configuration, for which a clear decrease in $P_\mathrm{th}$ with increasing $Z_\textrm{x-pt}$ is observed. The dependence of $P_\textrm{th}$ on divertor magnetic geometry is further investigated using a time-dependent probability density function (PDF) model and information geometry to elucidate the roles played by pedestal plasma turbulence and perpendicular velocity flows. The degree of stochasticity of the plasma turbulence is observed to be sensitive to the plasma heating rate. The calculated square of the information rate shows changes in the relative density fluctuations and perpendicular velocity PDFs begin 2–5 ms prior to the L–H transition for three plasmas; providing a crucial measurement of the dynamic timescale of external transport barrier formation. Additionally, both information length and rate provide potential predictors of the L–H transition for these plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Empirical probability and machine learning analysis of m , n = 2, 1 tearing mode onset parameter dependence in DIII-D H-mode scenarios

m, n = 2, 1 tearing mode onset empirical probability and machine learning analyses of a multiscenario DIII-D database of over 14 000 H-mode discharges show that the normalized plasma beta, the rotation profile, and the magnetic equilibrium shape have the strongest impact on the 2,1 tearing mode stability, in qualitative agreement with neoclassical tearing modes (m and n are the poloidal and toroidal mode numbers, respectively). In addition, 2,1 tearing modes are most likely to destabilize when n > 1 tearing modes are already present in the core plasma. The covariance matrix of tearing sensitive plasma parameters takes a nearly block-diagonal form, with the blocks incorporating thermodynamic, current and safety factor profile, separatrix shape, and plasma flow parameters, respectively. This suggests a number of paths to improved stability at fixed pressure and edge safety factor primarily by preserving a minimum of 1 kHz differential rotation, increasing the minimum safety factor above unity, using upper single null magnetic configuration, and reducing the core impurity radiation. In addition, lower triangularity, lower elongation, and lower pedestal pressure may also help to improve stability. Furthermore, the electron and ion temperature, collisionality, resistivity, internal inductance, and the parallel current gradient appear to only weakly correlate with the 2,1 tearing mode onsets in this database.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Divertor detachment characterization in negative triangularity discharges in DIII-D via 2D edge-plasma transport modeling

Edge fluid modeling of the first divertor-plasma detachment experiments in negative triangularity (NT) discharges in the DIII-D tokamak is presented using the 2D multifluid edge transport code UEDGE, including cross-field particle drifts. Experiments were performed where the lower single-null magnetic equilibrium had a strong NT (δ≈−0.5), that is, where the magnetic X-point is at a larger major radius than the core magnetic axis. Divertor-plasma detachment was induced by increasing the core plasma density in DIII-D via intrinsic gas puffing. Here density scans are performed with UEDGE to reach a detached plasma and to quantitatively recover the experimental rollover of the ion saturation current on the outer divertor target plate. The simulations cover experiments with both signs of the toroidal magnetic field, B T , where the ion magnetic Grad-B drifts are directed into (forward B T ) and out of (reverse B T ) the divertor region. Consistent with experiments with neutral beam power injection, the NT simulations reproduce: 40% higher density is needed to reach detachment onset with forward B T compared with reverse B T , and the absence of deep detachment is found with reverse B T . Similarly, comparison between Ohmic discharges in NT and positive triangularity (PT) shaping confirms that a substantially higher density is needed to achieve detachment in NT than in PT, with NT requiring an line-average density of at least the Greenwald density or higher. Simulation results suggest that higher densities are needed to reach detachment in negative compared to PT because these discharges have a shorter midplane-to-target distance along the total magnetic field B, a shorter outer divertor poloidal leg length (0.06 m vs 0.2 m), and reduced radial transport [near-scrape-off layer (SOL) D ⊥ /χ ⊥ =0.3/0.5 vs D ⊥ /χ ⊥ =1.0/1.0, all in (m 2 /s)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simulation of the SPARC plasma boundary with the UEDGE code

Here in this work, the UEDGE edge transport code is used to examine conditions in the SPARC divertor and edge plasma for various levels of carbon impurity and power from the core (P SOL ). A double-null magnetic configuration is simulated assuming up-down symmetry in geometry and physics. The anomalous heat and particle transport coefficients are tuned to match empirical predictions for SPARC's midplane density profiles, target plate heat flux profiles, and inner/outer divertor power sharing. Convective transport is included on the low-field side, while on the high-field side the transport is modeled as purely diffusive. Hydrogen neutrals are modeled as a fluid with inertial effects, and a carbon impurity is included using the fixed-fraction model. We find that detachment induced by impurity seeding could significantly reduce the heat flux to the divertor surfaces in the SPARC tokamak. At P SOL = 28 MW (the value predicted for SPARC's full-power H-mode scenario) cases with both divertor legs detached were obtained with a carbon impurity fraction between 0.3%–1.4%, far below Z eff limits for SPARC. When the plasma in the outer leg is detached, the peak heat flux density perpendicular to the target plate is below 1 MW m -2 , electron and ion temperatures are less than 1.5 eV, and momentum detachment is observed. However, the detachment state is found to be sensitive to the side-wall boundary conditions, the level of neutral pumping, and the target plate tilt. Finally, a broadly similar SOLPS simulation of SPARC is used to assess the appropriateness of the simpler impurity and neutral models used in UEDGE.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The effect of plasma shaping on high density H-mode SOL profiles and fluctuations in TCV

Abstract The impact of plasma shaping on the properties of high density H-mode scrape-off layer (SOL) profiles and transport at the outer midplane has been investigated on Tokamakà configuration variable. The experimental dataset has been acquired by evolving the upper triangularity while keeping the other parameters constant. The scan comprises δ u p values between 0.0 and 0.6, excluding negative triangularity scenarios. Within this study, a transition from type-I edge localised modes to the quasi-continuous exhaust regime takes place from low to high δ u p . The modification of the upstream SOL profiles has been assessed, in terms of separatrix quantities, within the α t turbulence control parameter theoretical framework (Eich et al 2020 Nucl. Fusion 60 056016). The target parallel heat load and the upstream near-SOL density profiles have been shown to broaden significantly for increasing α t . Correspondingly, in the far SOL a density shoulder formation is observed when moving from low to high δ u p . These behaviours have been correlated with an enhancement of the SOL fluctuation level, as registered by wall-mounted Langmuir probes as well as the thermal helium beam diagnostic. Specifically, both the background and the filamentary-induced fluctuating parts of the first wall ion saturation current signal are larger at higher δ u p , with filaments being ejected more frequently into the SOL. Comparison of two pulses at the extremes of the δ u p scan range, but with otherwise same input parameters, shows that the midplane neutral pressure does not change much during the H-mode phase of the discharge. This indicates that indirect effects of the change in geometry, linked to first wall recycling sources, should not play a significant role. The total core radiation increases at high δ u p , on account of a stronger plasma–wall interaction and resulting larger carbon impurity intake from the first wall. This is likely associated to the enhanced first wall fluctuations, as well as a smaller outer gap and the close-to-double-null magnetic topology at high shaping.

Stagni, A. (ORCID:0000000180841544)↗

On FIRE mode in KSTAR

We report on the status of Fast Ion Regulated Enhancement (FIRE) mode experiments in the Korea Superconducting Tokamak Advanced Research. This regime is being developed for high-performance, steady-state operation which features a stationary ion internal transport barrier, enabling a central ion temperature approaching 10 keV to be sustained for up to 50 s, without the need for delicate profile control and with no significant impurity accumulation. As its key novelty lies in the significant contribution of fast ions that stabilize core turbulence, the regime has been named FIRE mode. To achieve this regime, neutral beam injection is applied at moderate power levels near the L–H power threshold, while maintaining low plasma density to avoid the L–H transition. The scenario is typically established in diverted magnetic configurations. The core features of FIRE mode were investigated through power balance analysis and fluctuation measurements, revealing a clear transport bifurcation in the ion channel. At the plasma edge, FIRE mode occasionally exhibits I-mode characteristics, particularly in unfavorable magnetic null configurations with q 95 ∼ 4, including the presence of weakly coherent modes. In terms of MHD activity, sawtooth oscillations are observed but appear to be stabilized during the high-performance phase. Fast ion-driven Alfvénic eigenmodes (AEs), indicated by strong frequency chirping near 200 kHz, are also observed. Additionally, lower-frequency MHD activities, distinct from the fast ion-driven AEs, are present and have some influence on plasma performance. The enhancement of core confinement is primarily attributed to fast ion effects, which were evaluated with respect to dilution, alpha stabilization, and resonant interactions with turbulence using gyrokinetic analyses. Among these, the dilution effect was found to be the most dominant. The characteristics of FIRE mode were compared with those of other hot ion plasma scenarios, such as supershot and hot ion mode. While they share many similarities, FIRE mode is distinguished by the accessibility to conditions with T i ≈ T e , presence of I-mode edge features, and its long-duration sustainment. Predictive simulations of FIRE mode were performed using integrated transport modeling with TRIASSIC, employing the TGLF anomalous transport model. These simulations confirmed the critical role of fast ions in achieving this regime. The future prospect of FIRE mode for application in fusion reactors is discussed, with an emphasis on possibly extending the regime to higher density operation.

FIRE mode↗

Heating of the corona by magnetic singularities

Theoretical models of current-sheet formation and magnetic heating in the solar corona are examined analytically. The role of photospheric connectivity in determining the topology of the coronal magnetic field and its equilibrium properties is explored; nonequilibrium models of current-sheet formation (assuming an initially well connected field) are described; and particular attention is given to models with discontinuous connectivity, where magnetic singularities arise from smooth footpoint motions. It is shown that current sheets arise from connectivities in which the photospheric flux structure is complex, with three or more polarity regions and a magnetic null point within the corona.

Antiochos, Spiro K.↗

Reconnection of stressed magnetic fields

It is shown that magnetized plasma configurations under magnetic stress relax irreversibly to the state of minimum stress at a rate that is essentially Alfvenic provided a magnetic null is present. The relaxation is effected by the reconnection at the field null and proceeds at a rate proportional to the absolute value of ln(eta) exp-1, where eta is the resistivity. An analytic calculation in the linear regime is presented.

Hassam, A. B.↗

Ultraviolet Events Observed in Active Regions: An Interpretation of Flaring Arches and Associated Small Flares - 2

We analyze Hz, UV, and X-ray emissions in and around the spectacular arch system seen in the corona on 1980 March 27 during the Solar Maximum Mission. The flaring of the arch plasma is studied, and its dependence on triggering mechanisms related to the observed small limb flare in the arch footpoint is analyzed. To drive these events, we propose a mechanism in which small electric current circuits and the localized magnetic free energy are continuously generated at a magnetic null by a pressure gradient, which then compress or expand the plasma. This free energy dissipates by Joule effect and upward transport.

Fontenla, J.↗

Magnetic Roots and the Driving of Extended Coronal Heating

We report results from a continuation of a previous study, in which we found large bright coronal loops within active regions and extending from active regions that have one end rooted near an island of included magnetic polarity that is a site of enhanced coronal heating and microflares. This suggested that magnetic activity such as microflaring results in enhanced heating in both the compact core field around the island and in the large loops extending from it. We might expect that the intensity variations due to enhanced heating in the compact and extended structures would be correlated. However, although some ex- tended loops do respond to the largest events taking place in the core fields near their feet, they do not show a clear response to most smaller individual events nor to the overall envelope of coronal heating activity in the core fields at their feet as determined from longer-term observations. Thus, while it is clear that the extended loops' heating is being driven from their ends at the magnetic islands, much of this heating is apparently by some form of footpoint activity that is not strongly coupled to the heating in the footpoint core fields. One possibility is that the remote heating in the extended loops is driven by reconnection at the magnetic null over the island, and that this reconnection is driven mainly by core-field activity that produces little coronal heating within the core field itself, perhaps in the manner of the numerical simulations by Karpen, Antiochos, and DeVore.

Porter, Jason G.↗

H-alpha Proxies for EIT Crinkles: Further Evidence for Pre-Flare "Breakout"-Type Activity in an Ejective Solar Eruption

We present Halpha observations from Big Bear Solar Observatory of an eruptive flare in NOAA AR 8210, occurring near 22:30 UT on 1998 May 1. Previously, using the EUV Imaging Telescope (EIT) on the SOHO spacecraft, we found that a pattern of transient, localized brightenings, which we call "EIT crinkles," appears in the neighborhood of the eruption near the time of flare onset. These EIT crinkles occur at a location in the active region well separated from the sheared core magnetic fields, which is where the most intense features of the eruption are concentrated. We also previously found that high-cadence images from the Soft X-ray Telescope (SXT) on Yohkoh indicate that soft X-ray intensity enhancements in the core begin after the start of the EIT crinkles. With the Halpha data, we find remote flare brightening counterparts to the EIT crinkles. Lightcurves as functions of time of various areas of the active region show that several of the remote flare brightenings undergo intensity increases prior to onset of principle brightenings in the core region, consistent with our earlier findings from EIT and SXT data. These timing relationships are consistent with the eruption onset mechanism known as the breakout model, introduced by Antiochos and colleagues, which proposes that eruptions begin with reconnection at a magnetic null high above the core region. Our observations are also consistent with other proposed mechanisms which do not involve early reconnection in the core region. As a corollary, our observations are not consistent with the so-called tether cutting models, which say that the eruption begins with reconnection in the core. The Halpha data further show that a filament in the core region becomes activated near the time of EIT crinkle onset, but little if any of the filament actually erupts, despite the presence of a halo Coronal Mass Ejection (CME) associated with this event.

Sterling, Alphonse C.↗