Electron Acceleration Mechanism Research Articles

The observational evidence that all microflares that accelerate electrons to high energies are rooted in sunspots

Context. In general, large solar flares are more efficient at accelerating high-energy electrons than microflares. Nonetheless, sometimes microflares that accelerate electrons to high energies are observed. Their origin is unclear. Aims. We statistically characterized microflares with strikingly hard spectra in the hard X-ray (HXR) range, which means that they are efficient at accelerating high-energy electrons. We refer to these events as “hard microflares”. Methods. We selected 39 hard microflares, based on their spectral hardness estimated from the Solar Orbiter/STIX HXR quicklook light curves in two energy bands. The statistical analysis is built on spectral and imaging information from STIX combined with extreme ultraviolet (EUV) and magnetic field maps from SDO/AIA and SDO/HMI. Results. The key observational result is that all hard microflares in this dataset have one of the footpoint rooted directly within a sunspot (either in the umbra or the penumbra). This clearly indicates that the underlying magnetic flux densities are large. For the events with the classic two-footpoints morphology, the absolute value of the mean line-of-sight magnetic flux density (and vector magnetic field strength) at the footpoint rooted within the sunspot ranges from 600 to 1800 G (1500 to 2500 G), whereas the outer footpoint measures from 10 to 200 G (100 to 400 G), therefore about ten times weaker. In addition, approximately 78% of the hard microflares, which exhibited two HXR footpoints, have similar or even stronger HXR flux from the footpoint rooted within the sunspot. This contradicts the magnetic mirroring scenario. The median footpoint separation, measured through HXR observations, is approximately 24 Mm, which aligns with regular events of similar GOES classes. In addition, about 74% of the events could be approximated by a single-loop geometry, demonstrating that hard microflares typically have a relatively simple morphology. Out of these events, around 54% exhibit a relatively flat flare loop geometry. Conclusions. We conclude that all hard microflares are rooted in sunspots, which implies that the magnetic field strength plays a key role in efficiently accelerating high-energy electrons, with hard HXR spectra associated with strong fields. This key result will allow us to further constrain our understanding of the electron acceleration mechanisms in flares and space plasmas.

Electron Acceleration via Secondary Reconnection in the Separatrix Region of Magnetopause Reconnection

AbstractMagnetic reconnection is a fundamental process known to play a crucial role in electron acceleration and heating, however, the mechanism of electron energization during reconnection is still not fully understood. This study introduces a novel electron acceleration mechanism in which electrons can be accelerated by secondary reconnection in the separatrix region. The secondary reconnection occurs in a thin current sheet resulted from the shear of the out‐of‐plane Hall magnetic fields of the primary magnetopause reconnection. It results in the intense electron energy fluxes toward the primary X‐line. This mechanism will likely be an important piece in the puzzle of particle acceleration by reconnection.

Quantitative Analysis of Electron Heating and Acceleration in Coalescing Magnetic Flux Ropes at Earth's Magnetopause

AbstractCoalescence of magnetic flux ropes (MFRs) is suggested as a crucial mechanism for electron acceleration in various astrophysical plasma systems. However, how electrons are being accelerated/heated via MFR coalescence is not fully understood. In this paper, we quantitatively analyze electron heating and acceleration during the coalescence of three MFRs at Earth's magnetopause using in‐situ Magnetospheric Multiscale (MMS) observations. We find that suprathermal electrons are enhanced in the coalescing MFRs than those in the ambient magnetosheath and non‐coalescing MFRs. Both first‐order Fermi and E|| acceleration were responsible for this electron acceleration, while the overall effect of betatron process cooled the electrons. The most intense Fermi acceleration was observed in the trailing part of the middle MFR, while E|| acceleration occurred primarily at the reconnection sites between the coalescing MFRs. For non‐coalescing MFRs, the dominant mechanism for energizing electrons is the E|| acceleration. Our results further consolidate the important role of MFR coalescence in electron heating/acceleration in space plasma.

Statistical analysis of high-frequency whistler waves at Earth's bow shock: Further support for stochastic shock drift acceleration

We statistically investigate high-frequency whistler waves (with frequencies higher than ∼10% of the local electron cyclotron frequency) at Earth's bow shock using magnetospheric multi-scale (MMS) spacecraft observations. We focus specifically on the wave power within the shock transition layer, where we expect electron acceleration via stochastic shock drift acceleration (SSDA) to occur associated with efficient pitch-angle scattering by whistler waves. We find that the wave power is positively correlated with both the Alfvén Mach number in the normal incidence frame MA and in the de Hoffmann–Teller frame MA/cos θBn. The empirical relation with MA/cos θBn is compared with the theory of SSDA that predicts a threshold wave power proportional to (MA/cos θBn)−2. The result suggests that the wave power exceeds the theoretical threshold for MA/cos θBn≳30–60, beyond which efficient electron acceleration is expected. This aligns very well with previous statistical analysis of electron acceleration at Earth's bow shock [Oka et al., Geophys. Res. Lett. 33, 5–6 (2006)]. Therefore, we consider that this study provides further support for SSDA as the mechanism of electron acceleration at Earth's bow shock. At higher-Mach-number astrophysical shocks, SSDA will be able to inject electrons into the diffusive shock acceleration process for subsequent acceleration to cosmic-ray energies.

Analyzing electron acceleration mechanisms in magnetized plasma using Sinh–Gaussian pulse excitation

Analyzing electron acceleration mechanisms in magnetized plasma using Sinh–Gaussian pulse excitation

Over-30-GeV intense laser phase-locked direct electron acceleration

When an intense laser obliquely irradiates a solid, a pre-pulse will first ionize the solid surface, followed by the main pulse interacting with the plasma and ultimately being reflected by the plasma. Simultaneously, certain electrons within the plasma will be trapped in the accelerating phase of the laser field, subsequently gaining effective acceleration within the field, this phenomenon is known as phase-locked electron acceleration. Given the current intense lasers' electric field intensity nearing the TV/m range, electrons could potentially acquire energy levels on the order of hundreds of GeV or even TeV, provided they stay in the accelerating phase of the laser field long enough. Here, we initially use PIC (Particle-in-Cell) simulations to simulate the interaction process between laser pulses and plasma, thereby obtaining the properties of phase-locked electrons. In order to reduce computational demands, we turn to use a three-dimensional (3D) test particle model to calculate the subsequent interactions of these electrons with the reflected laser field. By this model, we obtain the data of the locked-phase electrons after having interacted with the reflected laser (Fig. (a)). Furthermore, we use this model to calculate the dynamical behavior of electrons under different initial conditions (Fig. (b)). Under the laser intensity of <inline-formula><tex-math id="M1">\begin{document}$ {a}_{0}=350 $\end{document}</tex-math></inline-formula>(<inline-formula><tex-math id="M2">\begin{document}$ {a}_{0} $\end{document}</tex-math></inline-formula> is the normalized laser vector potential), the energy of the electrons directly accelerated by the laser is enhanced to 32 GeV. In contrast, under the same laser intensity, the energy of the electrons accelerated by ponderomotive force is only 0.35 GeV. The research findings indicate that the strong laser with peak power around 10 PW can directly accelerate electrons to approximately 30 GeV. Additionally, this study outlines the optimal initial conditions for injecting electrons into the laser field and the final electron energy within the phase-locked acceleration mechanism, thereby establishing a calibration relationship with the laser field intensity. Given the continual enhancement of laser intensity and the potential application of the laser phase-locked electron acceleration mechanism to positron acceleration, this research holds promise for its implementation in fields such as miniaturized positron-electron colliders and high-energy gamma-ray sources.

Relativistic electron flux growth during storm and non-storm periods as observed by ARASE and GOES satellites

Variations of relativistic electron fluxes (E ≥ 1 MeV) and wave activity in the Earth magnetosphere are studied to determine the contribution of different acceleration mechanisms of the outer radiation belt electrons: ULF mechanism, VLF mechanism, and adiabatic acceleration. The electron fluxes were measured by Arase satellite and geostationary GOES satellites. The ULF power index is used to characterize the magnetospheric wave activity in the Pc5 range. To characterize the VLF wave activity in the magnetosphere, we use data from PWE instrument of Arase satellite. We consider some of the most powerful magnetic storms during the Arase era: May 27–29, 2017; September 7–10, 2017; and August 25–28, 2018. Also, non-storm intervals with a high solar wind speed before and after these storms for comparison are analyzed. Magnitudes of relativistic electron fluxes during these magnetic storms are found to be greater than that during non-storm intervals with high solar wind streams. During magnetic storms, the flux intensity maximum shifts to lower L-shells compared to intervals without magnetic storms. For the considered events, the substorm activity, as characterized by AE index, is found to be a necessary condition for the increase of relativistic electron fluxes, whereas a high solar wind speed alone is not sufficient for the relativistic electron growth. The enhancement of relativistic electron fluxes by 1.5–2 orders of magnitude is observed 1–3 days after the growth of the ULF index and VLF emission power. The growth of VLF and ULF wave powers coincides with the growth of substorm activity and occurs approximately at the same time. Both mechanisms operate at the first phase of electron acceleration. At the second phase of electron acceleration, the mechanism associated with the injection of electrons into the region of the magnetic field weakened by the ring current and their subsequent betatron acceleration during the magnetic field restoration can work effectively.Graphical

Hydrodynamic regime and cold plasmas hit by short laser pulses

AbstractWe briefly report and elaborate on some conditions allowing a hydrodynamic description of the impact of a very short and arbitrarily intense laser pulse onto a cold plasma, as well as the localization of the first wave-breaking due to the plasma inhomogeneity. We use a recently developed fully relativistic plane model whereby we reduce the system of the Lorentz–Maxwell and continuity PDEs into a 1-parameter family of decoupled systems of non-autonomous Hamilton equations in dimension 1, with the light-like coordinate $$\xi =ct\!-\!z$$ ξ = c t - z replacing time t as an independent variable. Apriori estimates on the Jacobian $$\hat{J}$$ J ^ of the change from Lagrangian to Eulerian coordinates in terms of the input data (initial density and pulse profile) are obtained applying Liapunov direct method to an associated family of pairs of ODEs; wave-breaking is pinpointed by the inequality $$\hat{J}\le 0$$ J ^ ≤ 0 . These results may help in drastically simplifying the study of extreme acceleration mechanisms of electrons, which have very important applications.

MMS Observation of Two‐Step Electron Acceleration at Earth's Bow Shock

AbstractWe use the Magnetospheric Multiscale mission to observe a bi‐directional electron acceleration event in the electron foreshock upstream of Earth's quasi‐perpendicular collisionless bow shock. The acceleration region is associated with a decrease in wave activity, inconsistent with common electron acceleration mechanisms such as Diffusive Shock Acceleration and Stochastic Shock Drift Acceleration. We propose a two‐step acceleration process where an electron field‐aligned beam acts as a seed population further accelerated by a shrinking magnetic bottle process, with the shock acting as the magnetic mirror(s).

On the impact of short laser pulses on cold diluted plasmas

We analytically study the impact of a (possibly, very intense) short laser pulse onto an inhomogeneous cold diluted plasma at rest, in particular: the duration of the hydrodynamic regime; the formation and the features of plasma waves (PWs); their wave-breakings (WBs); the motion of test electrons injected in the PWs.If the pulse is a plane wave travelling in the z-direction, and the initial plasma density (IPD) depends only on z, then suitable matched bounds on the maximum and relative variations of the IPD, as well as the intensity and duration of the pulse, ensure a strictly hydrodynamic evolution of the electron fluid during its whole interaction with the pulse, while ions can be regarded as immobile. This evolution is ruled by a family (parametrized by Z≥0) of decoupled systems of non-autonomous Hamilton equations with 1 degree of freedom, which determine how electrons initially located in the layer Z≤z<Z+dZ move; ξ=ct−z replaces time t as the independent variable. This family of ODEs is obtained by reduction from the Lorentz–Maxwell and continuity PDEs for the electrons’ fluid within the spacetime region where the change of the pulse is negligible. After the laser–plasma interaction the Jacobian of the map from Lagrangian to Eulerian coordinates is linear-quasi-periodic in ξ. We determine spacetime locations and features of the first wave-breakings of the wakefield PWs, the motion of test electrons (self-)injected in the PWs. The energy of those trapped in a single PW trough grows linearly with the distance gone, where the IPD is constant.If the pulse has cylindrical symmetry and a not too small radius, the same conclusions hold for the part of the plasma enclosed within the causal cone swept by it.This computationally light approach may help in a preliminary study of extreme acceleration mechanisms of electrons (LWFA, etc.), before 2D or 3D PIC simulations.

Effect of anode shape on neutron and x-ray emission in dense plasma focus

The neutron and x-ray production is investigated in various pulse-power devices for a deeper understanding of the ion and electron acceleration mechanisms and the application of pulsed neutron sources. We present the extensive results from an anode shape experiment carried out on the PFZ-200 plasma focus device. The various shapes of anodes were tested, including cylinders, tapers, or rounded tips. The experimental shots with a peak current above 200 kA were performed in pure deuterium working gas at 280–600 Pa pressure to obtain maximal neutron yield for each anode shape. The average neutron yields are in the range of (1–2) ×108 neutrons/shot. Outstanding findings about x-ray emission were obtained with the group of tapered anode tips. Using the scintillation detectors shielded by 5 cm thick lead bricks, we obtained the hard x-ray signals with photons exceeding 600 keV energy. Such relatively high x-ray energy indicates the optimized conditions for electron and ion acceleration. At the same time, the individual shots have been well reproducible. Therefore, we were able to study plasma dynamics with the schlieren images taken at different times at different shots.

The First AGILE Solar Flare Catalog

We report the Astro-rivelatore Gamma a Immagini LEggero (AGILE) observations of solar flares, detected by the onboard anticoincidence system in the 80–200 keV energy range, from 2007 May 1 to 2022 August 31. In more than 15 yr, AGILE detected 5003 X-ray, minute-lasting transients, compatible with a solar origin. A cross-correlation of these transients with the Geostationary Operational Environmental Satellites (GOES) official solar flare database allowed us to associate an intensity class (i.e., B, C, M, or X) to 3572 of them, for which we investigated the main temporal and intensity parameters. The AGILE data clearly revealed the solar activity covering the last stages of the 23rd cycle, the whole 24th cycle, and the beginning of the current 25th cycle. In order to compare our results with other space missions operating in the high-energy range, we also analyzed the public lists of solar flares reported by RHESSI and Fermi Gamma-ray Burst Monitor. This catalog reports 1424 events not contained in the GOES official data set, which, after statistical comparisons, are compatible with low-intensity, short-duration solar flares. Besides providing a further data set of solar flares detected in the hard X-ray range, this study allowed to point out two main features: a longer persistence of the decay phase in the high-energy regime, with respect to the soft X-rays, and a tendency of the flare maximum to be reached earlier in the soft X-rays with respect to the hard X-rays. Both these aspects support a two-phase acceleration mechanism of electrons in the solar atmosphere.

Electron Acceleration by Interaction of Two Filamentary Currents Within a Magnetopause Magnetic Flux Rope

AbstractTwo types of filamentary currents (FCs) were observed inside a magnetic flux rope at the magnetopause by the Magnetospheric Multiscale mission. The first FC is identified as an electron vortex, while the other is a reconnecting current sheet. Stochastic electric fields were generated within the FCs, resulting in electron acceleration up to a few keV, similar to recent simulations of electron acceleration inside vortex, which is a second‐order Fermi acceleration. Furthermore, two FCs propagated at different speeds, causing compression in the region between them. Energetic electrons up to 200 keV were detected in the compressed region and displayed a double power‐law spectrum. Observations suggest that the electrons were mainly accelerated by betatron mechanism in the compressed region. The formation, evolution, and interaction of FCs provide a novel mechanism for electron acceleration. These results clearly show the significance of electron‐scale dynamics within flux rope.

The Efficiency of Electron Acceleration during the Impulsive Phase of a Solar Flare

Solar flares are known to be prolific electron accelerators, yet identifying the mechanism(s) for such efficient electron acceleration in solar flare (and similar astrophysical settings) presents a major challenge. This is due in part to a lack of observational constraints related to conditions in the primary acceleration region itself. Accelerated electrons with energies above ∼20 keV are revealed by hard X-ray (HXR) bremsstrahlung emission, while accelerated electrons with even higher energies manifest themselves through radio gyrosynchrotron emission. Here, we show, for a well-observed flare on 2017 September 10, that a combination of RHESSI HXR and and the Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) EUV observations provides a robust estimate of the fraction of the ambient electron population that is accelerated at a given time, with an upper limit of ≲10−2 on the number density of nonthermal (≥20 keV) electrons, expressed as a fraction of the number density of ambient protons in the same volume. This upper limit is about 2 orders of magnitude lower than previously inferred from microwave observations of the same event. Our results strongly indicate that the fraction of accelerated electrons in the coronal region at any given time is relatively small but also that the overall duration of the HXR emission requires a steady resupply of electrons to the acceleration site. Simultaneous measurements of the instantaneous accelerated electron number density and the associated specific electron acceleration rate provide key constraints for a quantitative study of the mechanisms leading to electron acceleration in magnetic reconnection events.

Electron Heating in Magnetosheath Turbulence: Dominant Role of the Parallel Electric Field Within Coherent Structures

AbstractHow particles are being energized by turbulent electromagnetic fields is an outstanding question in plasma physics and astrophysics. This paper investigates the electron acceleration mechanism in strong turbulence (δB/B0 ∼ 1) in the Earth's magnetosheath based on the novel observations of the Magnetospheric Multiscale mission. We find that electrons are magnetized in turbulent fields for the majority of the time. By directly calculating the electron acceleration rate from Fermi, betatron mechanism, and parallel electric field, it is found that electrons are primarily accelerated by the parallel electric field within coherent structures. Moreover, the acceleration rate by parallel electric fields increases as the spatial scale reduces, with the most intense acceleration occurring over about one ion inertial length. This study is an important step toward fully understanding the turbulent energy dissipation in weakly collisional plasmas.

The role of laser chirp in relativistic electron acceleration using multi-electron gas targets

The role of multi-10 TW chirped laser pulses interacting with N2 gas jet targets, as a test case for multi-electron targets, is experimentally examined. Complementary measurements using He gas jet targets, which are fully ionized well before the laser pulse peak, are also presented for comparison with the measurements for the multi-electron N2 targets. It is found that for both gases positively chirped laser pulses accelerate electrons more efficiently compared to the Fourier transform-limited and negatively chirped pulses. Furthermore, multi-electron targets offer additional electron injection mechanisms for efficient electron acceleration as a function of the chirp, due to the dynamic ionization of inner-shell electrons near the peak of the laser pulse. Finally, we show that the background plasma density value plays a critical role in the efficient acceleration of positively chirped pulses as well as in the tuning of the positive chirp value for maximizing the electron energy. We clearly observe that larger plasma density values require higher positive chirp values for efficient electron acceleration.

Efficient Electron Acceleration Driven by Flux Rope Evolution during Turbulent Reconnection

Magnetic flux ropes or magnetic islands are important structures responsible for electron acceleration and energy conversion during turbulent reconnection. However, the evolution of flux ropes and the corresponding electron acceleration process still remain open questions. In this paper, we present a comparative study of flux ropes observed by the Magnetospheric Multiscale mission in the outflow region during an example of turbulent reconnection in Earth's magnetotail. Interestingly, we find the farther the flux rope is away from the X-line, the bigger the size of the flux rope and the slower it moves. We estimate the power density converted at the observed flux ropes via the three fundamental electron acceleration mechanisms: Fermi, betatron, and parallel electric field. The dominant acceleration mechanism at all three flux ropes is the betatron mechanism. The flux rope that is closest to the X-line, having the smallest size and the fastest moving velocity, is the most efficient in accelerating electrons. Significant energy also returns from particles to fields around the flux ropes, which may facilitate the turbulence in the reconnection outflow region.

Electron acceleration by laser plasma wedge interaction

A new electron acceleration mechanism is identified that develops when a relativistically intense laser irradiates the wedge of an over-dense plasma. This induces a diffracted electromagnetic wave with a significant longitudinal electric field that accelerates electrons from the plasma over long distances to relativistic energies. Well collimated, highly-charged (nC) electron bunches with energies up to 100's MeV are obtained using a laser beam with $I \lambda_0^2 =3.5\times 10^{19}\,{\rm W \mu m^2/cm^2}$. Multi-dimensional particle-in-cell simulations, supported by a simple analytical model, confirm the efficiency and robustness of the proposed acceleration scheme.

Intense Whistler-mode Waves at Foreshock Transients: Characteristics and Regimes of Wave−Particle Resonant Interaction

Thermalization and heating of plasma flows at shocks result in unstable charged-particle distributions that generate a wide range of electromagnetic waves. These waves, in turn, can further accelerate and scatter energetic particles. Thus, the properties of the waves and their implication for wave−particle interactions are critically important for modeling energetic particle dynamics in shock environments. Whistler-mode waves, excited by the electron heat flux or a temperature anisotropy, arise naturally near shocks and foreshock transients. As a result, they can often interact with suprathermal electrons. The low background magnetic field typical at the core of such transients and the large wave amplitudes may cause such interactions to enter the nonlinear regime. In this study, we present a statistical characterization of whistler-mode waves at foreshock transients around Earth’s bow shock, as they are observed under a wide range of upstream conditions. We find that a significant portion of them are sufficiently intense and coherent (narrowband) to warrant nonlinear treatment. Copious observations of background magnetic field gradients and intense whistler wave amplitudes suggest that phase trapping, a very effective mechanism for electron acceleration in inhomogeneous plasmas, may be the cause. We discuss the implications of our findings for electron acceleration in planetary and astrophysical shock environments.

Properties and Acceleration Mechanisms of Electrons Up To 200keV Associated With a Flux Rope Pair and Reconnection X-Lines Around It in Earth's Plasma Sheet.

The properties and acceleration mechanisms of electrons (<200keV) associated with a pair of tailward traveling flux ropes and accompanied reconnection X-lines in Earth's plasma sheet are investigated with MMS measurements. Energetic electrons are enhanced on both boundaries and core of the flux ropes. The power-law spectra of energetic electrons near the X-lines and in flux ropes are harder than those on flux rope boundaries. Theoretical calculations show that the highest energy of adiabatic electrons is a few keV around the X-lines, tens of keV immediately downstream of the X-lines, hundreds of keV on the flux rope boundaries, and a few MeV in the flux rope cores. The X-lines cause strong energy dissipation, which may generate the energetic electron beams around them. The enhanced electron parallel temperature can be caused by the curvature-driven Fermi acceleration and the parallel electric potential. Betatron acceleration due to the magnetic field compression is strong on flux rope boundaries, which enhances energetic electrons in the perpendicular direction. Electrons can be trapped between the flux rope pair due to mirror force and parallel electric potential. Electrostatic structures in the flux rope cores correspond to potential drops up to half of the electron temperature. The energetic electrons and the electron distribution functions in the flux rope cores are suggested to be transported from other dawn-dusk directions, which is a 3-dimensional effect. The acceleration and deceleration of the Betatron and Fermi processes appear alternately indicating that the magnetic field and plasma are turbulent around the flux ropes.