Betatron Mechanism Research Articles

Abstract It is widely recognized that adiabatic acceleration plays an essential role in the dynamics of the solar wind electron distribution. Nevertheless, the role of electron adiabatic cooling remains poorly understood, at least from an observational standpoint. Even the betatron cooling has never been verified in the solar wind. Here, we present a distinct event of simultaneous betatron cooling of halo and strahl electrons in a small-scale magnetic structure, probably due to a local expansion (weakening of magnetic field strength). The betatron cooling results in the drop of electron differential fluxes, which peaks in the quasi-perpendicular direction and smoothly decreases toward the field-aligned direction. The cooling processes of halo and strahl electrons via the betatron mechanism are well reproduced using an ideal adiabatic acceleration/cooling model.

A growing body of evidence from observations, theories, and simulations indicates that particles can be effectively accelerated in solar wind regions filled with dynamic small-scale flux ropes (FRs). The main acceleration mechanisms identified in simulations include parallel electric field acceleration, first-order Fermi acceleration, and generalized betatron acceleration in contracting or merging small-scale FRs. However, direct identification of these acceleration mechanisms from in situ measurements remains a challenge. Here we present a distinct event of local betatron acceleration within a contracting small-scale FR in the solar wind, due to a local compression. In this event, the lower-energy halo electrons were effectively accelerated through the betatron mechanism, whereas the higher-energy suprathermal electrons predominated by the superhalo component were almost not energized. The halo electron energization processes via the betatron mechanism are reproduced using an analytical model. Further examination of small-scale FRs in the vicinity of the heliospheric current sheet over the period 1995–2020 indicates that in situ signatures of the betatron acceleration process are essentially elusive.

Magnetic reconnection driven by a capacitor coil target is an innovative way to investigate low-β magnetic reconnection in the laboratory, where β is the ratio of particle thermal pressure to magnetic pressure. Low-β magnetic reconnection frequently occurs in the Earth’s magnetosphere, where the plasma is characterized by β ≲ 0.01. In this paper, we analyze electron acceleration during magnetic reconnection and its effects on the electron energy spectrum via particle-in-cell simulations informed by parameters obtained from experiments. We note that magnetic reconnection starts when the current sheet is down to about three electron inertial lengths. From a quantitative comparison of the different mechanisms underlying the electron acceleration in low-β reconnection driven by coil targets, we find that the electron acceleration is dominated by the betatron mechanism, whereas the parallel electric field plays a cooling role and Fermi acceleration is negligible. The accelerated electrons produce a hardened power-law spectrum with a high-energy bump. We find that injecting electrons into the current sheet is likely to be essential for further acceleration. In addition, we perform simulations for both a double-coil co-directional magnetic field and a single-coil one to eliminate the possibility of direct acceleration of electrons beyond thermal energies by the coil current. The squeeze between the two coil currents can only accelerate electrons inefficiently before reconnection. The simulation results provide insights to guide future experimental improvements in low-β magnetic reconnection driven by capacitor coil targets.

Abstract We analyzed changes in the height of the coronal hard X-ray (HXR) source for flares SOL2013-05-13T01:50 and SOL2013-05-13T15:51. Analysis of the Reuven Ramaty High Energy Solar Spectroscopic Imager data revealed the downward motion of the HXR source and the separation of the sources by energy and height. In the early stages of the flares, a negative correlation was found between the HXR source area in the corona and HXR flux. For the SOL2013-05-13T15:51 event, an increasing trend in the time delay spectra at the footpoints was obtained. For both events, the spectra of the time delays in the coronal HXR source showed a decreasing trend with energy in certain flare phases. To interpret the observed phenomena, we considered a flare model of collapsing traps and calculated the distribution functions of accelerated electrons along the magnetic loop using a nonstationary relativistic kinetic equation. This approach considers betatron and Fermi first-order acceleration mechanisms. The increasing trend of the time delay spectra at the footpoints was explained by the high mirror ratio in the magnetic loop and betatron acceleration mechanism. The observed features in the spatial and temporal behavior of the HXR sources, such as the negative correlation between the HXR source area and HXR flux, can be interpreted by the collapsing trap model.

Abstract Two 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 dramatic changes in the magnetic field at the dipolarization front (DF) provide a suitable environment for electron acceleration, which usually can cause the flux enhancement of energetic electrons behind the front. However, it is unknown whether energetic electrons observed at the DF are energized locally, and which mechanism accelerates the electrons at the DF is unclear. Our study performs a direct quantitative analysis to reveal the acceleration process of energetic electrons at the DF using the high-time-resolution data from NASA's Magnetospheric Multiscale mission. The fluxes of energetic electrons at 90° are enhanced at the front. Under adiabatic conditions, our quantitative analysis indicates that these electrons at the front could be locally accelerated to over 100 keV by betatron acceleration. Eventually, the electron temperature anisotropy formed via the betatron mechanism could provide the free energy to excite whistler waves at the DF. Our quantitative study provides, for the first time, strong direct evidence for the local electron acceleration at the DF.

Abstract How 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.

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.

The most recent findings on the dynamics of the outer radiation belt (ORB) and the physics of magnetospheric substorms are examined. Specifically, we investigate the relationship between storm time substorms and the energetic electron population that forms the ORB. Traditionally, storm time substorms have been considered as the primary source of energetic electrons, which are further accelerated during storms to contribute to the formation of the ORB. However, several observations have demonstrated that large magnetospheric substorms can generate high-energy electrons even in the absence of magnetic storms. Substorms introduce dispersionless injections of energetic electrons deep into the magnetosphere from the geosynchronous orbit during storm times. The injected electrons undergo additional acceleration via the betatron mechanism during the storm recovery phase, thus increasing the ORB population. To gain a better understanding of this process, it is crucial to study plasma sheet turbulence, substorm onset processes, and the brightening of auroral arcs. By analyzing the aforementioned findings, this study aims to highlight the need for reanalyzing of the role of auroral processes in the formation of the ORB.

The magnetic merging process related to pairwise magnetic islands coalescence is investigated by two-dimensional particle-in-cell simulations with a guide field. Owing to the force of attraction between parallel currents within the initial magnetic islands, the magnetic islands begin to approach each other and merge into one big island. We find that this newly formed island is unstable and can be divided into two small magnetic islands spontaneously. Lastly, these two small islands merge again. We follow the time evolution of this process, in which the contributions of three mechanisms of electron acceleration at different stages, including the Fermi, parallel electric field, and betatron mechanisms, are studied with the guide center theory.

We compare ESA PROBA-V observations of electron flux at LEO with those from the NASA Van Allen Probes mostly at MEO for October 2013. Dropouts are visible at all energy during four storms from both satellites. Equatorially trapped electron fluxes are higher than at LEO by 102 (<1MeV) to 105 (>2.5MeV). We observe a quite isotropic structure of the outer belt during quiet times, contrary to the inner belt, and pitch angle dependence of high energy injection. We find a very good overlap of the outer belt at MEO and LEO at ∼0.5MeV. We use test-particle simulations of the energetic electrons trapped in the terrestrial magnetic field to study the outer radiation belt electron flux changes during geomagnetic storms. We show that the Dst (Disturbance storm time) effect during the main phase of a geomagnetic storm results in a betatron mechanism causing outward radial drift and a deceleration of the electrons. This outward drift motion is energy independent, pitch angle-dependent, and represents a significant distance (∼1 L-shell at L=5 for moderate storms). At fixed L-shell, this causes a decay of the LEO precipitating flux (adiabatic outward motion), followed by a return to the normal state (adiabatic inward motion) during main and recovery phases. Dst effect, associated with magnetopause shadowing and radial diffusion can explain the main characteristics of outer radiation belt electron dropouts in October 2013. We also use Fokker-Planck simulations with event-driven diffusion coefficients at high temporal resolution, to distinguish instantaneous loss from the gradual scattering that depopulates the slot region and the outer belt after storms. Simulations reproduce the slot formation and the gradual loss in the outer belt. The typical energy dependence of these losses leads to the absence of scattering for relativistic and ultra-relativistic electrons in the outer belt, oppositely to dropouts.

Abstract A series of intermittent coherent structures was observed in magnetosheath turbulence in the form of magnetic peaks. These magnetic peaks are always accompanied with enhancement of local current density, and three of them are studied in detail because of their intense current density. Based on the magnetic field signals, magnetic curvatures, and the toroidal magnetic field lines, three peaks are identified as magnetic flux ropes. In each trailing part of these three peaks, an extremely thin electron current layer was embedded within a much broader ion‐scale current layer. The energy dissipation is evident within the peaks and direct evidence of magnetic reconnection was found within the thinnest electron current layer. The electrons were heated mainly in two regions of magnetic peaks, that is, the reconnecting current layer by parallel electric field and the trailing edges by Fermi and betatron mechanisms. These results suggest that the ion‐scale magnetic peaks are coherent structures associated with energy dissipation and electron heating in the magnetosheath. Thin current layers can be formed in magnetic peaks, and magnetic reconnection can play a significant role for the energy dissipation in magnetic peaks.

Abstract Although it has been shown that betatron and Fermi mechanisms contribute to electron acceleration at the dipolarization front (DF), the relative efficiency of these acceleration processes is unclear. In this paper, we directly calculate the electron adiabatic acceleration rate (the instantaneous acceleration) at DFs by using the data from the Magnetospheric Multiscale mission. We find that betatron acceleration dominates at the DF. Although the Fermi acceleration rate is smaller than the betatron acceleration rate, it is effective on a larger spatial scale than betatron acceleration, which is localized at the DF proper. The acceleration by the parallel electric field is negligible because it is far below the measurement uncertainties. The dependence of these acceleration rates on the DF normal, magnetic field, and thickness of the DF are analyzed. Our results provide important information for understanding the electron acceleration in the Earth's magnetotail.

Abstract A long‐standing problem concerning dipolarization front (DF) is why energetic electrons only appear in half the DF events? By analyzing MMS measurements, here we answer this question. We find a DF structure, behind which energetic‐electron fluxes are modulated by magnetosonic waves: At wave troughs (B‐minimum) electron fluxes are high; at wave crests (B‐maximum) electron fluxes are low. This phenomenon challenges the classical theory of betatron mechanism, so we need to propose a new theory to explain it. In our theory, there exists a magnetic bottle with time‐varying belly but steady neck behind the DF. When the belly expands, a magnetic bottle is formed, and electrons are trapped; when the belly contracts, the magnetic bottle disappears, and electrons are expelled. Quantitatively, we validate the existence of this bottle and estimate its size as 2–3 RE. Our theory can explain both the presence and absence of energetic electrons behind DFs.

Abstract Energetic electrons have frequently been observed in small‐scale flux ropes. However, whether these energetic electrons were energized directly within the flux rope or not is unknown. In this paper, we present concrete evidence provided by the Magnetospheric Multiscale mission that a secondary flux rope provided strong acceleration for electrons expelled by the reconnection X line. We find that the energetic electron fluxes inside the ion‐scale flux rope were larger than those outside the flux rope. Electrons were adiabatically accelerated by betatron and Fermi mechanisms inside the flux rope. The highest energy electrons (&gt;100 keV) were produced by betatron acceleration, whereas Fermi acceleration was unable to accelerate the electrons to high energy probably due to the finite distance of the acceleration region along the field‐aligned direction. These results confirm the essential role of ion‐scale flux ropes in producing energetic electrons.

In this paper, the particle acceleration processes around magnetotail dipolarization fronts (DFs) were reviewed. We summarize the spacecraft observations (including Cluster, THEMIS, MMS) and numerical simulations (including MHD, test-particle, hybrid, LSK, PIC) of these processes. Specifically, we (1) introduce the properties of DFs at MHD scale, ion scale, and electron scale, (2) review the properties of suprathermal electrons with particular focus on the pitch-angle distributions, (3) define the particle-acceleration process and distinguish it from the particle-heating process, (4) identify the particle-acceleration process from spacecraft measurements of energy fluxes, and (5) quantify the acceleration efficiency and compare it with other processes in the magnetosphere (e.g., magnetic reconnection and radiation-belt acceleration processes). We focus on both the acceleration of electrons and ions (including light ions and heavy ions). Regarding electron acceleration, we introduce Fermi, betatron, and non-adiabatic acceleration mechanisms; regarding ion acceleration, we present Fermi, betatron, reflection, resonance, and non-adiabatic acceleration mechanisms. We also discuss the unsolved problems and open questions relevant to this topic, and suggest directions for future studies.

Magnetic reconnection is considered to be one important source to produce energetic electrons. In this paper, two-dimensional (2D) particle-in-cell (PIC) simulations are performed to investigate electron acceleration during the merging process of multiple magnetic islands in a current sheet with a strong guide field. Due to the existence of the strong guide field, we can analyze the contributions of the parallel electric field, Fermi, and betatron mechanisms to the electron acceleration with the guiding-center theory. During the coalescence process of magnetic islands, the islands merge each other continuously until only one large island remains. Energetic electrons are generated during such process, and the electrons with sufficient high energy develop a power-law spectrum. We also investigate the dependence of the index of the power-law spectra on the shape of magnetic islands, electron plasma beta, the number of magnetic islands, and the guide field.

Abstract Magnetic reconnection—the process typically lasting for a few seconds in space—is able to accelerate electrons. However, the efficiency of the acceleration during such a short period is still a puzzle. Previous analyses, based on spacecraft measurements in the Earth’s magnetotail, indicate that magnetic reconnection can enhance electron fluxes up to 100 times. This efficiency is very low, creating an impression that magnetic reconnection is not good at particle acceleration. By analyzing Cluster data, we report here a remarkable magnetic reconnection event during which electron fluxes are enhanced by 10,000 times. Such acceleration, 100 times more efficient than those in previous studies, is caused by the betatron mechanism. Both reconnection fronts and magnetic islands contribute to the acceleration, with the former being more prominent.

A new combined Fermi, betatron, and turbulent electron acceleration mechanism is proposed in interaction of magnetic islands during turbulent magnetic reconnection evolution in explosive astrophysical phenomena at large temporal-spatial scale (LTSTMR), the ratio of observed current sheets thickness to electron characteristic length, electron Larmor radius for low-β and electron inertial length for high-β, is on the order of 1010–1011; the ratio of observed evolution time to electron gyroperiod is on the order of 107–109). The original combined acceleration model is known to be one of greatest importance in the interaction of magnetic islands; it assumes that the continuous kinetic-dynamic temporal-spatial scale evolution occurs as two separate independent processes. In this paper, we reconsider the combined acceleration mechanism by introducing a kinetic-dynamic-hydro full-coupled model instead of the original micro-kinetic or macro-dynamic model. We investigate different acceleration mechanisms in the vicinity of neutral points in magnetic islands evolution, from the stage of shrink and breakup into smaller islands (kinetic scale), to the stage of coalescence and growth into larger islands (dynamic scale), to the stages of constant and quasi-constant (contracting-expanding) islands (hydro scale). As a result, we give for the first time the acceleration efficiencies of different types of acceleration mechanisms in magnetic islands’ interactions in solar atmosphere LTSTMR activities (pico-, 10–2–105 m; nano-, 105–106 m; micro-, 106–107 m; macro-, 107–108 m; large-, 108–109 m).

The dynamics of high-energy electron fluxes (with energies over 40 keV) is analyzed in 13 events of magnetic field dipolization observed by the Cluster satellites in the near-tail of the Earth magnetosphere. In all of the events, the observed energetic electron fluxes are enhanced simultaneously with initial dipolization. Good correlation (correlation coefficient >0.6) is observed between the dynamics of the energetic electron fluxes with energies up to 90 keV and the B-Z component of the magnetic field. Electron fluxes with higher energies display a decline of correlation with the magnetic field. The increase in electron fluxes with energies up to 90 keV during dipolization development is shown to be mainly due to the mechanism of betatron acceleration. The dynamics of electron fluxes with higher energies is poorly described by the betatron scenario and requires consideration of other, probably nonadiabatic, mechanisms.