Flux Tubes Research Articles

Dynamics and emission properties of flux ropes from two-temperature GRMHD simulations with multiple magnetic loops

Flux ropes erupting in the vicinity of a black hole are thought to be a potential model for the flares observed in Sagittarius\,A$^*$. In this study, we examine the radiative properties of flux ropes that emerged in the vicinity of a black hole. We performed three-dimensional two-temperature general relativistic magnetohydrodynamic (GRMHD) simulations of magnetized accretion flows with alternating multiple magnetic loops and general relativistic radiation transfer (GRRT) calculations. In the GRMHD simulations, we implemented two different sizes of initial magnetic loops. In the small loop case, magnetic dissipation leads to a weaker excitement of magneto-rotational instability inside the torus, which generates a lower accretion rate compared to the large loop case. However, the small loop case generates more flux ropes due to frequent reconnection by magnetic loops with different polarities. By calculating the thermal synchrotron emission, we found that the variability of light curves and the emitting region are tightly related. At $230\ GHz$ and higher, the emission from the flux ropes is relatively stronger compared to the background, which is responsible for the filamentary structure in the images. At lower frequencies (e.g. $43\ GHz$), emission comes from more extended regions, which have a less filamentary structure in the image. Our study shows that self-consistent electron temperature models are essential for the calculation of thermal synchrotron radiation and the morphology of the GRRT images. Flux ropes contribute considerable emission at frequencies $ GHz$.

Assistance force-line of exosuit affects ankle multidimensional motion: a theoretical and experimental study

BackgroundThe talocrural joint and the subtalar joint are the two major joints of the ankle-joint complex. The position and direction of the exosuit force line relative to these two joint axes can influence ankle motion. We aimed to understand the effects of different force-lines on ankle multidimensional motion.MethodsIn this article, three assistance force line schemes for ankle exosuits were proposed: perpendicular to the talocrural joint axis (PT), intersecting with the subtalar joint axis (IS), and parallel to the triceps surae (PTS). A theoretical model was proposed to calculate the exosuit’s assistance moment. Seven participants completed four experimental tests of ankle plantarflexion, including three passive motions assisted by the PT, PTS and IS schemes, and one active motion without exosuit assistance (Active).ResultsThe simulation results demonstrated that all three exosuits were able to produce significant moments of ankle plantarflexion. Among these, the PT scheme exhibited the highest moments in all dimensions, followed by the PTS and IS schemes. The experimental findings confirmed the effectiveness of all three exosuit schemes in assisting ankle plantarflexion. Additionally, as the assistive force lines approached the subtalar joint, there was a decrease in ankle motion assisted by the exosuits in non-plantarflexion directions, along with a reduction in the average distance of ankle angle curves relative to active ankle motion. Furthermore, the linear correlation coefficients between inversion and plantarflexion, adduction and plantarflexion, and adduction and inversion gradually converged toward active ankle plantarflexion motion.ConclusionsOur research indicates that the position of the exosuit force line to the subtalar joint has a significant impact on ankle inversion and adduction. Among all three schemes, the IS, which has the closest distance to the subtalar joint axes, has the greatest kinematic similarity to active ankle plantarflexion and might be a better choice for ankle assistance and rehabilitation.

Eruption of a Million-Kelvin Warm Magnetic Flux Rope on the Sun

Solar magnetic flux rope (MFR) plays a central role in the physics of coronal mass ejections (CMEs). It mainly includes a cold filament at typical chromospheric temperatures (∼10,000 K) and a hot channel at high coronal temperatures (∼10 MK). The warm MFR at quiescent coronal temperatures of a million Kelvin is, however, rarely reported. In this study, using multiwavelength images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory and Extreme Ultraviolet Imager (EUVI) on board the Solar Terrestrial Relations Observatory-A, we present an eruption of a warm channel that represents an MFR with quiescent coronal temperatures (∼0.6–2.5 MK). On 2022 May 8, we observed the failed eruption of a hot channel, with the average temperature and emission measure (EM) of 10 MK and 1.1 × 1028 cm−5, using AIA high-temperature images in the active region (AR) 13007. This failed eruption was associated with a C8.2 flare, with no CME. Subsequently, we observed a warm channel that appeared in AIA and EUVI low-temperature images rather than in AIA high-temperature images. It then erupted and transformed into a semicircular shape. An associated C2.1 flare, along with the signatures of magnetic reconnection in AIA high-temperature images, were identified. Additionally, we observed a CME associated with this event. Compared with the hot channel, the warm channel is cooler and rarer with the average temperature and EM of 1.7 (1.6) MK and 2.0 × 1026 (2.3 × 1026) cm−5. All the results suggest an unambiguous observation of the million-Kelvin warm MFR that erupted as a CME and fill a gap in the temperature domain of coronal MFRs.

Pure gauge flux tube and running coupling from EMT at high temperature

Pure gauge flux tube and running coupling from EMT at high temperature

Super-X and Conventional divertor configurations in MAST-U ohmic L-mode; a comparison facilitated by interpretative modelling

Abstract Measurements are presented, alongside corresponding interpretative SOLPS-ITER simulations, of the first MAST-U experiments comparing ohmically heated L-mode fuelling scans in Conventional divertor (CD) and Super-X divertor (SXD) configurations. In experiment, at comparable outer mid-plane separatrix electron density, $n_{e,\rm{sep,OMP}}$, the maximum lower outer target heat load was found to be a factor 16$\pm7$ lower in SXD compared to CD. In simulation, a factor 26.8 reduction was found (slightly higher than the experimental range), suggesting an additional reduction in SXD compared to the factor 9.3 expected from geometric considerations alone. According to the simulations, this additional reduction in the SXD is due to a net radial transport of the energy remaining downstream of the $T_e=5$ eV location. This energy is carried out of the critical (highest heat load) flux tube by deuterium atoms, demonstrating the importance of a longer legged divertor which provides space for this to occur. Importantly, in both simulation and experiment, the SXD has minimal impact on the upstream $n_e$ and $T_e$ profiles. Spectral inferences of detachment front movement in SXD compare well between simulation and experiment. In regions of high magnetic field gradient, the parallel movement of the front towards the X-point becomes less sensitive to increasing $n_{e,\rm{sep,OMP}}$, in qualitative agreement with simplified models and previous predictive simulations. Additional aspects, regarding the target ion flux rollover, upstream separatrix temperature and drift effects, are also presented and discussed.

An Additional Note to “A New Insight into the Linear Theory of Magnetoacoustic Waves in the Homogeneous Flux Tubes with an Abrupt Boundary”

This is to address the criticism expressed in the article (Goedbloed & Poedts ) referred to as GP[24] about the work (Yelagandula ) referred to as Y[23]. It will be shown that the dispersion relation obtained in Y[23] is indeed correct within the framework of the ZSER model discussed in Y[23] despite the correct criticism of GP[24] about the electrodynamic boundary condition.

Internal magnetic field structures observed by PSP/WISPR in a filament-related coronal mass ejection

We investigated the coronal mass ejection (CME) related to an eruptive filament over the southwestern solar limb on December 8, 2022, at around 8 UT. We tracked localized density enhancements reflecting the magnetic structures using white-light data taken with the Wide-field Instrument for Solar PRobe (WISPR) aboard the Parker Solar Probe (PSP). We aim to investigate the 3D location, morphology and evolution of the internal magnetic fine structures of CMEs. Specifically, we focused on the physical origin of the features in the WISPR images, how the white-light structures evolve over time, and their relationship with the source region, filament, and the flux rope. The fast tangential motion of the PSP spacecraft during its perihelion permits a single event to be viewed from multiple angles in short times relative to the event's evolution. Hence, three-dimensional information of selected CME features can be derived from this single spacecraft using triangulation techniques. We grouped small-scale structures with roughly similar speeds, longitude, and latitude into three distinct morphological groups. We found twisted magnetic field patterns close to the eastern leg of the CME that may be related to "horns" outlining the edges of the flux-rope cavity. We identified aligned thread-like bundles close to the western leg, and they may be related to confined density enhancements evolving during the filament eruption. High density blob-like features (magnetic islands) are widely spread in longitude (sim 40°) close to the flanks and the rear part of the CME. We also note that the large-scale outer envelope of the CME, seen clearly from 1 AU, was not well observed by PSP. We demonstrate that CME flux ropes, apart from the blobs, may comprise different morphological groups with a cluster behavior; the blobs instead span a wide range of longitudes. This finding may hint at either the three-dimensionality of the post-CME current sheet (CS) or the influence of the ambient corona in the evolutionary behavior of the CS. Importantly, we show that the global appearance of the CME can be very different in WISPR (0.11--0.16 AU) and the instruments near 1 AU because of the shorter line-of-sight integration of WISPR.

Joint action of phase mixing and nonlinear effects in MHD waves propagating in coronal loops

The evolution of Alfv\'en waves in cylindrical magnetic flux tubes, which represent a basic model for loops observed in the solar corona, can be affected by phase mixing and turbulent cascade. Phase mixing results from transverse inhomogeneities in the Alfv\'en speed, causing different shells of the flux tube to oscillate at different frequencies, thus forming increasingly smaller spatial scales in the direction perpendicular to the guide field. Turbulent cascade also contributes to the dissipation of the bulk energy of the waves through the generation of smaller spatial scales. Both processes present characteristic timescales. Different regimes can be envisaged according to how those timescales are related and to the typical timescale at which dissipation is at work. We investigate the interplay of phase mixing and the nonlinear turbulent cascade in the evolution and dissipation of Alfv\'en waves using compressible magnetohydrodynamic numerical simulations. We consider perturbations in the form of torsional waves, both propagating and standing, or turbulent fluctuations, or a combination of the two. The main purpose is to study how phase mixing and nonlinear couplings jointly work to produce small scales in different regimes. We conducted a numerical campaign to explore the typical parameters, such as the loop length, the amplitude and spatial profile of the perturbations, and the dissipative coefficients. A pseudo-spectral code was employed to solve the three-dimensional compressible magnetohydrodynamic equations, modeling the evolution of perturbations propagating in a flux tube corresponding to an equilibrium configuration with cylindrical symmetry. We find that phase mixing takes place for moderate amplitudes of the turbulent component even in a distorted, nonaxisymmetric configuration, building small scales that are locally transverse to the density gradient. The dissipative time decreases with increasing the percentage of the turbulent component. This behavior is verified both for propagating and standing waves. Even in the fully turbulent case, a mechanism qualitatively similar to phase mixing occurs: it actively generates small scales together with the nonlinear cascade, thus providing the shortest dissipative time. General considerations are given to identify this regime in the parameter space. The turbulent perturbation also distorts the background density, locally increasing the Alfv\'en velocity gradient and further contributing to accelerating the formation of small scales. Our campaign of simulations is relevant for the coronal plasma where Reynolds and Lundquist numbers are extremely high. For sufficiently low perturbation amplitudes, phase mixing and turbulence work synergically, speeding up the dissipation of the perturbation energy: phase mixing dominates at early times and nonlinear effects at later times. We find that the dissipative time is shorter than those of phase mixing and the nonlinear cascade when individually considered.

Physical insights from the aspect ratio dependence of turbulence in negative triangularity plasmas

Abstract In this work, we study the impact of aspect ratio A = R0/r (the ratio of major radius R0 to minor radius r) on the confinement benefits of Negative Triangularity (NT) plasma shaping. We use high-fidelity flux tube gyrokinetic GENE simulations and consider several different scenarios: four of them inspired by TCV experimental data, a scenario inspired by DIII-D experimental data and a scenario expected in the new SMART spherical tokamak. The present study reveals a surprising and non-trivial dependence. NT improves confinement at any value of A for ITG turbulence, while for TEM turbulence confinement is improved only in the case of large and conventional aspect ratios. Additionally, through a detailed study of a large aspect ratio case with pure ITG drive, we develop an intuitive physical picture that explains the beneficial effect of NT at large and conventional aspect ratios. This picture does not hold in TEM-dominated regimes, where a complex synergistic effect of many factors is found. Finally, we performed the first linear gyrokinetic simulations of SMART, finding that both NT and PT scenarios are dominated by micro-tearing-mode (MTM) turbulence and that NT is more susceptible to MTMs at tight aspect ratio. However, we found that a regime where ITGs dominate in SMART can be found, and in this regime NT is more linearly stable.

How large is the space of covariantly constant gauge fields

The covariantly constant gauge fields are solutions of the sourceless Yang-Mills equation and represent classical vacuum fields. We found that the moduli space of the covariantly constant gauge fields is infinite-dimensional and is therefore much larger than the space of constant chromomagnetic fields. These solutions represent a space lattice of non-perturbative magnetic flux tubes/vertices oriented in the opposite directions, each of which has a Dirac quantum flux. The geometrical structure of the solutions is self-sustaining without presence of any Higgs field support. They are similar to a condensate of the Nielsen-Olesen magnetic flux tubes of opposite orientations. The solutions have a non-vanishing Hopf invariant density.

Solar magnetic flux rope identification with GUITAR: GUI for Tracking and Analysing flux Ropes

Modelling the early evolution of magnetic flux ropes (MFRs) in the solar atmosphere is crucial for understanding their destabilization and eruption mechanism. Identifying the relevant magnetic field lines in simulation data, however, is not straightforward. In previous work an extraction and tracking method was developed to facilitate this task. Here, we present the corresponding graphical user interface (GUI), called GUITAR (GUI for Tracking and Analysing flux Ropes), with the aim to offer a variety of tools to the community for identifying and tracking MFRs. The starting point is a map of a selected proxy parameter for MFRs, e.g., a map of the twist-parameter Tw, current density, etc. We showcase how the GUITAR tools can be used to disentangle a multi-MFR system and facilitate in-depth analysis of their properties and evolution by applying them on a time-dependent data-driven magnetofrictional model (TMFM) simulation of solar active region AR12473. We show the MFR extraction using Tw maps, together with targeted use of mathematical morphology algorithms and discuss the evolution of the system.

Safety First: Stability and Dissipation of Line-tied Force-free Flux Tubes in Magnetized Coronae

Magnetized plasma columns and extended magnetic structures with both footpoints anchored to a surface layer are an important building block of astrophysical dissipation models. Current loops shining in X-rays during the growth of plasma instabilities are observed in the corona of the Sun and are expected to exist in highly magnetized neutron star magnetospheres and accretion disk coronae. For varying twist and system sizes, we investigate the stability of line-tied force-free flux tubes and the dissipation of twist energy during instabilities using linear analysis and time-dependent force-free electrodynamics simulations. Kink modes (m = 1) and efficient magnetic energy dissipation develop for plasma safety factors q ≲ 1, where q is the inverse of the number of magnetic field line windings per column length. Higher-order fluting modes (m > 1) can distort equilibrium flux tubes for q > 1 but induce significantly less dissipation. In our analysis, the characteristic pitch μ˜0 of flux-tube field lines determines the growth rate ( ∝μ˜03 ) and minimum wavelength of the kink instability ( ∝μ˜0−1 ). We use these scalings to determine a minimum flux tube length for the growth of the kink instability for any given μ˜0 . By drawing analogies to idealized magnetar magnetospheres with varying regimes of boundary shearing rates, we discuss the expected impact of the pitch-dependent growth rates for magnetospheric dissipation in magnetar conditions.

Experimental investigation of tail void grouting pressure evolution for super-large diameter shield tunnels

The shield tunneling method is widely used in underground construction. Factors such as the variations in grouting pressure and stiffness/strength evolution over space and time directly affect ground deformation and system stability. To investigate the effect of grouting pressure variation, grouting influence zone, and hydromechanical properties on the model responses (e.g., surface settlement and lining forces), an innovative model test setup was developed to simulate the tunneling process wherein the lining could settle or float during grout injection. This setup included tunnel shrinking, loading-unloading, grout injection, and sample preparation systems. The experimental results show that the grouting pressure evolution law may be significantly affected by the tunnel translation. When the tunnel centerline was fixed in the traditional model tests, the resulting grouting pressure in the tail void was lower than that when the tunnel was free to move. This is because the tunnel translation changed the shape of the annular gap and contributed to the measured grouting pressure. The proposed setup is capable of revealing a more realistic law of grouting pressure evolution, and the subsequent spatio-temporal grouting-induced soil/lining behavior is currently being investigated.

Evolution of mechanical properties of shield tunnels induced by water-soil gushing

Water-soil gushing in shield tunnels has been a major threat to the safety of tunnel structures. However, traditional numerical methods cannot reasonably simulate large soil deformation around the tunnel caused by the water-soil gushing. Therefore, it is difficult to reveal the evolution of the internal force and deformation of tunnel structures. In this paper, based on the two-phase Material Point Method, the numerical analysis method for the water-soil gushing was established to investigate the development of water-soil pressure acting on the tunnel surface, and then the evolution of the tunnel mechanical behaviours in the process of tunnel gushing was further studied. The results indicate that during the “rapid gushing stage”, the tunnel surface pressures around the leakage point decrease sharply, whereas those on the tunnel invert increase significantly. This gives rise to a significant increase in the shear force and bending moment of the tunnel lining, with increase rates of 114% and 82%, respectively. In addition, the axial and angular deformation of Joint No.2 near the leakage point increased significantly, which may lead to serious longitudinal joint dislocation or even concrete crushing. Thus, close attention to the joint deformation is required.

Study of magnetic relaxation in MHD simulations of energetically different flares

The scenario of magnetic energy dissipation in solar flares due to reconnection merits investigation from the perspective of magnetohydrodynamic (MHD) relaxation. For this purpose, we carry out data-constrained MHD simulations with the EULAG-MHD numerical model for three energetically different flares, identified as B6.4, C4.0, and M1.1 in the GOES scheme. A magnetic field reconstruction in the solar atmosphere using a non-force-free field extrapolation model identifies magnetic null points for the B6.4 and C4.0 flares and a hyperbolic flux tube for the M1.1 flare as primary reconnection sites. The simulated evolution of the magnetofluid exhibits reconnection at these sites—exemplified by the slipping reconnection in the null point topology of the B6.4 flare. An estimation of the dissipated magnetic energy using three different volumes of integration within the computational domain amounts to ≈7%, 16.8%, and 33% of the available free magnetic energy in the simulation of B6.4, C4.0, and M1.1 flares. The angle (θ) between the current density and the magnetic field at the reconnection site decreases by 75.92°, 41.37°, and 40.13°, respectively, implying more alignment. The amount of dissipated magnetic energy in the simulated dynamics of each flare is in concurrence with the general energy relation between the classes of chosen flares. Furthermore, the increase in alignment at the reconnection sites suggests the occurrence of magnetic relaxation locally.

A New Type of Jovian Hectometric Radiation Powered by Monoenergetic Electron Beams

AbstractIn this study, we statistically analyze the Jovian auroral radio sources detected in situ by Juno/Waves at frequencies f below the electron cyclotron frequency fce. We first conduct a survey of Juno/Waves data over 1–40 MHz from 2016 to 2022. The 15 detected HectOMetric (HOM) sources all lie within 1–5 MHz and are both less frequent than the radio sources commonly observed slightly above fce and clustered in the southern hemisphere, within ∼90–270° longitudes. We analyze these emission regions with a growth rate analysis in the framework of the Cyclotron Maser Instability (CMI), which we apply to JADE‐E high cadence electron measurements. We show that the f < fce emissions correspond to crossed radio sources, ∼300 km wide. They are located in a hot and highly depleted auroral plasma environment, along flux tubes colocated with upward field‐aligned current and at the equatorward edge of the main auroral oval. The wave amplification is consistent with the CMI and its free energy source consists of a shell‐type electron distribution function (EDF) with characteristic energies of 0.2–5keV. More energetic, 5–50 keV, shell‐type EDFs were systematically observed at higher latitudes but without any radio counterpart. Various parameters for the f < fce HOM sources, reminiscent of the ones at Earth/Saturn, are compared. Other CMI‐unstable EDFs, primarily loss cone ones, are systematically observed during the same intervals, giving rise to emission observed at fce < f < fce + 0.5%. Our analysis thus reveals that different portions of the same EDF can be CMI‐unstable and simultaneously amplify radio waves below and above fce.

The Complexity of Emerging Magnetic Flux during the Lifetime of Solar Ephemeral Regions

As a relatively active region, the ephemeral region (ER) exhibits a highly complex pattern of magnetic flux emergence. We aim to study in detail the secondary flux emergences (SFEs), which we define as bipoles that appear close to ERs and finally coalesce with ERs after a period of time. We study SFEs during the whole process, from the emergence to the decay of five ERs observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. The maximum unsigned magnetic flux for each ER is around 1020 Mx. Each ER has tens of SFEs with an average emerging magnetic flux of approximately 5 × 1018 Mx. The frequency of normalized magnetic flux for all the SFEs follows a power-law distribution with an index of −2.08. The majority of SFEs occur between the positive and negative polarities of an ER, and their growth time is concentrated within 1 hr. The magnetic axis of SFE is found to exhibit a random distribution in the five ERs. We suggest that the relationship between SFEs and ERs can be understood by regarding the photospheric magnetic field observations as cross sections of an emerging magnetic structure. Tracking the evolution of ERs, we propose that these SFEs in ERs may have emerged consequentially from the bundle of flux tubes of ERs and that SFEs are partially emerged Ω-loops.

Magnetic flux eruptions at the root of time lags in low-luminosity active galactic nuclei

Sagittarius A$^ is a compact radio source at the center of the Milky Way that has not conclusively shown evidence to support the presence of a relativistic jet. Nevertheless, indirect methods at radio frequencies do indicate consistent outflow signatures. Temporal shifts between features in frequency bands are known as time lags, associated with flares or outflows of the accretion system. It is possible to gain information on the emission and outflow mechanics by interpreting these time lags. By means of a combined general-relativistic magnetrohydrodynamical and radiative transfer modeling approach, we studied the origin of the time lags for magnetically arrested disk models with three black hole spins ($a_ $). We exclusively modeled the emission from the source across a frequency range of $ GHz. Our study also includes a targeted ``slow light'' investigation for one of the best-fitting ``fast light'' windows. We were able to recover the observational time-lag relations in various windows of our simulated light curves. The theoretical interpretation of these most promising time-lag windows is threefold: i) a magnetic flux eruption perturbs the jet-disk boundary and creates a flux tube; ii) the flux tube orbits and creates a clear emission feature; and iii) the flux tube interacts with the jet-disk boundary. The best-fitting windows have an intermediate (i=30$^ inclination and zero black hole spin. The targeted slow light study did not produce better-fitting time lag results, which indicates that the fast versus slow light paradigm is often not intuitively understood and is likely to be influential in timing-sensitive black hole accretion studies. While previous studies have sought to interpret time-lag properties with spherical or jetted expansion models, we show that this picture is too simplistic. Sophisticated general-relativistic magnetrohydrodynamical models consistently capture the observational time-lag behavior, which is rooted in the complex dynamic interplay between the flux tube and coupled disk-jet system.

Analysis of BMR Tilt from AutoTAB Catalog: Hinting toward the Thin Flux Tube Model?

One of the intriguing mechanisms of the Sun is the formation of bipolar magnetic regions (BMRs) in the solar convection zone (CZ), which are observed as regions of concentrated magnetic fields of opposite polarity on the photosphere. These BMRs are tilted with respect to the equatorial line, which statistically increases with latitude. The thin flux tube model, employing the rise of magnetically buoyant flux loops and their twist by Coriolis force, is a popular paradigm for explaining the formation of tilted BMRs. In this study, we assess the validity of the thin flux tube model by analyzing the tracked BMR data obtained through the Automatic Tracking Algorithm for BMRs. Our observations reveal that the tracked BMRs exhibit the expected collective behaviors. We find that the polarity separation of BMRs increases over their normalized lifetime, supporting the assumption of a rising flux tube from the CZ. Moreover, we observe an increasing trend of the tilt with the flux of the BMR, suggesting that rising flux tubes associated with lower flux regions are primarily influenced by drag force and Coriolis force, while in higher flux regions, magnetic buoyancy dominates. Furthermore, we observe Joy’s law dependence for emerging BMRs from their first detection, indicating that at least a portion of the tilt observed in BMRs can be attributed to the Coriolis force. Notably, lower flux regions exhibit a higher amount of fluctuations associated with their tilt measurement compared to stronger flux regions, suggesting that lower flux regions are more susceptible to turbulent convection.

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.