Small-scale Magnetic Flux Research Articles

Connectivity between the solar photosphere and chromosphere in a vortical structure

Context. High-resolution solar observations have revealed the existence of small-scale vortices, as seen in chromospheric intensity maps and velocity diagnostics. Frequently, these vortices have been observed near magnetic flux concentrations, indicating a link between swirls and the evolution of the small-scale magnetic fields. Vortices have also been studied with magneto-hydrodynamic (MHD) numerical simulations of the solar atmosphere, revealing their complexity, dynamics, and magnetic nature. In particular, it has been proposed that a rotating magnetic field structure driven by a photospheric vortex flow at its footprint produces the chromospheric swirling plasma motion. Aims. We present a complete and comprehensive description of the time evolution of a small-scale magnetic flux concentration interacting with the intergranular vortex flow and affected by processes of intensification and weakening of its magnetic field. In addition, we study the chromospheric dynamics associated with the interaction, including the analysis of a chromospheric swirl and an impulsive chromospheric jet. Methods. We studied observations taken with the CRisp Imaging SpectroPolarimeter (CRISP) instrument and the CHROMospheric Imaging Spectrometer (CHROMIS) at the Swedish Solar Telescope (SST) in April 2019. The data were recorded at quiet-Sun disc centre, consisting of full Stokes maps in the Fe I line at 6173 Å and in the Ca II infrared triplet line at 8542 Å, as well as spectroscopic maps in the lines of Hα 6563 Å and Ca II K 3934 Å. Utilising the multi-wavelength data and performing height-dependent Stokes inversion, based on methods of local correlation tracking and wavelet analysis, we studied several atmospheric properties during the event lifetime. This approach allowed us to interpret the spatial and temporal connectivity between the photosphere and the chromosphere. Results. We identified the convective collapse process as the initial mechanism of magnetic field intensification, generating a re-bound flow moving upwards within the magnetic flux concentration. This disturbance eventually steepens into an acoustic shock wave that dissipates in the lower chromosphere, heating it locally. We observed prolonged magnetic field amplification when the vortex flow disappears during the propagation of the upward velocity disturbance. We propose that this type of magnetic field amplification could be attributed to changes in the local vorticity. Our analysis indicates the rotation of a magnetic structure that extends from the photosphere to the chromosphere, anchored to a photospheric magnetic flux concentration. It appears to be affected by a propagating shock wave and its subsequent dissipation process could be related to the release of the jet.

A Tempered Fractional Kinetic Transport Theory for Energetic Particle Interaction with Quasi-two-dimensional Turbulence in the Large-scale Solar Wind

Observational evidence is accumulating that turbulence in the solar wind is intermittent (non-Gaussian) because of the strong presence of a quasi-two-dimensional (quasi-2D), low-frequency turbulence component containing nonpropagating, closed, small-scale magnetic flux ropes with open meandering field lines in between. le Roux & Zank showed how one can derive fractional focused and Parker-type transport equations that model large-scale anomalous transport in the solar wind as the outcome of energetic particle interaction with quasi-2D turbulence. In this follow-up paper this theory is developed further to address certain limitations. (i) The second moment of the Lévy probability distribution function (PDF) specified in the theory for the particle step size is infinite, indicating unphysical transport. (ii) The expected transition of energetic particle transport from anomalous to normal diffusion beyond a certain critical transport distance was not included. (iii) The competition between anomalous diffusion and advection is not properly sustained at late times. Shortcomings (i) and (ii) are addressed by introducing an exponentially truncated Lévy PDF for the energetic particle step size in the theory, resulting in revised tempered fractional focused and Parker-type transport equations featuring tempered fractional derivatives that enable modeling of tempered Lévy flights. Furthermore, these equations are cast in a tempered fractional telegrapher form to investigate whether the fractional wave equation part of the equation can restore causality in unscattered particle transport during early times and in Lévy flights during intermediate times (Lévy walks). They are also transformed into a tempered fractional Fokker–Planck form to overcome limitation (iii).

Connecting Solar Wind Velocity Spikes Measured by Solar Orbiter and Coronal Brightenings Observed by SDO

The Parker Solar Probe's discovery that magnetic switchbacks and velocity spikes in the young solar wind are abundant has prompted intensive research into their origin(s) and formation mechanism(s) in the solar atmosphere. Recent studies, based on in situ measurements and numerical simulations, argue that velocity spikes are produced through interchange magnetic reconnection. Our work studies the relationship between interplanetary velocity spikes and coronal brightenings induced by changes in the photospheric magnetic field. Our analysis focuses on the characteristic periodicities of velocity spikes detected by the Proton Alpha Sensor on the Solar Orbiter during its fifth perihelion pass. Throughout the time period analyzed here, we estimate their origin along the boundary of a coronal hole. Around the boundary region, we identify periodic variations in coronal brightening activity observed by the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory. The spectral characteristics of the time series of in situ velocity spikes, remote coronal brightenings, and remote photospheric magnetic flux exhibit correspondence in their periodicities. Therefore, we suggest that the localized small-scale magnetic flux within coronal holes fuels a magnetic reconnection process that can be observed as slight brightness augmentations and outward fluctuations or jets. These dynamic elements may act as mediators, bonding magnetic reconnection with the genesis of velocity spikes and magnetic switchbacks.

Small-scale magnetic flux emergence preceding a chain of energetic solar atmospheric events

Advancements in instrumentation have revealed a multitude of small-scale extreme-ultraviolet (EUV) events in the solar atmosphere and considerable effort is currently undergoing to unravel them. Our aim is to employ high-resolution and high-sensitivity magnetograms to gain a detailed understanding of the magnetic origin of such phenomena. We used coordinated observations from the Swedish 1-m Solar Telescope (SST), the Interface Region Imaging Spectrograph ( and the Solar Dynamics Observatory ( to analyze an ephemeral magnetic flux emergence episode and the following chain of small-scale energetic events. These unique observations clearly link these phenomena together. The high-resolution (0 $) magnetograms obtained with SST/CRISP allowed us to reliably measure the magnetic field at the photosphere and to detect the emerging bipole that caused the subsequent eruptive atmospheric events. Notably, this small-scale emergence episode remains indiscernible in the lower resolution SDO/HMI magnetograms (0 $). We report the appearance of a dark bubble in related to the emerging bipole, a sign of the canonical expanding magnetic dome predicted in flux emergence simulations. Evidence of reconnection are also found, first through an Ellerman bomb and later by the launch of a surge next to a UV burst. The UV burst exhibits a weak EUV counterpart in the coronal SDO/AIA channels. By calculating the differential emission measure (DEM), its plasma is shown to reach a temperature beyond 1 MK and to have densities between the upper chromosphere and transition region. Our study showcases the importance of high-resolution magnetograms in revealing the mechanisms that trigger phenomena such as EBs, UV bursts, and surges. This could hold implications for small-scale events similar to those recently reported in the EUV using Solar Orbiter. The finding of temperatures beyond 1 MK in the UV burst plasma strongly suggests that we are examining analogous features. Therefore, we recommend caution when drawing conclusions from full-disk magnetograms that lack the necessary resolution to reveal their true magnetic origin.

Axial Flux Evolution of Small-scale Magnetic Flux Ropes from 0.06 to 10 au

Small-scale magnetic flux ropes (SMFRs) fill much of the solar wind, but their origin and evolution are debated. We apply our recently developed, improved Grad–Shafranov algorithm for the detection and reconstruction of SMFRs to data from Parker Solar Probe, Solar Orbiter, Wind, and Voyager 1 and 2 to detect events from 0.06 to 10 au. We observe that the axial flux density is the same for SMFRs of all sizes at a fixed heliocentric distance but decreases with distance owing to solar wind expansion. Additionally, using the difference in speed between SMFRs, we find that the vast majority of SMFRs will make contact with others at least once during the 100 hr transit to 1 au. Such contact would allow SMFRs to undergo magnetic reconnection, allowing for processes such as merging via the coalescence instability. Furthermore, we observe that the number of SMFRs with higher axial flux increases significantly with distance from the Sun. Axial flux is conserved under solar wind expansion, but the observation can be explained by a model in which SMFRs undergo turbulent evolution by stochastically merging to produce larger SMFRs. This is supported by the observed log-normal axial flux distribution. Lastly, we derive the global number of SMFRs above 1015 Mx near the Sun to investigate whether SMFRs begin their journey as small-scale solar ejections or are continuously generated within the outer corona and solar wind.

A Closer Look at Small-scale Magnetic Flux Ropes in the Solar Wind at 1 au: Results from Improved Automated Detection

Small-scale interplanetary magnetic flux ropes (SMFRs) are similar to ICMEs in magnetic structure, but are smaller and do not exhibit coronal mass ejection plasma signatures. We present a computationally efficient and GPU-powered version of the single-spacecraft automated SMFR detection algorithm based on the Grad–Shafranov (GS) technique. Our algorithm can process higher resolution data, eliminates selection bias caused by a fixed 〈B〉 threshold, has improved detection criteria demonstrated to have better results on an MHD simulation, and recovers full 2.5D cross sections using GS reconstruction. We used it to detect 512,152 SMFRs from 27 yr (1996–2022) of 3 s cadence Wind measurements. Our novel findings are the following: (1) the SMFR filling factor (∼ 35%) is independent of solar activity, distance to the heliospheric current sheet, and solar wind plasma type, although the minority of SMFRs with diameters greater than ∼0.01 au have a strong solar activity dependence; (2) SMFR diameters follow a log-normal distribution that peaks below the resolved range (≳104 km), although the filling factor is dominated by SMFRs between 105 and 106 km; (3) most SMFRs at 1 au have strong field-aligned flows like those from Parker Solar Probe measurements; (4) the radial density (generally ∼1 detected per 106 km) and axial magnetic flux density of SMFRs are higher in faster solar wind types, suggesting that they are more compressed. Implications for the origin of SMFRs and switchbacks are briefly discussed. The new algorithm and SMFR dataset are made freely available.

Calcium Bright Knots and the Formation of Chromospheric Anemone Jets on the Sun

Space-based observations show that the solar atmosphere from the solar chromosphere to the solar corona is filled with small-scale jets and is linked with small-scale explosions. These jets may be produced by mechanisms similar to those of large-scale flares and such jets may be related to the heating of the corona and chromosphere as well as the acceleration of solar wind. The chromospheric anemone jets on the Sun remain puzzling because their footpoints (or bright knots) have not been well resolved and the formation process of such enigmatic small-scale jets remains unclear. We propose a new model for chromospheric jets using the 3D magnetohydrodynamic simulations, which show that the continuous, upward rising of small-scale twisted magnetic flux ropes in a magnetized solar chromosphere drives small-scale magnetic reconnection and the launching of several small-scale jets during the evolution of the chromospheric anemone jets. Our new, self-consistent, 3D computer modeling of small-scale, but ever-changing flux rope emergence in the magnetized solar atmosphere is fully consistent with observations and provides a universal mechanism for nanoflare and jet formation.

Series of Small-scale Low Plasma β Magnetic Flux Ropes Originating from the Same Longitudinal Region: Parker Solar Probe Observations

In this study, we report on small-scale magnetic flux ropes (SMFRs) observed as a compact series in a narrow Carrington longitudinal range during three Parker Solar Probe (PSP) encounters. First, during ∼1.5 days of PSP's inbound part of Encounter 4, we identified a series of 11 SMFRs within 1.°4 in longitude over the radial distance of ∼8.4 R ☉ (from ∼44 to 35 R ☉). The identified SMFRs lasted from ∼0.5 to 1.8 hr, and adjacent events were separated mostly by a few hours and up to ∼6.5 hr at the longest, but some events were very closely spaced with intervals of a few ∼tens of minutes or less apart. Most of the identified SMFRs are successfully fitted to the force-free model. The SMFRs are clearly distinguished from the surroundings by a notable reduction in plasma β, which itself was comparably low (less than unity) in the background plasma. Furthermore, the magnetic field and plasma flow within the SMFRs fluctuated significantly less than the more turbulent surroundings. The fluctuations in the surrounding medium exhibited occasional Br polarity reversal (possibly switchbacks) and were Alfvénic to a large extent with far weaker compressional components. The majority of these key features with some differences have also been found in the series of SMFRs and their surroundings identified within 1.°3 or less in longitude during Encounters 1 and 5. We speculate that these SMFRs were repetitively generated by successive reconnection within a very narrow angular zone located close to the Sun but not necessarily at the same radial position.

Nature of Turbulence inside Small-scale Magnetic Flux Ropes near the Sun: Parker Solar Probe Observations

In this study, we probe the turbulence characteristic within the small-scale magnetic flux ropes (SSMFRs) close to the Sun using Parker Solar Probe (PSP) magnetic field data. The study includes 50 SSMFRs observed by PSP during Encounter 1, 2, and 3 between 35.74 R ☉ and 142.29 R ☉ distance from the Sun. We observed that the average spectral index for all the selected SSMFR events is –1.49 ± 0.21. In line with expectations, we also saw average ∣σ m ∣ values close to zero throughout the inertial range. We also observed that the size of the eddy at the highest frequency is much smaller than the size of the SSMFRs, indicating anisotropy within it. Thus, our finding supports anisotropic models that feature the Iroshnikov–Kraichnan index. Our findings agree with the turbulence properties of the solar wind near the Sun. We also observe low ∼0.1 compressibility, indicating SSMFRs are dominant by Alfvénic fluctuations. In light of this, we believe such an incompressible MHD spectrum results from nonlinear interactions between Alfvénic fluctuations. As a result, our research contributes to understanding the energy cascade process and its transport in solar plasma within the inner heliosphere.

Variability of the slow solar wind: New insights from modelling and PSP-WISPR observations

Aims. We analyse the signature and origin of transient structures embedded in the slow solar wind, and observed by the Wide-Field Imager for Parker Solar Probe (WISPR) during its first ten passages close to the Sun. WISPR provides a new in-depth vision on these structures, which have long been speculated to be a remnant of the pinch-off magnetic reconnection occurring at the tip of helmet streamers. Methods. We pursued the previous modelling works of Réville et al. (2020, ApJ, 895, L20; 2022, A&A, 659, A110) that simulate the dynamic release of quasi-periodic density structures into the slow wind through a tearing-induced magnetic reconnection at the tip of helmet streamers. Synthetic WISPR white-light (WL) images are produced using a newly developed advanced forward modelling algorithm that includes an adaptive grid refinement to resolve the smallest transient structures in the simulations. We analysed the aspect and properties of the simulated WL signatures in several case studies that are typical of solar minimum and near-maximum configurations. Results. Quasi-periodic density structures associated with small-scale magnetic flux ropes are formed by tearing-induced magnetic reconnection at the heliospheric current sheet and within 3 − 7 R⊙. Their appearance in WL images is greatly affected by the shape of the streamer belt and the presence of pseudo-streamers. The simulations show periodicities on ≃90 − 180 min, ≃7 − 10 h, and ≃25 − 50 h timescales, which are compatible with WISPR and past observations. Conclusions. This work shows strong evidence for a tearing-induced magnetic reconnection contributing to the long-observed high variability of the slow solar wind.

Anomalous Transport of Energetic Particles Interacting with Dynamic Small-Scale Magnetic Flux Rope Structures

le Roux and Zank [25] showed previously how one can derive from first principles a pitch-angle dependent fractional diffusion-advection kinetic equation to model the anomalous diffusion of energetic particles interacting with small-scale magnetic flux ropes (SMFRs) in the inner heliosphere on the basis of the standard focused transport equation. This equation has the following limitations: (1) The asymptotic power law of a Lévy distribution was specified to model the non-Gaussian statistics of the disturbed energetic particle trajectories generated during energetic particle interaction with numerous SMFRs. The second moment (variance) and higher moments of the Lévy distribution are infinite, indicating over-efficient non-local transport that is scale-free. (2) The theory does not naturally allow for a transition of anomalous transport to normal diffusion, or to a different anomalous diffusion state. An outline of a derivation is presented in which an exponentially truncated Lévy distribution was specified instead, resulting in a tempered fractional diffusion-advection kinetic equation that addresses these two concerns.

Novel Approach to Forecasting Photospheric Emergence of Active Regions

One key aspect of understanding the solar dynamo mechanism and the evolution of solar magnetism is to properly describe the emergence of solar active regions. In this Letter, we describe the Lagrangian photospheric flows dynamics during a simulated flux emergence that produces an active region formed by pores. We analyze the lower photospheric flow organization prior, during and following the rise of an active region, uncovering the repelling and attracting photospheric structures that act as sources and sinks for magnetic element transport. Our results show that around 10 hr before the simulated emergence, considerable global changes are taking place on mesogranular scales indicated by an increase of the number of regions acting as a source to the multiple and scattered emergences of small-scale magnetic flux. At the location of active region’s appearance, the converging flows become weaker and there is an arising of a diverging region 8 hr before the emergence time. Our study also indicates that the strong concentration of magnetic field affects the flow dynamics beyond the area of the actual simulated pores, leading to complex and strongly diverging flows in the neighboring regions. Our findings suggest that the Lagrangian analysis is a powerful tool to describe the changes in the photospheric flows due to magnetic flux emergence.

Parallel and Momentum Superdiffusion of Energetic Particles Interacting with Small-scale Magnetic Flux Ropes in the Large-scale Solar Wind

A recently developed time-dependent fractional Parker transport equation is solved to investigate the parallel and momentum superdiffusion of energetic charged particles in an inner heliospheric region containing dynamic small-scale flux ropes (SMFRs). Both types of superdiffusive transport are investigated with fractional transport terms containing a fractional time integral combined with normal spatial or momentum derivatives. Just as for normal diffusion, accelerated particles form spatial peaks with a maximum amplification factor that increases with particle energy. Instead of growth of the spatial peaks until a steady state is reached as for normal diffusion, parallel superdiffusion causes the peaks to dissipate into plateaus followed by a rollover at late times. The peaks dissipate at a faster rate when parallel transport is more superdiffusive. Furthermore, the accelerated particle spectral distribution function inevitably becomes an f 0 ∝ p −3 spectrum at late times in the test particle limit near the particle source despite the potential for spectral steepening from other transport terms. All this is a product of the growing domination of parallel spatial and especially momentum superdiffusion over other transport terms with time. Such extreme late time effects can be avoided by a transition to a normal diffusive state. Finally, fitting spatial peaks observed during SMFR acceleration events with the solution of the fractional Parker transport equation can potentially be used as a diagnostic for estimating the level of spatial and momentum superdiffusion in these events and how the levels of superdiffusion vary with distance from the Sun.

Statistical Study of Ejections in Coronal Hole Regions As Possible Sources of Solar Wind Switchbacks and Small-scale Magnetic Flux Ropes

The omnipresence of transient fluctuations in the solar wind, such as switchbacks (SBs) and small-scale magnetic flux ropes (SMFRs), have been well observed by the in situ observation of Parker Solar Probe (PSP), yet their sources are not clear. Possible candidates fall into two categories: solar origin and in situ generation in the solar wind. Among the solar-origin scenarios, the small-scale activities (such as ejections and eruptions) in coronal hole (CH) regions, where solar wind originates, are suggested as candidates. Using full-disk extreme ultraviolet images from Atmospheric Imaging Assembly on board the Solar Dynamic Observatory, we identify small-scale ejections in CH regions during PSP Encounters 5, 7, and 8, and study their statistical properties. These ejections belong to two categories: standard jets and blowout jets. With 27,832 ejections identified in 24 days (about 2/3 of them are blowout jets), we updated the expected frequency for PSP to detect their counterparts in the heliospace. The ejections we identified are comparable to the frequency of PSP-detected SMFRs, but they are insufficient to serve as the only producer of SBs or SB patches. Certain smaller events missed by this study, such as jetlets, may fill the gap.

The Chromosphere Underneath a Coronal Bright Point

Coronal bright points (CBPs) are sets of small-scale coronal loops, connecting opposite magnetic polarities, primarily characterized by their enhanced extreme-ultraviolet (EUV) and X-ray emission. Being ubiquitous, they are thought to play an important role in heating the solar corona. We aim at characterizing the barely explored chromosphere underneath CBPs, focusing on the related spicular activity and on the effects of small-scale magnetic flux emergence on CBPs. We used high-resolution observations of a CBP in Hβ and Fe i 617.3 nm from the Swedish 1 m Solar Telescope in coordination with the Solar Dynamics Observatory. This work presents the first high-resolution observation of spicules imaged in Hβ. The spicules were automatically detected using advanced image processing techniques, which were applied to the Dopplergrams derived from Hβ. Here we report their abundant occurrence close to the CBP “footpoints” and find that the orientation of such spicules is aligned along the EUV loops, indicating that they constitute a fundamental part of the whole CBP magnetic structure. Spatiotemporal analysis across multiple channels indicates that there are coronal propagating disturbances associated with the studied spicules, producing transient EUV intensity variations of the individual CBP loops. Two small-scale flux emergence episodes appearing below the CBP were analyzed, one of them leading to quiet-Sun Ellerman bombs and enhancing the nearby spicular activity. This paper presents unique evidence of the tight coupling between the lower and upper atmosphere of a CBP, thus helping to unravel the dynamic phenomena underneath CBPs and their impact on the latter.

Small-scale Magnetic Flux Ropes in Stream Interaction Regions from Parker Solar Probe and Wind Spacecraft Observations

Using in situ measurements from the Parker Solar Probe and Wind spacecraft, we investigate the small-scale magnetic flux ropes (SFRs) and their properties inside stream interaction regions (SIRs). Within SIRs from ∼0.15 to 1 au, SFRs are found to exist in a wide range of solar wind speeds with more frequent occurrences after the stream interface, and the Alfvénicity of these structures decreases significantly with increasing heliocentric distances. Furthermore, we examine the variation of five corresponding SIRs from the same solar sources. The enhancements of suprathermal electrons within these SIRs persist at 1 au and are observed multiple times. An SFR appears to occur repeatedly with the recurring SIRs and is traversed by the Wind spacecraft at least twice. This set of SFRs has similarities in variations of the magnetic field components, plasma bulk properties, density ratio of solar wind alpha and proton particles, and unidirectional suprathermal electrons. We also show, through the detailed time-series plots and Grad–Shafranov reconstruction results, that they possess the same chirality and carry comparable amounts of magnetic flux. Lastly, we discuss the possibility for these recurring SFRs to be formed via interchange reconnection, maintain the connection with the Sun, and survive up to 1 au.

Small-scale dynamo in cool stars

Context. Some of the small-scale solar magnetic flux can be attributed to a small-scale dynamo (SSD) operating in the near-surface convection. The SSD fields have consequences for solar granular convection, basal flux, and chromospheric heating. A similar SSD mechanism is expected to be active in the near-surface convection of other cool main-sequence stars, but this has not been investigated thus far. Aims. We aim to investigate changes in stratification and convection due to inclusion of SSD fields for F3V, G2V, K0V, and M0V spectral types in the near-surface convection. Methods. We studied 3D magnetohydrodynamic (MHD) models of the four stellar boxes, covering the subsurface convection zone up to the lower photosphere in a small Cartesian box, based on the MURaM radiative-MHD simulation code. We compared the SSD runs against reference hydrodynamic runs. Results. The SSD is found to efficiently produce magnetic field with energies ranging between 5% to 80% of the plasma kinetic energy at different depths. This ratio tends to be larger for larger Teff. The relative change in density and gas pressure stratification for the deeper convective layers due to SSD magnetic fields is negligible, except for the F-star. For the F-star, there is a substantial reduction in convective velocities due to Lorentz force feedback from magnetic fields, which, in turn, reduces the turbulent pressure. Conclusions. The SSD in near-surface convection for cool main-sequence stars introduces small but significant changes in thermodynamic stratification (especially for the F-star) due to a reduction in the convective velocities.

Investigating Particle Acceleration by Dynamic Small-scale Flux Ropes behind Interplanetary Shocks in the Inner Heliosphere

We recently extended our Parker-type transport equation for energetic particle interaction with numerous dynamic small-scale magnetic flux ropes (SMFRs) to include perpendicular diffusion in addition to parallel diffusion. We present a new analytical solution to this equation assuming heliocentric spherical geometry with spherical symmetry for all SMFR acceleration mechanisms present in the transport theory. With the goal of identifying the dominant mechanism(s) through which particles are accelerated by SMFRs, a search was launched to identify events behind interplanetary shocks that could be explained by our new solution and not classical diffusive shock acceleration. Two new SMFR acceleration events were identified in situ for the first time within heliocentric distances of 1 astronomical unit (au) in Helios A data. A Metropolis–Hastings algorithm is employed to fit the new solution to the energetic proton fluxes so that the relative strength of the transport coefficients associated with each SMFR acceleration mechanism can be determined. We conclude that the second-order Fermi mechanism for particle acceleration by SMFRs is more important than first-order Fermi acceleration due to the mean compression of the SMFRs regions during these new events. Furthermore, with the aid of SMFR parameters determined via the Grad–Shafranov reconstruction method, we find that second-order Fermi SMFR acceleration is dominated by the turbulent motional electric field parallel to the guide/background field. Finally, successful reproduction of energetic proton flux data during these SMFR acceleration events also required efficient particle escape from the SMFR acceleration regions.

Near-orthogonal Orientation of Small-scale Magnetic Flux Ropes Relative to the Background Interplanetary Magnetic Field

Small-scale magnetic flux ropes (SMFRs) have been identified at a large range of heliospheric distances from the Sun. Their features are somewhat similar to those of larger-scale flux rope structures such as magnetic clouds (MCs), while their occurrence rate is far higher. In this work, we examined the orientations of a large number of SMFRs that were identified at 1 au by fitting to the force-free model. We find that, while most of the SMFRs lie mostly close to the ecliptic plane, as previously known, their azimuthal orientations relative to the Sun–Earth line are found largely at two specific angles (slightly less than 45° and 225°). This latter feature in turn leads to a strong statistical trend in which the axis of SMFRs lies at a large tilt angle relative to (most often nearly orthogonal to) the corresponding background interplanetary magnetic field directions in the ecliptic plane. This feature is different from previous reports on SMFRs—and in stark contrast to the cases of MCs. This is an important observational constraint that should be considered for understanding SMFR generation and propagation.

Effects of Pressure Anisotropy on the Geometry of Magnetic Flux Rope

This paper aims to examine the effects of pressure anisotropy on the geometry of magnetic flux rope using the newly developed two-dimensional magnetohydrostatic reconstruction associated with pressure anisotropy. A small-scale magnetic flux rope observed by the Magnetospheric Multiscale mission, in the magnetosheath reconnection outflow during an outbound magnetopause crossing, is demonstrated. At the center of the flux rope, the magnetic field strength was enhanced with decreasing plasma pressure. The entire flux rope was mostly occupied by the pressure anisotropy of p ⊥ > p ∥, where the subscripts ∥ and ⊥ denote the components parallel and perpendicular to the local magnetic field, respectively. The estimated aspect ratio of the width to the length of the flux rope from reconstruction was ∼0.326 for p ⊥ > p ∥ and ∼0.389 for isotropic pressure. By comparing the magnetic field map from the isotropic Grad–Shafranov reconstruction, the results show for p ⊥ > p ∥ that (1) the width of the flux rope is reduced, leading to a small aspect ratio of the flux rope, and (2) the circular field line of the flux rope is contracted. Moreover, an experiment is conducted for p ∥ > p ⊥ by exchanging p ⊥ and p ∥ of the flux rope, for which the isotropic pressure is less affected. The experimental results indicate that the effects of p ∥ > p ⊥ on the geometry of the flux rope are opposite to that of p ⊥ > p ∥. The overall finding may provide new insight into charged particle acceleration within magnetic flux ropes/islands in anisotropic plasmas.