Tangential Discontinuity Research Articles

Revisiting the Superstorm on 6–7 April 2000 Caused by an Extraordinary Corotating Interaction Region (With an Embedded Coronal Jet?)

AbstractThe 6–7 April 2000 superstorm of SYM‐H intensity = −319 nT discussed in Meng et al. (2019; https://doi.org/10.1029/2018JA026425) was misidentified as being due to an interplanetary coronal mass ejection associated with a solar flare. The interplanetary cause was a highly unusual corotating interaction region (CIR) bounded by a strong fast forward shock (FS) with magnetosonic Mach number Mms = 4.6 and a fast reverse shock (RS) with Mms = 1.9. The exceptionally strong FS caused a ∼3‐factor interplanetary magnetic field (IMF) magnitude amplification in the leading half of the CIR with peak southward IMF Bz = −27 nT causing the superstorm. A plasma region between a tangential discontinuity and the stream interface had a scale size of ∼0.096 AU. We hypothesize that this is the first detection of a coronal jet at 1 AU. The jet/Gold magnetic tongue (1959; https://doi.org/10.1029/JZ064i011p01665) was embedded within the CIR, contained the southward Bz and caused the magnetic storm. We hypothesize that a shrinking coronal hole and magnetic reconnection caused the formation and release of the jet.

Formation of Standing Whistler Wave in Earth's Magnetosheath

AbstractThe dispersion of shock is universal in various media, and in plasmas, standing whistler waves represent the dispersion of collisionless shocks. These standing whistler waves are usually observed upstream of low Mach number planetary bow shocks and interplanetary shocks. However, our understanding of the plasma behavior and electric field properties within these waves remains limited. Using conjoint THEMIS and Magnetospheric Multiscale (MMS) observations, we report the first observation of standing whistler wave upstream of a fast shock in Earth's magnetosheath resulting from the interaction between a solar wind tangential discontinuity and the bow shock. High‐resolution MMS measurements provide unprecedented insights into these waves, characterizing their circular polarization, near‐parallel propagation to the shock normal, and fixed phase relative to the shock ramp. The observed field and particle characteristics are discussed in detail.

Observations and Simulations of a Double‐Core Hot Flow Anomaly

AbstractHot Flow anomalies (HFAs), one of the most well‐analyzed transient phenomena in the Earth's foreshock, are known as kinetic structures driven by tangential discontinuities (TDs). Recently, a 2‐dimensional (2D) magnetohydrodynamics (MHD) model reproduced HFAs with either a high‐ or low‐density core. Further investigation of an HFA with two cores observed by the Magnetospheric Multiscale (MMS) mission is reported. The observation via the Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) mission suggests this MHD HFA is associated with a foreshock density hole‐like structure. The trailing flux tube in simulation may propagate with a TD in the foreshock. Our work suggests that HFAs with two low‐density cores can also be achieved in MHD process. Results show the total ram pressure can be an excellent diagnostic for the presence of transient structures, such as HFAs, at the bow shock.

Hermite Quartic Splines for Smoothing and Sampling a Roughing Curvilinear Spiral Toolpath

From an industrial point of view, the milling of 2.5D cavities is a frequent operation, consuming time and presenting optimization potential, especially through a judicious choice of the tool trajectory. Among the different types of trajectories, some have a general spiral-like aspect and can potentially offer a reduced machining time. They are called curvilinear trajectories and are obtained by interpolation between structure curves, which are the numerical solutions of a partial differential equation. In this case, the machine tool will connect points, and the trajectory will be made up of small segments. While these trajectories exhibit all the necessary qualities on a macroscopic level for rapid tool movement, the tangential discontinuities at a microscopic scale, inherent in the discretization, significantly increase the machining time. This article proposes a method to reparameterize the structure curves of the curvilinear spiral with a set of C2 connected Hermit quartic spline patches. This creates a smooth toolpath that can be machined at an average feedrate closer to the programmed one and will, de facto, reduce the machining time. This article shows that the proposed method increases on two representative geometries of cavities and toolpath quality indicators, and reduces the milling time from 10% to 18% as compared to the PDE curvilinear spiral generation method proposed by Bieterman and Sandström. In addition, the proposed method is suitable for any non-convex pocket, with or without island(s).

Hybrid Kinetic Modeling of the Magnetosheath Impulsive Plasma Cloud Penetration Through the Magnetopause and Comparison With MMS and Other Spacecraft Observations

AbstractThis research examines the plasma processes under penetration of the plasma clouds (plasmoids) across the magnetopause which is modeled as a tangential discontinuity (TD). Cases with the parallel magnetic field in both sides out of the TD are under investigation. Plasma parameters and magnetic field were chosen from the MMS mission and other spacecraft observations. The results are important for understanding the following basic space plasma physics problems: (a) plasma cloud deformation and strong phase mixing with magnetospheric plasma; (b) the transfer of mass, momentum and energy of magnetosheath and magnetic cloud plasma into magnetospheric plasmas; (c) necessary conditions for plasma cloud penetration via the magnetopause; (d) wave generation by plasma clouds inside the magnetopause.

Enhanced Ion Acceleration Due To High‐Shear Tangential Discontinuities Upstream of Quasi‐Perpendicular Shocks

AbstractCollisionless shock waves are efficient ion accelerators. Previous numerical and observational studies have shown that quasi‐parallel (Q‖) shocks are more effective than quasi‐perpendicular (Q⊥) shocks at generating energetic ions under steady upstream conditions. Here, we use a local, 2D, hybrid particle‐in‐cell model to investigate how ion acceleration at super‐critical Q⊥ shocks is modulated when tangential discontinuities (TDs) with large magnetic shear are present in the upstream plasma. We show that such TDs can significantly increase the ion acceleration efficiency of 2D Q⊥ shocks, up to a level comparable to Q‖ shocks. Using data from the hybrid model and test particle simulations, we show that the enhanced energization is related to the magnetic field change associated with the discontinuity. When shock‐reflected ions cross the TD during their upstream gyromotion, the sharp field change causes the ions to propagate further upstream, and gain additional energy from the convection electric field associated with the upstream plasma flow. Our findings illustrate that the presence of upstream discontinuities can lead to bursts of energetic ions, even when they do not trigger the formation of foreshock transients. These results emphasize the importance of time‐variable upstream conditions when considering ion energization at shocks.

2.5‐D Local Hybrid Simulations of Hot Flow Anomalies Under Various Magnetic Field Geometries

AbstractHot flow anomalies are ion kinetic phenomena that play an important role in geoeffects and particle acceleration. They form due to the currents driven by demagnetized foreshock ions around a tangential discontinuity (TD). To understand the profile of such currents around a TD with foreshock ions on both sides, we use 2.5‐D local hybrid simulations of TDs, interacting with a planar shock with various shock geometries. We find that the electric field direction relative to the TD plane provides information about how the foreshock ion‐driven currents affect the magnetic field around the TD. For TDs embedded in the quasi‐parallel shock on both sides, the foreshock ions from one side of TD can cross it determining the current profile on the other side. In contrast, for TDs embedded in the quasi‐perpendicular shock, sheath‐leaked ions enter the TD and determine the current profile. We find that the foreshock ultra‐low frequency waves can periodically modulate how foreshock ions interact with the TD and thus the current profile. Studying the effects of various magnetic field configurations allows us to build a more comprehensive model of hot flow anomalie formation.

2.5‐D Local Hybrid Simulations of Discontinuity‐Driven Compressional Boundaries Under Various Magnetic Field Geometries

AbstractIn the ion foreshock, there are many foreshock transients driven by back streaming foreshock ions. When the foreshock ions interact with tangential discontinuities (TDs), hot flow anomalies form if the foreshock ion‐driven current decreases field strength at TDs, but the opposite situation has been paid little attention. Using 2.5‐D local hybrid simulations, we show that a compressional boundary with enhanced field strength and density can form. We examine how the foreshock ions interact with TDs under various magnetic field geometries to drive currents that lead to compressional boundaries. The current driven by the foreshock ions should peak on its initial side of a TD so that the enhanced field strength at the TD in turn increases this current by keeping more foreshock ions on their initial side. Which side the current peaks can be determined by whether the foreshock ions initially cross the TD and/or how their velocity is projected into the local perpendicular direction. Additionally, the foreshock ion‐driven currents from two sides could compete, and whether a compressional boundary forms is determined by the net current profile. Because such compressive structures in the foreshock can drive magneto sheath jets and cause many geoeffects, it is necessary to fully understand their formation.

Temperature Intermittent Structures in the Fast Solar Wind

In the solar wind turbulence, proton temperature fluctuations are highly intermittent, especially at small scales in the inertial range. This phenomenon may contain information about solar wind intermittent heating. However, the physical nature of the temperature intermittency is not yet clear. Based on the measurements from Solar Orbiter between 2020 September and 2022 September, we identify 185 temperature intermittent structures at the scale of 24 s with well-defined minimum variance direction in the fast solar wind and study the nature and kinetic effects of them. According to the variations of proton temperature, the intermittent structures are classified into four types, including temperature bump, step, dip, and chain. When considering the magnetic field configuration together with other plasma properties, we find that, among the bump cases, 46 of them are linear magnetic holes (LMHs) that are mainly related to mirror-mode (MM) instability, and 43 of them are current sheets (CSs) with local temperature enhancement. The step cases are found to be associated with shock-like structures (13 cases) and tangential discontinuities (eight cases) that separate two different parcels of plasma. For the dip cases, 21 of them could be associated with the MM instability, and the rest of the 16 ones may prefer soliton scenario. The 38 chain cases are identified as compressive vortex-like structures and a mixture of LMHs and CSs. These results will help to further understand the intermittent dissipation process in the solar wind turbulence.

Solar Wind Charge-Exchange X-ray Emissions from the O5+ Ions in the Earth’s Magnetosheath

The spectra and global distributions of the X-ray emissions generated by the solar wind charge-exchange (SWCX) process in the terrestrial magnetosheath are investigated based on a global hybrid model and a global geocoronal hydrogen model. Solar wind O6+ ions, which are the primary charge state for oxygen ions in solar wind, are considered. The line emissivity of the charge-exchange-borne O5+ ions is calculated by the Spectral Analysis System for Astrophysical and Laboratory (SASAL). It is found that the emission lines from O5+ range from 105.607 to 118.291 eV with a strong line at 107.047 eV. We then simulate the magnetosheath X-ray emission intensity distributions with a virtual camera at two positions of the north pole and dusk at six stages during the passing of a perpendicular interplanetary shock combined with a tangential discontinuity structure through the Earth’s magnetosphere. During this process, the X-ray emission intensity increases with time, and the maximum value is 27.11 keV cm−2 s−1 sr−1 on the dayside, which is 4.5 times that before the solar wind structure reached the Earth. A clear shock structure can be seen in the magnetosheath and moves earthward. The maximum emission intensity seen at dusk is always higher than that seen at the north pole.

Cross‐Comparison of Observations With the Predictions of Global Hybrid Simulations for Multiple IMF Discontinuities Impacting the Bow Shock and Magnetosheath

AbstractWe use the three‐dimensional (3‐D) global hybrid code ANGIE3D to simulate the interaction of four solar wind tangential discontinuities (TDs) observed by ARTEMIS P1 from 0740 UT to 0800 UT on 28 December 2019 with the bow shock, magnetosheath, and magnetosphere. We demonstrate how the four discontinuities produce foreshock transients, a magnetosheath cavity‐like structure, and a brief magnetopause crossing observed by THEMIS and MMS spacecraft from 0800 UT to 0830 UT. THEMIS D observed entries into foreshock transients exhibiting low density, low magnetic field strength, and high temperature cores bounded by compressional regions with high densities and high magnetic field strengths. The MMS spacecraft observed cavities with strongly depressed magnetic field strengths and highly deflected velocity in the magnetosheath downstream from the foreshock. Dawnside THEMIS A magnetosheath observations indicate a brief magnetosphere entry exhibiting enhanced magnetic field strength, low density, and decreased and deflected velocity (sunward flow). The solar wind inputs into the 3‐D hybrid simulations resemble those seen by ARTEMIS. We simulate the interaction of four oblique TDs with properties similar to those in the observation. We place virtual spacecraft at the locations where observations were made. The hybrid simulations predict similar characteristics of the foreshock transients, a magnetosheath cavity, and a magnetopause crossing with characteristics similar to those observed by the multi‐spacecraft observations. The detailed and successful comparison of the interaction involving multiple TDs will be presented.

Triggering the Magnetopause Reconnection by Solar Wind Discontinuities

Magnetic reconnection is one of the most universal processes in space plasma that is responsible for charged particle acceleration and the mixing and heating of plasma populations. In this paper we consider a triggering process of reconnection that is driven by interaction of two discontinuities: solar wind rotational discontinuity and tangential discontinuity at Earth’s magnetospheric boundary, the magnetopause. Combining multispacecraft measurements and global hybrid simulations, we show that solar wind discontinuities may drive the magnetopause reconnection and cause the mixing of the solar wind and magnetosphere plasmas around the magnetopause, well downstream of the solar wind flow. Since large-amplitude discontinuities are frequently observed in the solar wind and predicted for various stellar winds, our results of reconnection driven by the discontinuity–discontinuity interaction may have a broad application beyond the magnetosphere.

Solar Wind Current Sheets: MVA Inaccuracy and Recommended Single‐Spacecraft Methodology

AbstractWe present the analysis of 1,831 current sheets (CS) observed aboard four Cluster spacecraft in a pristine solar wind. Four‐spacecraft estimates of the CS normal and propagation velocity are compared with different single‐spacecraft estimates. The Minimum Variance Analysis (MVA) of the magnetic field is shown to be highly inaccurate in estimating the normal. The MVA normal often differs by more than 60° from the normal obtained by multi‐spacecraft timing method, likely due to ambient turbulent fluctuations. In contrast, the cross‐product of magnetic fields at the CS boundaries delivers the normal with an uncertainty of less than 15° at the confidence level of 90%. The CSs are essentially frozen into plasma flow, since their propagation velocity is consistent with local ion flow velocity within 20% at the confidence level of 90%. The single‐spacecraft methodology based on the cross‐product method and frozen‐in assumption delivers the CS thickness and current density amplitude within 20% of their actual values at the confidence level of 90%. The CSs are kinetic‐scale structures with half‐thickness λ from a few tenths to tens of local proton inertial length λp and scale‐dependent shear angle and current density amplitude, and . The classification of the CSs in terms of tangential and rotational discontinuities remains a challenge, because even the four‐spacecraft normal has too large uncertainties to reveal the actual normal magnetic field component. The presented results will be valuable for the analysis of solar wind CSs, when only single‐spacecraft measurements are available.

Effects of charge exchange on plasma flow in the heliosheath and astrosheathes

ABSTRACT Shock boundary layers are regions bounded by a shock wave on the one side and tangential discontinuity on the other side. These boundary layers are commonly observed in astrophysics. For example, they exist in the regions of the interaction of the stellar winds with the surrounding interstellar medium. Additionally, the shock layers (SLs) are often penetrated by the flows of interstellar atoms, as, for instance, in the astrospheres of the stars embedded by the partially ionized interstellar clouds. This paper presents a simple toy model of an SL that aims to qualitatively describe the influence of charge exchange with interstellar hydrogen atoms on the plasma flow in astrospheric SLs. To clearly explore this effect, magnetic fields are neglected, and the geometry is kept as simple as possible. The model explains why the cooling of plasma due to charge exchange in the inner heliosheath leads to an increase in plasma density in front of the heliopause. It also demonstrates that the source of momentum causes changes in the pressure profile within the SL. The paper also discusses the decrease in plasma density near the astropause in the outer SL in the case of layer heating, which is particularly relevant in light of the Voyager measurements in the heliospheric SL.

Five-axis path smoothing based on sliding convolution windows for CNC machining

Tiny linear toolpaths widely used in five-axis CNC machine tools only meet G0 continuity at the junctions of adjacent paths, the tangential and curvature discontinuities at the corners result in decelerations and fluctuations of machine tools. Although the corner smoothing for the three-axis tool path is relatively mature, the five-axis tool pose path smoothing is still difficult to plan due to the nonlinear motions of the rotational axes and the parameter synchronization between the tool center point (TCP) path and the tool orientation vector (TOV) path. Therefore, this paper aims to extend the smoothing scopes of previously presented mixed tiny path smoothing method based on sliding convolution windows for three-axis CNC machining (Zhang et al. in Journal of Manufacturing Process 102:685–699, [19]). Compared with the previous work, this paper converts the five-axis tool pose path into the tool position signal and tool orientation signal, and the interpolation points of the two path signals in the convolution window are directly processed on the basis of the synchronous motions of all axes. The original parameter synchronization relationship between the TCP path and the TOV path is still maintained. Besides, the smoothing error prediction model is constructed. The proposed five-axis path smoothing method has been integrated into a self-developed open-architecture CNC system and its effectiveness for the five-axis path optimization is validated via the simulation and experiment.

Maximum Aligned Directional Derivative (MADD) Technique for Planar Structure Analysis in Space

Interplanetary discontinuities are the most common intermittent structures in the solar winds, whose jump conditions conform to the Rankine–Hugoniot relations. The identification and analysis of such planar structures rely on an accurate determination of the normal vectors. In this study, we perform a benchmark test of a technique designed to estimate the dimensionality and orientation of the magnetic fields based on four spacecraft measurements. Such a technique operates on the fact that in a strictly planar magnetic field, three columns of ∇ B are all aligned and the characteristic direction corresponding to the maximum aligned directional derivative (MADD; i.e., the maximum of ∣∇B·r^∣ ) can be considered the normal vector of the structure. A benchmark test of this technique, using both the simulation data and numerical models of planar structures, shows that the MADD technique can identify planar magnetic field structures efficiently. For a discontinuity with translational and rotational motion, MADD is able to estimate its normal vector with second-order precision and the speed of motion with first-order precision. Two demonstrations of the MADD application to the tangential discontinuity and shock structures are presented to show its efficiency and superiority. In principle, MADD is suitable for all types of planar structures in space. Compared with the minimum variance analysis and timing techniques, MADD is superior in the study of intermediate shocks that exhibit magnetic coplanarity and rapid spatial evolution.

Are Switchback Boundaries Observed by Parker Solar Probe Closed?

Switchbacks are sudden and large deflections in the magnetic field that Parker Solar Probe frequently observes in the inner heliosphere. Their ubiquitous occurrence has prompted numerous studies to determine their nature and origin. Our goal is to describe the boundary of these switchbacks using a series of events detected during the spacecraft’s first encounter with the Sun. Using FIELDS and SWEAP data, we investigate different methods for determining the boundary normal. The observed boundaries are arc-polarized structures with a rotation that is always contained in a plane. Classical minimum variance analysis gives misleading results and overestimates the number of rotational discontinuities. We propose a robust geometric method to identify the nature of these discontinuities, which involves determining whether or not the plane that contains them also includes the origin ( B = 0). Most boundaries appear to have the same characteristics as tangential discontinuities in the context of switchbacks, with little evidence for having rotational discontinuities. We find no effect of the size of the Parker spiral deviation. Furthermore, the thickness of the boundary is within MHD scales. We conclude that most of the switchback boundaries observed by Parker Solar Probe are likely to be closed, in contrast to previous studies. Our results suggest that their erosion may be much slower than expected.

Mixed tiny path smoothing method based on sliding convolution windows for CNC machining

The machining toolpaths of complex free-form surface parts are generated using computer-aided manufacturing (CAM) systems and programmed by a series of mixed tiny paths composed of tiny lines, arcs, and non-uniform rational B-spline (NURBS). The mixed tiny paths need to be smoothed to eliminate the tangential discontinuities at corners. This paper proposes a mixed tiny path smoothing method based on sliding convolution windows (MSSCW). In this method, the mixed tiny path is firstly converted into a positional signal along the travel length in the spatial domain, and then sliding convolution windows, which centered on each original interpolation point, are used to generate high-order continuous smoothed toolpath. Finally, the smoothing error is checked and corrected by modifying the length duration of the sliding convolution windows. Compared with conventional path smoothing method, the MSSCW method is suitable for various computer numerical control (CNC) machining toolpaths, and the continuity of the smoothed toolpath can be adjusted according to user requirements. Consequently, the feasibility and effectiveness of the proposed method are validated in simulations and experimental results which realize the improvement of the machining quality of complex free-form surfaces.

Dynamics of Benjamin–Ono Solitons in a Two-Layer Ocean with a Shear Flow

The results of a theoretical study on Benjamin–Ono (BO) soliton evolution are presented in a simple model of a two-layer ocean with a shear flow and viscosity. The upper layer is assumed to move with a constant speed relative to the lower layer with a tangential discontinuity in the flow profile. It is shown that in the long-wave approximation, such a model can be appropriate. If the flow is supercritical, i.e., its speed (U) exceeds the speed of long linear waves (c1), then BO solitons experience “explosive-type” enhancement due to viscosity, such that their amplitudes increase to infinity in a finite time. In the subcritical regime, when U<c1, BO solitons experience very slow decay due to viscosity. Soliton amplitude decays with time as A∼t−1/2 or A∼t−1/3, depending on whether both layers are weakly viscous (the former case) or only the lower layer is viscous (the latter case). Estimates of "explosion time" are presented for real oceanic parameters.

Transport and Acceleration of O+ Ions in Upstream Solar Wind Due To Impact of an IMF Discontinuity: 3D Global Hybrid Simulation

AbstractBased on the predictions of global 3D hybrid simulations, we present a new transport/acceleration path for escaped O+ ions in the upstream solar wind region resulting from the impact of a particular IMF tangential discontinuity (TD) with negative (positive) IMF Bz on the discontinuity's anti‐sunward (sunward) side. For O+ ions escaping to the duskside magnetosheath and with gyro‐radii larger than the TD thickness, when they encounter the TD, they can first go sunward into the upstream solar wind. They then gyrate clockwise to the pre‐noon side and get accelerated within the solar wind region and circulate back to the dawnside magnetosphere. These ions may be accelerated to well within the ring current energy range depending on the solar wind electric field strength. This new transport/acceleration path can bring some of the escaped ions into the inner magnetosphere, thus providing a new mechanism for generating an O+ ring current population.