Cusp Region Research Articles

A novel method for measuring the direction and angle of Central ray and predicting rotation center via panorama phantom.

The aim of this study is to propose and evaluate a novel method for measuring the central ray direction and detecting the rotation center of panoramic radiography using the panorama phantom. To determine the central ray direction, two points passing through the same x-coordinate in a panoramic radiograph were identified and connected. The angles formed by the central ray with the midline and the angle to the arch form were measured using mathematical calculations. Further, by analyzing the continuous changes in the central ray obtained in this manner, the movement of the rotation center was detected and visualized. The angle between the central ray and the midline exhibited a progressive decrease from the anterior to the posterior direction. With regards to the arch form, the angle of the central ray exhibited an increasing pattern as it moved from the anterior to the posterior direction, culminating in its peak value at the lower second premolar cusp region, followed by a consistent decrease. The rotation center approximately started from the distolateral aspect of the coronoid process and then anteromedially moved to the midline in a curved line passing between the mandibular notch and coronoid process. By using the panorama phantom, we successfully obtained the central ray direction and detected the rotation center of the panoramic radiography.

Multiple Satellite Observations of the High‐Latitude Cusp Aurora During Northward IMF Conditions

AbstractCusp auroras poleward of the typical auroral oval are ascribed to high‐latitude lobe reconnection when the Interplanetary Magnetic Field (IMF) Bz is predominantly northward. In this study, we further investigate the ionospheric characteristics of a unique high‐latitude cusp region employing multiple satellite observations. A cusp aurora event with wide spatial spread was observed in the postnoon polar cap region. It was found to be associated with northward IMF Bz and positive By components. The cusp aurora was located from 68° to 86° in magnetic latitude and within 15–17 hr in magnetic local time. This broad coverage in the polar cap indicates direct precipitating particles from the magnetosheath. Particle energy is different between the equatorward and poleward edges of the cusp aurora. The precipitating ions at the equatorward side maintain magnetosheath particle characteristics as expected, while ions with higher energies occurred in the poleward side. Further, the poleward edge of the cusp aurora was nearly situated in the center of a convection shear and was associated with an upward field‐aligned current. These observations suggest a lobe cell circulation, hence we attribute the formation of the cusp aurora to the high‐latitude lobe reconnection. Simultaneous observations in the southern hemisphere indicate the absence of cusp aurora. The auroral presence only in the northern hemisphere is probably due to the combination of large dipole tilt angle and positive IMF Bz, which facilitates the lobe reconnection.

Investigating the Basis Set Convergence of Diagrammatically Decomposed Coupled-Cluster Correlation Energy Contributions for the Uniform Electron Gas.

We investigate the convergence of coupled-cluster (CC) correlation energies and related quantities with respect to the employed basis set size for the uniform electron gas (UEG) to gain a better understanding of the basis set incompleteness error (BSIE). To this end, coupled-cluster doubles (CCD) theory is applied to the three-dimensional UEG for a range of densities, basis set sizes, and electron numbers. We present a detailed analysis of individual diagrammatically decomposed contributions to the amplitudes at the level of CCD theory. In particular, we show that only two terms from the amplitude equations contribute to the asymptotic large-momentum behavior of the transition structure factor, corresponding to the cusp region at short interelectronic distances. However, due to the coupling present in the amplitude equations, all decomposed correlation energy contributions show the same asymptotic convergence behavior to the complete basis set limit. These findings provide an additional rationale for the success of a recently proposed correction to the BSIE of CC theory. Lastly, we examine the BSIE in the CCD plus perturbative triples [CCD(T)] method, as well as in the newly proposed CCD plus complete perturbative triples [CCD(cT)] method.

Multi‐Instrument Analysis of the Formation and Segmentation of Tongue of Ionization Into Two Consecutive Polar Cap Patches

AbstractThis paper investigates the formation and segmentation of the tongue of ionization into two consecutive polar cap patches using multi‐instrument observations from 27 February 2014. We provide insights into how the interplanetary magnetic field (IMF) variations influence the formation and segmentation of these patches. Our findings reveal that the entry of dayside dense plasma into the polar cap is predominantly driven by the modified convection near the cusp region, which is controlled by the transition of IMF By or the sudden drop of IMF Bz. Furthermore, we observe a rapid north‐westward plasma flow within the patch segmentation region, accompanied by equatorward‐expanded and enhanced convection near the cusp region. This fast‐moving flow, approximately 1.5 km/s, is characterized by low density and high electron temperature and shows a signature of a Subauroral Polarization Stream. This suggests that the fast‐westward flow, in conjunction with the expansion and contraction of ionospheric convection, plays a crucial role in the segmentation of polar cap patches from the dayside plasma reservoir. This study provides a comprehensive observation of the evolution of polar cap patches, thereby advancing our understanding of the dynamic mechanisms governing patch formation and segmentation.

Kinetic Signatures, Dawn‐Dusk Asymmetries, and Flux Transfer Events Associated With Mercury's Dayside Magnetopause Reconnection From 3D MHD‐AEPIC Simulations

AbstractMercury possesses a miniature yet dynamic magnetosphere driven primarily by magnetic reconnection occurring regularly at the magnetopause and in the magnetotail. Using the newly developed Magnetohydrodynamics with Adaptively Embedded Particle‐in‐Cell (MHD‐AEPIC) model coupled with planetary interior, we have performed a series of global simulations with a range of upstream conditions to study in detail the kinetic signatures, asymmetries, and flux transfer events (FTEs) associated with Mercury's dayside magnetopause reconnection. By treating both ions and electrons kinetically, the embedded PIC model reveals crescent‐shaped phase‐space distributions near reconnection sites, counter‐streaming ion populations in the cusp region, and temperature anisotropies within FTEs. A novel metric and algorithm are developed to automatically identify reconnection X‐lines in our 3D simulations. The spatial distribution of reconnection sites as modeled by the PIC code exhibits notable dawn‐dusk asymmetries, likely due to such kinetic effects as X‐line spreading and Hall effects. Across all simulations, simulated FTEs occur quasi‐periodically every 4–9 s. The properties of simulated FTEs show clear dependencies on the upstream solar wind Alfvénic Mach number (MA) and the interplanetary magnetic field orientation, consistent with MESSENGER observations and previous Hall‐MHD simulations. FTEs formed in our MHD‐AEPIC model tend to carry a large amount of open flux, contributing ∼3%–36% of the total open flux generated at the dayside. Taken together, our MHD‐AEPIC simulations provide new insights into the kinetic processes associated with Mercury's magnetopause reconnection that should prove useful for interpreting spacecraft observations, such as those from MESSENGER and BepiColombo.

Validation of Simulated Statistical Characteristics of Magnetosphere‐Ionosphere Coupling in Global Geospace Simulations Over an Entire Carrington Rotation

AbstractWe study the statistical features of magnetosphere‐ionosphere (M‐I) coupling using a two‐way M‐I model, the GT configuration of the Multiscale Atmosphere Geospace Environment (MAGE) model. The M‐I coupling characteristics, such as field‐aligned current, polar cap potential, ionospheric Joule heating, and downward Alfvénic Poynting flux, are binned according to the interplanetary magnetic field clock angles over an entire Carrington Rotation event between 20 March and 16 April 2008. The MAGE model simulates similar distributions of field‐aligned currents compared to empirical Weimer/AMPS models and Iridium observations and reproduces the Region 0 current system. The simulated convection potential agrees well with the Weimer empirical model and displays consistent two‐cell patterns with SuperDARN observations, which benefit from more extensive data sets. The Joule heating structure in MAGE is generally consistent with both empirical Cosgrove and Weimer models. Moreover, our model reproduces Joule heating enhancements in the cusp region, as presented in the Cosgrove model and observations. The distribution of the simulated Alfvénic Poynting flux is consistent with that observed by the FAST satellite in the dispersive Alfvén wave regime. These M‐I coupling characteristics are also binned by the Kp indices, indicating that the Kp dependence of these patterns in the M‐I model is more effective than the empirical models within the Carrington Rotation. Furthermore, the MAGE simulation exhibits an improved M‐I current‐voltage relation that closely resembles the Weimer model, suggesting that the updated global model is significantly improved in terms of M‐I coupling.

TRICE‐2/SuperDARN Observations and Comparison With the Associated MMS Magnetopause Crossing

AbstractTwo sounding rockets, designated TRICE‐2, were launched on 8 December 2018 into the northern cusp region. The two rockets were designated the high‐ and low‐flyers, respectively, and launched 2 min apart to investigate cusp structures, specifically their spatial or temporal nature. 2 hr prior to the cusp encounter by the TRICE‐2 rockets, the MMS satellites, located in the magnetopause boundary layer, observed switching ion beams under very similar IMF conditions as later observed by TRICE‐2. The observed ion beam switch in the boundary layer defined the location of the primary dayside X‐line. Both, TRICE‐2 and MMS, also observed the signatures of multiple X‐lines at the magnetopause, overlapping ion‐energy dispersions in the cusp and counterstreaming ion beams in the magnetopause boundary layer, respectively. In addition to the TRICE‐2 cusp observations, ionospheric convection patterns from the SuperDARN radar are used to explain the vastly different cusp ion signatures observed by the TRICE‐2 rockets. While the high‐flyer rocket progressed north through the center of the cusp, the low‐flyer rocket drifted off to the east and crossed into the dusk convection cell, traveling perpendicular to the ionospheric convection direction before reaching the poleward oriented section of the convection cell also observed by the high‐flyer counterpart.

Mid- and High-Latitude Electron Temperature Dependence on Solar Activity in the Topside Ionosphere through the Swarm B Satellite Observations and the International Reference Ionosphere Model

This study focuses on the open question of the electron temperature (Te) variation with solar activity in the topside ionosphere at mid- and high latitudes. It takes advantage of in situ observations taken over a decade (2014–2023) from Langmuir probes on board the low-Earth-orbit Swarm B satellite and spanning an altitude range of 500–530 km. The study also includes a comparison with Te values modeled using the International Reference Ionosphere (IRI) model and with Millstone Hill (42.6° N. 71.5° W) incoherent scatter radar observations. The largest Te variation with solar activity was found at high latitudes in the winter season, where Te shows a marked decreasing trend with solar activity in the polar cusp and auroral regions and, more importantly, at sub-auroral latitudes in the nightside sector. Differently, in the summer season, Te increases with solar activity in the polar cusp and auroral regions, while for equinoxes, variations are smaller and less clear. Mid-latitudes generally show negligible Te variations with solar activity, which are mostly within the natural dispersion of Te observations. The comparison between measured and modeled values highlighted that future implementations of the IRI model would benefit from an improved description of the Te dependence on solar activity, especially at high latitudes.

Large‐Scale Traveling Ionospheric Disturbances Over the European Sector During the Geomagnetic Storm on March 23–24, 2023: Energy Deposition in the Source Regions and the Propagation Characteristics

AbstractMultiple Large‐Scale Traveling Ionospheric Disturbances (LSTIDs) are observed in the European sector in both day‐time and night‐time during the magnetic storm on March 23–24, 2023. The Total Electron Content (TEC) observation from a network of GNSS receivers shows the propagation of LSTIDs with amplitudes between around 0.5 and 1 TECU originating from auroral and polar cusp regions down to southern Europe (35°N) with velocities between around 500 and 1,600 [m/s]. We study the energy deposition to the LSTIDs in the source regions and the resulting horizontal propagation over storm‐time background density by using continuous measurements of EISCAT incoherent scatter radars in northern Norway and Svalbard that allow for estimating the source energy to the thermosphere‐ionosphere system via Joule heating and particle precipitation. Both EISCAT and GNSS TEC data show that the electron density decreased to 50% in the auroral zone after the storm onset. The ionospheric heating caused a nearly 250% increase in the electron temperature above 200 km altitude and the ion temperature above 100 km altitude. We find that Joule Heating acts as a primary energy source for the night‐time LSTIDs triggered in the auroral region, while the day‐time LSTIDs can be also driven by precipitating particles in the polar cusp. We also find that a significant background density decrease over the whole European sector is caused by this storm for the following day, during which almost no clear LSTIDs are observed.

Observations of Geomagnetic Crochet at High‐Latitudes Due To X1.5 Class Solar Flare on 3 July 2021

AbstractOn 3 July 2021, an X1.5 solar flare from the National Oceanic and Atmospheric Administration solar Active Region AR12838 (24°N, 88°W) occurred at 14:18 UT, peaked at 14:29 UT, and decayed at 14:34 UT. The study of this X1.5 solar flare is significant due to its unique geomagnetic crochet feature at high latitudes and its effective signature on Earth. The study examined X‐rays, the extreme ultraviolet spectrum, ionospheric equivalent current (IEC), and geomagnetic field components. The study reveals a sudden increase in IEC during the X1.5 flare episode, forming a zonal current region and producing a geomagnetic crochet signature in geomagnetic field components at high latitudes (50°–80°N) along the 11°–26°E longitude sector during the flare peak time. All three geomagnetic field components show different sensitivity to the solar flare effect (sfe), and the amplitude and phase of the geomagnetic crochet across latitudes (for a given longitude) are consistent with the variations in the IEC. The present study is the first to appraise geomagnetic crochets of low magnitude (8–40 nT) and short duration (10–15 min) at high latitudes, particularly in the polar cusp region, during the X‐class limb flare.

Localized Hybrid Simulation of Martian Crustal Magnetic Cusp Regions: Vertical Electric Potential Drop and Plasma Dynamics

AbstractThe localized crustal magnetic fields of Mars play an important role in the planet’s ionosphere‐solar wind interaction. Various physical processes in the induced magnetosphere, such as particle precipitation, field‐aligned currents, and ion outflow, are usually associated with the crustal magnetic cusp regions, where field lines are mostly vertical and open to space. Due to the small spatial scale (a few hundred km) of the Martian crustal magnetic cusps, localized models with high spatial resolutions and ion kinetics are needed to understand the physical processes. We adapt the simulation platform HYB developed at the Finnish Meteorological Institute to a moderately strong magnetic cusp above the Martian exobase with a 2‐D simulation domain assuming periodic boundary conditions on the third dimension. Two plasma sources are included in the simulation: hot protons from the induced magnetosphere and cold heavy ions (O+) from the ionosphere. Our model results can qualitatively reproduce the vertical electric potential drop, particle transport, and field aligned current in the cusp region. The vertical electric potential is built up mostly by the Hall electric field as a result of the separation between ion and electron fluxes of the downward plasma flow. By varying the model inputs, we found that the vertical potential drop depends on ionospheric ion density and magnetic field strength. These results tell us that energy is transferred from magnetospheric plasma to ionospheric plasma through the vertical electric potential buildup in magnetic cusps and how this process may affect electron precipitation, ion escape, and ionosphere conditions at Mars.

SMILE Winter Campaign

ABSTRACT This white paper is highly topical as it relates to the upcoming solar wind magnetosphere ionosphere link explorer (SMILE) mission: SMILE is a joint mission between the European Space Agency and the Chinese Academy of Sciences and it aims to build a more complete understanding of the Sun–Earth connection by measuring the solar wind and its dynamic interaction with the magnetosphere. It is a fully funded mission with a projected launch in 2025. This paper outlines a plan for action for SMILE’s first Northern hemisphere winter campaign using ground-based instruments. We outline open questions and which data and techniques can be employed to answer them. The science themes we discuss are: (i) Earth’s magnetosheath, magnetopause, and magnetic cusp impact on the ionospheric cusp region; (ii) defining the relationship between auroral processes, solar wind, and magnetospheric drivers; (iii) understanding the interhemispheric properties of the Earth’s magnetosphere–ionosphere system. We discuss open questions (different to the mission goals) which may be answered using existing ground-based instrumentation together with SMILE data to leverage the maximum scientific return of the mission during the first winter after launch. This paper acts as a resource for planning, and a call to collaborative action for the scientific community.

Electrical transport mechanism of manganite-based trilayer heterostructures in the Cusp and insulating regions

In the present study, efforts are made to study the temperature dependent resistivity (ρ-T) variations of manganites (La0.7Sr0.3MnO3 (LSMO) single layer) and manganites-based systems ((LSMO/γ-Fe2O3/LSMO) trilayer heterostructures) in two distinct regions (Cusp region and Insulating region). Cusp region is an intermediate region between Metallic region and Insulating region. The resistivity-temperature curves are studied and analysed by various resistive models and fitting equations. The co-existence of ferromagnetic clusters and polarons manifests in the Cusp region. The Insulating region is explored and fitted under two regimes: Low Temperature Insulating region and High Temperature Insulating region. Various mathematical models viz. Thermal Activation model, Small Polaron Hopping model and Variable Range Hopping model were employed to study the ρ-T variations under various temperature ranges for LSMO (60 nm) single layer system and LSMO/γ-Fe2O3/LSMO (150 nm) trilayer heterostructures. In Insulating region, the deviations in the fitted curves from the experimental data is due to intrinsic disorder at the R/A site in case of LSMO single layer system while in case of trilayer system disorder exists at both R/A and B sites. The study is crucial to understand the microscopic picture of electrical transport behavior in both the systems near and above Metal-Insulator Transition.

Latituditual Structure of Dayside Polar Cusp Precipitation

The results of observations of low-altitude spacecraft crossing the daytime sector of the auroral zone and of high-apogee spacecraft in the equatorial plane of the magnetosphere were analyzed in order to identify the main processes leading to the formation of dayside polar cusps. Observations from the DMSP F7 spacecraft were used to analyze the latitudinal characteristics of ion precipitation in the cusp region and to study the latitudinal profile of ion pressure in the cusp depending on the IMF parameters. A significant difference was found in identifying the cusp boundaries using an automated data processing system and direct analysis of spacecraft observations. It is shown that for small negative values of the Bz-component of the IMF (〈Bz〉 = –3.0 nT), an ordinary feature of the cusp is the latitudinal profile of the ion pressure (Pi) with a width of ~1° of latitude with two maxima, one of which is located in the equatorward and the other in the poleward of the cusp. For large negative Bz values (–6, –8 nT), the polar maximum in the latitudinal profile Pi disappears; only the equatorial maximum remains, the Pi level at the maximum increases, and the width of the cusp decreases to ~0.7°. For Bz IMF 0, the most characteristic is the Pi profile with a maximum ion pressure in the polar part of the cusp. The cusp for Bz 0 is located at higher latitudes than for Bz 0, and its average latitudinal width increase to ~1.4° of latitude. In the prenoon sector MLT, the most typical for periods with a large negative By-component of the IMF (〈By〉 = –6.3 nT, 〈Bz〉 = –1.7 nT) is a cusp with a width of ~1.4° of latitude with a flat top in the latitudinal Pi profile. Comparison of the pressure distributions observed at low heights with data from high-apogee satellites confirmed the possibility of describing the formation of the cusp as a diamagnetic cavity and using observations in the cusp to determine the ion pressure in the magnetosheath.

Trajectory optimization method based on ellipse model for dynamic motion control of piezoelectric transducer in an optical resonance cavity

External-cavity diode laser (ECDL) can continuously change the output wavelength by scanning its optical resonance cavity (ORC), which is a piezoelectric transducer (PZT) actuated mechanical system. However, because of the inherent hysteresis characteristic of PZT and limited system bandwidth, the dynamic response of the ORC system exhibits both the nonlinearity and vibration while high-frequency triangular wave scanning, thereby resulting in the degradation of the output wavelength performance of the ECDL. As a result, a trajectory optimization method is presented to improve the scanning characteristics of the ORC system. Firstly, the hysteresis behavior of PZT is described by the elliptic model to generate a compensation voltage for the PZT. Secondly, the cusp region of the compensation voltage is optimized by a frequency domain objective function to greatly reduce the high-order harmonic components of the compensation voltage. Finally, an optimal voltage trajectory for driving the ORC system is obtained. The experimental results demonstrate the validity of our proposed trajectory optimization method for simultaneously suppressing the nonlinearity and vibration of the ORC system within the scanning frequency of 100 Hz.

Effects of Coronal Magnetic Field Configuration on Particle Acceleration and Release during the Ground Level Enhancement Events in Solar Cycle 24

Ground level enhancements (GLEs) are extreme solar energetic particle (SEP) events that are of particular importance in space weather. In solar cycle 24, two GLEs were recorded on 2012 May 17 (GLE 71) and 2017 September 10 (GLE 72), respectively, using a range of advanced modern instruments. Here we conduct a comparative analysis of the two events by focusing on the effects of large-scale magnetic field configuration near active regions on particle acceleration and release. Although the active regions are both located near the western limb, temporal variations of SEP intensities and energy spectra measured in situ display different behaviors at early stages. By combining a potential field model, we find the coronal mass ejection (CME) in GLE 71 originated below the streamer belt, while in GLE 72 it originated near the edge of the streamer belt. We reconstruct the CME shock fronts with an ellipsoid model based on nearly simultaneous coronagraph images from multiple viewpoints and further derive the 3D shock geometry at the GLE onset. The highest-energy particles are primarily accelerated in the shock–streamer interaction regions, i.e., likely at the nose of the shock in GLE 71 and the eastern flank in GLE 72, due to quasi-perpendicular shock geometry and confinement of closed fields. Subsequently, they are released to the field lines connecting to near-Earth spacecraft when the shocks move through the streamer cusp region. This suggests that magnetic structures in the corona, especially shock–streamer interactions, may have played an important role in the acceleration and release of the highest-energy particles in the two events.

Computed Tomographic Evaluation of Buccal Shelf Dimensions in South Indian Patients With Sagittal Skeletal Class III Malocclusion: A Retrospective Study.

Background Computed tomographic evaluation of mandibular buccal shelf region in skeletal class III malocclusion cone beam computed tomography (CBCT) studies have been reported to have great alteration in the thickness of mandibular buccal shelf region owing to the different growth patterns and ethnic variations. The aim of this study was to determine the total and cortical bone thicknessin the mandibularbuccal shelf(MBS) region for extra-alveolar mini-screw placement in South Indian patients with sagittal skeletal class III malocclusion. Material and methods This retrospective computed tomographic study consisted of archived files of the Dravidian population with class III skeletal base that met the eligibility criteria. The total bone and cortical bone thickness of the buccal shelf regions were evaluated in relation to three anatomical sites at various depths and angulations. One-way ANOVA and Tukey honestly significant difference (HSD) post hoc tests were used for statistical analysis. Pearson correlation coefficient was performed to compare if any relation existed between bone thickness and the growth pattern. Results The maximum bone thickness in the buccal shelf region in our study was found at the distal portion of the second molar root, 8-12 mm from its cementoenamel junction (CEJ) and at 30-45 ° angulation (p-value<0.005). There was a positive correlation between the hypo-divergent growth pattern and the thickness of the bone. Conclusion Based on the sites recorded, the preferred site for mini screw placement in Class III patients is the distobuccal cusp region with respect to the second molarat a depth of 8-12 mmand at angulation of 30-45 °. There was a moderate correlation with hypo-divergent growth patterns, suggestive of a wider and thicker mandibular buccal shelf region in these subjects.

Direct numerical simulations of methane, ammonia-hydrogen and hydrogen turbulent premixed flames

Three turbulent premixed flames with the same unstretched laminar flame speeds and thicknesses are analyzed and compared using 3D Direct Numerical Simulation (DNS) in a slot burner configuration at atmospheric conditions: a CH4/air flame at ϕ=1, an NH3−H2/air (46% vol. H2) at ϕ=1 and an H2/air flame at ϕ=0.45.While both stoichiometric methane and ammonia-hydrogen flames behave similarly, the lean hydrogen flame brush is twice as short with less flame surface, and exhibits significant alteration of its local flame structure: for the H2 flame, the thickness of flamelets decreases significantly while burning rates increase drastically. This is observed for flame elements convexly curved with respect to fresh reactants (positive curvature) because of preferential diffusion, where thermo-diffusive instabilities generate long-tail structures that continuously head toward the fresh gases, and also for near-flat flame elements because of local strain effects. Opposite behaviors are observed for flame elements concavely curved (negative curvature) where fuel depletion caused by unfocusing of hydrogen and strain effects are unable to increase the consumption, even leading to near-extinction of the flame. The turbulent methane and ammonia-hydrogen flames studied in this work do not exhibit the instabilities seen in the pure hydrogen flame. However, local flame-flame interactions are observed in the cusp regions of all three flames, which significantly increase the displacement speed as well as flame surface destruction.A 1D-3D comparison indicates that strain effects in regions of low curvature and preferential diffusion effects in regions of positive curvature can be modeled using counterflow flamelets to account for stretch effects on the turbulent hydrogen flame propagation in addition to turbulent wrinkling.

Gaussian functions with odd power of r produced by the free complement theory.

We investigate, in this paper, the Gaussian (G) function with odd powers of r, rxaybzcexp(-αr2), called the r-Gaussian or simply the rG function. The reason we investigate this function here is that it is generated as the elements of the complement functions (cf's) when we apply the free complement (FC) theory for solving the Schrödinger equation to the initial functions composed of the Gaussian functions. This means that without the rG functions, the Gaussian set of functions cannot produce the exact solutions of the Schrödinger equation, showing the absolute importance of the rG functions in quantum chemistry. Actually, the rG functions drastically improve the wave function near the cusp region. This was shown by the applications of the present theory to the hydrogen and helium atoms. When we use the FC-sij theory, in which the inter-electron function rij is replaced with its square sij=rij2 that is integrable, we need only one- and two-electron integrals for the G and rG functions. The one-center one- and two-electron integrals of the rG functions are always available in a closed form. To calculate the integrals of the multi-centered rG functions, we proposed the rG-NG expansion method, in which an rG function is expanded by a linear combination of the G functions. The optimal exponents and coefficients of this expansion were given for N = 2, 3, 4, 5, 6, and 9. To show the accuracy and the usefulness of the rG-NG method, we applied the FC-sij theory to the hydrogen molecule.

Lateral Confinement and the Remarkably Self-similar Nature of Coronal Pseudostreamer Mass Ejections

Coronal mass ejections (CMEs) that originate from pseudostreamers, which separate coronal holes of the same magnetic polarity, are characterized by a narrow (∼5°–30°), fan-shaped appearance in white-light coronagraph images. Despite this striking morphological similarity, a wide variety of underlying eruptions are observed, including not only coronal jets, but also larger-scale filament eruptions, footpoint flares, and even extreme-ultraviolet (EUV) waves that reflect off the coronal hole boundaries. Using EUV images recorded by the Solar Dynamics Observatory during the early rising phase of cycle 25 (2020–2022), we describe examples of the different kinds of underlying eruptions and identify the corresponding fan-like ejections in Large Angle and Spectrometric Coronagraph images. We attribute the narrowness of the white-light CMEs to lateral confinement by the like-polarity open flux surrounding the pseudostreamer and point out that, although the multipolar topology facilitates the “breakout” of material through the cusp region, it also tends to inhibit the eruption of the pseudostreamer as a whole. We also note that the self-similar “continuum” formed by the pseudostreamer mass ejections does not include the larger, more space-weather-effective CMEs associated with helmet streamers, which are surrounded by open flux of opposite polarity and undergo much greater lateral expansion.