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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Effect of spatial density variation and O+ concentration on the growth and evolution of electromagnetic ion cyclotron waves

We simulate electromagnetic ion cyclotron (EMIC) wave growth and evolution within three regions, the plasmasphere (or plasmaspheric plume), the plasmapause, and the low-density plasmatrough outside the plasmapause. First, we use a ring current simulation with a plasmasphere model to model the particle populations that give rise to the instability for conditions observed on 9 June 2001. Then, using two different models for the cold ion composition, we do a full scale hybrid code simulation in dipole coordinates of the EMIC waves on a meridional plane at MLT = 18 and at 1900 UT within a range of L shell from L = 4.9 to 6.7. EMIC waves were observed during June 9, 2001 by Geostationary Operational Environmental Satellite (GOES) spacecraft. While an exact comparison between observed and simulated spectra is not possible here, we do find significant similarities between the two, at least at one location within the region of largest wave growth. We find that the plasmapause is not a preferred region for EMIC wave growth, though waves can grow in that region. The density gradient within the plasmapause does, however, affect the orientation of wave fronts and wave vector both within the plasmapause and in adjacent regions. There is a preference for EMIC waves to be driven in the He+ band (frequencies between the O+ and He+ gyrofrequencies) within the plasmasphere, although they can also grow in the plasmatrough. If present, H+ band waves are more likely to grow in the plasmatrough. This fact, plus L dependence of the frequency and possible time evolution toward lower frequency waves, can be explained by a simple model. Large O+ concentration limits the frequency range of or even totally quenches EMIC waves. This is more likely to occur in the plasmatrough at solar maximum. Such large O+ concentration significantly affects the H+ cutoff frequency and hence the width in frequency of the stop band above the He+ gyrofrequency. EMIC wave surfaces predicted by cold plasma theory are altered by the finite temperature of the ring current H+.

58 GEOSCIENCES↗
DOE OSTI2016

Measurement and modeling of the refilling plasmasphere during 2001

The Naval Research Laboratory SAMI3 (Sami3 is Also a Model of the Ionosphere) and the RAM-CPL (Ring current Atmosphere interaction Model-Cold PLasma) codes are used to model observed plasmasphere dynamics during 25 November 2001 to 1 December 2001 and 1–5 February 2001. Model results compare well to plasmasphere observations of electron and mass densities. Comparison of model results to refilling data and to each other shows good agreement, generally within a factor of 2. We find that SAMI3 plasmaspheric refilling rates and ion densities are sensitive to the composition and temperature of the thermosphere and exosphere, and to photoelectron heating. Furthermore, results also support our previous finding that the wind-driven dynamo significantly impacts both refilling rates and plasmasphere dynamics during quiet periods.

58 GEOSCIENCES↗
DOE OSTI2024

Simulating Long–Term Dynamics of Radiation Belt Electrons Using DREAM3D Model

Here, we compared the performance of DREAM3D simulations in reproducing the long-term radiation belt dynamics observed by Van Allen Probes over the entire year of 2017 with various boundary conditions (BCs) and model inputs. Specifically, we investigated the effects of three different outer boundary conditions, two different low-energy boundary conditions for seed electrons, four different radial diffusion (RD) coefficients (DLL), four hiss wave models, and two chorus wave models from the literature. Using the outer boundary condition driven by GOES data, our benchmark simulation generally well reproduces the observed radiation belt dynamics inside L* = 6, with a better model performance at lower μ than higher μ, where μ is the first adiabatic invariant. By varying the boundary conditions and inputs, we find that: (a) The data-driven outer boundary condition is critical to the model performance, while adding in the data-driven seed population doesn't further improve the performance. (b) The model shows comparable performance with DLL from Brautigam and Albert (2000, https://doi.org/10.1029/1999ja900344), Ozeke et al. (2014, https://doi.org/10.1002/2013ja019204), and Liu et al. (2016, https://doi.org/10.1002/2015gl067398), while with DLL from Ali et al. (2016, https://doi.org/10.1002/2016ja023002) the model shows less RD compared to data. (c) The model performance is similar with data-based hiss models, but the results show faster loss is still needed inside the plasmasphere. (d) The model performs similarly with the two different chorus models, but better capturing the electron enhancement at higher μ using the Wang et al. (2019, https://doi.org/10.1029/2018ja026183) model due to its stronger wave power, since local heating for higher energy electrons is under-reproduced in the current model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Comparison of electron loss models in the inner magnetosphere during the 2013 St. Patrick's Day geomagnetic storm

Electrons with energies in the keV range play an important role in the dynamics of the inner magnetosphere. Therefore, accurately modeling electron fluxes in this region is of great interest. However, these calculations constitute a challenging task since the lifetimes of electrons that are available have limitations. In this study, we simulate electron fluxes in the energy range of 20 eV-100 keV to assess how well different electron loss models can account for the observed electron fluxes during the GEM Challenge Event of the 2013 St. Patrick's Day storm. Three models (Case 1, Case 2, and Case 3) of electron lifetimes due to wave-induced pitch angle scattering are used to compute the fluxes, which are compared with measurements from the Van Allen Probes. The three models consider electron losses due to interactions with whistler mode hiss waves inside the plasmasphere and with whistler mode chorus waves outside the plasmasphere. The Case 1 (historical) model produces excessive loss at low L shells before and after the storm, suggesting that it overestimates losses due to hiss during quiet times. During the storm main phase and early recovery all three models show good agreement with the observations, indicating that losses due to chorus during disturbed times are in general well accounted for by the models. Furthermore, the more recent Case 2 and Case 3 models show overall better agreement with the observed fluxes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Cross-scale observations of the 2015 St. Patrick's day storm: THEMIS, Van Allen Probes, and TWINS

In this paper, we present cross-scale magnetospheric observations of the 17 March 2015 (St. Patrick's Day) storm, by Time History of Events and Macroscale Interactions during Substorms (THEMIS), Van Allen Probes (Radiation Belt Storm Probes), and Two Wide-angle Imaging Neutral-atom Spectrometers (TWINS), plus upstream ACE/Wind solar wind data. THEMIS crossed the bow shock or magnetopause 22 times and observed the magnetospheric compression that initiated the storm. Empirical models reproduce these boundary locations within 0.7 R E . Van Allen Probes crossed the plasmapause 13 times; test particle simulations reproduce these encounters within 0.5 R E . Before the storm, Van Allen Probes measured quiet double-nose proton spectra in the region of corotating cold plasma. About 15 min after a 0605 UT dayside southward turning, Van Allen Probes captured the onset of inner magnetospheric convection, as a density decrease at the moving corotation-convection boundary (CCB) and a steep increase in ring current (RC) proton flux. During the first several hours of the storm, Van Allen Probes measured highly dynamic ion signatures (numerous injections and multiple spectral peaks). Sustained convection after ~1200 UT initiated a major buildup of the midnight-sector ring current (measured by RBSP A), with much weaker duskside fluxes (measured by RBSP B, THEMIS a and THEMIS d). A close conjunction of THEMIS d, RBSP A, and TWINS 1 at 1631 UT shows good three-way agreement in the shapes of two-peak spectra from the center of the partial RC. A midstorm injection, observed by Van Allen Probes and TWINS at 1740 UT, brought in fresh ions with lower average energies (leading to globally less energetic spectra in precipitating ions) but increased the total pressure. Finally, the cross-scale measurements of 17 March 2015 contain significant spatial, spectral, and temporal structure.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

The Characteristic Response of Whistler Mode Waves to Interplanetary Shocks

Magnetospheric whistler mode waves play a key role in regulating the dynamics of the electron radiation belts. Recent satellite observations indicate a significant influence of interplanetary (IP) shocks on whistler mode wave power in the inner magnetosphere. In this study, we statistically investigate the response of whistler mode chorus and plasmaspheric hiss to IP shocks based on Van Allen Probes and THEMIS satellite observations. Immediately after the IP shock arrival, chorus wave power is usually intensified, often at postmidnight to prenoon sector, while plasmaspheric hiss wave power predominantly decreases near the dayside but intensifies near the nightside. We conclude that chorus wave intensification outside the plasmasphere is probably associated with the suprathermal electron flux enhancement caused by the IP shock. Through a simple ray tracing modeling assuming the scenario that plasmaspheric hiss is originated from chorus, we find that the solar wind dynamic pressure increase changes the magnetic field configuration to favor ray penetration in the nightside and promote ray refraction away from the dayside, potentially explaining the magnetic local time–dependent responses of plasmaspheric hiss waves following IP shock arrivals.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Simulations of Van Allen Probes Plasmaspheric Electron Density Observations

Here we simulate equatorial plasmaspheric electron densities using a physics-based model (Cold PLasma, CPL; used in the ring current-atmosphere interactions model) of the source and loss processes of refilling and erosion driven by empirical inputs. The performance of CPL is evaluated against in situ measurements by the Van Allen Probes (Radiation Belt Storm Probes) for two events: the 31 May to 5 June and 15 to 20 January 2013 geomagnetic storms observed in the premidnight and postmidnight magnetic local time (MLT) sectors, respectively. Overall, CPL reproduces the radial extent of the plasmasphere to within a mean absolute difference of |ΔL avg |=0.5 ± 0.1 L. The model electric field responsible for E × B convection and the parameterization of geomagnetic conditions (under the Kp-index and solar wind properties) implemented by CPL did not account for localized enhancements in the duskward electric field during increased activity. Rather, it was found to be largely dependent on the measure of the quiet time background. Finally, this property indicates that the agreement between these simulations and observations does not account for the complete set of physical processes during extreme (strong or weak) geomagnetic conditions impacting the plasmasphere. Nevertheless, at the presented resolution of the model CPL does provide good agreement in reproducing Radiation Belt Storm Probes observations of plasmaspheric density and plasmapause location.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Characteristic energy range of electron scattering due to plasmaspheric hiss

In this paper, we investigate the characteristic energy range of electron flux decay due to the interaction with plasmaspheric hiss in the Earth's inner magnetosphere. The Van Allen Probes have measured the energetic electron flux decay profiles in the Earth's outer radiation belt during a quiet period following the geomagnetic storm that occurred on 7 November 2015. The observed energy of significant electron decay increases with decreasing L shell and is well correlated with the energy band corresponding to the first adiabatic invariant μ = 4–200 MeV/G. The electron diffusion coefficients due to hiss scattering are calculated at L = 2–6, and the modeled energy band of effective pitch angle scattering is also well correlated with the constant μ lines and is consistent with the observed energy range of electron decay. Using the previously developed statistical plasmaspheric hiss model during modestly disturbed periods, we perform a 2-D Fokker-Planck simulation of the electron phase space density evolution at L = 3.5 and demonstrate that plasmaspheric hiss causes the significant decay of 100 keV–1 MeV electrons with the largest decay rate occurring at around 340 keV, forming anisotropic pitch angle distributions at lower energies and more flattened distributions at higher energies. Finally, our study provides reasonable estimates of the electron populations that can be most significantly affected by plasmaspheric hiss and the consequent electron decay profiles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

2015 Los Alamos Space Weather Summer School Research Reports

The fifth Los Alamos Space Weather Summer School was held June 1st - July 24th, 2015, at Los Alamos National Laboratory (LANL). With renewed support from the Institute of Geophysics, Planetary Physics, and Signatures (IGPPS) and additional support from the National Aeronautics and Space Administration (NASA) and the Department of Energy (DOE) Office of Science, we hosted a new class of five students from various U.S. and foreign research institutions. The summer school curriculum includes a series of structured lectures as well as mentored research and practicum opportunities. Lecture topics including general and specialized topics in the field of space weather were given by a number of researchers affiliated with LANL. Students were given the opportunity to engage in research projects through a mentored practicum experience. Each student works with one or more LANL-affiliated mentors to execute a collaborative research project, typically linked with a larger ongoing research effort at LANL and/or the student’s PhD thesis research. This model provides a valuable learning experience for the student while developing the opportunity for future collaboration. This report includes a summary of the research efforts fostered and facilitated by the Space Weather Summer School. These reports should be viewed as work-in-progress as the short session typically only offers sufficient time for preliminary results. At the close of the summer school session, students present a summary of their research efforts. Titles of the papers included in this report are as follows: Full particle-in-cell (PIC) simulation of whistler wave generation, Hybrid simulations of the right-hand ion cyclotron anisotropy instability in a sub-Alfvénic plasma flow, A statistical ensemble for solar wind measurements, Observations and models of substorm injection dispersion patterns, Heavy ion effects on Kelvin-Helmholtz instability: hybrid study, Simulating plasmaspheric electron densities with a two-component electric field model, Ion and electron heating by whistler turbulence: parametric studies via particle-in-cell simulation, and The statistics of relativistic electron pitch angle distribution in the Earth’s radiation belt based on the Van Allen Probes measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Assessment of Variability of the TEC in the Equatorial Anomaly Region with a Focus over Africa Using Rz and F10.7 as Input Drivers

This paper mainly intends to address the assessment of altitudinal variability of the vertical total electron content (VTEC) extracted from the Global Positioning System (GPS), the new versions of the International Reference Ionosphere Extended to the Plasmasphere (IRI-Plas 2017), and a quick-run ionospheric electron density (NeQuick 2) model in the equatorial anomaly region with a focus over Africa. This is manipulated employing the daily sunspot number (Rz) and 10.7 cm solar radio flux (F10.7) indices as the driver for the models during 2013–2016. The results show that the GPS-derived VTEC values are generally smaller than the modeled VTEC (IRI-Plas 2017 and NeQuick 2 VTEC) values, especially while utilizing the models with the Rz index. The modeled VTEC values are closer to the GPS VTEC values while using the models with the F10.7 index than Rz. The VTEC values obtained while using both models with the F10.7 index tend to increase while traversing from the high to the low solar activity years (especially in the March equinox and December solstice). The top-side ionospheric and plasmaspheric layers contribute the highest and lowest values to the total VTEC. Hence, the signal propagation through the ionosphere is largely affected when the signal crosses the top-side layer. Unlike other layers, due to the limited impact of the EUV on the ionization of neutral particles in the plasmasphere, the VTEC in the plasmaspheric layer (ECpl) shows smooth pattern with similar hourly values. Moreover, the IRI-Plas 2017 model does not effectively respond to the geomagnetic storm time variability of the VTEC with altitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Modeling of the cold electron plasma density for radiation belt physics

This review focusses strictly on existing plasma density models, including ionospheric source models, empirical density models, physics-based and machine-learning density models. This review is framed in the context of radiation belt physics and space weather codes. The review is limited to the most commonly used models or to models recently developed and promising. A great variety of conditions is considered such as the magnetic local time variation, geomagnetic conditions, ionospheric source regions, radial and latitudinal dependence, and collisional vs. collisionless conditions. These models can serve to complement satellite observations of the electron plasma density when data are lacking, are for most of them commonly used in radiation belt physics simulations and can improve our understanding of the plasmasphere dynamics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Evolution of chorus emissions into plasmaspheric hiss observed by Van Allen Probes

The two classes of whistler mode waves (chorus and hiss) play different roles in the dynamics of radiation belt energetic electrons. Chorus can efficiently accelerate energetic electrons, and hiss is responsible for the loss of energetic electrons. Previous studies have proposed that chorus is the source of plasmaspheric hiss, but this still requires an observational confirmation because the previously observed chorus and hiss emissions were not in the same frequency range in the same time. In this paper, we report simultaneous observations form Van Allen Probes that chorus and hiss emissions occurred in the same range ~300–1500 Hz with the peak wave power density about 10 -5 nT 2 /Hz during a weak storm on 3 July 2014. Chorus emissions propagate in a broad region outside the plasmapause. Meanwhile, hiss emissions are confined inside the plasmasphere, with a higher intensity and a broader area at a lower frequency. A sum of bi-Maxwellian distribution is used to model the observed anisotropic electron distributions and to evaluate the instability of waves. A three-dimensional ray tracing simulation shows that a portion of chorus emission outside the plasmasphere can propagate into the plasmasphere and evolve into plasmaspheric hiss. Moreover, hiss waves below 1 kHz are more intense and propagate over a broader area than those above 1 kHz, consistent with the observation. Finally, the current results can explain distributions of the observed hiss emission and provide a further support for the mechanism of evolution of chorus into hiss emissions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Penetration of magnetosonic waves into the plasmasphere observed by the Van Allen Probes

During the small storm on 14–15 April 2014, Van Allen Probe A measured a continuously distinct proton ring distribution and enhanced magnetosonic (MS) waves along its orbit outside the plasmapause. Inside the plasmasphere, strong MS waves were still present but the distinct proton ring distribution was falling steeply with distance. We adopt a sum of subtracted bi-Maxwellian components to model the observed proton ring distribution and simulate the wave trajectory and growth. MS waves at first propagate toward lower L shells outside the plasmasphere, with rapidly increasing path gains related to the continuous proton ring distribution. The waves then gradually cross the plasmapause into the deep plasmasphere, with almost unchanged path gains due to the falling proton ring distribution and higher ambient density. These results present the first report on how MS waves penetrate into the plasmasphere with the aid of the continuous proton ring distributions during weak geomagnetic activities.

58 GEOSCIENCES↗
DOE OSTI2014

High and low frequency instabilities driven by counter-streaming electron beams in space plasmas

A four-component plasma composed of a drifting (parallel to ambient magnetic field) population of warm electrons, drifting (anti-parallel to ambient magnetic field) cool electrons, stationary hot electrons, and thermal ions is studied in an attempt to further our understanding of the excitation mechanisms of broadband electrostatic noise (BEN) in the Earth's magnetospheric regions such as the magnetosheath, plasmasphere, and plasma sheet boundary layer (PSBL). Using kinetic theory, beam-driven electrostatic instabilities such as the ion-acoustic, electron-acoustic instabilities are found to be supported in our multi-component model. The dependence of the instability growth rates and real frequencies on various plasma parameters such as beam speed, number density, temperature, and temperature anisotropy of the counter-streaming (relative to ambient magnetic field) cool electron beam are investigated. It is found that the number density of the anti-field aligned cool electron beam and drift speed play a central role in determining which instability is excited. Using plasma parameters which are closely correlated with the measurements made by the Cluster satellites in the PSBL region, we find that the electron-acoustic and ion-acoustic instabilities could account for the generation of BEN in this region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Scattering by whistler-mode waves during a quiet period perturbed by substorm activity

We study the dynamics of radiation belt electrons during a 10-day quiet period perturbed by substorm activity and preceding a high-speed stream (HSS), aiming at a global description of the radiation belts in L-shell, L in [2, 6], and energy [0.1, 10] MeV. We combine Van Allen Probes observations and Fokker-Planck numerical simulations of pitch-angle diffusion. The Fokker-Planck model uses event-driven pitch angle diffusion coefficients from whistler-mode waves, built from the wave properties and the ambient plasma density measurements from the Van Allen Probes. We first find this event has some similar characteristics to regular quiet times previously studied; a widely extended plasmasphere within which we observe strong and varying whistler-mode waves. These ambient conditions lead to strong pitch-angle scattering, which contributes to the creation of a wide slot region as well as a significant decay of the outer radiation belts, which are observed and qualitatively well simulated. In addition, we find the substorm activity causes short duration (within ± 4h) decay of the plasma density and a lowering amplitude of the whistler-mode waves within the plasmasphere, both causing opposite effects in terms of pitch angle diffusion. This leads to a diminution of pitch-angle diffusion at the time of the main substorm activity. Conversely, whistler-mode waves become enhanced in the time periods between the substorm injections. All effects cumulated, we find an enhancement of pitch angle diffusion by whistler-mode waves above L~4.7 during the 10-day period. This directly relates to the combination of quietness and substorm activity which allows pitch angle diffusing of up to 1 MeV electrons in the outer belt. Relativistic electrons of 1–2 MeV remain trapped in the outer belt, from L~4.7 to L~5.2, forming, in both the observations and the simulations, a distinct pocket of remnant electrons.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Generation of Subauroral Longitudinally Extended Emissions Following Intensifications of the Poleward Boundary of the Substorm Bulge and Streamer Production

Observations showing the development of Subauroral Longitudinally Extended Emigerssions on a global scale are presented. It is demonstrated that they occur as a separation of an east-west arc-like band of luminosity that detaches away from the equatorward edge of the auroral distribution following episodes of auroral streamer production. They persist for time intervals on the order of ~30 min and devolve into patchy disjointed segments before they fade. Emissions are seen in both 557.7 nm OI and 391.4 nm N + 2 1NG lines, and 630.0 nm emissions are often observed equatorward. The 391.4 nm emissions are typically weaker and fade away more quickly than the 557.7 nm emissions, suggesting that an auroral precipitation source is initially present but is rapidly depleted as the forms age. All cases are associated with enhanced Subauroral Polarization Stream (SAPS) flows, and one event shows clear association with large-scale Giant Undulations (GUs) and the formation of spur-like forms that fold equatorward under the main oval. A model is proposed for the production of subauroral longitudinally extended forms in which nonlinear growth of SAPS-induced surface waves on the plasmapause results in a disruption of the boundary. It is suggested that hot plasma of plasma sheet origin becomes entrained in the plasmasphere to produce transient precipitation-associated auroral emissions that may decay into STEVE emissions and that cold dense plasma from the plasmasphere becomes entrained onto open drift paths to feed long-lived drainage plumes. This process may occur quasi periodically during intense substorms and storm-time conditions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Key Elements of Auroral Substorm Development and their Relationship to Recent Observations of Detached Sub-Auroral Phenomena Including STEVE-like Emissions

Since Akasofu introduced the concept of the substorm in 1964, numerous refinements have been added to the phenomenological model of how auroral substorms develop. Here, we review several of the most important of these including; polar cap patches, intensifications of the Polar Activated Band (PAB) at the poleward edge of the bulge, the development of new arcs poleward, the generation of auroral streamers, the evolution of streamers into auroral torches and omega bands, the association of streamers with particle injection and BBF activity in the tail, and wedgelet-like magnetic perturbations on the ground. We also review the concept of “contact breakups” which are breakups that appear to be triggered by the arrival of streamer-like forms in the equatorward regions of the oval. Finally, we remind the community that the addition of detached sub-auroral emissions was made to the phenomenological picture of substorm develop in the late 1960s along with the concept of auroral streamers. Newer observations of detached sub-auroral (STEVE-like emissions) from the Viking/UVI and POLAR/VIS imagers are presented which confirm that they are east-west aligned bands of emission that separate away from the equatorward edge of the auroral oval in response to intensifications of the poleward edge of the bulge and subsequent streamer production. We propose a new model for the formation of detached sub-auroral (STEVE-like) emissions in which a non-linear growth of a SAPS-driven instability (e.g. like the shear-flow/ballooning instability) at the plasmapause results in the disruption of the boundary separating hot plasma sheet particle from the cold plasmaspheric plasma. It is proposed that the resulting intermixing of plasma populations leads to both the observed STEVE-like emissions and also provides a source of cold plasma on open drift paths that can feed the long-lived drainage plumes that have recently been discovered.

58 GEOSCIENCES↗
DOE OSTI2021

Propagation of Chorus Waves Generated in Minimum‐B Pockets

Abstract We present the first ray tracing results of chorus waves generated in minimum‐B pockets. A new ray tracer is developed to accommodate an arbitrary magnetic field model, which enables us to construct minimum‐B pocket geometries using the Tsyganenko (1989) model. Rays with different frequencies and initial wave normal angles are launched from minimum‐B pockets and traced under different geomagnetic activity and hot electron density conditions. Our results indicate that chorus waves generated from minimum‐B pockets are usually highly localized and thus are unlikely to be detected unless the spacecraft is very close to the source region. These waves are also very unlikely to propagate into the plasmasphere. The propagation distances generally decrease with increasing geomagnetic activity.

Kang, Ning↗