Ultralow Frequency Waves Research Articles

Energetic Electron and Proton Interactions with Pc5 Ultra Low Frequency (ULF) Waves during the Great Geomagnetic Storm of 15–16 July 2000

The dynamics of the outer zone radiation belt has received a lot of attention mainly due to the correlation between the occurrence of enhancing relativistic electron flux and spacecraft operation anomalies or even failures (e.g., Baker et al. 1994). Relativistic electron events are often observed during great storms associated with ultra low frequency (ULF) waves. For example, a large buildup of relativistic electrons was observed during the great storm of March 24, 1991 (e.g., Li et al. 1993; Hudson et al. 1995; Mann et al. 2013). However, the dominant processes which accelerate magnetospheric radiation belt electrons to MeV energies are not well understood. In this paper, we present observations of Pc5 ULF waves in the recovery phase of the Bastille day storm of July 16, 2000 and electron and proton flux simultaneously oscillating with the same frequencies as the waves. The mechanism for the observed electron and proton flux modulations is examined using groundbased and satellite observations. During this storm time, multiple packets of discrete frequency Pc5 ULF waves appeared associated with energetic particle flux oscillations. We model the drift paths of electrons and protons to determine if the particles drift through the ULF wave to understand why some particle fluxes are modulated by the ULF waves and others are not. We also analyze the flux oscillations of electrons and protons as a function of energy to determine if the particle modulations are caused by a ULF wave drift resonance or advection of a particle density gradient. We suggest that the energetic electron and proton modulations by Pc5 ULF waves provide further evidence in support of the important role that ULF waves play in outer radiation belt dyanamics during storm times.

On the Role of ULF Waves in the Spatial and Temporal Periodicity of Energetic Electron Precipitation

AbstractEnergetic electron precipitation to the Earth's atmosphere is a key process controlling radiation belt dynamics and magnetosphere‐ionosphere coupling. One of the main drivers of precipitation is electron resonant scattering by whistler‐mode waves. Low‐altitude observations of such precipitation often reveal quasi‐periodicity in the ultra‐low‐frequency (ULF) range associated with whistler‐mode waves, causally linked to ULF‐modulated equatorial electron flux and its anisotropy. Conjunctions between ground‐based instruments and equatorial spacecraft show that low‐altitude precipitation concurrent with equatorial whistler‐mode waves also exhibits a spatial periodicity as a function of latitude over a large spatial region. Whether this spatial periodicity might also be due to magnetospheric ULF waves spatially modulating electron fluxes and whistler‐mode chorus has not been previously addressed due to a lack of conjunctions between equatorial spacecraft, low earth orbit spacecraft, and ground‐based instruments. To examine this question, we combine ground‐based and equatorial observations magnetically conjugate to observations of precipitation at the low‐altitude, polar‐orbiting CubeSats Electron Losses and Fields Investigation‐A and ‐B. As they sequentially cross the outer radiation belt with a temporal separation of minutes to tens of minutes, they can easily reveal the spatial quasi‐periodicity of electron precipitation. Our combined data sets confirm that ULF waves may modulate whistler‐mode wave generation within a large magnetic local time and L‐shell domain in the equatorial magnetosphere, and thus lead to significant aggregate energetic electron precipitation exhibiting both temporal and spatial periodicity. Our results suggest that the coupling between ULF and whistler‐mode waves is important for outer radiation belt dynamics.

Identifying the Structure and Propagation of Dawnside Pc5 ULF Waves Using Space‐Ground Conjunctions

AbstractPc5 ultralow frequency waves are important for transferring energy between the magnetosphere and ionosphere. While many observations have been performed on Pc5 waves properties, it has been difficult to determine the source region, signal propagation path, and the two‐dimensional structure of Pc5 waves beyond coverage by a small number of satellites. Pc5 waves often show a dawn‐dusk asymmetry, but the cause of the asymmetry is under debate. To address these issues, we used conjunction events between the THEMIS satellites and all‐sky imagers and analyzed two Pc5 wave events that were stronger on the dawnside. For both events, the Pc5 waves propagated from dawnside magnetopause toward the nightside magnetosphere. The Pc5 waves were also associated with dawnside magnetopause surface waves, which were probably induced by the Kelvin‐Helmholtz instability. The ionospheric equivalent currents identified multiple vortices on the dawnside associated with quasi‐periodic auroral arcs and much weaker perturbations on the duskside. Global auroral imaging also presented a similar dawn‐dusk asymmetry with multiple arcs on the dawnside, while only one or two major arcs existed on the duskside. Pc5 waves in the magnetosphere had an anti‐phase relation between the total magnetic field and thermal pressure, with a slower propagation velocity compared with magnetohydrodynamic waves. The Poynting flux was anti‐sunward with an oscillating field‐aligned component. These properties suggest that Pc5 waves were slow or drift mirror mode waves coupled with standing Alfven waves. The ground‐based and multi‐satellite observations provide crucial information for determining the Pc5 waves properties, possible source region, and signal propagation path.

Editorial: Sources and propagation of ultra-low frequency waves in planetary magnetospheres

Editorial: Sources and propagation of ultra-low frequency waves in planetary magnetospheres

Low Frequency ULF Waves in the Earth's Inner Magnetosphere: Power Spectra During High Speed Streams and Quiet Solar Wind and Seeding of EMIC Waves.

Here, we extend the scope of the Gamayunov and Engebretson (2021, hereinafter Paper 1), https://doi.org/10.1029/2021JA029247 work by analyzing the low frequency ultra-low-frequency (ULF) wave power spectra in the Earth's inner magnetosphere during high speed stream (HSS) and quiet solar wind (QSW) driving conditions in the upstream solar wind (SW) and comparing our results to the results of Paper 1, where the statistics of ULF wave power spectra during coronal mass ejections (CMEs) are presented. The most important results of our statistical and comparative analyses are as follows. (a) During CMEs, HSSs, and QSW, the magnetic field power spectra of the transverse and compressional fluctuations are well approximated by power laws in the ∼mHz-Hz frequency range, where on average the parameters of power law fits during CMEs and HSSs are close, and those during QSW differ considerably from the respective parameters during CMEs and HSSs. (b) The dominance of the average compressional power over the average transverse power for the low frequency ULF waves during the 0<SYM/H≲25nT geomagnetic conditions may serve as a proxy of HSSs in the upstream SW, whereas the opposite relation between the average powers is an indication of CMEs. (c) Independently of the SW driving conditions, a turbulent energy cascade from low frequencies in the ULF wave frequency range into the higher frequency range exists in the Earth's inner magnetosphere, supplying the nonthermal electromagnetic seed fluctuations needed for the growth of electromagnetic ion cyclotron waves (∼Hz) due to relaxation of unstable distributions of energetic magnetospheric ions.

Simultaneous Cross‐Energy Ion Response and Wave Generation After the Impact of an Interplanetary Shock

AbstractInterplanetary (IP) shocks have substantial impact on particles and electromagnetic fields when arriving at the Earth's magnetosphere. In this study, we have examined the dynamics of cross‐energy ions and plasma waves observed by Van Allen Probe B near the equator at the noon sector inside the geosynchronous orbit after the impact of an IP shock on 27 February 2014. We found that the Ultra‐Low Frequency (ULF) and electromagnetic ion cyclotron (EMIC) waves are induced, and the differential fluxes of protons of various energies have different responses after the IP shock arrival. The perpendicular flux increased dramatically for low‐energy ions (10–100 eV) due to the electric field drift and betatron acceleration. These adiabatic processes also accounted for the evident proton flux decrease at 30–80 keV energies and increase at energies higher than 100 keV, caused by the positive or negative gradient in phase space density before the IP shock arrival. The short‐lived ULF waves triggered by the IP shock also interacted with the ∼100 keV protons, resulting in the stripes in their pitch angle distribution. The anisotropic distribution of &gt;50 keV protons excited EMIC waves after the shock arrival. This study provides a comprehensive picture of the IP shock effects on the ions of different energies and plasma waves inside the geosynchronous orbit, which shed new lights on the cross‐energy responses of ions and plasma waves in the inner magnetosphere to solar wind discontinuities.

Energetic Electron Flux Predictions in the Near‐Earth Plasma Sheet From Solar Wind Driving

AbstractSuprathermal electrons in the near‐Earth plasma sheet are important for inner magnetosphere considerations. They are the source population for outer radiation belt electrons and they pose risks to geosynchronous satellites through their contribution to surface charging. We use empirical modeling to address relationships between solar driving parameters and plasma sheet electron flux. Using Time History of Events and Macroscale Interactions during Substorms, OMNI, and Flare Irradiance Spectral Model Version 2 data, we develop a neural network model to predict differential electron flux from 0.08 to 93 keV in the plasma sheet, at distances from 6 to 12 RE. Driving parameters include solar wind (SW) density and speed, interplanetary magnetic field (IMF) BZ and BY, solar extreme ultraviolet flux, IMF BZ ultra‐low frequency (ULF) wave power, SW‐magnetosphere coupling functions Pα1 and NXCF, and the 4‐hr time history of these parameters. Our model predicts overall plasma sheet electron flux variations with correlation coefficients of between 0.59 and 0.77, and median symmetric accuracy in the 41%–140% range (depending on energy). We find that short time‐scale electron flux variations are not reproduced using short time‐scale inputs. Using a recently published technique to extract information from neural networks, we determine the most important drivers impacting model prediction are VSW, VBS, and IMF BZ. SW‐magnetosphere coupling functions that include IMF clock angle, IMF BZ ULF wave power, and IMF BY have little impact in our model of electron flux in the near‐Earth plasma sheet. The new model, built directly on differential flux, outperforms an existing model that derives fluxes from plasma moments, with the performance improvement increasing with increasing energy.

Extreme Energy Spectra of Relativistic Electron Flux in the Outer Radiation Belt.

Electron diffusion by whistler-mode chorus waves is one of the key processes controlling the dynamics of relativistic electron fluxes in the Earth's radiation belts. It is responsible for the acceleration of sub-relativistic electrons injected from the plasma sheet to relativistic energies as well as for their precipitation and loss into the atmosphere. Based on analytical estimates of chorus wave-driven quasi-linear electron energy and pitch-angle diffusion rates, we provide analytical steady-state solutions to the corresponding Fokker-Planck equation for the relativistic electron distribution and flux. The impact on these steady-state solutions of additional electromagnetic ion cyclotron waves, and of ultralow frequency waves are examined. Such steady-state solutions correspond to hard energy spectra at 1-4MeV, dangerous for satellite electronics, and represent attractors for the system dynamics in the presence of sufficiently strong driving by continuous injections of 10-300keV electrons. Therefore, these analytical steady-state solutions provide a simple means for estimating the most extreme electron energy spectra potentially encountered in the outer radiation belt, despite the great variability of injections and plasma conditions. These analytical steady-state solutions are compared with numerical simulations based on the full Fokker-Planck equation and with relativistic electron flux spectra measured by satellites during one extreme event and three strong events of high time-integrated geomagnetic activity, demonstrating a good agreement.

Dynamics of Earth's bow shock under near-radial interplanetary magnetic field conditions

We investigate the dynamics of Earth's quasi-parallel terrestrial bow shock based on measurements from the Magnetospheric MultiScale (MMS) spacecraft constellation during a period of near-radial interplanetary magnetic conditions, when the interplanetary magnetic field and the solar wind (SW) velocity are nearly anti-parallel. High-speed earthward ion flows with properties that are similar to those of the pristine SW are observed to be embedded within the magnetosheath-like plasma. These flows are accompanied by Interplanetary Magnetic Field (IMF) intensity of less than about 10 nT, compared to nearby magnetosheath intensities of generally greater than 10 nT. The high-speed flow intervals are bounded at their leading and trailing edges by intense fluxes of more energetic ions and large amplitude quasi-sinusoidal magnetic oscillations, similar to ultra-low frequency waves known to steepen and pileup on approach toward Earth to form the quasi-parallel bow shock. The MMS string-of-pearls configuration is aligned with the outbound trajectory and provides inter-spacecraft separations of several hundred km along its near 103 length, allowing sequential observation of the plasma and magnetic field signatures during the event by the four spacecraft. The SW-like interval is most distinct at the outer-most MMS-2 and sequentially less distinct at each of the trailing MMS spacecraft. We discuss the interpretation of this event alternatively as MMS having observed a quasi-rigid bow shock contraction/expansion cycle, ripples or undulations propagating on the bow shock surface, or a more spatially local evolution in the context of either a deeply deformed shock surface or a porous shock surface, as in the three-dimensional patchwork concept of the quasi-parallel bow shock, under the extant near-radial IMF condition.

Ionospheric Oxygen Outflows Directly Injected Into the Inner Magnetosphere: Van Allen Probes Statistics

AbstractIonospheric oxygen outflows (IOOs) are frequently observed in Earth's inner magnetosphere. As a potential fast mass source of the inner magnetosphere, they have been extensively studied for decades. In this study, we identified 271 IOO events from 6‐year Van Allen Probes (VAPs) data and conducted a statistical study to reveal when, where, and how they occur. All the events are observed in the nightside magnetosphere, with the occurrence rate peaking at the L‐shells corresponding to the auroral oval. The spatial scale of IOOs in the equatorial plane is estimated from the two‐spacecraft configuration of the VAP mission. The results show that, in statistics, IOOs are 3.9‐hr wide in magnetic local time and 1.0‐Earth radius wide in L‐shell. Further investigation shows that IOOs would shift to lower L‐shells and occupy a larger L‐shell extent as the AE index increases. Analysis of the environment conditions reveals that IOOs are statistically associated with AE‐index enhancements, ultra‐low‐frequency (ULF) waves, and magnetic field dipolarization, but not with any systematic variations in the SYM‐H index and the solar wind parameters. From this observation, we suggest that geomagnetic substorms and substorm‐associated processes (e.g., ULF waves) are potential triggers of inner‐magnetosphere IOOs.

Response of Electric Field in Terrestrial Magnetosphere to Interplanetary Shock

Electric field impulses generated by interplanetary shocks can cause a series of dynamic processes in the Earth’s magnetosphere and were previously explained by either fast-mode wave propagation or flow related to compression of the magnetopause. Based on a Space Weather Modeling Framework simulation, we suggest a new scenario in which the evolution of the impulse is due to both the propagation of the fast-mode wave and the compression of the magnetopause, which can explain the simulation and observations in previous related studies. The onset of the electric field impulse is determined by the propagation of the fast-mode wave in the magnetosphere while the peak of the impulse is determined by the propagation of the compression of the magnetopause. The new understanding of the impulse is important for the generation of subsequent ultralow frequency waves through the coupling of the fast-mode to Alfvén waves and field line resonances and related radiation-belt electron acceleration.

A global view of Pc3 wave activity in near-Earth space: Results from hybrid-Vlasov simulations

Ultra-low frequency (ULF) waves in the Pc3 range, with periods between 10–45 s, are routinely observed in Earth’s dayside magnetosphere. They are thought to originate in the foreshock, which extends upstream of the quasi-parallel bow shock and is populated with shock-reflected particles. The foreshock is permeated with ULF waves generated by ion beam instabilities, most notably the “30-s” waves whose periods match those of the Pc3 waves and which are carried earthward by the solar wind flow. However, the global picture of Pc3 wave activity from the foreshock to the magnetosphere and its response to changing solar wind conditions is still poorly understood. In this study, we investigate the global distribution and properties of Pc3 waves across near-Earth space using global simulations performed with the hybrid-Vlasov model Vlasiator. The simulations enable us to study the waves in their global context, and compare their properties in the foreshock, magnetosheath and dayside magnetosphere, for different sets of upstream solar wind conditions. We find that in all three regions the Pc3 wave power peaks at higher frequencies when the interplanetary magnetic field (IMF) strength is larger, consistent with previous studies. The Pc3 wave power is significantly enhanced in all three regions for higher solar wind Alfvén Mach number. As this parameter is known to affect the shock properties but has little impact inside the magnetosphere, this brings further support to the magnetospheric waves originating in the foreshock. Other parameters that are found to influence the foreshock wave power are the solar wind density and the IMF cone angle. Inside the magnetosphere, the wave power distribution depends strongly on the IMF orientation, which controls the foreshock position upstream of the bow shock. The wave power is largest when the angle between the IMF and the Sun-Earth line is smallest, suggesting that wave generation and transmission are most efficient in these conditions.

Convolutional Neural Networks for Automated ULF Wave Classification in Swarm Time Series

Ultra-low frequency (ULF) magnetospheric plasma waves play a key role in the dynamics of the Earth’s magnetosphere and, therefore, their importance in Space Weather phenomena is indisputable. Magnetic field measurements from recent multi-satellite missions (e.g., Cluster, THEMIS, Van Allen Probes and Swarm) are currently advancing our knowledge on the physics of ULF waves. In particular, Swarm satellites, one of the most successful missions for the study of the near-Earth electromagnetic environment, have contributed to the expansion of data availability in the topside ionosphere, stimulating much recent progress in this area. Coupled with the new successful developments in artificial intelligence (AI), we are now able to use more robust approaches devoted to automated ULF wave event identification and classification. The goal of this effort is to use a popular machine learning method, widely used in Earth Observation domain for classification of satellite images, to solve a Space Physics classification problem, namely to identify ULF wave events using magnetic field data from Swarm. We construct a Convolutional Neural Network (ConvNet) that takes as input the wavelet spectrum of the Earth’s magnetic field variations per track, as measured by Swarm, and whose building blocks consist of two alternating convolution and pooling layers, and one fully connected layer, aiming to classify ULF wave events within four different possible signal categories: (1) Pc3 wave events (i.e., frequency range 20–100 MHz), (2) background noise, (3) false positives, and (4) plasma instabilities. Our preliminary experiments show promising results, yielding successful identification of more than 97% accuracy. The same methodology can be easily applied to magnetometer data from other satellite missions and ground-based arrays.

A review of the theory of 3‐D Alfvén (field line) resonances

This review article aims to summarise recent developments in Alfvén resonance theory, with a focus on applications to magnetospheric ultra-low frequency (ULF) waves, though many of the ideas are relevant for applications in other fields as well. The key aspect we treat is how Alfvén resonance manifests in a fully 3-D varying medium. The prerequisite ideas are developed in a reasonably comprehensive introduction, which would be a good starting point for any interested reader looking to gain an understanding of the Alfvén resonance process, as well as where to find associated reading. The main part of the review is split into three sections. We firstly consider results from numerical simulations of relatively simple magnetic field geometries, such as 2-D and 3-D dipoles, to develop the fundamental properties of 3-D Alfvén resonances. Secondly, we review previous simulations in more general magnetic field geometries, reconciling these results with those from the simpler dipole cases. Thirdly, in light of these numerical results, we review theoretical studies using various analytical methods to find approximate solutions to the pertinent magnetohydrodynamic (MHD) equations. The review is concluded with a discussion of these different approaches, as well as linking these ideas to their importance for observations. Finally, we discuss potential future developments in this research area.

Magnetospheric responses to solar wind Pc5 density fluctuations: Results from 2D hybrid Vlasov simulation

Ultra-low frequency (ULF) waves are routinely observed in Earth’s dayside magnetosphere. Here we investigate the influence of externally-driven density variations in the near-Earth space in the ULF regime using global 2D simulations performed with the hybrid-Vlasov model Vlasiator. With the new time-varying boundary setup, we introduce a monochromatic Pc5 range periodic density variation in the solar wind. A breathing motion of the magnetopause and changes in the bow shock standoff position are caused by the density variation, the time lag between which is found to be consistent with propagation at fast magnetohydrodynamic speed. The oscillations also create large-scale stripes of variations in the magnetosheath and modulate the mirror and electromagnetic ion cyclotron modes. We characterize the spatial-temporal properties of ULF waves at different phases of the variation. Less prominent EMIC and mirror mode wave activities near the center of magnetosheath are observed with decreasing upstream Mach number. The EMIC wave occurrence is strongly related to pressure anisotropy and β‖, both vary as a function of the upstream conditions, whereas the mirror mode occurrence is highly influenced by fast waves generated from upstream density variations.

Electron Flux Variability and Ultra‐Low Frequency Wave Activity in the Outer Radiation Belt Under the Influence of Interplanetary Coronal Mass Ejections and High‐Speed Solar Wind Streams: A Statistical Analysis From the Van Allen Probes Era

AbstractThe ultra‐low frequency (ULF) waves can stochastically accelerate radiation belt electrons. Radial diffusion is a well‐established mechanism that can enhance or reduce the electron population in combination with other processes. Using data from the Van Allen Probes, we investigated the response of the 2.10 MeV energy electrons and ULF waves to two types of solar wind structures interacting with Earth's magnetosphere, namely, interplanetary coronal mass ejections (ICMEs) and High‐Speed solar wind streams (HSS). We use measured electron differential flux and ULF waves in the Pc4–Pc5 frequency range from October 2012 to May 2019. We examine 155 events with changes in the outer radiation belt electron differential flux. Results considering all ICMEs and HSSs during the Van Allen Probes era show that for both solar wind structures, solar wind interplanetary magnetic field Bz, solar wind proton density, and speed are related to the outer radiation belt relativistic electrons' response. The persistent ULF power is present during enhancement cases, while for reduction, the ULF waves power is concentrated at the initial reduction on the outer radiation belt electron flux.

Automatic detection of auroral Pc5 geomagnetic pulsation using machine learning approach guided with discrete wavelet transform

Geomagnetic micropulsations are ultra-low frequency (ULF) signals observed in the magnetosphere as well as on the ground. These signals offer us an effective means to study the coupling of the magnetosphere-ionosphere processes in the space field. The most prominent observed type of such ULF waves is the Pc5 pulsations (with a frequency range of 1–7 mHz), known to have their maximum amplitude in the auroral oval. The low magnitude of Pc5 signals withstands against distinguishing them from the background noise. This study presents a machine learning approach for the automatic detection of geomagnetic Pc5 pulsations in the auroral zone using artificial neural networks (ANN) guided by discrete wavelet transform. Our ANN algorithm is validated and tested using a huge amount of datasets of auroral ground-based geomagnetic records from the Svalbard network during the two solar cycles 23 and 24. The wavelet-based coherence was used to determine the signal’s consistency detected by the magnetometer stations of the Svalbard network; since they are sensitive to all sorts of space wave-related phenomena that left their footprint on the magnetic field time series. The Daubechies wavelet transform was utilized to classify and extract Pc5 signals from the artificial noise and the results are correlated with the geomagnetic pulsation records as detected by our ANN-based model. The ANN-based model showed a good correlation of an average of 98% for the different phases of the two studied solar cycles. The statistical regression analysis of the post-processed results yielded a high coefficient of determination of R2 = 0.9 and norms of residuals of 8–21 nT. The Pc5 events detected by the ANN-based algorithm during the two solar cycles showed a good correlation with the Kp index, which enables our model for space weather forecasting.

On the Estimation of Resonance Widths of Field Line Resonances Using Ground Magnetometer Data

This paper presents a comparison of three methods to estimate the latitudinal resonance width of field line resonant, ultra-low frequency waves detected at the ground. These are a spatial domain, full-width half-maximum method and frequency domain amplitude-phase and amplitude-division methods. These methods were used to estimate the resonance width of several field line resonant intervals occurring on 26 November 2001, 1 October 2012, and 19 June 2015. The 19 June 2015 interval used data from one low, two mid, and one high latitudes. It was found that the resonance width estimates were different for each method and with how the data were processed. The most suitable methods and data processing were determined from a damped driven harmonic oscillator model. The amplitude-division methods yielded the most accurate results when the ground magnetic field data were processed with a boxcar window function or a frequency domain, exponential smoothing taper. The amplitude-phase method tended to underestimate the resonance width. The full-width half-maximum method gave accurate results for a high spatial resolution linear piece-wise curve fitted to the spectral amplitude with latitude profile. An accurate estimate of the latitudinal resonance width requires a correct choice of data processing, estimate method, resonance profile with latitude, and resonance model.

Nonlinear Wave Growth Analysis of Chorus Emissions Modulated by ULF Waves

AbstractWe present Van Allen Probes observations of periodic chorus wave emissions in the troughs of compressional ultralow frequency (ULF) waves. During this event, the spectral gap of chorus waves gradually widens as the spacecraft moves from the equatorial source region towards higher latitudes. Moreover, chorus wave intensity increases and frequency range widens after a substorm injection. We show that the periodic occurrence of chorus waves is attributed to the modulation of threshold amplitude for nonlinear growth of chorus waves by the second spatial derivative of ULF compressional magnetic field. The widening gap can be interpreted in terms of the nonlinear damping mechanism. A good agreement is also found between the nonlinear wave growth theory and the observations regarding the influence of substorm injection on the chorus. These findings support the applicability of the nonlinear theory in describing the chorus wave generation and damping, together with their modulations by ULF waves.

Estimating Inner Magnetospheric Radial Diffusion Using a Hybrid-Vlasov Simulation

Radial diffusion coefficients quantify non-adiabatic transport of energetic particles by electromagnetic field fluctuations in planetary radiation belts. Theoretically, radial diffusion occurs for an ensemble of particles that experience irreversible violation of their third adiabatic invariant, which is equivalent to a change in their Roederer L* parameter. Thus, the Roederer L* coordinate is the fundamental quantity from which radial diffusion coefficients can be computed. In this study, we present a methodology to calculate the Lagrangian derivative of L* from global magnetospheric simulations, and test it with an application to Vlasiator, a hybrid-Vlasov model of near-Earth space. We use a Hamiltonian formalism for particles confined to closed drift shells with conserved first and second adiabatic invariants to compute changes in the guiding center drift paths due to electric and magnetic field fluctuations. We investigate the feasibility of this methodology by computing the time derivative of L* for an equatorial ultrarelativistic electron population travelling along four guiding center drift paths in the outer radiation belt during a 5 minute portion of a Vlasiator simulation. Radial diffusion in this simulation is primarily driven by ultralow frequency waves in the Pc3 range (10–45 s period range) that are generated in the foreshock and transmitted through the magnetopause to the outer radiation belt environment. Our results show that an alternative methodology to compute detailed radial diffusion transport is now available and could form the basis for comparison studies between numerical and observational measurements of radial transport in the Earth’s radiation belts.