Relativistic Electron Dynamics Research Articles

A study of the wave dynamics of the space–time fractional nonlinear evolution equations of beta derivative using the improved Bernoulli sub-equation function approach

The space–time fractional nonlinear Klein-Gordon and modified regularized long-wave equations explain the dynamics of spinless ions and relativistic electrons in atom theory, long-wave dynamics in the ocean, like tsunamis and tidal waves, shallow water waves in coastal sea areas, and also modeling several nonlinear optical phenomena. In this study, the improved Bernoulli sub-equation function method has been used to generate some new and more universal closed-form traveling wave solutions of those equations in the sense of beta-derivative. Using the fractional complex wave transformation, the equations are converted into nonlinear differential equations. The achieved outcomes are further inclusive of successfully dealing with the aforementioned models. Some projecting solitons waveforms, including, kink, singular soliton, bell shape, anti-bell shape, and other types of solutions are displayed through a three-dimensional plotline, a plot of contour, and a 2D plot for definite parametric values. It is significant to note that all obtained solutions are verified as accurate by substituting the original equation in each case using the computational software, Maple. Additionally, the results have been compared with other existing results in the literature to show their uniqueness. The proposed technique is effective, computationally attractive, and trustworthy to establish more generalized wave solutions.

Prompt Appearance of Large‐Amplitude EMIC Waves Induced by Solar Wind Dynamic Pressure Enhancement and the Subsequent Relativistic Electron Precipitation

AbstractElectromagnetic ion cyclotron (EMIC) waves play an important role in relativistic electron dynamics. In this study, we find a large‐amplitude EMIC wave event induced by the prompt enhancement of solar wind dynamic pressure on 6 November 2015. These large‐amplitude EMIC waves are simultaneously observed by multiple satellites over 13 hr in magnetic local time (MLT) with a peak amplitude of ∼4 nT. Satellites at different locations observed different bands of EMIC waves, implying the importance of background plasma density in EMIC wave generation. Electron pitch angle distributions show obvious responses to EMIC wave activities. During EMIC wave appearance, the fluxes of relativistic electrons with pitch angles around 90° increase, while the fluxes of field‐aligned relativistic electrons decrease, showing distinct “bite‐out” signatures, indicating pitch angle scattering by EMIC waves, and the scattering efficiency depends on the amplitude and polarization of EMIC waves. Combined with phase space density profiles of electrons that are nearly constant at energies below the minimum resonant energy of electrons (Emin) but show dropout at energies above the Emin after EMIC wave activities, we conclude that large‐amplitude EMIC waves can cause rapid electron loss down to several hundred keV. In addition, simultaneous observations of hundreds of keV electron precipitation and tens of keV proton precipitation by Polar Operational Environmental Satellites near the region where EMIC waves are observed, provide direct evidence of relativistic electron precipitation caused by the large‐amplitude EMIC waves, ultimately driven by solar wind structures.

The Effects of Geomagnetic Activities on Acceleration Regions of Radiation Belt Electrons

AbstractSolar wind and magnetospheric processes play important roles in relativistic electron acceleration in the Earth's outer radiation belt. However, how geomagnetic activity affects the acceleration region of relativistic electrons is still not clear. Here we first report the local acceleration regions during the strong storm of 1 June 2013. The first local acceleration region occurs at the lower L shell (L* ∼ 4.0) during the early recovery phase, which is associated with non‐continuous substorm activities. The second local acceleration region occurs at the higher L shell (L* ∼ 5.0) during the late recovery phase, which is associated with continuous substorm activities. To provide a more comprehensive picture, we additionally analyze two storm events with different geomagnetic activities. These events suggest that (a) the strong storm makes it possible for the local acceleration regions to occur at different L shells; (b) the timing, intensity, and duration of substorms during the recovery phase are crucial to the location and dynamics of the local acceleration region. These results can help us further understand the dynamics of relativistic electrons in the Earth's outer radiation belt.

Rapid Enhancements of Relativistic Electrons in the Earth's Outer Radiation Belt Caused by the Intense Substorms: A Statistical Study

AbstractUsing the data from Van Allen Probe A and B, we investigate rapid enhancements of relativistic electrons in the Earth's outer radiation belt caused by the intense substorms (AEmax > ∼900 nT) for 29 events from January 2013 to April 2015. These intense substorms may occur during the storm main phase or recovery phase. Based on the different substorm evolution characteristics, the intense substorms are divided into non‐continuous intense substorm activities and continuous intense substorm activities. In this study, we set a criterion for rapid enhancements when the electron phase space densities for μ = 1,096, 2,290, and 3,311 MeV/G increased by more than two times in 9 hr. In the time interval of 9 hr, the local acceleration by chorus waves is the dominant process for accelerating the seed populations (hundred kiloelectron volts) up to MeV energies. Our statistical results show that enhanced chorus waves and seed electrons during the intense substorms are observed in the outer radiation belt. Continuous intense substorm activities can more rapidly (<9 hr) and efficiently accelerate relativistic electrons in the outer radiation belt than non‐continuous intense substorm activities. During the intense substorms, the electric field acceleration could contribute to rapid enhancements of relativistic electrons in the outer radiation belt. Our statistical study suggests that the intense substorms during geomagnetic storms have a significant effect on the rapid variations of relativistic electron dynamics.

Band structure for relativistic charge carriers submitted to a helical electric field

We study the relativistic dynamics of electrons submitted to a uniform harmonic electric fields longitudinally applied to the electron velocity. In order to obtain explicitly the set of time-dependent equations for the bi-spinors components, we write down the corresponding Dirac equation for this system. By performing a suitable transformation to this set of equations, we get a matrix equation whose eigenvalues can be found directly. We found analytically the band structure and show a break of degeneracy and the existence of three bands: two total and one partial. The thicker band preventing from the Schwinger mechanisms can be shortened by proper combination of the frequency and amplitude of the applied electric field.

Spinorial dynamics of relativistic electrons during ponderomotive scattering in intense laser pulses

Spinorial dynamics of relativistic electrons during ponderomotive scattering in intense laser pulses

Waveform Control of Relativistic Electron Dynamics in Laser-Plasma Acceleration

The interaction of ultraintense laser pulses with an underdense plasma is used in laser-plasma acceleration to create compact sources of ultrashort pulses of relativistic electrons and x rays. The accelerating structure is a plasma wave, or wakefield, that is excited by the laser ponderomotive force, a force that is usually assumed to depend solely on the laser envelope and not on its exact waveform. Here, we use near-single-cycle laser pulses with a controlled carrier-envelope phase to show that the actual waveform of the laser field has a clear impact on the plasma response. The beam pointing of our relativistic electron beam oscillates in phase with the carrier-envelope phase of the laser, at an amplitude of 15 mrad, or 30% of the beam divergence. Numerical simulations explain this observation through asymmetries in the injection and acceleration of the electron beam, which are locked to the carrier-envelope phase. These results imply that we achieve waveform control of relativistic electron dynamics. Our results pave the way to high-precision, subcycle control of electron injection in plasma accelerators, enabling the production of attosecond relativistic electron bunches and x rays.Received 26 May 2021Revised 10 December 2021Accepted 11 January 2022DOI:https://doi.org/10.1103/PhysRevX.12.011036Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasHigh intensity laser-plasma interactionsLaser wakefield accelerationPonderomotive effectsUltrashort pulsesAccelerators & BeamsPlasma PhysicsAtomic, Molecular & Optical

Relativistic electron dynamics in magnetic fields with low-degree of field nonlinearity

Abstract We study the relativistic bound state dynamics of electrons in the presence of electromagnetic fields within the framework of a novel class of nonlinear Dirac wave equations. In 2 + 1 space–time dimensions, we address a specific interacting electron model in a homogeneous magnetic field providing the allowed nonlinear ground-state Landau energy levels. We concentrate on the regime of laboratory high magnetic fields, and thus, comment on the relevance of this approach to study 2D electron systems.

Electron Acceleration by Magnetosonic Waves in the Deep Inner Belt (L = 1.5–2) Region During Geomagnetic Storm of August 2018

AbstractThe relativistic electron acceleration in the inner radiation belt have received little attention in the past due to sparse measurements. The 90° minimum pitch angle distributions of electrons in extremely low L‐shells during storms are speculated to be preferentially heated by fast magnetosonic waves. The high‐quality measurements of relativistic electrons by instruments onboard Van Allen Probes and ZH–1 provide a great opportunity to investigate the dynamics of relativistic electrons in the inner radiation belt. At extremely low L‐shells (L 2), a weak flux enhancement (increased by 2–3 times) of 100s keV electrons and the corresponding formation of butterfly PADs are observed during the major geomagnetic storm (minimum Dst ≈ −179 nT) occurred in August 2018. Simultaneously the magnetosonic waves, accompanied with weak hiss waves, were observed also in such low L‐shells. Combining with a numerical simulation of wave and particle interaction model, magnetosonic waves are thought to play an important role in electron acceleration and formation of butterfly PADs during this storm, which is the first direct observation in such low L‐shells.

The Energy Spectra of Electron Microbursts Between 200 keV and 1 MeV

AbstractThis study investigates the energy spectrum of electron microbursts observed by the Focused Investigations of Relativistic Electron Burst Intensity, Range, and Dynamics II (FIREBIRD‐II, henceforth FIREBIRD) CubeSats. FIREBIRD is a pair of CubeSats, launched in January 2015 into a low Earth orbit, which focuses on studying electron microbursts. High‐resolution electron data from FIREBIRD‐II consist of 5 differential energy channels between 200 keV and 1 MeV and a 1 MeV integral channel. This covers an energy range that has not been well studied from low Earth orbit with good energy and time resolution. This study aims to improve the understanding of the scattering mechanism behind electron microbursts by investigating their spectral properties and their relationship with the equatorial electron population under different geomagnetic conditions. Microbursts are identified in the region of the North Atlantic where FIREBIRD only observes electrons in the bounce loss cone. The electron flux and exponential energy spectrum of each microburst are calculated using a FIREBIRD instrument response modeled in GEANT4 (GEometry ANd Tracking) and compared with the near‐equatorial electron spectra measured by the Van Allen Probes. Microbursts occurring when the Auroral Electrojet (AE) index is enhanced tend to carry more electrons with relatively higher energies. The microburst scattering mechanism is more efficient at scattering electrons with lower energies; however, the difference in scattering efficiency between low and high energy is reduced during periods of enhanced AE.

A Strong Correlation Between Relativistic Electron Microbursts and Patchy Aurora

AbstractIn this letter, we present the results of a conjunction between the Solar Anomalous and Magnetospheric Particle Explorer (SAMPEX) satellite and a Time History of Events and Macroscale Interactions during Substorms (THEMIS) all‐sky imager in Gillam, Canada, showing a high correlation between relativistic, MeV, electron microbursts and a type of pulsating aurora called patchy aurora. The correlation was 0.8, and is not serendipitous. While the relationship between pulsating aurora and 10–100s keV microbursts has been previously predicted, here we show a strong association between keV and MeV electron dynamics, possibly spanning two orders of magnitude. Importantly, this result shows that the dynamics of relativistic radiation belt electrons are at times intimately tied to keV electron precipitation, and cannot be studied in isolation.

Radiative polarization dynamics of relativistic electrons in an intense electromagnetic field

We propose a self-consistent model which utilizes the polarization vector to theoretically describe the evolution of spin polarization of relativistic electrons in an intense electromagnetic field. The variation of radiative polarization due to instantaneous no photon emission is introduced into our model, which extends the applicability of the polarization vector model derived from the nonlinear Compton scattering under local constant crossed-field approximation to the complex electromagnetic environment in laser plasma interaction. According to this model, we develop a Monte Carlo method to simulate the electron spin under the influence of radiation and precession simultaneously. Our model is consistent with the quantum physical picture that spin can only be described by a probability distribution before measurement, and it contains the entire information on the spin. The correctness of our model is confirmed by the successful reproduction of the Sokolov-Ternov effect and the comparison of the simulation results with other models in the literature. The results show the superiority in accuracy, applicability, and computational efficiency of our model, and we believe that our model is a better choice to deal with the electron spin in particle-in-cell simulation for laser plasma interaction.

Estimating the Impacts of Radiation Belt Electrons on Atmospheric Chemistry Using FIREBIRD II and Van Allen Probes Observations

AbstractThis study considers the impact of electron precipitation from Earth's radiation belts on atmospheric composition using observations from the NASA Van Allen Probes and NSF Focused Investigations of Relativistic Electron Burst Intensity, Range, and Dynamics (FIREBIRD II) CubeSats. Ratios of electron flux between the Van Allen Probes (in near‐equatorial orbit in the radiation belts) and FIREBIRD II (in polar low Earth orbit) during spacecraft conjunctions (2015–2017) allow an estimate of precipitation into the atmosphere. Total Radiation Belt Electron Content, calculated from Van Allen Probes RBSP‐ECT MagEIS data, identifies a sustained 10‐day electron loss event in March 2013 that serves as an initial case study. Atmospheric ionization profiles, calculated by integrating monoenergetic ionization rates across the precipitating electron flux spectrum, provide input to the NCAR Whole Atmosphere Community Climate Model in order to quantify enhancements of atmospheric HOx and NOx and subsequent destruction of O3 in the middle atmosphere. Results suggest that current APEEP parameterizations of radiation belt electrons used in Coupled Model Intercomparison Project may underestimate the duration of events as well as higher energy electron contributions to atmospheric ionization and modeled NOx concentrations in the mesosphere and upper stratosphere.

Traveling-wave Thomson scattering for electron-beam spectroscopy

We propose a method to use traveling-wave Thomson scattering for spatiotemporally-resolved electron spectroscopy. This can enable ultrafast time-resolved measurements of the dynamics of relativistic electrons in the presence of extremely intense light fields, either in vacuum or in plasma, such as in laser wakefield accelerators. We demonstrate, with test-particle simulation and analysis, the capability of this technique for measurements of various high field phenomena: radiation reaction of electrons due to scattering, dephasing of a laser wakefield accelerator, and acceleration of electrons in multiple buckets by a laser wakefield.

Energetic Electron Precipitation Observed by FIREBIRD‐II Potentially Driven by EMIC Waves: Location, Extent, and Energy Range From a Multievent Analysis

AbstractWe evaluate the location, extent, and energy range of electron precipitation driven by ElectroMagnetic Ion Cyclotron (EMIC) waves using coordinated multisatellite observations from near‐equatorial and Low‐Earth‐Orbit (LEO) missions. Electron precipitation was analyzed using the Focused Investigations of Relativistic Electron Burst Intensity, Range and Dynamics (FIREBIRD‐II) CubeSats, in conjunction either with typical EMIC‐driven precipitation signatures observed by Polar Orbiting Environmental Satellites (POES) or with in situ EMIC wave observations from Van Allen Probes. The multievent analysis shows that electron precipitation occurred in a broad region near dusk (16–23 MLT), mostly confined to 3.5–7.5 L‐shells. Each precipitation event occurred on localized radial scales, on average ∼0.3 L. Most importantly, FIREBIRD‐II recorded electron precipitation from ∼200 to 300 keV to the expected ∼MeV energies for most cases, suggesting that EMIC waves can efficiently scatter a wide energy range of electrons.

Relativistic electron dynamics in ion channel guiding in the presence of a helical ‎wiggler and an external oblique magnetic field ‎

In this paper, the electron acceleration and its relativistic dynamics in an ion-channel formed due to the laser pulse propagation through the plasma and under influence of the ion channel space-charge and a heliacal wiggler as well as the oblique magnetic field have been investigated. The equations for investigation of the electron dynamics are the tree-dimension Lorentz equations. For analytical analysis of the obtained equations, a three-dimension single particle code and forth order Runge-Kutta method is used as well. The electron energy gain and the relativistic electron dynamics drastically are affected by the ion-channel potential and the helical wiggler and also the external oblique magnetic field. The results of this paper can be significant in the selection of the appropriate parameters for plasma-based accelerators design.

Modeling advective transport of radiation belt electrons

The relativistic electron dynamics in the radiation belts falls into two categories: diffusive processes, in which particles are scattered randomly, and advective processes, in which particles are collectively driven in one direction in energy or space. In this work, we focus on advection which can occur on a timescale faster than diffusion for CME shock compressions of the dayside magnetosphere. Test-particle simulations are done in the electric and magnetic fields generated by the LFM global MHD model, and the advection coefficient is calculated. Then, the advection coefficient is applied to the transport equation with advection term included and solved for phase space density time evolution. The calculation is done for 17 March 2015 and 6–7 September 2017 CME-shock events, using realistic initial conditions measured by Van Allen Probes, all showing inward motion of electrons on the time scale of minutes. The result is compared with the phase space density calculated based on full test-particle simulations in MHD fields. The inward shift in phase space density is found to be comparable for both methods, while solving the transport equation is much faster once advection coefficients are modeled.

Evidence of radial Weibel instability in relativistic intensity laser-plasma interactions inside a sub-micron thick liquid target

Super-intense laser plasma interaction has shown great promise as a platform for next generation particle accelerators and sources for electron, x-rays, ions and neutrons. In particular, when a relativistic intense laser focus interacts with a thin solid density target, ionized electrons are accelerated to near the speed of light (c) within an optical cycle and are pushed in the forward and transverse directions away from focus, carrying a significant portion of the laser energy. These relativistic electrons are effectively collisionless, and their interactions with the ions and surrounding cold electrons are predominantly mediated by collective electromagnetic effects of the resulting currents and charge separation. Thus, a deeper understanding of subsequent high energy ions generated from various mechanisms and their optimization requires knowledge of the relativistic electron dynamics and the fields they produce. In addition to producing MV/m quasi-static fields, accelerating the ions and confining the majority of the electrons near the bulk of the laser target, these relativistic electron currents are subject to plasma instabilities like the Weibel instability as they propagate through the thermal population in the bulk target. In this work, we present high temporal (100 fs) and spatial (1 μm) resolution shadowgraphy video capturing relativistic radial ionization front expansion and the appearance of filamentation radiating from the laser spot within a sub-micron thick liquid sheet target. Filamentation within the region persists for several picoseconds and seeds the eventual recombination and heating dynamics on the nanosecond timescale. A large scale three-dimensional particle-in-cell (PIC) simulation of the interaction revealed the presence of strong magnetic fields characteristic of Weibel Instability, and corroborated the relativistic radial expansion of the ionization front, whose speed was determined to be 0.77c. Both the experimental and simulation results strongly point towards the target field ionization and the outward expanding hot electron current as the cause of the radial expansion.

ReSpect: Relativistic spectroscopy DFT program package.

With the increasing interest in compounds containing heavier elements, the experimental and theoretical community requires computationally efficient approaches capable of simultaneous non-perturbative treatment of relativistic, spin-polarization, and electron correlation effects. The ReSpect program has been designed with this goal in mind and developed to perform relativistic density functional theory (DFT) calculations on molecules and solids at the quasirelativistic two-component (X2C Hamiltonian) and fully relativistic four-component (Dirac-Coulomb Hamiltonian) level of theory, including the effects of spin polarization in open-shell systems at the Kramers-unrestricted self-consistent field level. Through efficient algorithms exploiting time-reversal symmetry, biquaternion algebra, and the locality of atom-centered Gaussian-type orbitals, a significant reduction of the methodological complexity and computational cost has been achieved. This article summarizes the essential theoretical and technical advances made in the program, supplemented by example calculations. ReSpect allows molecules with >100 atoms to be efficiently handled at the four-component level of theory on standard central processing unit-based commodity clusters, at computational costs that rarely exceed a factor of 10 when compared to the non-relativistic realm. In addition to the prediction of band structures in solids, ReSpect offers a growing list of molecular spectroscopic parameters that range from electron paramagnetic resonance parameters (g-tensor, A-tensor, and zero-field splitting), via (p)NMR chemical shifts and nuclear spin-spin couplings, to various linear response properties using either conventional or damped-response time-dependent DFT (TDDFT): excitation energies, frequency-dependent polarizabilities, and natural chiroptical properties (electronic circular dichroism and optical rotatory dispersion). In addition, relativistic real-time TDDFT electron dynamics is another unique feature of the program. Documentation, including user manuals and tutorials, is available at the program's website http://www.respectprogram.org.

Solar activity phase dependence of the magnetospheric processes and relativistic electron flux at geostationary orbit

This study aims to investigate the effects of the solar activity phases on the magnetospheric processes in relation to daily relativistic electron ($E>2$ MeV) dynamics at geosynchronous orbit (GEO) during Solar Cycles 23–24. GOES observations indicate that in the descending phase the electron fluxes are seasonally dependent with largest flux in equinoctial periods, relatively high, and 27-day recurrent, while in the maximum phases they are relatively low and nonrecurrent. The electron fluxes are relatively low and partially recurrent in the ascending phases. The cross correlation coefficients (c.c.s) of daily $K_{\textrm{p}}$–$V_{\textrm{sw}}$, $K_{\textrm{p}}$–$AE$, $K_{\textrm{p}}$–$AL$ evolve in the similar trend for both solar cycles: highest during the descending phases, lower in the ascending phases, and lowest in the maximum and minimum phases. The correlation of $K_{\textrm{p}}$–viscous term is strongest during descending phases and weakest around the maximum phases. The correlation of $K_{\textrm{p}}$–merging term slightly varies in a chaotic way from one solar phase to another, but drops to its lowest value in the solar minimum. The correlation analysis results signify the role of the solar activity in controlling the solar wind–magnetosphere couplings. Two case studies during maximum (2000) and descending (2017) phases indicate that the solar activity dependence of the magnetospheric processes and relativistic electrons is characterized by substorm activity and solar wind drivers. Most of the substorms induced by coronal mass ejections in the maximum phase exhibit strong but short and non-repetitive features that associate with low electron fluxes at GEO. In contrast, high intensity, prolonged, and repetitive substorm activities induced by high-speed solar winds are the main cause of the relativistic electron enhancements during the descending phases. The enhancements strongly depend on $V_{\textrm{sw}}$ and $\Sigma K_{\textrm{p}}$ in which only appropriate $V_{\textrm{sw}}$ and $\Sigma K_{\textrm{p}}$ are required. In the descending phase, the requirements for the flux enhancements to $\geq 10^{3}$ cm−2 sr−1 s−1 are the simultaneity of $V_{\textrm{sw}}>500$ km/s and the prolongation of $\Sigma K_{\textrm{p}}>220$ and to $\geq 10^{4}$ cm−2 sr−1 s−1 when $V_{\textrm{sw}}\geq 630$ km/s and $\Sigma K_{\textrm{p}}>227$. Furthermore, the correlations of $\Sigma K_{\textrm{p}}$ and log-electron fluxes are stronger in the descending/ascending phases than in the maximum phase, while the time lag between them is longer in the maximum phase. The remarkable correlations of $V_{\textrm{sw}}$–$K_{\textrm{p}}$ and in the descending phase indicate appropriate magnetospheric convection in association with the repetitive substorms that can effectively trigger the stochastic mechanisms of electron acceleration. The results are extensively discussed in the light of observations and current theories of radiation belt dynamics.