Relativistic Electron Dynamics Research Articles

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.

A Framework for Understanding and Quantifying the Loss and Acceleration of Relativistic Electrons in the Outer Radiation Belt During Geomagnetic Storms

AbstractWe present detailed analysis of the global relativistic electron dynamics as measured by total radiation belt content (RBC) during coronal mass ejection (CME) and corotating interaction region (CIR)‐driven geomagnetic storms. Recent work has demonstrated that the response of the outer radiation belt is consistent and repeatable during geomagnetic storms. Here we build on this work to show that radiation belt dynamics can be divided into two sequential phases, which have different solar wind dependencies and which when analyzed separately reveal that the radiation belt responds more predictably than if the overall storm response is analyzed as a whole. In terms of RBC, in every storm we analyzed, a phase dominated by loss is followed by a phase dominated by acceleration. Analysis of the RBC during each of these phases demonstrates that they both respond coherently to solar wind and magnetospheric driving. However, the response is independent of whether the storm response is associated with either a CME or CIR. Our analysis shows that during the initial phase, radiation belt loss is organized by the location of the magnetopause and the strength of Dst and ultralow frequency wave power. During the second phase, radiation belt enhancements are well organized by the amplitude of ultralow frequency waves, the auroral electroject index, and solar wind energy input. Overall, our results demonstrate that storm time dynamics of the RBC is repeatable and well characterized by solar wind and geomagnetic driving, albeit with different dependencies during the two phases of a storm.

Ultrafast Plasma Electron Dynamics: A Route to Terahertz Pulse Shaping

Intense ultrafast laser interaction with solid-density plasma can lead to relativistic transient electron dynamics that are favorable for the generation of high-field terahertz (THz) pulses. We investigate the temporal characteristics of such THz pulses. Single-shot electro-optic measurements enable us to record the complete temporal profiles of the THz pulses emanating from planar $\mathrm{Cu}$ and aligned $\mathrm{Cu}$-nanorod-array plasma. The temporal properties of the THz pulses exhibit several transients. Fully relativistic two-dimensional particle-in-cell simulations corroborate experimental observations and reveal that these features originate from electron microbunch emission from the target. Our results demonstrate that target nanostructuring provides a route to control such ultrafast electron dynamics and hence THz-pulse properties in the time domain.

The FIREBIRD-II CubeSat mission: Focused investigations of relativistic electron burst intensity, range, and dynamics.

FIREBIRD-II is a National Science Foundation funded CubeSat mission designed to study the scale size and energy spectrum of relativistic electron microbursts. The mission consists of two identical 1.5 U CubeSats in a low earth polar orbit, each with two solid state detectors that differ only in the size of their geometric factors and fields of view. Having two spacecraft in close orbit allows the scale size of microbursts to be investigated through the intra-spacecraft separation when microbursts are observed simultaneously on each unit. Each detector returns high cadence (10 s of ms) measurements of the electron population from 200 keV to >1 MeV across six energy channels. The energy channels were selected to fill a gap in the observations of the Heavy Ion Large Telescope instrument on the Solar, Anomalous, and Magnetospheric Particle Explorer. FIREBIRD-II has been in orbit for 5 years and continues to return high quality data. After the first month in orbit, the spacecraft had separated beyond the expected scale size of microbursts, so the focus has shifted toward conjunctions with other magnetospheric missions. FIREBIRD-II has addressed all of its primary science objectives, and its long lifetime and focus on conjunctions has enabled additional science beyond the scope of the original mission. This paper presents a brief history of the FIREBIRD mission's science goals, followed by a description of the instrument and spacecraft. The data products are then discussed along with some caveats necessary for proper use of the data.

Nondispersive analytical solutions to the Dirac equation

This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first family of solutions describe the shape-preserving translation of a wavepacket along any desired trajectory in the x-y plane. In particular, we show that the dispersionless motion of a Gaussian wavepacket along both elliptical and circular paths can be achieved with rather simple electromagnetic field configurations. A second family of solutions involves a plane electromagnetic wave and a combination of generally inhomogeneous electric and magnetic fields. The novel analytical solutions of the Dirac equation given here provide important insights into the connection between the quantum relativistic dynamics of electrons and the underlying geometry of the Lorentz group.

Squeezed momentum distributions of relativistic electrons in intense laser fields with arbitrary polarization

We investigate the dynamics of relativistic electrons interacting with intense laser fields in a linear or circular polarization. First, we study the momentum distributions of a single spatially localized wave packet. We find that these distributions are squeezed in the polarization plane ($y\text{\ensuremath{-}}z$) as well as along the laser propagation ($x$) direction. In a chosen gauge, the squeezing direction is controlled by the laser vector potential $\mathbf{A}$ and the electron initial momentum. For the case when the electron initial momentum is zero the squeezing occurs directly along the direction of $\mathbf{A}$. We obtain analytical expressions within linear momentum approximation that explain the squeezing features very well by defining a squeezing vector and rotational angle of the squeezed momentum distribution. We analyze the symmetric properties of the momentum distributions viewed in different momentum planes and discuss the effects of different helicity of circular laser polarizations and the direction of the spin quantization. An unexpected feature of bending of momentum distribution is found for very intense laser fields. We extend our investigation to the momentum distribution of two spatially separated wave packets, particularly the orientations of two crossing distributions. It is found that the absolute phase of the initial laser field affects the orientation of the electron momentum distributions while quantum superposition of two states with the same spin gives interference in the momentum distributions that depends on the quantum phase of the electron.

Direct Observation of Subrelativistic Electron Precipitation Potentially Driven by EMIC Waves

AbstractElectromagnetic ion cyclotron (EMIC) waves are known to typically cause electron losses into Earth's upper atmosphere at >~1 MeV, while the minimum energy of electrons subject to efficient EMIC‐driven precipitation loss is unresolved. This letter reports electron precipitation from subrelativistic energies of ~250 keV up to ~1 MeV observed by the Focused Investigations of Relativistic Electron Burst Intensity, Range and Dynamics (FIREBIRD‐II) CubeSats, while two Polar Operational Environmental Satellites (POES) observed proton precipitation nearby. Van Allen Probe A detected EMIC waves (~0.7–2.0 nT) over the similar L shell extent of electron precipitation observed by FIREBIRD‐II, albeit with a ~1.6 magnetic local time (MLT) difference. Although plasmaspheric hiss and magnetosonic waves were also observed, quasi‐linear calculations indicate that EMIC waves were the most efficient in driving the electron precipitation. Quasi‐linear theory predicts efficient precipitation at >0.8–1 MeV (due to H‐band EMIC waves), suggesting that other mechanisms are required to explain the observed subrelativistic electron precipitation.

Equatorial Magnetosonic Waves Observed by Cluster Satellites: The Chirikov Resonance Overlap Criterion

AbstractMagnetosonic waves play an important role on the overall dynamics of relativistic radiation belt electrons. Numerical codes modeling the evolution of the radiation belts often account for wave‐particle interaction with magnetosonic waves. The diffusion coefficients incorporated in these codes are generally estimated based on the results of statistical surveys of the occurrence and amplitude of these waves. These statistical models assume that the spectrum of the magnetosonic waves can be considered as continuous in frequency space. This assumption can only be valid if the discrete nature of the waves satisfy the Chirikov overlap criterion. Otherwise, the assumption of a continuous frequency spectrum could produce erroneous results in wave models and hence estimates of the electron diffusion coefficients used in numerical models of the inner magnetosphere. Recently, it was demonstrated, through a case study conducted on a single short (10 s) period snapshot within a longer wave event, that the discrete nature of the equatorial magnetosonic waves do satisfy the Chirikov overlap criterion and so the assumption of a continuous frequency spectrum is valid for the calculation of diffusion coefficients. This paper expands this study to a broader range of time with many magnetosonic wave events to determine whether the discrete nature of the waves always satisfy the Chirikov overlap criterion. The results show that most, but not all, discrete magnetosonic emissions satisfy the Chirikov overlap criterion. Therefore, the use of the continuous spectrum, employed in quasi‐linear theory, may not always be justified.

Cyclotron Acceleration of Relativistic Electrons Through Landau Resonance With Obliquely Propagating Whistler‐Mode Chorus Emissions

AbstractEfficient acceleration of relativistic electrons at Landau resonance with obliquely propagating whistler‐mode chorus emissions is confirmed by theory, simulation, and observation. The acceleration is due to the perpendicular component of the wave electric field. We first review theoretical analysis of nonlinear motion of resonant electrons interacting with obliquely propagating whistler‐mode chorus. We have derived formulae of inhomogeneity factors for Landau and cyclotron resonances to analyze nonlinear wave trapping of energetic electrons by an obliquely propagating chorus element. We performed test particle simulations to confirm that nonlinear wave trapping by both Landau and cyclotron resonances can take place for a wide range of energies. For an element of large amplitude chorus waves observed by the Van Allen Probes, we have performed detailed analyses of the wave form data based on theoretical framework of nonlinear trapping of resonant electrons. We compare the efficiencies of accelerations by cyclotron and Landau resonances. We find significant acceleration can take place both in Landau and cyclotron resonances. What controls the dynamics of relativistic electrons in the Landau resonance is the perpendicular field components rather than the parallel electric field of the oblique chorus wave. In evaluating the efficiency of nonlinear trapping, we have taken into account variation of the wave trapping potential structure controlled by the inhomogeneity factors.

Dynamics of Megaelectron Volt Electrons Observed in the Inner Belt by PROBA‐V/EPT

AbstractUsing the observations of the EPT (Energetic Particle Telescope) onboard the satellite PROBA‐V, we study the dynamics of inner and outer belt electrons from 500 keV to 8 MeV during quiet periods and geomagnetic storms. This high time‐resolution (2‐s) spectrometer operating at the altitude of 820 km on a low polar orbit is providing continuously valuable electrons fluxes for already 5 years. We emphasize especially that some megaeleactron volt electrons are observed in low quantities in the inner belt, even during periods when they are not observed by Van Allen Probes. We show that they are not due to proton contamination but to clear injections of particles from the outer belt during strong geomagnetic storms of March and June 2015, and September 2017. Electrons with lower energy are injected also during less strong storms and the L shell of the electron flux peak in the outer belt shifts inward with a high dependence on the electron energy. With the new high‐resolution EPT instrument, we can study the dynamics of relativistic electrons, including megaelectron volt electrons in the inner radiation belt, revealing how and when such electrons are injected into the inner belt and how long they reside there before being scattered into the Earth's atmosphere or lost by other mechanisms.

Spin trapping and flipping in FeCO through relativistic electron dynamics.

Transition metal compounds are very versatile, and their characteristics can differ profoundly depending on their electronic structure. Compounds in which a spin transition from a low-spin to a high-spin state can be achieved through means of an optical excitation are particularly intriguing, as a controlled spin-flip opens promising avenues in areas such as sensing, information technology, molecular switches and energy technology. The fundamental mechanisms in spin crossover and spin transitions remain unanswered, due to the complexity of electronic structure and interplay of relativistic effects. Presented here is a new approach that allows the first direct study of spin flip dynamics through a mapping of spin-mixed to spin-pure states. The method is applied to FeCO and addresses the spin-flip dynamics during a spin transition. Wave packets that combine different spin states are generated through optical excitation and relevant mechanisms in optically triggered spin transitions are discussed.

Dynamics of Electron in TEM Wave Field

Big amount of works deals with solution of differential equations, associated with electron motion in electromagnetic field, using methods of classical electrodynamics. Solution of equation of an electron motion in TEM wave field is interesting task because this equation is mathematical model of big number of wave processes, which are used for researches of different physical processes. The proposed work dedicated to finding the solution for the equation of an electron motion in TEM wave field in laboratory system of coordinates using the theory of almost periodic functions. The work demonstrates that the projections of electron velocity on coordinate axis conform to the wave equation, and, consequently, could be expanded into generalized Fourier series at any value of the wave and electron parameters. In the present work, the formulas received before for electron velocity projection on coordinate axis, are transformed to a well-behaved form, and are broken down into non-perfect generalized Fourier series. Non-perfect Fourier series for projections of electron velocity on coordinate axis are found by means of plotting of complex series, which are called in the theory of almost periodic functions as ”closure of set”. For approximate computation of electron velocity it is possible to restrict oneself to finite number of series harmonics. Application of method of electron velocity components transformation into generalized Fourier series made it possible to find in electron velocity components series terms, which do not depend on time and are equal to average magnitudes of the respective values. Electron velocity components present functions of initial magnitudes of electron velocity components, of generalized phase magnitude and of the wave parameters. Initial magnitudes are not preset at random, but calculated from the equations, the type of which is specified in the work. Electron trajectory in coordinate space is calculated by integrating of the respective expressions for velocity projections on coordinate axis. For demonstration purpose the work deals with the example of electron dynamics in wave polarization plane with consideration of only permanent addends and first harmonics of Fourier series for electron velocity projections on coordinate axis. An approximate solution of the equations of electron dynamics in the plane of polarization of the wave is given. Solution for the equation of electron motion in TEM wave field in the laboratory coordinate system using the theory of almost periodic functions made it possible to solve the problem of dynamics of relativistic electron in the field of progressing TEM wave. It made it possible to demonstrate the availability of time-independent summands in the value of the speed of the electron, which moves in TEM wave. A very important circumstance is also the fact, that the theory makes it possible to investigate electron dynamics depending on the original wave intensity.

Stochastic electron heating in the laser and quasi-static electric and magnetic fields

The dynamics of relativistic electrons in the intense laser radiation and quasi-static electromagnetic fields both along and across the laser propagating direction are studied in the 3/2 dimensional (3/2D) Hamiltonian framework. It is shown that the unperturbed oscillations of the relativistic electron in these electric fields could exhibit a long tail of the amplitude of harmonics which makes an onset of stochastic electron motion be a primary candidate for electron heating. Chirikov-like mappings which describe the recurrence relations of electron energy and time passing through zero canonical momentum plane are derived, and then, the criteria for instability are obtained. It follows that for both transverse and longitudinal electric fields, there exist upper limits of the stochastic electron energy depending on the laser intensity and electric field strength. These maximum energies could be increased by a weak electric field. However, the maximum energy is reduced for the superluminal phase velocity in both cases. The impacts of the magnetic fields on the electron dynamics are different for these two cases and discussed qualitatively. These analytic results are confirmed by the numerical simulations of solving the 3/2D Hamiltonian equations directly.

Surface plasmons in superintense laser-solid interactions

We review studies of superintense laser interactions with solid targets where the generation of propagating surface plasmons (or surface waves) plays a key role. These studies include the onset of plasma instabilities at the irradiated surface, the enhancement of secondary emissions (protons, electrons, and photons as high harmonics in the XUV range) in femtosecond interactions with grating targets, and the generation of unipolar current pulses with picosecond duration. The experimental results give evidence of the existence of surface plasmons in the nonlinear regime of relativistic electron dynamics. These findings open up a route to the improvement of ultrashort laser-driven sources of energetic radiation and, more in general, to the extension of plasmonics in a high field regime.

Laser-driven relativistic electron dynamics in a cylindrical plasma channel**Project supported by the National Natural Science Foundation of China (Grant Nos. 11475027, 11765017, 11764039, 11305132, and 11274255), the Natural Science Foundation of Gansu Province, China (Grant No. 17JR5RA076), and the Scientific Research Project of Gansu Higher Education, China (Grant No. 2016A-005).

The energy and trajectory of the electron, which is irradiated by a high-power laser pulse in a cylindrical plasma channel with a uniform positive charge and a uniform negative current, have been analyzed in terms of a single-electron model of direct laser acceleration. We find that the energy and trajectory of the electron strongly depend on the positive charge density, the negative current density, and the intensity of the laser pulse. The electron can be accelerated significantly only when the positive charge density, the negative current density, and the intensity of the laser pulse are in suitable ranges due to the dephasing rate between the wave and electron motion. Particularly, when their values satisfy a critical condition, the electron can stay in phase with the laser and gain the largest energy from the laser. With the enhancement of the electron energy, strong modulations of the relativistic factor cause a considerable enhancement of the electron transverse oscillations across the channel, which makes the electron trajectory become essentially three-dimensional, even if it is flat at the early stage of the acceleration.

The Relativistic Geometry and Dynamics of Electrons

Atiyah and Sutcliffe (Proc R Soc Lond Ser A 458:1089–1115, 2002) made a number of conjectures about configurations of N distinct points in hyperbolic 3-space, arising from ideas of Berry and Robbins (Proc R Soc Lond Ser A 453:1771–1790, 1997). In this paper we prove all these conjectures, purely geometrically, but we also provide a physical interpretation in terms of Electrons.

The effects of magnetospheric processes on relativistic electron dynamics in the Earth's outer radiation belt

AbstractUsing the electron phase space density (PSD) data measured by Van Allen Probe A from January 2013 to April 2015, we investigate the effects of magnetospheric processes on relativistic electron dynamics in the Earth's outer radiation belt during 50 geomagnetic storms. A statistical study shows that the maximum electron PSDs for various μ (μ = 630, 1096, 2290, and 3311 MeV/G) at L*~4.0 after the storm peak have good correlations with storm intensity (cc~0.70). This suggests that the occurrence and magnitude of geomagnetic storms are necessary for relativistic electron enhancements at the inner edge of the outer radiation belt (L* = 4.0). For moderate or weak storm events (SYM‐Hmin > ~−100 nT) with weak substorm activity (AEmax < 800 nT) and strong storm events (SYM‐Hmin ≤ ~−100 nT) with intense substorms (AEmax ≥ 800 nT) during the recovery phase, the maximum electron PSDs for various μ at different L* values (L* = 4.0, 4.5, and 5.0) are well correlated with storm intensity (cc > 0.77). For storm events with intense substorms after the storm peak, relativistic electron enhancements at L* = 4.5 and 5.0 are observed. This shows that intense substorms during the storm recovery phase are crucial to relativistic electron enhancements in the heart of the outer radiation belt. Our statistics study suggests that magnetospheric processes during geomagnetic storms have a significant effect on relativistic electron dynamics.

Multiple‐Satellite Observation of Magnetic Dip Event During the Substorm on 10 October 2013

AbstractWe present a multiple‐satellite observation of the magnetic dip event during the substorm on 10 October 2013. The observation illustrates the temporal and spatial evolution of the magnetic dip and gives a compelling evidence that ring current ions induce the magnetic dip by enhanced plasma beta. The dip moves with the energetic ions in a comparable drift velocity and affects the dynamics of relativistic electrons in the radiation belt. In addition, the magnetic dip provides a favorable condition for the electromagnetic ion cyclotron (EMIC) wave generation based on the linear theory analysis. The calculated proton diffusion coefficients show that the observed EMIC wave can lead to the pitch angle scattering losses of the ring current ions, which in turn partially relax the magnetic dip in the observations. This study enriches our understanding of magnetic dip evolution and demonstrates the important role of the magnetic dip for the coupling of radiation belt and ring current.

Relativistic electron dynamics produced by azimuthally localized poloidal mode ULF waves: Boomerang‐shaped pitch angle evolutions

AbstractWe present an analysis of “boomerang‐shaped” pitch angle evolutions of outer radiation belt relativistic electrons observed by the Van Allen Probes after the passage of an interplanetary shock on 7 June 2014. The flux at different pitch angles is modulated by Pc5 waves, with equatorially mirroring electrons reaching the satellite first. For 90° pitch angle electrons, the phase change of the flux modulations across energy exceeds 180° and increasingly tilts with time. Using estimates of the arrival time of particles of different pitch angles at the spacecraft location, a scenario is investigated in which shock‐induced ULF waves interact with electrons through the drift resonance mechanism in a localized region westward of the spacecraft. Numerical calculations on particle energy gain with the modified ULF wavefield reproduce the observed boomerang stripes and modulations in the electron energy spectrogram. The study of boomerang stripes and their relationship to drift resonance taking place at a location different from the observation point adds new understanding of the processes controlling the dynamics of the outer radiation belt.

High-Order-Harmonic Generation from a Relativistic Circularly Polarized Laser Interacting with Over-Dense Plasma Grating**Supported by the National Natural Science Foundation of China under Grant Nos 11375265, 11475259 and 11675264, the National Basic Research Program of China under Grant No 2013CBA01504, and the Science Challenge Project under Grant No JCKY2016212A505.

The simple surface current model is extended to study the generation of high-order harmonics for a relativistic circularly polarized laser pulse interacting with a plasma grating surface. Both exact relativistic electron dynamics and optical interference of surface periodic structure are considered. It is found that high order harmonics in the specular direction are obviously suppressed whereas the harmonics of the grating periodicity are strongly enhanced and folded into small solid angles with respect to the surface direction. The conversion efficiency of certain harmonics is five orders of magnitude higher than that of the planar target cases. It provides an effective approach to generate a coherent radiation within the so-called ‘water window’ while maintaining high conversion efficiency and narrow angle spread.