Wave-particle Interactions Research Articles

Low-latitude Auroras: Insights from 2023 April 23 Solar Storm

In 2023 April, a low-latitude aurora observed by the all-sky camera at Hanle, Ladakh, India (33°14’N geographic latitude), generated significant interest. This was the first such aurora recorded from the Indian region in the space era and occurred during a moderate solar storm. This study explores this low-latitude auroral sighting, which happened during the sheath-region passage of an interplanetary coronal mass ejection. We analyze in situ multispacecraft particle measurements and geomagnetic field observations from both ground-based and satellite-based magnetometers. The auroral observations at Hanle coincided with intense substorm activity. Our findings indicate that the aurora did not actually reach India; the equatorward boundary was beyond 50°N geographic latitude. Enhanced electron fluxes with energies below 100 eV were detected at 54°N geographic latitude at about 830 km altitude in the predawn sector (4–5 hr local time). In the midnight sector, the equatorward boundary is estimated to be around 52°N geographic latitude, based on Hanle observations and considering emission altitudes of 600–650 km due to low-energy electrons. Thus, the low-latitude red aurora observed from India resulted from the emissions at higher altitudes due to low-energy electron precipitation in the auroral oval and a slight equatorward expansion of the auroral oval. The low-energy electrons likely originated from the plasma sheet and were precipitated due to enhanced wave–particle interactions from strong magnetosphere compression during high solar wind pressure. This study is crucial in understanding low-latitude auroras in the modern space era.

Hamiltonian for complex plasmas

The Hamiltonian for a complex plasma involving dust spinning motion in a magnetic field is proposed. The formulation is in a classical limit of a quantum mechanical approach based on the Dirac equation, a relativistic wave equation in which the spin of particles is considered. The quantum mechanical spin term –γs·B [γ=gq/2m, g=2(Lande´ g−factor),q is a charge, m is a mass of a particle, and s = spin operator] is replaced by –γs·B [γ with g=1, s = I(ω+γB), I is the moment of inertia of a dust particle, and ω is the spinning angular velocity of a dust particle] in a classical limit. The wave–particle interaction involving spin motion is described as an interaction between particles and quasiparticles by the second quantization. The equation of motion with a damping term shows the relaxation of spinning dust particles aligning with the magnetic field.

Interaction of driven ‘cold’ electron plasma wave with thermal bulk via ion spatial inhomogeneity

Abstract Using high resolution Vlasov - Poisson simulations, evolution of driven ``cold" electron plasma wave (EPW) in the presence of stationary inhomogeneous background of ions is studied. Mode coupling dynamics between ``cold'' EPW with phase velocity $v_{\phi}$ greater than thermal velocity i.e $v_{\phi} \gg v_{thermal}$ and its inhomogeneity induced sidebands is illustrated as an initial value problem. In driven cases, formation of BGK like phase space structures corresponding to sideband modes due to energy exchange from primary mode to bulk particles via wave-wave and wave-particle interactions leading to particle trapping is demonstrated for inhomogeneous plasma. Qualitative comparison studies between initial value perturbation and driven problem is presented, which examines the relative difference in energy transfer time between the interacting modes. Effect of variation in background ion inhomogeneity amplitude as well as ion inhomogeneity scale length on the driven EPWs is reported.

Investigating the fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation: an iterative framework for nonlinear wave dynamics

Abstract This paper addresses the solution of the fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation using the Conformable Laplace Decomposition Method (CLDM). The CDGSK equation, a fundamental model in wave dynamics and fluid mechanics, is explored for its applications in quantum mechanics and nonlinear optics. By employing fractional calculus, we demonstrate how fractional derivatives influence the physical characteristics of wave propagation in both optical and quantum systems. The exact solutions obtained provide insight into soliton behavior, essential for understanding wave-particle interactions in quantum fields and light–matter interactions in optics. The fractional nature of the equation allows for more accurate modeling of non-integer order dynamics commonly found in optical fibers and quantum waveguides. The CLDM method proves to be highly effective, providing approximate solutions with minimal computational effort. These findings offer significant contributions to the fields of quantum mechanics and nonlinear optics, where the fractional CDGSK equation can be applied to solve complex wave equations with great accuracy.

Ultra-relativistic electron flux enhancement under persistent high speed solar wind stream

The physical mechanisms usually applied to explain the relativistic electron enhancement have been delved into to elucidate non-adiabatic electron acceleration resulting in the ultra-relativistic electron population observed in the outer radiation belt. We considered multisatellite observations of the solar wind parameters, magnetospheric waves, and particle flux to report an unusual local acceleration of ultra-relativistic electrons under a prolonged high-speed solar wind stream (HSS). A corotating interaction region reaches the Earth’s bowshock on August 3, 2016, causing a minor geomagnetic storm. Following this, the magnetosphere was driven for 72 h by a long-term HSS propagating at 600 km/s. During this period, the magnetosphere sustained both ultra-low frequency (ULF) and very-low frequency (VLF) waves in the outer radiation belt region. Besides the waves, the relativistic and ultra-relativistic electron fluxes were enhanced with different time lags regarding the magnetic storm main phase. The efficiency of wave-particle interaction in enhancing ultrarelativistic electrons is evaluated by the diffusion coefficient rates, considering both ULF and VLF waves together with phase space density analyses. Results show that local acceleration by whistler mode chorus waves can occur in a time scale of 2–4 h, whereas ULF waves take around 10’s of hours and magnetosonic waves take a time scale of days. This result is confirmed by the phase space density analysis. Accordingly, it shows that peaks of local acceleration of 1 MeV electrons are consistent with the observation of the highest chorus wave amplitude at the same L-shell and MLT. Thus, we argue that whistler mode chorus waves interacting with relativistic electrons are the main physical mechanisms leading to ultra-relativistic electron enhancement, while ULF and fast magnetosonic waves are found as secondary physical processes. Lastly, our analysis contributes to understanding how whistler and ULF waves can contribute to ultra-relativistic electrons showing up in the inner magnetosphere under the HSS driver.

Detection of bifurcation in phase-space perturbative structures across transient wave–particle interaction in laboratory plasmas

A key ingredient for realizing a magnetically confined tritium-deuterium plasma fusion reactor is plasma heating by fusion-born high-energy helium ions, as a chained cycle of "nuclear burning." Efficient collisionless plasma heating by high-energy particles is anticipated when their energy is directly transferred to the plasma through waves. Those processes often involve nonlinear structure formations in phase-space, spanned by real-space and velocity-space coordinates, that significantly influence heating efficiency. To date, experimental knowledge of phase-space structure formation physics is severely limited, due to lack of experimental diagnostic schemes. Here, state-of-the-art hardware and software approaches for phase-space perturbative structure detection are introduced. A bifurcation in the phase-space structure formation is found, which affects the plasma heating efficiency. A confinement magnetic field structure is shown to be a potential knob for nuclear-burning control through phase-space manipulation.

Backward test particle simulation of nonlinear cyclotron wave-particle interactions in the radiation belts

Wave-particle interaction plays a crucial role in the dynamics of the Earth’s radiation belts. Cyclotron resonance between coherent whistler mode electromagnetic waves and energetic electrons of the radiation belts is often called a coherent instability. Coherent instability leads to wave amplification/generation and particle acceleration/scattering. The effect of wave on particle’s distribution function is a key component of the instability. In general, whistler wave amplitude can grow over threshold of quasi-linear (linear) diffusion theory which analytically tracks the time-evolution of a particle distribution. Thus, a numerical approach is required to model the nonlinear wave induced perturbations on particle distribution function. A backward test particle model is used to determine the energetic electrons phase space dynamics as a result of coherent whistler wave instability. The results show the formation of a phase space features with much higher resolution than is available with forward scattering models. In the nonlinear regime the formation of electron phase space holes upstream of a monochromatic wave is observed. The results validate the nonlinear phase trapping mechanism that drives nonlinear whistler mode growth. The key differences in phase-space perturbations between the linear and nonlinear scenarios are also illustrated. For the linearized equations or for low (below threshold) wave amplitudes in the nonlinear case, there is no formation of a phase-space hole and both models show features that can be characterized as linear striations or ripples in phase-space.

Numerical simulations of temperature anisotropy instabilities stimulated by suprathermal protons

Context. The new in situ measurements of the Solar Orbiter mission contribute to the knowledge of the suprathermal populations in the solar wind, especially of ions and protons whose characterization, although still in the early phase, seems to suggest a major involvement in the interaction with plasma wave fluctuations. Aims. Recent studies point to the stimulating effect of suprathermal populations on temperature anisotropy instabilities in the case of electrons already being demonstrated in theory and numerical simulations. Here, we investigate anisotropic protons, addressing the electromagnetic ion-cyclotron (EMIC) and the proton firehose (PFH) instabilities. Methods. Suprathermal populations enhance the high-energy tails of the Kappa velocity (or energy) distributions measured in situ, enabling characterization by contrasting to the quasi-thermal population in the low-energy (bi-)Maxwellian core. We use hybrid simulations to investigate the two instabilities (with ions or protons as particles and electrons as fluid) for various configurations relevant to the solar wind and terrestrial magnetosphere. Results. The new simulation results confirm the linear theory and its predictions. In the presence of suprathermal protons, the wave fluctuations reach increased energy density levels for both instabilities and cause faster and/or deeper relaxation of temperature anisotropy. The magnitude of suprathermal effects also depends on each instability’s specific (initial) parametric regimes. Conclusions. These results further strengthen the belief that wave-particle interactions govern space plasmas. These provide valuable clues for understanding their dynamics, particularly the involvement of suprathermal particles behind the quasi-stationary non-equilibrium states reported by in situ observations.

Relaxation of weakly collisional plasma: Continuous spectra, discrete eigenmodes, and the decay of echoes.

The relaxation of a weakly collisional plasma, which is of fundamental interest to laboratory astrophysical plasmas, can be described by the self-consistent Boltzmann-Poisson equations with the Lenard-Bernstein collision operator. We perform a perturbative (linear and second-order) analysis of the Boltzmann-Poisson equations and obtain exact analytic solutions which resolve some longstanding controversies regarding the impact of weak collisions on the continuous spectra, the discrete Landau eigenmodes, and the decay of plasma echoes. We retain both damping and diffusion terms in the collision operator throughout our treatment. We find that the linear response is a temporal convolution of two types of contribution: a continuum that depends on the continuous velocities of particles (crucial for the plasma echo), and another, consisting of discrete modes that are coherent modes of oscillation of the entire system. The discrete modes are exponentially damped over time due to collective effects or wave-particle interactions (Landau damping), as well as collisional dissipation. The continuum is also damped by collisions but somewhat differently than the discrete modes. Up to a collision time, which is the inverse of the collision frequency ν_{c}, the continuum decay is driven by the diffusion of particle velocities and is cubic exponential, occurring over a timescale ∼ν_{c}^{-1/3}. After a collision time, however, the continuum decay is driven by the collisional damping of particle velocities and diffusion of their positions and occurs exponentially over a timescale ∼ν_{c}. This slow exponential decay causes perturbations to damp the most on scales comparable to the mean free path but very slowly on larger scales. This establishes the local thermal equilibrium, which is the essence of the fluid limit. The long-term decay of the linear response is driven by the discrete modes on scales smaller than the mean free path but, on larger scales, is governed by a combination of the slowly decaying continuum and the least damped discrete mode. This slow exponential decay implies that the echo, which results from the interference of the continuum response to two subsequent pulses, is detectable even on scales comparable to the mean free path, as long as the second pulse is introduced within a few phase-mixing timescales after the first.

Electrostatic Waves and Electron Holes in Simulations of Low-Mach Quasi-perpendicular Shocks

Collisionless low-Mach-number shocks are abundant in astrophysical and space plasma environments, exhibiting complex wave activity and wave–particle interactions. In this paper, we present 2D Particle-in-Cell (PIC) simulations of quasi-perpendicular nonrelativistic (v sh ≈ (5500–22000) km s−1) low-Mach-number shocks, with a specific focus on studying electrostatic waves in the shock ramp and precursor regions. In these shocks, an ion-scale oblique whistler wave creates a configuration with two hot counterstreaming electron beams, which drive unstable electron acoustic waves (EAWs) that can turn into electrostatic solitary waves (ESWs) at the late stage of their evolution. By conducting simulations with periodic boundaries, we show that the EAW properties agree with linear dispersion analysis. The characteristics of ESWs in shock simulations, including their wavelength and amplitude, depend on the shock velocity. When extrapolated to shocks with realistic velocities (v sh ≈ 300 km s−1), the ESW wavelength is reduced to one-tenth of the electron skin depth and the ESW amplitude is anticipated to surpass that of the quasi-static electric field by more than a factor of 100. These theoretical predictions may explain a discrepancy, between PIC and satellite measurements, in the relative amplitude of high- and low-frequency electric field fluctuations.

Electron acceleration by stochastic wave fields in a bounded plasma system

We investigate the electron acceleration dynamics in spatially stochastic wave fields. For a bounded system, the spectra (frequency and wave number) of the stochastic wave fields are discrete so that they can form spatiotemporal “singular” structures once their phases are in synchronization. As a consequence, the electrons will experience significant scattering by these singular structures, which is an in-phase effect of an ensemble of non-resonant wave–particle interactions. In the presence of parallel symmetry breaking, it is found that the governing Fokker–Planck equation has a structure similar to that of the resonant wave–particle interaction but with a broader parameter regime in the velocity/energy space of the electron distribution function.

The Independence of Magnetic Turbulent Power Spectra to the Presence of Switchbacks in the Inner Heliosphere

An outstanding gap in our knowledge of the solar wind is the relationship between switchbacks and solar wind turbulence. Switchbacks are large fluctuations, even reversals, of the background magnetic field embedded in the solar wind flow. It has been proposed that switchbacks may form as a product of turbulence and decay via coupling with the turbulent cascade. In this work, we examine how properties of solar wind magnetic field turbulence vary in the presence or absence of switchbacks. Specifically, we use in situ particle and fields measurements from Parker Solar Probe to measure magnetic field turbulent wave power, separately in the inertial and kinetic ranges, as a function of switchback magnetic deflection angle. We demonstrate that the angle between the background magnetic field and the solar wind velocity in the spacecraft frame (θ vB ) strongly determines whether Parker Solar Probe samples wave power parallel or perpendicular to the background magnetic field. Further, we show that θ vB is strongly modulated by the switchback magnetic deflection angle. In this analysis, we demonstrate that switchback deflection angle does not correspond to any significant increase in wave power in either the inertial range or at kinetic scales. This result implies that switchbacks do not strongly couple to the turbulent cascade in the inertial or kinetic ranges via turbulent wave–particle interactions. Therefore, we do not expect switchbacks to contribute significantly to solar wind heating through this type of energy conversion pathway although contributions via other mechanisms, such as magnetic reconnection, may still be significant.

A hybrid Eulerian-Lagrangian Vlasov method for nonlinear wave-particle interaction in weakly inhomogeneous magnetic field

We present a hybrid Eulerian-Lagrangian (HEL) Vlasov method for nonlinear resonant wave-particle interactions in weakly inhomogeneous magnetic field. The governing Vlasov equation is derived from a recently proposed resonance tracking Hamiltonian theory. It gives the evolution of the distribution function with a scale-separated Hamiltonian that contains the fast-varying coherent wave-particle interaction and slowly-varying motion about the resonance frame of reference. The hybrid scheme solves the fast-varying phase space evolution on Eulerian grid with an adaptive time step and then advances the slowly-varying dynamics by Lagrangian method along the resonance trajectory. We apply the HEL method to study the frequency chirping of whistler-mode chorus wave in the magnetosphere and the self-consistent simulations reproduce the chirping chorus wave and give high-resolution phase space dynamics of energetic particles at low computational cost. The scale-separated HEL approach could provide additional insights of the wave instabilities and wave-particle nonlinear coherence compared to the conventional Vlasov and particle-in-cell methods.

Flat Spectra of Energetic Particles in Interplanetary Shock Precursors

The observed energy spectra of accelerated particles at interplanetary shocks often do not match the diffusive shock acceleration (DSA) theory predictions. In some cases, the particle flux forms a plateau over a wide range of energies, extending upstream of the shock for up to seven flux e-folds before submerging into the background spectrum. Remarkably, at and downstream of the shock we have studied in detail, the flux falls off in energy as ϵ −1, consistent with the DSA prediction for a strong shock. The upstream plateau suggests a particle transport mechanism different from those traditionally employed in DSA models. We show that a standard (linear) DSA solution based on a widely accepted diffusive particle transport with an underlying resonant wave–particle interaction is inconsistent with the plateau in the particle flux. To resolve this contradiction, we modify the DSA theory in two ways. First, we include a dependence of the particle diffusivity κ on the particle flux F (nonlinear particle transport). Second, we invoke short-scale magnetic perturbations that are self-consistently generated by, but not resonant with, accelerated particles. They lead to the particle diffusivity increasing with the particle energy as ∝ϵ 3/2 that simultaneously decreases with the particle flux as 1/F. The combination of these two trends results in the flat spectrum upstream. We speculate that nonmonotonic spatial variations of the upstream spectrum, apart from being time-dependent, may also result from non-DSA acceleration mechanisms at work upstream, such as stochastic Fermi or magnetic pumping acceleration.

Overview of Large Helical Device experiments of basic plasma physics for solving crucial issues in reaching burning plasma conditions

Abstract Recently, experiments on basic plasma physics issues for solving future problems in fusion energy have been performed on a Large Helical Device. There are several problems to be solved in future devices for fusion energy. Emerging issues in burning plasma are: alpha-channeling (ion heating by alpha particles), turbulence and transport in electron dominant heating helium ash exhaust, reduction of the divertor heat load. To solve these problems, understanding the basic plasma physics of (1) wave–particle interaction through (inverse) Landau damping, (2) characteristics of electron-scale (high-k) turbulence, (3) ion mixing and the isotope effect, and (4) turbulence spreading and detachment, is necessary. This overview discusses the experimental studies on these issues and turbulent transport in multi-ion plasma and other issues in the appendix.

Earth's ambipolar electrostatic field and its role in ion escape to space.

Cold plasma of ionospheric origin has recently been found to be a much larger contributor to the magnetosphere of Earth than expected1-3. Numerous competing mechanisms have been postulated to drive ion escape to space, including heating and acceleration by wave-particle interactions4 and a global electrostatic field between the ionosphere and space (called the ambipolar or polarization field)5,6. Observations of heated O+ ions in the magnetosphere are consistent with resonant wave-particle interactions7. By contrast, observations of cold supersonic H+ flowing out of the polar ionosphere8,9 (called the polar wind) suggest the presence of an electrostatic field. Here we report the existence of a +0.55 ± 0.09 V electric potential drop between 250 km and 768 km from a planetary electrostatic field (E∥⊕ = 1.09 ± 0.17 μV m-1) generated exclusively by the outward pressure of ionospheric electrons. We experimentally demonstrate that the ambipolar field of Earth controls the structure of the polar ionosphere, boosting the scale height by 271%. We infer thatthis increases the supply of cold O+ ions to the magnetosphere by more than 3,800%, in which other mechanisms such as wave-particle interactions can heat and further accelerate them to escape velocity. The electrostatic field of Earth is strong enough by itself to drive the polar wind9,10 and is probably the origin of the cold H+ ion population1 that dominates much of the magnetosphere2,3.

Fast nonlinear scattering of runaway electron beams through resonant interactions with plasma waves

Abstract The resonant interaction between a runaway electron (RE) beam and a reactor-grade background plasma is investigated through two-dimensional particle-in-cell simulations, employing a simplified model of the system. The temporal evolutions of the electron momentum distribution function for two separate initial beam energies (1 and 10 MeV) are tracked, revealing the occurrence of plasma wave growth concomitant with pitch angle scattering or momentum distribution diffusion within the RE beam. Notably, we identify and confirm the dependence of the dominant resonance condition on the initial kinetic energy of the RE beam. Furthermore, we quantify the effect of particle-wave interactions on the RE momentum distribution diffusion by assessing the average kinetic energy flux from the RE distribution function.

Statistical Distributions of Plasma Density and Pressure in the Jovian Plasma Sheet

The Jovian plasma sheet is a key region of the Jovian magnetosphere populated by a mix of warm and hot plasma. It is the main channel for radial transport of mass and energy in the Jovian magnetosphere and provides a favorable environment for magnetic reconnection and wave–particle interactions although the understanding of its plasma properties is incomplete. This study combines observations from the Jovian Auroral Distributions Experiment and Juno Energetic Particle Detector Instrument on board the Juno spacecraft during its first 31 orbits to analyze the plasma properties of the Jovian plasma sheet from 20 R J to 100 R J. Our results indicate that the plasma number density decreases from 1 cm−3 at 20 R J to 0.005 cm−3 at 100 R J, while the plasma pressure decreases from 2 nPa at 20 R J to 0.02 nPa at 100 R J. The plasma pressure inside the plasma sheet is comparable to the magnetic pressure in the lobe region, suggesting a rough balance between the two. In the plasma sheet with r > 70 R J, the H+ density and pressure remain relatively constant, likely due to other plasma sources such as the solar wind. Additionally, we find that the pressure (density) ratios for heavy ions between the center and the edge of the plasma sheet are generally an order of magnitude, while that for H+ decreases with radial distance. These findings contribute to a more comprehensive understanding of the plasma properties of the Jovian plasma sheet.

Complete quasilinear model for the acceleration-driven lower hybrid drift instability and a computational assessment of its validity.

A complete quasilinear model is derived for the electrostatic acceleration-driven lower hybrid drift instability in a uniform two-species low-beta plasma in which current is perpendicular to the background magnetic field. The model consists of coupled nonlinear velocity space diffusion equationsfor the volume-averaged ion and electron distribution functions. Each species' diffusion coefficient depends on a time-evolving spectral density of the electric-field energy per unit volume and a time-evolving dispersion relation. The dispersion relation is expressed analytically in integral form without the use of asymptotic limits and applies to arbitrary distribution functions, so long as they can be expressed as a function of one velocity coordinate, e.g., f(v_{y}) or f(v_{⊥}). The quasilinear model conserves energy and is complete in that it fully describes the evolution of the distribution functions, including resonant and nonresonant particle-wave interactions, while accounting for distribution-function-dependent mixed-complex frequencies. The quasilinear diffusion model is solved numerically and self-consistently using a Crank-Nicolson temporal discretization and a second-order finite-volume velocity-space discretization. Numerical solutions are compared to nonlinear fourth-order accurate continuum kinetic Vlasov-Poisson simulations. Evolution of electric-field energy, growth rates, distribution functions, and diffusion coefficients are shown to be in agreement with Vlasov simulations. The quasilinear model is shown to predict anomalous transport terms, like resistivity and heating, to within a factor of order unity. Discrepancies between the quasilinear model and Vlasov simulations are assessed and attributed primarily to lack of damping in the quasilinear description and to the use of unperturbed-orbit susceptibilities in the linear theory dispersion relation. The results illuminate the predictive accuracy of the quasilinear model, place approximate bounds on its validity, and provide much needed vetting of quasilinear theory's ability to predict the nonlinear state of a microturbulent plasma.

Variability of energetic proton flux and pitch angle distributions in the Earth's radiation belt modulated by geomagnetic storms

Energetic protons trapped in the radiation belt, as a vital component of the ring current system, are observationally and theoretically modulated by geomagnetic disturbances. Utilizing Van Allen Probe observations, we statistically analyzed their temporal variations at 55–489 keV as well as their pitch angle distributions (PADs) index n (fitted by sinn∂, where ∂ is the pitch angle) in response to geomagnetic storms. It shows that protons at low energies are more easily accelerated during storms. The threshold of accelerations becomes greater for high-energy protons, while a large value of n can persist for a few days to months. Further investigations suggest that one-quarter of the storms increase the proton flux at all energy channels (55–489 keV) both inside and outside the plasmapause location (Lpp). Specifically, more than half of the storms enhance the flux for protons at Ek > 400 keV inside and close to the Lpp as well as protons at Ek < 100 keV deep inside the Lpp. Comparably, protons at larger pitch angles (near 90°) are more easily lost outside the Lpp, which results in more pronounced pancake PADs with larger n. The index n preferentially decreases at L > 5 during 75% of the storms on the dayside, while it decreases at L = ∼4 during 50% of the storms on the nightside, showing significant day–night asymmetry. Further detailed investigations revealed that source and loss processes, including radial diffusion, magnetopause shadowing, and wave–particle interactions, account for the statistical results. The present study provides quantitative information on the overall characteristics of energetic proton fluxes, which can enhance the comprehension of the radiation belts.