Wave-particle Interactions Research Articles

Stress Wave Propagation and Decay Based on Micro-Scale Modelling in the Topology of Polymer Composite with Circular Particles.

This article deals with stress wave decay performance, analysing the stress wave propagation generated by an impulsive unit load in a 2D representative unit cell (RUC) of a polymer composite with circular particles representing spherical particles, elliptical particles, and short fibres. The micro-scale numerical simulation uses explicit finite element analysis (FEA). The micro-response to an impulsive unit load creates a stress wave amplitude interacting with the material structure and tends to weaken and absorb energy. The stress wave damping is determined by the decaying amplitudes of Mises stress at the front of the stress wave. The stress wave damping is evaluated for different ratios of tensile modules and material densities of matrix and reinforcing material and other factors, such as percentage and particle size, applied to nine topologies of RUCs, and even the presence of an interfacial region is analysed. Moreover, the article visualises the phases of stress wave decay in various particle distributions, i.e., various topologies. Analysing the different topologies of the same particle volume (area) percentage, the study proved that the composite topology and resulting wave-particle and wave-wave interactions are other sources of material damping. The presence of even a small percentage, 3.5 area%, of reinforcing circular particles in the matrix brings a significant increase in stress wave damping up to about 40-43% (depending on the topology) compared to a homogeneous matrix with stress wave damping of 12.5% under the same conditions. Moreover, the topology with the same volume (area) percentage can increase particle stress wave damping by 15.3%.

Design of the electron cyclotron resonance (ECR) plasma source for the space plasma environment research facility.

The Space Plasma Environment Research Facility (SPERF) was built in Harbin to study the three-dimensional magnetic reconnection and wave-particle interactions relevant to space physics in laboratory settings. A 2.45GHz Electron Cyclotron Resonance (ECR) plasma source is adopted in the device to simulate the Earth's magnetosphere and achieve the scientific goals. In this paper, the design of the ECR plasma source is presented. The structures of the microwave source, the microwave transfer system, and the antenna are introduced. Additionally, the resonant surfaces are computed to predict the locations of microwave absorption. The absorption mechanisms of the microwave in the SPERF are also discussed. The discharge experiment demonstrates the utility of the ECR source in simulating the Earth's magnetosphere. The successful operation of the source indicates that the ECR discharge is a powerful tool for creating a plasma environment in a large plasma experimental device.

A multi-satellite survey scheme for addressing open questions on the Earth’s outer radiation belt dynamics

The Earth’s outer radiation belt is highly dynamic, containing relativistic electron fluxes that can increase by several orders of magnitude during magnetospheric disturbances. This greatly increases the likelihood of spacecraft malfunction or failure and significantly influences the solar-terrestrial system’s energy and mass coupling, highlighting the importance of fully understanding the mechanisms governing these dynamics from both theoretical and practical perspectives. Although many theories have been proposed, further research is essential to quantify the specific contributions of different dynamic mechanisms for improving space weather forecasting. To address this, observations of the outer radiation belt with high spatial–temporal resolution to distinguish the spatial and temporal variations are essential. We introduce a 10-CubeSat constellation survey scheme in the geosynchronous transfer orbit (GTO) to achieve this required observation. Three baseline instruments are proposed to be employed: the high energy electron detector (HEED), the search coil wave detector (SCWD), and the magnetometer (MAG). Two groups of physical processes will be investigated: wave-particle interactions involving charged particles interacting with whistler-mode waves, electromagnetic ion cyclotron (EMIC) waves, and ultra-low frequency (ULF) waves; and radial transport encompassing shock-induced injections, substorm injections, storm convection and magnetopause shadowing. The performance parameters of instruments and platform of the constellation are presented. Additionally, aligned with the concept of constellation survey, we outline the COSPAR-coordinated space program, COnstellation of Radiation BElt Survey (CORBES), which will provide a crucial scientific contribution in the absence of the Van Allen Probes. The program’s excellent observational capability enables a comprehensive understanding of the underlying physical mechanisms governing the outer radiation belt dynamics and improved space weather forecasting.

Characteristics of radiation belt energetic protons and the movement of their core location in response to geomagnetic disturbances

The energetic protons trapped within the Earth's radiation belt play a crucial role in substantially impacting the behavior of the ring current, which in turn affects the dynamics of energetic particles. Here, we statistically analyze and discuss the global distributions and temporal evolutions of them at energies from 55 keV to 489 keV by using 7-year (2012–2019) observations by radiation belt storm probes ion composition experiment onboard Van Allen Probes. The observations show that low-energy protons (55–148 keV) are distributed at higher L shells (L > 4), which can deeply penetrate during intense storms. The high-energy protons (221–489 keV) are mainly located at L < 4.5 and are comparably stable. Moreover, the core location (i.e., Lc, the L shell with the peak flux) of them is typically energy-dependent and can be displaced due to geomagnetic storms. Detailed analysis reveals that the Lc for low-energy protons is primarily outside the plasmapause location (Lpp), which can rapidly radially move. However, the Lc for high-energy protons is essentially inside Lpp and is harder to move. The Lc for intermediate-energy protons exhibits fluctuations around Lpp, indicating a clear competition between source and loss processes. In addition, alternative mechanisms, such as wave–particle interactions, are primarily responsible for the gradual variation of them after storms. Our study provides the total configuration of the radiation belt energetic protons measured in the Van Allen Probe era, which would be useful for better understanding the variation of trapped particles in the inner magnetosphere.

Theory of the anomalous momentum exchange from wave–particle interactions in Hall-effect ion accelerators and comparisons with measurements

Theory of the anomalous momentum exchange from wave–particle interactions in Hall-effect ion accelerators and comparisons with measurements

Fast ion relaxation in ITER mediated by Alfvén instabilities

We address the critical issue for future burning plasmas of whether high-energy fusion products or auxiliary heating-beam ions will be confined for a sufficiently long time to compensate for thermal plasma energy losses. This issue can be mitigated by one of the most deleterious collective phenomena—the instability of low, sub-cyclotron frequency Alfvén eigenmodes (AEs), such as toroidicity-induced AEs and reversed-shear AEs in the ITER steady-state scenario. Using a revised quasi-linear (QL) theory applied to energetic particle (EP) relaxation in the presence of AEs, we find that the AE instabilities can affect both neutral beam ions and alpha particles, although the resulting fast ion transport is expected to be modest if classical particle slowing down is assumed. On the other hand, the QL theory predicts that the AE amplitudes will be enhanced by the background microturbulence, although this topic remains outside our scope due to the significant numerical effort required to evaluate these effects. We report our results for EP relaxation dynamics obtained utilizing several tools: (i) a comprehensive linear stability study of the sub-cyclotron Alfvénic spectrum as computed by ideal magnetohydrodynamic NOVA simulations for the AE eigenproblem, (ii) drift kinetic NOVA-C calculations for wave–particle interaction and AE growth/damping rates, and (iii) predictive QL modeling coupled with the global transport code TRANSP to assess the EP relaxation on the equilibrium timescale.

ULF Wave Transport of Relativistic Electrons in the Van Allen Belts: Criteria for Transition to Radial Diffusion

AbstractRelativistic electrons in the radiation belts can be transported as a result of wave‐particle interactions (WPI) with ultra‐low frequency (ULF) waves. Such WPI are often assumed to be diffusive, parametric models for the radial diffusion coefficient often being used to assess the rates of radial transport. However, these WPI transition from initially coherent interactions to the diffusive regime over a finite time, this time depending on the ULF wave power spectral density, and local resonance conditions. Further, in the real system on the timescales of a single storm, interactions with finite discrete modes may be more realistic. Here, we use a particle‐tracing model to simulate the dynamics of outer radiation belt electrons in the presence of a finite number of discrete frequency modes. We characterize the point of the onset of diffusion as a transition from separate discrete interactions in terms of wave parameters by using the “two‐thirds” overlap criterion (Lichtenberg & Lieberman, 1992, https://doi.org/10.1007/978‐1‐4757‐2184‐3), a comparison between the distance between, and the widths of, the electron's primary resonant islands in phase space. Further, we find the particle decorrelation time in our model system with typical parameters to be on the timescale of hours, which only afterward can the system be modeled by one‐dimensional radial diffusion. Direct comparison of particle transport rates in our model with previous analytic diffusion coefficient formulations show good agreement at times beyond the decorrelation time. These results are critical for determining the time periods and conditions under which ULF wave radial diffusion theory can be applied.

The excitation of whistler waves and wave-particle interaction in magnetic reconnection

A 2.5D PIC kinetic code is executed to simulate the excitation of electron whistlers and ion cyclotron whistler (L wave) during magnetic reconnection. Our simulation results suggest that quasi-parallel and anti-parallel whistler waves can be excited in the separatrix region near X-Line and in the outflow region, respectively. Electron whistlers play a crucial role in energy release and transfer, as the small mass of electrons allows them to move rapidly under the perturbation of a magnetic field during magnetic reconnection. The L wave excited near the separatrix region far from X-Line, it propagate obliquely to the local magnetic field. Velocity distribution functions (VDFs) indicate that these waves are associated with temperature anisotropy instabilities of electron-beams (ion-beam). The electron whistler in the separatrix region is excited by cyclotron resonance due to the electron beam. The electron whistler observed in the outflow region is generated by Landau resonance owing to beam-mode, where the v∥ is close to the phase speed vph of the wave. Regarding L wave, their excitation mechanism is attributed to significant perpendicular temperature anisotropy instability (Ti⊥>Ti∥) of ion-beam, and satisfies cyclotron resonance condition. Meanwhile, our simulation results illustrate that the existence of energy conversion between particles and waves during the wave excitation by using the Wave-Particle Interaction Analyzer (WPIA).

Prompt extinction of bump-on-tail energy spectra for radiation belt electron phase space density

The bump-on-tail electron flux energy spectral distributions in the Earth's radiation belt are widely observed and have been proven to be generated by plasmaspheric hiss-led wave–particle interactions. Here, we report and discuss the prompt disappearance of them induced by the high solar wind dynamic pressure (Pdyn) combined with substorms on 12–13 March 2014. To remove the potential adiabatic influence, the electron fluxes are all converted to phase space density in the TS04 geomagnetic coordinate. Immediately after the Pdyn reached its maximum accompanied by the intensifying of substorms, the initial bump-on-tail spectra of the phase space density at L* (the third adiabatic invariant) from 3.8 to 4.4 were destroyed and rapidly smoothed to the exponential distributions, with a distinct ascent for lower energy electrons and a sharp decline for higher energy electrons. The balance line between the source and loss processes was located at μ = 50–200 MeV/G (μ is the first adiabatic invariant), which is sensitive to the spatial location. Further investigation of the temporal evolution of the phase space density along with L* and the plasma wave distributions provided evidence that the loss processes dominated at higher L* for electrons at μ ≳ 100 MeV/G, while the source processes became stronger at lower L* for electrons at μ ≲ 10 MeV/G. Our study provides new insight into the rapid change of the radiation belt electron spectral types in response to solar wind disturbances, which could be fully considered in further radiation belt particle modeling.

Wave–particle interactions in tokamaks

Transport consequences of the wave–particle interactions in the quasilinear plateau (QP) regime are presented. Eulerian approach is adopted to solve the drift kinetic equation that includes the physics of the nonlinear trapping (NT) and QP regimes. The localization of the perturbed distribution simplifies the test particle collision operator. It is shown that a mirror force like term responsible for the flattening of the distribution in the NT regime is subdominant in the QP regime, and controls the transition between these two regimes. Transport fluxes, flux-power relation, and nonlinear damping or growth rate are all calculated. There is no explicit collision frequency dependence in these quantities; however, the width of the resonance does. Formulas that join the asymptotic results of these two regimes to facilitate thermal and energetic particle transport, and nonlinear wave evolution of a single mode are presented.

Langmuir wave dynamics and plasma instabilities: Insights from generalized coupled nonlinear Schrödinger equations

This study aims to tackle the generalized coupled nonlinear Schrödinger ([Formula: see text] – [Formula: see text]) equations, with a focus on understanding their physical significance and stability, especially in the realm of plasma physics. These equations are crucial for grasping the complex dynamics of wave interactions within plasma systems, which are fundamental for phenomena like wave-particle interactions, turbulence, and magnetic confinement. We employ analytical methods such as the generalized rational ([Formula: see text]at) and Khater II ([Formula: see text]hat.II) techniques, along with characterizing the system using Hamiltonian principles, to carefully examine the stability of solutions. The relevance of this model extends across various plasma phenomena, including electromagnetic wave propagation, Langmuir wave dynamics, and plasma instabilities. By applying these analytical techniques, we derive solutions and investigate their stability using Hamiltonian dynamics, providing valuable insights into the fundamental behavior of nonlinear plasma waves. Our findings reveal the existence of stable solutions under specific conditions, thus advancing our understanding of plasma dynamics significantly. This research carries significant implications for fields such as plasma physics, astrophysics, and fusion research, where a deep understanding of plasma wave stability and dynamics is crucial. Essentially, our study represents a scholarly effort to offer fresh perspectives on the behavior of [Formula: see text] – [Formula: see text] equations within plasma systems, contributing to the academic discourse on plasma wave phenomena.

Unusually Low-frequency Whistler-mode Waves and Their Association with High-energy Protons Observed Upstream of Martian Bow Shock

Whistler-mode waves upstream of planetary bow shock are often referred to as “1-Hz waves” due to the center of their observed frequency range being at ∼1 Hz. A series of whistler-mode waves were observed upstream of the Martian bow shock by MAVEN on 2015 August 14, with unusually low frequencies centered at ∼0.4 Hz. These waves were accompanied (though not synchronized) by the significant flux enhancement of high-energy protons up to ∼10 keV. By analyzing the wave dispersion property and the wave–particle interaction condition, we find that the observed whistler-mode waves have the potential of resonating with protons of ∼1 keV with large pitch angles up to nearly perpendicular to the background magnetic field, thereby providing a feasible means of accounting for proton acceleration. Our results indicate the possible origin of energized protons in the Martian environment through the interaction with whistler-mode waves, and their potential relationship with the unique upstream conditions.

The fractional soliton solutions of dynamical system arising in plasma physics: The comparative analysis

In light of fractional theory, this paper presents several new effective solitonic formulations for the Langmuir and ion sound wave equations. Prior to this study, no previous research has presented the comparision and obtained the generalized fractional soliton solutions of this kind with power law kernel and Mittag-Leffler kernel. The ion sound and Langmuir wave equations are essential in plasma physics, offering insights into the collective behavior of charged particles in plasmas and enabling diagnostics and control of these complex, ionized gas systems. The two distinct fractional order differential operators are substituted for the traditional order derivative to reshape the examined model. The Atangana-Baleanu non-singular and non-local operator and conformable fractional operator are the fractional-order operators that are used to create the fractional complex system equations for Langmuir waves and ion sound. A constructive approach new auxiliary equation method utilizes to obtain the exact analytical soliton solutions for ion sound and Langmuir wave equation. A wide range of soliton solutions is obtained, including mixed complex solitary shock solutions, singular solutions, mixed shock singular solutions, mixed trigonometric solutions, mixed singular solutions, exact solutions, mixed periodic solutions, and mixed hyperbolic solutions, dark soliton, bright soliton, trigonometric solutions, periodic results, and hyperbolic results. The solitons solution of the ion sound and Langmuir wave equations lies in their ability to maintain wave stability, their role in modeling wave propagation and nonlinear effects, their potential use as diagnostic tools, and their relevance in wave-particle interactions in plasma physics. The solitons provide a valuable framework for understanding the behavior of waves in plasmas and offer insights into the complex dynamics of these charged particle systems. A graphical comparison analysis of a few solutions is also shown here, taking into account appropriate parametric values through the use of the software package. Moreover, the results of this study have important implications for Hamilton's equations and generalized momentum, where solitons are employed in long-range interactions.

Anomalous Resistivity and Electron Heating by Lower Hybrid Drift Waves during Magnetic Reconnection with a Guide Field.

The lower hybrid drift wave (LHDW) has been a candidate for anomalous resistivity and electron heating inside the electron diffusion region of magnetic reconnection. In a laboratory reconnection layer with a finite guide field, quasielectrostatic LHDW (ES-LHDW) propagating along the direction nearly perpendicular to the local magnetic field is excited in the electron diffusion region. ES-LHDW generates large density fluctuations (δn_{e}, about 25% of the mean density) that are correlated with fluctuations in the out-of-plane electric field (δE_{Y}, about twice larger than the mean reconnection electric field). With a small phase difference (∼30°) between two fluctuating quantities, the anomalous resistivity associated with the observed ES-LHDW is twice larger than the classical resistivity and accounts for 20% of the mean reconnection electric field. After we verify the linear relationship between δn_{e} and δE_{Y}, anomalous electron heating by LHDW is estimated by a quasilinear analysis. The estimated electron heating is about 2.6±0.3 MW/m^{3}, which exceeds the classical Ohmic heating of about 2.0±0.2 MW/m^{3}. This LHDW-driven heating is consistent with the observed trend of higher electron temperatures when the wave amplitude is larger. Presented results provide the first direct estimate of anomalous resistivity and electron heating power by LHDW, which demonstrates the importance of wave-particle interactions in magnetic reconnection.

Dynamics of the breather and solitary waves in plasma using the generalized variable coefficient Gardner equation

This paper presents an analytical approach to study the generalized variable coefficient Gardner equation, aiming to investigate the behaviour of plasma phenomena, which presents challenges due to the non-linear nature of the Gardner equation. The point symmetry group associated with the proposed equation is determined by Lie symmetry analysis. The Exp-function method is employed to construct exact travelling wave solutions and to obtain anomalous solutions with non-zero amplitude. Additionally, conservation laws are derived and analysed from the equation in the frame of Noether symmetry. Through simulation, breather, periodic, and localized solitary wave solutions are also presented in graphical form. Our results are expected to elucidate the impact of the equation in the study of the propagation of Alfvén waves with non-uniform density, temperature, and wave-particle interactions in a magnetized plasma.

Quantifying the diffusion of suprathermal electrons by whistler waves between 0.2 and 1 AU with Solar Orbiter and Parker Solar Probe

Context. The evolution of the solar wind electron distribution function with heliocentric distance exhibits different features that are still unexplained, in particular, the fast decrease in the electron heat flux and the increase in the Strahl pitch angle width. Wave-particle interactions between electrons and whistler waves are often proposed to explain these phenomena. Aims. We aim to quantify the effect of whistler waves on suprathermal electrons as a function of heliocentric distance. Methods. We first performed a statistical analysis of whistler waves (occurrence and properties) observed by Solar Orbiter and Parker Solar Probe between 0.2 and 1 AU. The wave characteristics were then used to compute the diffusion coefficients for solar wind suprathermal electrons in the framework of quasi-linear theory. These coefficients were integrated to deduce the overall effect of whistler waves on electrons along their propagation. Results. About 110 000 whistler wave packets were detected and characterized in the plasma frame, including their direction of propagation with respect to the background magnetic field and their radial direction of propagation. Most waves are aligned with the magnetic field and only ∼0.5% of them have a propagation angle greater than 45°. Beyond 0.3 AU, it is almost exclusively quasi-parallel waves propagating anti-sunward (some of them are found sunward but are within switchbacks with a change of sign of the radial component of the background magnetic) that are observed. Thus, these waves are found to be Strahl-aligned and not counter-streaming. At 0.2 AU, we find both Strahl-aligned and counter-streaming quasi-parallel whistler waves. Conclusions. Beyond 0.3 AU, the integrated diffusion coefficients show that the observed waves are sufficient to explain the measured Strahl pitch angle evolution and effective in isotropizing the halo. Strahl diffusion is mainly attributed to whistler waves with a propagation angle of θ ∈ [15.45]°, although their origin has not yet been fully determined. Near 0.2 AU, counter-streaming whistler waves are able to diffuse the Strahl electrons more efficiently than the Strahl-aligned waves by two orders of magnitude.

Modeling Ion Conic Formation in Io's Auroral Footprint

AbstractEnergetic ions outflowing from Jupiter's atmosphere was observed during Juno's 12th perijove crossing (PJ12) in the vicinity of Io's auroral footprint and reported by prior studies. It was hypothesized that Wave‐Particle Interactions (WPI) with ion cyclotron waves observed coincident with the ion outflow may be responsible for the heating and subsequent outflow. This study uses numerical simulation and data model comparison to test whether ion cyclotron resonant heating is indeed a plausible mechanism to explain the intense ion outflow observed. Our simulations assume that the wave heating is of limited duration due to Io's footprint motion. The simulations are moreover compared to the previously published Jupiter Energetic Particle Detector Instruments (JEDI) observations at high energies, and the lower energy Jovian Auroral Distributions Experiment (JADE) observations that were not previously reported. We find that the ion cyclotron resonant heating mechanism can indeed lead to ion conic formation and strong vertical transport under certain assumptions about the distribution of wave power with altitude. We also find that the ion outflow is energized quickly with very rapid formation of the ion conic distribution. The implications of the intense ion outflow are also examined and it is found that such strong wave heating can lead to a depletion of the topside ionosphere.

A Hamiltonian theory for nonlinear resonant wave–particle interaction in weakly inhomogeneous magnetic field

We develop a Hamiltonian theory for the nonlinear resonant interactions between energetic particles and nonlinear frequency chirping waves in the weakly inhomogeneous magnetic field. A canonical transformation is constructed to separate the fast and slowly varying scales, and the Hamiltonian of the resonant particle is transformed to the local resonance reference frames. The Vlasov equation of the local distribution function moving at the local resonance velocity is obtained using Liouville's theorem. The evolution for the slowly varying wave envelope is derived from the Ampère's law with both cold plasma and energetic particle currents. The Vlasov equation coupled with the wave envelope equation self-consistently describes the dynamics of the deeply trapped resonant particles and the slowly varying coherent wave envelope. The application of the theory to the frequency chirping chorus wave in magnetospheric plasmas is also discussed.

Ultra-relativistic Electron Acceleration during High-intensity Long-duration Continuous Auroral Electrojet Activity Events

Magnetospheric relativistic electrons are accelerated during substorms and strong convection events that occur during high-intensity long-duration continuous auroral electrojet activity (HILDCAA) events, associated with solar wind high-speed streams (coming from coronal holes). From an analysis of ∼2–20 MeV electrons at L ∼ 2–7 measured by the Van Allen Probe satellite, it is shown that ∼3.4–4.1 days long HILDCAA events are characterized by ∼7.2 MeV electron acceleration in the L ∼ 4.0–6.0 region, which occurs ∼2.9–3.4 days after the onset of HILDCAA. The dominant acceleration process is due to wave–particle interactions between magnetospheric electromagnetic chorus waves and substorm-injected ∼100 keV electrons. The longer the HILDCAA and chorus last, the higher the maximum energy of the accelerated relativistic electrons. The acceleration to higher and higher energies is due to a bootstrap mechanism.

Ion cyclotron emission in Maxwellian plasmas

Destabilization of ion cyclotron waves—waves with frequencies close to ion cyclotron harmonics—in inhomogeneous plasmas with Maxwell velocity distribution is considered. A new mechanism of destabilization of these waves is found, whereas the known interaction between cyclotron waves and drift waves is shown to be hardly able to lead to instabilities in realistic tokamak plasmas. Our finding is that the resonance wave–particle interaction in the presence of temperature gradient can change the diamagnetic drift frequency in such a way that the destabilizing influence of the diamagnetic drift exceeds Landau damping. This occurs when the energy of resonance particles is sufficiently high, which is always the case due to the infinite tail of the Maxwell distribution. Particles with higher energies provide a larger ratio of drive to damping, but the number of resonance particles and, thus, instability growth rates are exponentially small when particle energy is very high. Therefore, only moderately suprathermal particles can lead to observable instabilities. A condition for instabilities driven by these particles is obtained. Destabilization of electrostatic cyclotron waves and ordinary cyclotron waves is studied.