Perpendicular Wavenumber Research Articles

Gyrokinetic linear simulation of feedback instability in dipole magnetosphere

We perform a novel linear simulation of the feedback instability by applying a gyrokinetic model to the magnetosphere, where the geomagnetic field is modeled by a dipole magnetic field. In order to avoid huge numerical calculation costs, the effect of the fluctuating mirror force is neglected. It is found that kinetic effects, such as the finite Larmor radius effect and the electron Landau damping, strongly stabilize the feedback instability and form a peak in the perpendicular wave number spectrum of the growth rate. During the linear growth, it is observed that electron free energy has a much larger value than the electromagnetic field perturbation energy. Since such large electron free energy may lead to electron heating and acceleration, it is important to understand its generation mechanism. Analyses based on the energy conservation reveal that the coupling of the non-uniformity of the equilibrium fields along the geomagnetic field and the fluctuating electron distribution gives rise to thermodynamic power generating the electron free energy. A fine velocity space structure around an average Alfvén velocity of the fluctuating electron distribution mainly contributes to drive the thermodynamic power.

Detection of a low-frequency ion instability in a magnetic nozzle

Abstract A low-frequency ion instability, with frequency f I between the ion gyrofrequency and the lower hybrid frequency f c , i < f I ≪ f LH , is detected in an argon plasma expanding in a magnetic nozzle for magnetic fields between 240 < B z , max < 700 G. The frequency of the instability exhibits a linear dependence with magnetic field strength, and the wave amplitude has a radial maximum that would match the location of a conical density structure, i.e. high-density cones. For all of the magnetic field cases analysed, the high-frequency spectra showed upper and lower sidebands centred around the driving frequency and at a separation equal to the instability frequency, 27.12 MHz ± f I kHz. Measurements of the perpendicular wavenumber would satisfy, for certain magnetic field strengths, the dispersion relation of both an electrostatic ion cyclotron wave (ICW) and of an ion acoustic wave. It is hypothesised that the observed low-frequency wave could be an acoustic-like instability propagating perpendicular to the magnetic field, which develops as an ICW at some magnetic field strengths. From the data collected, it is suggested that the high-frequency sidebands may be caused by modulation of the low-frequency wave.

Statistical Observations of Proton‐Band Electromagnetic Ion Cyclotron Waves in the Outer Magnetosphere: Full Wavevector Determination

AbstractElectromagnetic Ion Cyclotron (EMIC) waves mediate energy transfer from the solar wind to the magnetosphere, relativistic electron precipitation, or thermalization of the ring current population, to name a few. How these processes take place depends on the wave properties, such as the wavevector and polarization. However, inferring the wavevector from in‐situ measurements is problematic since one needs to disentangle spatial and time variations. Using 8 years of Magnetospheric Multiscale (MMS) mission observations in the dayside magnetosphere, we present an algorithm to detect proton‐band EMIC waves in the Earth's dayside magnetosphere, and find that they are present roughly 15% of the time. Their normalized frequency presents a dawn‐dusk asymmetry, with waves in the dawn flank magnetosphere having larger frequency than in the dusk, subsolar, and dawn near subsolar region. It is shown that the observations are unstable to the ion cyclotron instability. We obtain the wave polarization and wavevector by comparing Single Value Decomposition and Ampere methods. We observe that for most waves the perpendicular wavenumber (k⊥) is larger than the inverse of the proton gyroradius (ρi), that is, k⊥ρi > 1, while the parallel wavenumber is smaller than the inverse of the ion gyroradius, that is, k‖ρi < 1. Left‐hand polarized waves are associated with small wave normal angles (θBk < 30°), while linearly polarized waves are associated with large wave normal angles (θBk > 30°). This work constitutes, to our knowledge, the first attempt to statistically infer the full wavevector of proton‐band EMIC waves observed in the outer magnetosphere.

Characterization of Turbulent Fluctuations in the Sub-Alfvénic Solar Wind

Parker Solar Probe (PSP) observed sub-Alfvénic solar wind intervals during encounters 8–14, and low-frequency magnetohydrodynamic (MHD) turbulence in these regions may differ from that in super-Alfvénic wind. We apply a new mode decomposition analysis to the sub-Alfvénic flow observed by PSP on 2021 April 28, identifying and characterizing entropy, magnetic islands, forward and backward Alfvén waves, including weakly/nonpropagating Alfvén vortices, forward and backward fast and slow magnetosonic (MS) modes. Density fluctuations are primarily and almost equally entropy- and backward-propagating slow MS modes. The mode decomposition provides phase information (frequency and wavenumber k) for each mode. Entropy density fluctuations have a wavenumber anisotropy of k ∥ ≫ k ⊥, whereas slow-mode density fluctuations have k ⊥ > k ∥. Magnetic field fluctuations are primarily magnetic island modes (δ B i ) with an O(1) smaller contribution from unidirectionally propagating Alfvén waves (δ B A+) giving a variance anisotropy of 〈δBi2〉/〈δBA2〉=4.1 . Incompressible magnetic fluctuations dominate compressible contributions from fast and slow MS modes. The magnetic island spectrum is Kolmogorov-like k⊥−1.6 in perpendicular wavenumber, and the unidirectional Alfvén wave spectra are k∥−1.6 and k⊥−1.5 . Fast MS modes propagate at essentially the Alfvén speed with anticorrelated transverse velocity and magnetic field fluctuations and are almost exclusively magnetic due to β p ≪ 1. Transverse velocity fluctuations are the dominant velocity component in fast MS modes, and longitudinal fluctuations dominate in slow modes. Mode decomposition is an effective tool in identifying the basic building blocks of MHD turbulence and provides detailed phase information about each of the modes.

Switching Between Whistler‐Mode Waves on Inhomogeneities of the Plasma Density and Magnetic Field

AbstractWe present results from the investigation of a transition between two whistler‐mode waves with the same frequency and the parallel wavelength but different perpendicular wavenumbers in the inhomogeneous media consisting of the plasma density and the background magnetic field. We consider transverse inhomogeneities of these quantities. We demonstrate that there are critical values of the plasma density and the magnetic field (which depend on the wave frequency and the parallel wavelength) and the switching between two whistler‐mode waves occurs in the vicinity of these values. We analyze this problem assuming that these critical values are reached inside the finite‐size transition layer between two regions where all the background quantities are homogeneous. We found analytical criteria for the mode switching and we confirmed our results with time‐dependent simulations of the electron‐MHD equations describing whistler‐mode waves in the magnetospheric plasma. We also investigate numerically the dependency of various parameters of the wave switching on the size of the transition region containing critical values of the plasma density and the magnetic field.

Resonant decay of kinetic Alfvén waves and implication on spectral cascading

A general equation describing the resonant nonlinear mode-coupling among kinetic Alfvén waves (KAWs) is derived using nonlinear gyrokinetic theory, which can be applied to study the potentially strong spectral energy transfer of KAWs. As a first application, the parametric decay of a pump KAW into two sideband KAWs is studied, with particular emphasis on cascading in the perpendicular wavenumber. It is found that, for the “co-propagating” cases with all three KAWs propagating in the same direction along the equilibrium magnetic field line, it exhibits a dual cascading character in the perpendicular wavenumber space; while for the “counter-propagating” cases with one sideband propagating in the opposite direction with respect to the pump wave, it instead, can exhibit both dual and inverse cascading behaviors. Furthermore, the implications of these findings on shear Alfvén waves regarding instability, nonlinear saturation, and charged particle transport in fusion plasmas are also discussed.

Introducing electromagnetic effects in Soledge3X

AbstractIn the pedestal region, electromagnetic effects affect the evolution of micro‐instabilities and plasma turbulence. The transport code Soledge3X developed by the CEA offers an efficient framework for turbulent 3D simulation on an electrostatic model with a fixed magnetic field. The physical accuracy of the model is improved with electromagnetic induction, driven by the local value of the parallel component of the electromagnetic vector potential , known from Ampère's law. It is solved implicitly in a coupled system with the vorticity equation on the electric potential . The consequence is a basic electromagnetic behavior in the form of shear Alfvén waves. A finite electron mass prevents unphysical speeds but requires solving for the time evolution of the parallel current density in the generalized Ohm's law. This term can be analytically included with little computational overhead in the system on and and improves its numerical condition, facilitating the iterative solving procedure. Simulations on a periodic slab case let us observe the predicted bifurcation of the wave propagation speed between the Alfvén wave and the electron thermal wave speeds for varying perpendicular wavenumbers. The first results on a circular geometry with a limiter attest to the feasibility of turbulent electromagnetic scenarios.

Small-amplitude Compressible Magnetohydrodynamic Turbulence Modulated by Collisionless Damping in Earth’s Magnetosheath: Observation Matches Theory

Plasma turbulence is a ubiquitous dynamical process that transfers energy across many spatial and temporal scales and affects energetic particle transport. Recent advances in the understanding of compressible magnetohydrodynamic (MHD) turbulence demonstrate the important role of damping in shaping energy distributions on small scales, yet its observational evidence is still lacking. This study provides the first observational evidence of substantial collisionless damping (CD) modulation on the small-amplitude compressible MHD turbulence cascade in Earth’s magnetosheath using four Cluster spacecraft. Based on an improved compressible MHD decomposition algorithm, turbulence is decomposed into three eigenmodes: incompressible Alfvén modes and compressible slow and fast (magnetosonic) modes. Our observations demonstrate that CD enhances the anisotropy of compressible MHD modes because CD has a strong dependence on wave propagation angle. The wavenumber distributions of slow modes are mainly stretched perpendicular to the background magnetic field ( B 0) and weakly modulated by CD. In contrast, fast modes are subjected to a more significant CD modulation. Fast modes exhibit a weak, scale-independent anisotropy above the CD truncation scale. Below the CD truncation scale, the anisotropy of fast modes enhances as wavenumbers increase. As a result, fast-mode fractions in the total energy of compressible modes decrease with the increase of perpendicular wavenumber (to B 0) or wave propagation angle. Our findings reveal how the turbulence cascade is shaped by CD and its consequences for anisotropies in the space environment.

An E-band multi-channel Doppler backscattering system on EAST.

An E-band (60-90 GHz) multi-channel Doppler backscattering (DBS) system with X-mode polarization has been installed on the Experimental Advanced Superconducting Tokamak (EAST), which can measure the turbulence at five different radial locations simultaneously. This system can launch 31 fixed microwave frequencies in the range of 60-90 GHz with a 1GHz interval into the plasma, and five probing signals are selected by employing a reference signal and multiple filters. During experiments, the frequency of the reference signal is tunable in the E-band, and the selected probing signals can be changed as needed without any other adjustments, which can be performed in one shot or between shots. Furthermore, the incident angle can be adjusted from -10° to 20°, and the wavenumber range is 4-25cm-1 with a wavenumber resolution of Δk/k ≤ 0.35. Ray tracing simulations are employed to calculate the scattering locations and the perpendicular wavenumber. In this article, the hardware design, ray tracing, and initial results obtained from the EAST plasma will be presented.

Oblique Bernstein wave propagation in electron‐ion plasma with electron quantization effects

AbstractWe have studied the role of electron quantization effects on the dispersion characteristics of the oblique electron Bernstein wave (EBW) in an electron‐ion plasma using Vlasov‐Poisson model. Our analysis shows that large thermal effects (as compared to quantization effects) give rise to the usual classical results while in the limit of strong magnetic field, the dispersion characteristics changes. The existence of a quantum Bernstein mode has been proposed which appears purely due to the electron quantization effects. The damping of the oblique EBW has also been analyzed in detail and we found that the magnitude of the damping of the wave decreases as we decrease the obliqueness parameter (parallel to perpendicular wavenumber ratio) which agrees with the earlier theoretical and experimental findings. Moreover, the strong quantization effects () also tend to suppress the damping of EBW which contributes to the stabilization of the waves. The present findings are relevant to the laboratory laser‐produced plasmas where strong external magnetic fields exist, and also to the dense astrophysical plasma environments.

Anisotropic Energy Transfer and Conversion in Magnetized Compressible Turbulence

We present a spatial filtering (or coarse-graining) analysis on 3D magnetized magnetohydrodynamic (MHD) turbulence simulations. The filtered compressible MHD formulae show transfer of kinetic and magnetic energies from large to small scales, as well as energy conversion between kinetic, magnetic, and thermal energies. The anisotropic filtering enables separate analyses of the energy flows perpendicular and parallel to the global mean magnetic field. Anisotropy in energy cascade is demonstrated by the larger perpendicular energy cascade rate and also the larger perpendicular wavenumbers associated with the peak energy transfer rate. We also find that the “inertial range” along the parallel (perpendicular) direction in the anisotropic energy cascade formulation is no longer strictly dissipation-free, because it includes the dissipation in the perpendicular (parallel) direction. A change in the driving force (kinetic only versus kinetic and magnetic) affects the energy conversion between kinetic and magnetic energies. While the compressibility of the driving force changes the partition of different channels of energy transfer and conversion, and also increases the total energy transfer rate, the global energy flow remains unaffected by compressibility qualitatively. Our analysis can be applied to multispacecraft observations of turbulence in the solar wind or a planetary magnetosphere.

Generation of an obliquely propagating shear alfven wave in dusty plasma by an ion beam

AbstractIon beam‐dusty plasma interaction leads to significant changes in the dispersion relation of shear Alfven wave depending on the beam, dust grain, and plasma parameters. Hydrogen ion beam particles interact with the shear Alfven wave via cyclotron interaction when they counter‐propagate with the wave and they can also interact with the co‐propagating wave via Cerenkov interaction. The interaction causes beam as well as plasma density fluctuations and gives rise to perpendicular currents. We have analytically obtained the dispersion relation and the growth/damping rate expressions for obliquely propagating shear Alfven waves in dusty plasma. The effect of beam velocity, magnetic field, wave number, dust particle density, and dust charge fluctuations are discussed. It is shown that both the wave frequency and the maximum growth rate decrease with an increase in beam velocity and the variations are different for parallel and perpendicular wave numbers. The dust particles enhance the frequency and maximum growth rate while the dust charge fluctuations induce damping. The results are in good agreement with the experimental observations.

Receiver circuit improvement of dual frequency-comb ka-band Doppler backscattering system in the large helical device (LHD).

Doppler-backscattering (DBS) has been used in several fusion plasma devices because it can measure the perpendicular velocity of electron density perturbation v⊥, the radial electric field Er, and the perpendicular wavenumber spectrum S(k⊥) with high wavenumber and spatial resolution. In particular, recently constructed frequency comb DBS systems enable observation of turbulent phenomena at multiple observation points in the radial direction. A dual-comb microwave DBS system has been developed for the large helical device plasma measurement. Since it is desirable to control the gain of each frequency-comb separately, a frequency-comb DBS system was developed with a function to adjust the gain of the scattered signal intensity of each channel separately. A correction processing method was also developed to correct the amplitude ratio and the phase difference between the in-phase and quadrature-phase signals of the scattered signals. As a result, the error in Doppler-shift estimation required to observe vertical velocity and the radial electric field was reduced, which enables more precise measurements.

Numerical implementation of the improved Sugama collision operator using a moment approach

The numerical implementation of the linearized gyrokinetic and drift-kinetic improved Sugama (IS) collision operators, recently introduced by Sugama et al. [Phys. Plasmas 26, 102108 (2019)], is reported. The IS collision operator extends the validity of the widely used original Sugama (OS) operator [Sugama et al., Phys. Plasmas 16, 112503 (2009)] to the Pfirsch–Schlüter collisionality regime. Using a Hermite–Laguerre velocity–space decomposition of the perturbed gyrocenter distribution function that we refer to as the gyro-moment approach, the IS collision operator is written in a form of algebraic coefficients that depend on the mass and temperature ratios of the colliding species and perpendicular wavenumber. A comparison between the IS, OS, and Coulomb collision operators is performed, showing that the IS collision operator is able to approximate the Coulomb collision operator in the case of trapped electron mode in H-mode pedestal conditions better than the OS operator. In addition, the IS operator leads to a level of zonal flow residual which has an intermediate value between the Coulomb and the OS collision operators. The IS operator is also shown to predict a parallel electrical conductivity that approaches the one of the Coulomb operator within less than 1%, while the OS operator can underestimate the parallel electron current by at least 10%. Finally, closed analytical formulas of the lowest order gyro-moments of the IS, OS, and Coulomb operators are given, which are ready to use to describe the collisional effects in reduced gyro-moment fluid models.

Simulating the filamentation of smoothed laser beams with three-dimensional nonlinear dynamics

In a plasma, the ponderomotive force of an inhomogeneous electromagnetic field expels plasma from regions of high intensity. When a laser propagates through a plasma, this force creates density wells that subsequently modify the index of refraction. The beam refracts and focuses into these wells and may filament. In extreme cases, the laser beam will spray due to increasing angular divergence of the beam. The threshold for ponderomotive self-focusing is well established for isolated laser hotspots or speckles. Here, we define a practical threshold for characterizing the filamentation of thousands of speckles that are found in the focal plane of high-power laser beams spatially smoothed with random phase plates as used at high energy and power laser facilities studying inertial confinement fusion. This threshold is tested against three-dimensional simulations of speckled laser light propagating through plasma. Four metrics are applied to assess filamentation: the fraction of power above five times the average intensity, an effective f-number, the mean-squared perpendicular wavenumber, and the fraction of rarefied density with deviation from the initial density exceeding |δn/n| = 0.1. The speckled beams studied are generated by random phase plates, both with and without additional polarization smoothing, in a parameter regime of relevance to indirect drive experiments. While filamentation has been discussed extensively in the literature, we believe this to be the first published simulation study with three-dimensional nonlinear hydrodynamics that addresses the onset threshold of ponderomotive filamentation and establishes the lengths and time scales necessary to reach a statistical steady state.

Quantum edge plasmon excitations and electron spill-out effect

In this paper, by using the effective Schrödinger–Poisson model, we investigate quantum edge plasmon excitations and electron spill-out effect in an arbitrary degenerate electron gas in the presence of perpendicular electron drift momentum. It is found that the single-electron Schrödinger equation solution produces a nonoscillatory electron number density distribution on the interface showing characteristic surface-dipole and electron spill-out effects. However, the Schrödinger–Poisson model produces large amplitude dual-tone density distribution due to both wave-like and particle-like plasmon dispersion other than surface-dipole and electron spill-out effects. The variations in the density structure are investigated in terms of different parameters such as the chemical potential, temperature, quantum electron tunneling parameter, and perpendicular electron de Broglie's wavenumber. Furthermore, we extend our study to the case of collective electron tunneling and reveal that the interface potential energy significantly differs from the case of single-electron quantum tunneling and strongly depends on the electron gas parameters. The current study reveals interesting features of the transverse plasmon excitations and electron spill-out in a current carrying narrow metal slab or metal–dielectric quantum sandwich interfaces incorporating both single-electron and collective quantum tunneling.

Investigation of Kinetic Ballooning Instability in 2D Harris Sheet Equilibrium With Finite Normal B z Field

Substorm onset is believed to be a fundamental process for magnetic and plasma energy transport in both magnetosphere and ionosphere. In this regard, the ballooning instability is considered to be one of the key trigger mechanism for the substorm onset scenario in the near-Earth plasma sheet. Here, the kinetic ballooning instability (KBI) in the near-Earth magnetotail is analyzed using the two-dimensional (2D) generalized Harris sheet and Voigt equilibrium models. The corresponding kinetic ballooning mode is unstable in the intermediate range of perpendicular wave number (ky) and the equatorial beta (βeq). We further note that the growth rate of the ballooning mode reduces significantly with the increase in electron-to-ion temperatures ratio (Te/Ti) and wave number ky. The kinetic ballooning mode is found to be most unstable in a thin current sheet region at the equatorial location xe ∼ (8.5 − 10)RE, where the ballooning drive term (βeq/LpRc) is dominant on stiffening effect due to minimum in normal magnetic field. Because of the stabilizing effect as caused by the field line stiffening and the strong field line stabilization, the ballooning mode is stable (marginally unstable) close (away) from the Earth. The magnitude of the KBI growth rates as a function of the equatorial beta βeq and location xe for a wide and thin current sheets using the Voigt equilibrium model are smaller than the Harris sheet counterpart, which are used for modeling the near-Earth plasma sheet configuration for the slow and fast substorm growth phases, respectively. The results suggest that the excitation of KBI through the local current sheet thinning may also be an effective trigger mechanism for the substorm onset in the near-Earth magnetotail. This article is protected by copyright. All rights reserved.

Three-dimensional Hybrid Simulation Results of a Variable Magnetic Helicity Signature at Proton Kinetic Scales

Abstract Three-dimensional hybrid kinetic simulations are conducted with particle protons and warm fluid electrons. Alfvénic fluctuations initialized at large scales and with wavevectors that are highly oblique with respect to the background magnetic field evolve into a turbulent energy cascade that dissipates at proton kinetic scales. Accompanying the proton scales is a spectral magnetic helicity signature with a peak in magnitude. A series of simulation runs are made with different large-scale cross helicity and different initial fluctuation phases and wavevector configurations. From the simulations a so-called total magnetic helicity peak is evaluated by summing contributions at a wavenumber perpendicular to the background magnetic field. The total is then compared with the reduced magnetic helicity calculated along spacecraft-like trajectories through the simulation box. The reduced combines the helicity from different perpendicular wavenumbers and depends on the sampling direction. The total is then the better physical quantity to characterize the turbulence. On average the ratio of reduced to total is 0.45. The total magnetic helicity and the reduced magnetic helicity show intrinsic variability based on initial fluctuation conditions. This variability can contribute to the scatter found in the observed distribution of solar wind reduced magnetic helicity as a function of cross helicity.

Determining Parameters of Whistler Waves Trapped in High‐Density Ducts

AbstractWe investigate the possibility of identifying the perpendicular and parallel wavelengths (or wave numbers) of the very‐low‐frequency (VLF) whistler‐mode waves trapped inside the high‐density duct. This will be done by using information about the wave frequency, background magnetic field, and plasma density inside and outside of the duct. This data is collected from observations by the Van Allen Probes satellites. We developed a three‐step procedure based on the analysis of the whistler wave dispersion relation and numerical simulations of the electron‐magnetohydrodynamics model. We use this model to identify the parallel and perpendicular wave numbers of the “most trapped” wave. The first two steps of this procedure identify the ranges of the parallel and perpendicular wavelengths of the waves trapped inside the duct. The third step uses numerical simulations to determine the parameters of the “most trapped” wave from the aforementioned ranges. This procedure has been applied to the retrieved data from the Van Allen Probes in order to analyze the structure of VLF waves observed in the equatorial magnetosphere.

Kinetic Alfvén waves in a deuterium-tritium fusion plasma with slowing-down distributed α-particles

The dispersion relation and damping rate of kinetic Alfvén waves (KAWs) in a deuterium-tritium fusion plasma with slowing-down distributed α-particles are investigated using the kinetic theory. The variations of wave frequency and damping rate with respect to the α concentration (nα /n e) and perpendicular wave number (k ⊥) are studied from a numerical way. The results show that the fluctuation of α concentration slightly affects the frequency and damping rate of KAWs at low nα /n e. In addition, the frequency and the damping rate increase as the k ⊥ and the background temperature T e increase. For comparison, the calculations are performed also in the case of α-particles following an equivalent Maxwellian distribution. For a given k ⊥, the value of the frequency obtained in the slowing-down distribution case is smaller than that obtained in the Maxwellian distribution case. Conversely, the value of the damping rate obtained in the slowing-down distribution case is slightly larger than that obtained in the Maxwellian distribution case.