Loss-cone Distribution Research Articles

Implications of Asymmetric Loss Cone Distribution on Whistler‐Driven Electron Precipitation at Mercury

AbstractMercury has a large loss cone difference in its two hemispheres due to the northward shifted magnetic dipole. The precipitation difference of energetic electrons in both hemispheres is poorly understood. We show that the northern precipitation is 2.5‐times higher than for a symmetric loss cone due to the effects of the enhanced whistler instability at the southern hemisphere with the larger loss cone. Simulations including nonlinear pitch angle scattering by the whistler‐mode waves show rapid (tens of milliseconds) electron flux modulation related to the wave subpacket structures by repeated interactions within a discrete wave element. The difference in the nonlinear whistler instability in the two hemispheres should enhance the electron precipitation, which, along with the direct impact effects of solar wind, contributes to Mercury's surface–magnetosphere coupling. Electrons hitting the planet's surface may be a possible factor in the formation of water through the formation of hydroxyl groups.

Modulation instability of whistler wave with electron loss cone distribution in magnetized plasma

Abstract The modulation instability of whistler mode waves caused by thermal electron anisotropy is studied. Based on MHD equations, the nonlinear schrödinger equation (NLSE) that describes the nonlinear modulation of whistler waves is derived by Using the Krylov-Bogoliubov-Mitropolsky (KBM) method. The condition for wave modulation instability is obtained from the loss cone distribution function of thermal electron anisotropy, revealing that the nonlinear growth of the waves tends towards electron perpendicular temperature anisotropy. By setting up continuous background waves and introducing small ion low frequency perturbations, we find that the change in the amplitude of the modulated wave is related with wave number. This finding has been validated through simulations that align with our analytical results. Additionally, we also calculate the maximum amplitude of the wave with loss cone angle and times, which revealed that the electron vertical temperature anisotropy will lead to the modulation instability of the whistler wave. This further confirms the occurrence of the modulation instability of the whistler wave in laboratory plasmas and strengthens their credibility.

Variation of Electron Lifetime Due To Scattering by Electrostatic Electron Cyclotron Harmonic Waves in the Inner Magnetosphere With Electron Distribution Parameters

AbstractThrough resonant wave‐particle interactions with electrostatic electron cyclotron harmonic (ECH) waves, low‐energy plasma sheet electrons can be scattered into the atmospheric loss cone and precipitate. This process can be investigated by calculating bounce‐averaged quasi‐linear diffusion coefficients. However, the numerical calculation of ECH wave‐induced scattering rates requires the specification of several parameters, including the properties of the hot plasma sheet electrons responsible for the wave excitation. The dependence of the diffusion coefficients on these parameters and the exact contribution of scattering by ECH waves to diffuse auroral precipitation is still poorly understood and has not been carefully quantified yet. In this study, we calculate bounce‐averaged quasi‐linear scattering rates and compare the resulting lifetimes to the strong diffusion limit. We vary the temperature, plasma density, and loss cone parameters of the hot component in the electron loss cone distribution over a large range based on previous studies and observations. By adopting a new model that derives the wave normal angle from the midpoint and the angular width of the growth rate profile, our findings suggest that the electron lifetime near the loss cone is not significantly affected by the hot electron temperature and loss cone parameters. However, there is an increase in electron lifetimes with increasing plasma density. For an electric field amplitude of 1 mV/m, the electron lifetime is below or equal to the lifetime calculated using the strong diffusion limit up to E = 0.25 keV when n = 1.5 cm−3, and up to E = 0.22 keV when n = 9 cm−3.

Effect of Beam Velocity on Firehose Instability in Earth’s Magneto-plasma with General Loss-Cone Distribution Function

The dynamics of firehose instability (FHI) in the presence of beams is investigated by applying kinetic theory and general loss cone distribution (GLCD) function. It is explained how ion/electron beams affect the growth rate and length of the FHI in low beta homogeneous plasma. The energy of the transversely heated ions is found to be reduced by the ion beam, whereas the temperature anisotropy arranges free energy, to begin with, and accelerates the growth rate of the instability. It has been discovered that the firehose instability results from the extraction of energy from ions heated perpendicularly in the presence of upflowing ion beams in the asymmetrical magneto-plasma. In the auroral acceleration region, the findings are expressed in terms of the firehose instability. The findings may be checked and then may be applied in dusty and multi-component space plasma also.

Electrostatic Waves Around a Magnetopause Reconnection Secondary Electron Diffusion Region Modulated by Whistler and Lower‐Hybrid Waves

AbstractWe investigate electrostatic waves in a magnetopause reconnection event around a secondary electron diffusion region. Near the current sheet mid‐plane, parallel electron beam‐mode waves are modulated by whistler waves. We conclude that the anisotropy of energized electrons in the reconnection exhaust excites whistler waves, which produce spatially modulated electron beams through nonlinear Landau resonance, and these beams excite beam‐mode electrostatic waves. In the separatrix region, parallel propagating electrostatic waves associated with field‐aligned electron beams and perpendicular propagating electron cyclotron harmonic waves with loss cone distributions exhibit modulation frequencies in the lower‐hybrid wave (LHW) frequency range. We infer that LHWs scatter electrons to produce beams and alter loss cones to modulate electrostatic waves. The results advance our understanding about the regimes and mechanisms of electrostatic waves in reconnection, with an emphasis on their coupling with lower‐frequency electromagnetic waves.

Electrostatic upper-hybrid mode instability driven by a ring electron distribution

Quasi electrostatic fluctuations in the upper-hybrid frequency range are commonly detected in the planetary magnetospheric environment. The origin of such phenomena may relate to the instability driven by a loss-cone feature associated with the electrons populating the dipole-like magnetic field. The present paper carries out a one-dimensional electrostatic particle-in-cell simulation accompanied by a reduced quasilinear kinetic theoretical analysis to investigate the dynamics of the upper-hybrid mode instability driven by an initial ring electron distribution function, which is a form of loss-cone distribution. A favorable comparison is found between the two approaches, which shows that the reduced quasilinear theory, which is grounded in the concept of a model of the particle distribution function that is assumed to maintain a fixed mathematical form except that the macroscopic parameters that define the distribution are allowed to evolve in time, can be an effective tool in the study of plasma instabilities, especially if it is guided by and validated against the more rigorous simulation result.

Toward developing a comprehensive algorithm for solving kinetic plasma dispersion relations for parallel propagation with a kappa distribution

In general, it is challenging to numerically solve all the roots of plasma wave dispersion relations. The velocity distributions of multi-component particles in an anisotropic high-energy plasma can be better described by a drift loss-cone bi-Kappa distribution or a mixed drift loss-cone distribution containing bi-Kappa and bi-Maxwellian plasma in space and laboratories. In this work, we have developed a code with a new numerical algorithm to solve all roots of the kinetic dispersion relation for parallel propagation in hot magnetized plasmas with drift loss-cone bi-Kappa distribution. Solving all roots of the rational expansions of the kinetic dispersion relation is equivalent to a matrix eigenvalue problem of a linear system. We have performed detailed numerical solutions for three kinds of plasmas: bi-Maxwellian, bi-Kappa, and cold plasmas. We have also proposed a unified numerical method to solve the mixed dispersion relation based on the bi-Kappa and bi-Maxwellian distributions. The numerical results and benchmark studies demonstrate that the new algorithm is in agreement with the data from previous studies. This is a crucial step toward revealing a full picture of kinetic plasma waves and instabilities.

Analytical evaluation of the Dnestrovskii functions occurring in weakly relativistic, magnetized, and thermal plasmas

AbstractIn this paper, we established an effective formula for Dnestrovskii functions based on the binomial expansion theorem which frequently appears in a weakly relativistic loss cone distribution, relativistic, magnetized, and thermal plasmas. The obtained formulas are expressed in terms of binomial coefficients and incomplete Gamma functions. Therefore, the proposed approach is a fully useful method to evaluate Dnestrovskii functions and related physical properties of plasmas. Calculation results of the Dnestrovskii functions are compared with other numerical and theoretical models and indicated acceptable agreement. The results of the calculations demonstrate that the derived formula is valid for a wide range of parameters.

Excitation of Saturnian ECH Waves Within Remote Plasma Injections: Cassini Observations

AbstractBased on Cassini observations, we report representative electrostatic electron cyclotron harmonic (ECH) wave events observed in Saturn's magnetosphere within remote plasma injections. Unlike local injections, remote injections are “older” injection events that have evolved to form a dispersed signature in particle energy spectrum. We show that Saturnian ECH waves within remote injections present a strong fundamental band and much weaker high harmonic bands. By calculating the linear wave growth rates based on the measured electron velocity distributions, we indicate that Saturnian ECH waves can be excited by the loss cone distribution of remotely injected, hot electrons of ∼100 eV to several keV. We find that ECH waves tend to intensify with increased fluxes of injected hot electrons but weakening with increased evolution time of the flux tubes, which is consistent with the results of wave growth rates and improves the current understanding of the generation of ECH waves at Saturn.

Electron distribution-controlled electron cyclotron harmonic wave generation in the magnetosphere

Electron cyclotron harmonic (ECH) waves, contributing significantly to magnetospheric dynamics, usually appear as a series of harmonics between the multiples of electron gyrofrequency. Previous studies have demonstrated that ECH waves are the electron Bernstein mode excited by the electron loss cone distribution. To investigate how the electron distribution controls the frequency and wave normal angle of excited ECH waves, we derive a concise analytic formula for ECH growth rates using the bi-Maxwellian distribution. Parametric studies show that the expansion of the loss cone size could effectively enlarge ECH growth rates and move the peak growth rates to a smaller wave number k (higher frequency) region, while the deepening of the loss cone can only increase the growth rates. It is also found that the growth rate pattern in the k space exhibits different trends on the two sides of 1.5 fce because the dominant resonance orders on the two sides are different. This study further develops our understanding of the generation mechanism of ECH waves.

Zebra Stripes with High Gyro-Harmonic Numbers

Solar radio zebras are used in the determination of the plasma density and magnetic field in solar flare plasmas. Analyzing observed zebra stripes and assuming their generation by the double-plasma resonance (DPR) instability, high values of the gyro-harmonic number are found. In some cases they exceed one hundred, in disagreement with the DPR growth rates computed up to now, which decrease with increasing gyro-harmonic number. We address the question of how zebras with high values of the gyro-harmonic numbers s are generated. For this purpose, we compute the growth rates of the DPR instability in a very broad range of s, considering a loss-cone kappa-distribution of superthermal electrons and varying the loss-cone angle, electron energies, and background plasma temperature. We have numerically calculated the dispersion relations and the growth rates of the upper-hybrid waves and found that the growth rates increase with increasing gyro-harmonic numbers if the loss-cone angles are sim80^{circ}. The highest growth rates for these loss-cone angles are obtained for velocity v_{kappa}= 0.15,c. The growth rates as a function of the gyro-harmonic number still show well distinct peaks, which correspond to zebra-stripe frequencies. The contrast between peak growth rates and surrounding growth rate levels increases as the kappa index increases and the background temperature decreases. Zebras with high values of s can be generated in regions where loss-cone distributions of superthermal electrons with large loss-cone angles (sim80^{circ}) are present. Furthermore, owing to the high values of s, the magnetic field is relatively weak and has a small spatial gradient in such regions.

Wavelength Measurements of Electron Cyclotron Harmonic Waves in Earth's Magnetotail

AbstractElectron cyclotron harmonic (ECH) waves, potential drivers for diffuse aurora precipitation, have been extensively investigated for decades. The generation mechanism of ECH waves, however, remains an open question. Theoretical work in 1970s has demonstrated that ECH waves can be excited by loss cone distributions of hot plasma sheet electrons. Recent THEMIS spacecraft observations, however, indicate that the waves can also be excited by low energy electron beams. Utilizing interferometry techniques to analyze the phase difference between electric potentials measured by individual probes on Electric Field Instrument antenna pairs on THEMIS spacecraft, we compute the wavenumber of both beam‐driven ECH waves and loss‐cone‐driven ECH waves. These wavenumber measurements as well as other wave properties obtained from spacecraft measurements prove to be consistent with expectation from linear instability analysis. This provides us with independent verification of the generation mechanism and linear dispersion relation of beam‐driven and loss‐cone‐driven ECH waves. Our statistical results demonstrate that the median value of the wave vectors of beam‐driven ECH waves, characterized by wave normal angles () less than 80°, is 0.011 m−1; and that of loss‐cone‐driven ECH waves, characterized by wave normal angles larger than 85°, is 0.00765 m−1. Direct wavenumber measurements of ECH waves allow us to better understand the interaction between ECH waves and electrons in Earth's magnetosphere.

Kinetic simulations of collision-less plasmas in open magnetic geometries *

Laboratory plasmas in open magnetic geometries can be found in many different applications such as (a) scrape-of-layer (SOL) and divertor regions in toroidal confinement fusion devices, (b) linear divertor simulators, (c) plasma-based thrusters and (d) magnetic mirrors etc. A common feature of these plasma systems is the need to resolve, in addition to velocity space, at least one physical dimension (e.g. along flux lines) to capture the relevant physics. In general, this requires a kinetic treatment. Fully kinetic particle-in-cell (PIC) simulations can be applied but at the expense of large computational effort. A common way to resolve this is to use a hybrid approach: kinetic ions and fluid electrons. In the present work, the development of a hybrid PIC computational tool suitable for open magnetic geometries is described which includes (a) the effect of non-uniform magnetic fields, (b) finite fully-absorbing boundaries for the particles and (c) volumetric particle sources. Analytical expressions for the momentum transport in the paraxial limit are presented with their underlying assumptions and are used to validate the results from the PIC simulations. A general method is described to construct discrete particle distribution functions in a state of mirror-equilibrium. This method is used to obtain the initial state for the PIC simulation. Collisionless simulations in a mirror geometry are performed. The results show that the effect of magnetic compression is correctly described and momentum is conserved. The self-consistent electric field is calculated and is shown to modify the ion velocity distribution function in a manner consistent with analytic theory. Based on this analysis, the ion distribution function is understood in terms of a loss-cone distribution and an isotropic Maxwell-Boltzmann distribution driven by a volumetric plasma source. Finally, the inclusion of a Monte Carlo based Fokker-Planck collision operator is discussed in the context of future work.

Harmonic Maser Emissions from Electrons with Loss-cone Distribution in Solar Active Regions

Abstract Electron cyclotron maser emission (ECME) is regarded as a plausible source for coherent radio radiations from solar active regions (e.g., solar radio spikes). In this Letter, we present a 2D3V fully kinetic electromagnetic particle-in-cell simulation to investigate the wave excitations and subsequent nonlinear processes induced by the energetic electrons in the loss-cone distribution. The ratio of the plasma frequency to the electron gyrofrequency ω pe/Ωce is set to 0.25, adequate for solar active region conditions. As a main result, we obtain strong emissions at the second-harmonic X mode (X2). While the fundamental X mode (X1) and the Z mode are amplified directly via the electron cyclotron maser instability, the X2 emissions can be produced by nonlinear coalescence between two Z modes and between Z and X1 modes. This represents a novel generation mechanism for the harmonic emissions in plasmas with a low value of ω pe/Ωce, which may resolve the escaping difficulty of explaining solar radio emissions with the ECME mechanism.

Nonlocal Theory of Excitation of Electron Bernstein Waves by a Relativistic Electron Beam in Plasma with Loss-Cone Distribution of Electron

A nonlocal theory of excitation of electron Bernstein waves in a magnetized plasma slab by a relativistic electron beam with loss-cone distribution of electrons is presented. Kinetic theory is employed to obtain the susceptibility of plasma electrons whereas fluid theory is used to obtain the susceptibility of beam electrons. The mode structure and growth rate of the electron Bernstein wave are obtained. The growth rate in the case of Cerenkov and slow cyclotron interactions are proportional to $${{\omega }_{b0}}^{1/3}$$ and $${\omega }_{b0}$$ , respectively. For typical parameter, the normalized growth rate attains maximum value at $$b\approx 1.743$$ with different normalized beam velocities. These parameters control the growth rate due to nonlocality which rapidly decreases. The present theoretical scheme may be possible application in the field of heating of spherical torus plasmas.

Evidence of Nonlinear Interactions Between Magnetospheric Electron Cyclotron Harmonic Waves

AbstractElectron cyclotron harmonic (ECH) waves play an important role in the magnetosphere‐ionosphere coupling. They are usually considered to be generated by the Bernstein‐mode instability with electron loss cone distributions. By analyzing the Van Allen Probes wave data, we present the direct evidence of the nonlinear interactions between ECH waves in the magnetosphere. Substorm‐injected electrons excite primary ECH waves in a series of structureless bands between multiples of the electron gyrofrequency. Nonlinear interactions between the primary ECH waves produce secondary waves at sum‐ and difference‐frequencies of the primary waves. Our results suggest that the nonlinear wave‐wave interactions can redistribute the primary ECH wave energy over a broader frequency range and hence potentially affect the magnetospheric electrons over a broader range of pitch angles and energies.

Particle‐in‐Cell Simulation of Electron Cyclotron Harmonic Waves Driven by a Loss Cone Distribution

AbstractElectron Cyclotron Harmonic (ECH) waves driven by a loss cone distribution are studied in this work by self‐consistent particle‐in‐cell simulations. These waves have been suggested to play an important role in diffuse auroral precipitation in the outer magnetosphere. However, particle simulation of this instability is difficult because the saturation amplitude of the wave driven by a realistic size loss cone distribution is very small. In this work we use an extraordinarily large number of particles to reduce simulation noise so that the growth and saturation of ECH waves can be investigated. Our simulation results are consistent with linear theory in terms of growth rate, and with observation in terms of wave amplitude. We demonstrate that the heating of cold electrons is negligible and nonresonant, different from previous conclusions, and suggest that the saturation of the wave is caused by the filling of the loss cone of hot electrons.

Study of relativistic beam of electron on whistler mode waves for subtracted distribution in Saturnian magnetosphere

Very low frequency electromagnetic waves in the magnetosphere of Saturn are the focus of the present study. Hot injected beam effect on these waves like whistler mode waves for relativistic and non-relativistic subtracted bi-Maxwellian distribution function have been studied in the presence of perpendicular A.C electric field. By using the method of characteristics solutions and kinetic approach, expression for dispersion relation and growth rate has been derived via detailed calculations and derivations. By changing parameters of plasma like: ac frequency, thermal anisotropy, number density, parametric analysis has been done. The influence of AC frequency on Doppler shift is analyzed, and the comparative study of the effects of oblique and parallel propagating waves on the growth rate has been done. Some different results were found using the subtracted bi-Maxwellian distribution function discussed with the results of bi-Maxwellian distribution function. It can be seen that the effective parameters for generating whistler mode waves are not only temperature anisotropy, but also relativistic factor, alternating field frequency, subtracted distribution amplitude and the width of the loss cone distribution function, which have been discussed in the results and discussion section.

Effect of the Temperature of Background Plasma and the Energy of Energetic Electrons on Z-mode Excitation

Abstract It has been suggested that the Z-mode instability driven by energetic electrons with a loss-cone type velocity distribution is one candidate process behind the continuum and zebra pattern of solar type-IV radio bursts. Both the temperature of background plasma (T 0) and the energy of energetic electrons (v e ) are considered to be important to the variation of the maximum growth rate (γ max). Here we present a detailed parameter study on the effect of T 0 and v e , within a regime of the frequency ratio ( ). In addition to γ max, we also analyze the effect on the corresponding wave frequency ( ) and propagation angle (θ max). We find that (1) γ max generally decreases with increasing v e , while its variation with T 0 is more complex depending on the exact value of v e . (2) With increasing T 0 and v e , presents stepwise profiles with jumps separated by gradual or very weak variations, and due to the warm plasma effect on the wave dispersion relation can vary within the hybrid band (the harmonic band containing the upper hybrid frequency) and the higher band. (3) The propagation is either perpendicular or quasi-perpendicular, and θ max presents variations in line with those of , as constrained by the resonance condition. We also examine the profiles of γ max with for different combinations of T 0 and v e to clarify some earlier calculations which show inconsistent results.

Whistler Instability Driven by Electron Thermal Ring Distribution With Magnetospheric Application

AbstractThe loss cone electron distribution function can be unstable to the excitation of whistler instability, which can be effective in pitch angle diffusion, thus rapidly filling up the loss cone and removing the free energy source. The present paper carries out a combined quasi‐linear analysis and one‐dimensional particle‐in‐cell simulation in order to investigate the dynamical consequences of the excitation of whistler instability. Thermal ring distribution can be considered as a simple substitution for the actual loss cone distribution. It is found according to both the reduced quasi‐linear theory and the particle‐in‐cell simulation that while the whistler instability is effective in pitch angle diffusion of the initial loss cone distribution, the complete isotropization is not achieved such that substantial loss cone persists in the saturation stage. This finding may explain the fundamental question of why weak loss cone feature persists in the magnetosphere and, more importantly, why charged particles trapped in dipole field do not steadily undergo pitch angle scattering and be lost eventually.