Loss-cone Distribution Research Articles

Study of kinetic Alfven wave (KAW) in plasma – sheet-boundary- layer

The effect of parallel electric field with general loss-cone distribution function on the dispersion relation and damping rate/growth rate of the kinetic Alfven wave (KAW) is evaluated by kinetic approach. The generation of KAW by the combined effect of parallel electric field and loss-cone distribution indices (J) at a particular range of k⊥ρi (k⊥ρi <1 and k⊥ρi >1) is noticed, where k⊥ is perpendicular wave number and ρi is the ion-gyro radius. Thus the propagation of KAW and loss of the Poynting flux from plasma sheet boundary layer (PSBL) to the ionosphere can be explained on the basis of present investigation. It is found that the present study also shows that the loss-cone distribution index is an important parameter to study KAW in the PSBL.

Foreshock-like density cavity in the outflow region of magnetotail reconnection

Abstract. During Cluster spacecraft crossing of the magnetotail, a novel density depleted cavity in association with magnetic compressions in the outflow region of reconnection was observed. It contains intense reflected field-aligned particles, which are produced by a generation mechanism similar to that of the terrestrial foreshock, and hence manifests a foreshock-like morphology. In this cavity, reflected field-aligned proton beams were observed and simultaneously the feature of magnetic-mirror loss-cone proton distributions were found. Magnetic field fluctuations, especially quasi-monochromatic oscillations, were recorded. Both the leading egde and the ULF wave boundary of the ion foreshock are identified from the time sequence of proton and magnetic field observations. Just upstream of the leading egde of the ion foreshock, reflected field-aligned electrons were detected, whose distribution has a narrow bump-on-tail pattern. However, close to the shock front, reflected electrons with a broad bump-on-tail pattern was measured. These two different manifestations of reflected electrons reveal the differences in their microscopic physics of the reflecting process. Moreover, a part of incident ions was further accelerated in the cavity due to trans-time magnetic pumping which provides another possible mechanism in the multi-step acceleration processes in reconnection.

Whistler Waves Excited by Loss-cone Distribution Electrons

利用一维粒子模拟方法研究了损失锥电子速度分布激发的哨声波非线性演化过程, 并与双麦克斯韦电子分布激发哨声波的情况进行了比较. 结果表明, 这两种情况下, 在线性增长阶段哨声波的主导频率 (能量最集中的一个频率) 是一样的, 波动的激发使得平行于背景磁场方向的电子温度有所提高. 比较而言,在损失锥分布情况下, 哨声波具有主导频率的波模可较早地被激发, 而在线性增长阶段, 哨声波的能量更倾向于集中在高频(短波长)波段. 部分粒子被散射到损失锥中, 而使损失锥分布得以补充. 本文还研究了不同各向异性分布和磁场强度条件下的激发过程.

Shear Driven Kinetic Alfven Wave with General Loss-Cone Distribution Function in the Plasma Sheet Boundary Layer

Expressions for the dispersion relation and growth rate of the KAW are derived for weak and strong shear regimes using the kinetic approach in view of the simultaneous observations of the large earthward Alfvenic Poynting flux, small-scale kinetic Alfven wave (KAW), earthward flowing electrons and upward flowing ions, at the substorm event in the plasma sheet boundary layer (PSBL). General loss-cone distribution function is adopted to describe the velocity distribution of the plasma particles. The results explain the generation of the observed KAW in the PSBL by the weak shear at the substorm onset. It is found that during the substorm expansion phase the cyclotron damping of KAW may lead to the upward flowing ion. Whereas, it’s Landau damping that may lead to the parallel energisation of the electrons that explains the observed loss of Alfvenic Poynting flux. It is also noted that the loss-cone distribution index changes the profiles of the frequency and growth rate plots of the shear-driven KAW. The loss-cone distribution function is therefore, an important factor for the excitation of KAW in the active region of the magnetosphere at the PSBL. Results are consistent with the finding of Wu and Seyler (J Geophys Res 108A6:1236, 2003) concerning kinetic Alfven wave generation and its stabilization by the sheared flow.

Shear-driven kinetic Alfven wave in the plasma sheet boundary layer

Abstract Shear-driven kinetic Alfven waves (KAWs) at the plasma sheet boundary layer (PSBL) were investigated for substorm events in the presence of a parallel electric field using the general loss-cone distribution function. Using a kinetic approach, we derived the expressions for dispersion relation and growth length of the KAW in the presence of the parallel electric field using the general loss-cone distribution function for both, weak and strong shear regimes. The frequency of the KAW obtained is in agreement with observed values of 0.1–4 Hz in the PSBL. The results explain the generation of the energetic KAWs at the PSBL by the shear at substorm onset. The parallel electric field associated with the energetic KAWs at substorm onset may heat the field-aligned electrons, leading to parallel electron energisation that ultimately causes an intense aurora. The electric field along magnetic field lines enhances the frequency of KAW but decreases the growth length in the case of weak shear. We also found that the parallel electric field can reflect KAW towards the PSBL. The loss-cone distribution index changes the profiles of frequency and growth length plots of the shear-driven KAW. Hence, the loss-cone distribution function is an important factor in the excitation of KAW in the active region of the magnetosphere, such as the PSBL and the auroral acceleration region.

EMIC waves around the plasma-pause region

Electromagnetic ion-cyclotron (EMIC) instability has been studied using the general loss-cone distribution function by investigating the trajectories of charged particles and using the method of particle aspect analysis. A low β (ratio of plasma pressure to magnetic pressure) plasma consisting of resonant and non-resonant particles has been considered. It is assumed that the resonant particles participate in energy exchange with the wave, whereas non-resonant particles support the oscillatory motion of the wave. The wave is assumed to propagate parallel to the static magnetic field. The effects of steepness of loss-cone distribution with thermal anisotropy are discussed. The growth rate, perpendicular and parallel resonant energies of the particles and marginal instability condition are derived. The effect of general loss-cone distribution function is to enhance the growth rate of EMIC waves. The results are interpreted for the space plasma parameters appropriate to the plasma-pause region of the earth's magnetoplasma. The results of the work is consistent for EMIC emissions observation by SAMPEX and CRRES satellite around the plasma-pause region as reported by Bortnik et al. [Bortnik, J., Thorne, R.M., O’Brien, T.P., Green, J.C., Strongeway, R.J., Shprits, Y.Y., Baker, D.N., 2006. Observation of two distinct, rapid loss mechanisms during the 20 November 2003 radiation belt dropout event. J. Geophys. Res. 111, A12216, doi:10.1029/2006JA011802] and Xinlin et al. [Xinlin, Li., Baker, D.N., O’Brien, T.P., Xie, L., Zong, Q.G., 2006. Correlation between the inner edge of outer radiation belt electrons and the innermost plasmapause location. Geophys. Res. Lett. 33, L14107, doi:10.1029/2006GL026294].

Ion and electron beam effects on kinetic Alfven wave with general loss-cone distribution function—kinetic approach

This work studies the effect of ion and electron beam on kinetic Alfven wave (KAW) with general loss-cone distribution function. The kinetic theory has been adopted to evaluate the dispersion relation and damping rate of the wave in the presence of loss-cone distribution indices J. The variations in wave frequency ω and damping rate with perpendicular wave number k⊥ρi, (k⊥ is perpendicular wave number and ρi is ion gyroradius) and parallel wave number k|| are studied. It is found that the distribution index J and ion beam velocity enhance the wave frequency at lower k⊥ρi, whereas the electron beam velocity enhances the wave frequency at higher k⊥ρi. The calculated values of frequency correspond to the observed values in the range 0.1–4 Hz. Increase in damping rate due to higher distribution indices J and ion beam velocity is observed. The effect of electron beam is to reduce the damping rate at higher k⊥ρi. The plasma parameters appropriate to plasma sheet boundary layer are used. The results may explain the transfer of Poynting flux from the magnetosphere to the ionosphere. It is also found that in the presence of the loss-cone distribution function the ion beam becomes a sensitive parameter to reduce the Poynting flux of KAW propagating towards the ionosphere.

A Broadband Microwave Burst Produced by Electron Beams

The theoretical and experimental study of fast electron beams attracts much attention in astrophysics and the laboratory. In the case of solar flares, the problem of reliable beam detection and diagnostics is of exceptional importance. This paper explores the fact that electron beams moving obliquely to the magnetic field or along the field with some angular scatter around the beam's propagation direction can generate microwave continuum bursts through the gyrosynchrotron mechanism. The characteristics of the microwave bursts produced by beams differ from those in the case of isotropic or loss-cone distributions, which suggests a new quantitative diagnostic for beams in the solar corona. To demonstrate the potential of this tool, we analyze a radio burst that occurred during an impulsive class 1B/M6.7 flare on 2001 March 10 (NOAA AR 9368; N27 degrees, W42 degrees). Based on detailed analysis of the spectral, temporal, and spatial relationships, we obtain firm evidence that the microwave continuum burst was produced by electron beams. We develop and apply a new forward-fitting algorithm based on the exact gyrosynchrotron formulae and employing both total-power and polarization measurements to solve the inverse problem of the beam diagnostics. The burst is found to have been generated by an oblique beam in a region of reasonably strong magnetic field (similar to 200-300 G) and observed at a quasi-transverse viewing angle. We find that the lifetime of the emitting electrons in the radio source was relatively short, tau(l) approximate to 0.5 s, consistent with a single reflection of the electrons from a magnetic mirror at the footpoint with the stronger magnetic field. We discuss the implications of these findings for electron acceleration in flares and beam diagnostics.

Effect of the general loss-cone distribution function on kinetic Alfvén waves—a kinetic approach

AbstractKinetic Alfvén waves are investigated in the presence of a general loss-cone distribution function including finite electron pressure and ion-gyroradius effects. The dispersion relation and damping/growth rate are evaluated for different electron to ion temperature ratios, Te/Ti, using a kinetic approach. The wave frequency ω and damping/growth rate γL are evaluated for two regimes of propagation, k⊥ρi &lt; 1 and k⊥ρi &gt; 1, where k⊥ is the perpendicular wave number and ρi is the ion-gyroradius. An enhancement of the wave frequency and a reduction in the damping rate are predicted by steep loss-cone distribution indices and Te/Ti. The growth of the wave is also noticed at higher values of the distribution index and lower Te/Ti. Plasma parameters appropriate to the plasma sheet boundary layer (PSBL) are used to discuss the propagation of kinetic Alfvén waves from the PSBL to the auroral ionosphere.

Numerical study of electrostatic electron cyclotron harmonic waves due to Maxwellian ring velocity distributions

Abstract Excitation of electrostatic electron cyclotron harmonic (ECH) waves is studied by performing linear dispersion analysis and particle-in-cell computer simulation. The ECH wave emissions can be excited by a positive slope in a velocity distribution function perpendicular to the ambient magnetic field, such as that due to a loss cone or ring velocity distribution. However, there exists no analytic expression for integration of Maxwellian ring velocity distribution functions. Here we present a method to solve the linear dispersion relations of Maxwellian ring velocity distribution functions with numerical integration. The obtained dispersion relations are confirmed by particle-in-cell simulation.

Effect of general loss-cone distribution function on the shear-driven electrostatic ion-cyclotron instability

The shear-driven electrostatic ion-cyclotron instability (EICI) is studied using the loss-cone distribution function by particle aspect analysis. The effect of the loss-cone distribution on the dispersion relation and growth rate of weak shear-driven EICI is studied. The whole plasma is considered to consist of resonant and non-resonant particles. The wave is assumed to propagate obliquely to the static magnetic field. It is found that the frequency of the EICI is Doppler shifted due to the transverse inhomogeneous flow in the direction of the magnetic field. It is also found that for anisotropic plasma the critical velocity shear needed to excite EICI depends upon the loss-cone distribution index ( J). With the increasing values the loss-cone distribution indices ( J), the critical value of normalized velocity shear needed to generate EICI in anisotropic plasma, decreases and is of the order of the weak shear. The loss-cone distribution acts as a source of free energy and generates the weak shear-driven EICI at longer perpendicular perturbations. It also lowers the transverse and parallel energy of the resonant ions. The study may explain the frequently observed EICI in the auroral acceleration region.

Whistler-mode instability in magnetospheres of Uranus and Neptune

Whistler-mode instability in the magnetospheres of the outer planets Uranus and Neptune is investigated using an anisotropic kappa loss-cone distribution and comparisons have been made with the observations made by Voyager 2. Normalized temporal growth rates have been evaluated numerically at two representative radial distances at each planet. Parametric studies have been performed by changing plasma parameters: cold and hot electron densities, hot electron temperature and temperature anisotropy. It is found that whistler-mode emissions observed at lower radial distances cannot be reproduced in our calculations. Electron pitch-angle diffusion and energy diffusion coefficients have been obtained using the calculated growth rates. The present calculations show that electrons of energy above about 20 keV may be able to precipitate into the planetary atmospheres of both planets. Present studies should be helpful in making estimates on scattering properties of whistler-mode waves and thus contribute to a better understanding of the auroral activity in the planetary atmospheres.

Ring current instabilities excited by the energetic oxygen ions

The ring current instabilities driven by the energetic oxygen ions are investigated during the magnetic storm. The electrons and protons are considered to have Maxwellian distributions, while energetic oxygen ions are having loss-cone distribution. Dispersion relation for the quasielectrostatic modes with frequencies ω&amp;gt;ωcp (proton cyclotron frequency) and propagating obliquely to the magnetic field is obtained. Dispersion relation is studied numerically for the storm time ring current parameters and it is found that these instabilities are most prominent during intense storms when the oxygen ions become the dominant constituents of the ring current plasma. For some typical storm-time ring current parameters, these modes can produce quasielectrostatic noise in the range of 17–220Hz, thus providing a possible explanation of the electrostatic noise observed at the inner boundary of the ring current during magnetic storms. Further, these modes can attain saturation electric fields of the order of 100–500μV∕m, and therefore, are expected to scatter O+ ions into the loss-cone giving rise to their precipitation into the atmosphere, thus contributing to the ring current decay.

Two dimensional simulation of amplitude modulated electron plasma waves

Highly modulated waves near electron plasma frequency with both parallel and perpendicular polarization have been observed near diffusion region at dayside and in the tail region. In this paper, two dimensional Particle-In-Cell (PIC) simulation was performed to study the possible generation mechanism of these modulated electron plasma waves. It is shown that weak beam instability could generate the modulated Langmuir wave and the ambient magnetic field plays an important role in the formation of modulation. When the weak beam has loss cone distribution, highly modulated upper hybrid waves are generated and propagate with large angle to the ambient magnetic field. The properties of these modulated waves are discussed and compared with observations.

Particle‐in‐cell simulation of Maxwellian ring velocity distribution

Electrostatic electron cyclotron harmonic (ECH) and electromagnetic whistler wave emissions are sometimes observed simultaneously in the near‐Earth nightside equatorial magnetotail region. The excitation mechanism for these two wave emissions, however, is quite different with ECH waves excited by a positive slope in the velocity distribution function perpendicular to the ambient magnetic field (such as due to a loss cone or ring velocity distribution), while whistler waves are excited by a temperature anisotropy whereby the perpendicular temperature is larger than the parallel temperature. Here we examine, using a two‐dimensional electromagnetic particle‐in‐cell computer simulation, the excitation of both waves as a consequence of a warm electron ring distribution in the presence of cold background electrons. Initially, ECH waves are excited by the ring distribution in the linear stage, which results in heating of the cold electrons and smearing of the ring distribution. During a nonlinear consequence of the ECH excitation and ensuing electron wave‐particle interactions, whistler waves are also excited by the different instability. Thus both waves are excited during the same simulation run, which may account for the magnetospheric observations of both ECH and whistler waves at the same location where electron loss cone distributions form in the equatorial magnetotail at about 6–9 RE from the Earth.

Evidence of Jovian active longitude: 2. A parametric study

In a previous work, we developed a model allowing a theoretical location of the Io‐controlled decameter radio sources (Io‐A, Io‐B, Io‐C, and Io‐D) in the central meridian longitude‐Io phase diagram. This model considers the cyclotron maser instability to be at the origin of most auroral planetary radio emissions. We derive the efficiency of this theoretical mechanism at the footprint of the Io flux tube during a complete revolution of the satellite around Jupiter, and we show that some longitudes in the northern and southern hemispheres favor the radio decameter emission and lead to a probability of higher occurrence. In order to make the calculation easier, we suppose that electrons are accelerated in the neighborhood of Io and follow an adiabatic motion along magnetic field lines carried by the satellite. We also assume that the source of free energy needed by the cyclotron maser instability to amplify the waves derives from a loss cone distribution function built up by electrons which have disappeared in Jupiter's ionosphere. We study the effect of several parameters on the theoretical location of the sources in the central meridian longitude‐Io phase diagram, in particular the Jovicentric declination of the Earth and the frequency of emission.

Beam effect on electromagnetic ion-cyclotron waves with general loss – cone distribution function in an anisotropic plasma-particle aspect analysis

Abstract. The effect of upgoing ion beam and temperature anisotropy on the dispersion relation, growth rate, parallel and perpendicular resonant energies, and marginal instability of the electromagnetic ion cyclotron (EMIC) waves, with general loss-cone distribution function, in a low β homogeneous plasma, is discussed by investigating the trajectories of the charged particles. The whole plasma is considered to consist of resonant and non-resonant particles. The resonant particles participate in an energy exchange with the waves, whereas the non-resonant particles support the oscillatory motion of the waves. The effects of the steepness of the loss-cone distribution, ion beam velocity, with thermal anisotropy on resonant energy transferred, and the growth rate of the EMIC waves are discussed. It is found that the effect of the upgoing ion beam is to reduce the energy of transversely heated ions, whereas the thermal anisotropy acts as a source of free energy for the EMIC waves and enhances the growth rate. It is found that the EMIC wave emissions occur by extracting energy of perpendicularly heated ions in the presence of an upflowing ion beam and a steep loss-cone distribution function in the anisotropic magnetoplasma. The effect of the steepness of the loss-cone is also to enhance the growth rate of the EMIC waves. The results are interpreted for EMIC emissions in the auroral acceleration region.

Effect of general loss-cone distribution function on electrostatic ion-cyclotron instability in an inhomogeneous plasma: particle aspect analysis

The electrostatic ion-cyclotron instability (EICI) in low β (ratio of plasma to magnetic pressure), anisotropic, inhomogeneous plasma is studied by investigating the trajectories of the particles using the general loss-cone distribution function (Dory-Guest-Harris type) for the plasma ions. In particular, the role of the loss-cone feature as determined by the loss-cone indices, in driving the drift-cyclotron loss-cone (DCLC) instability is analysed. It is found that for both long and short wavelength DCLC mode the loss-cone indices and the perpendicular thermal velocity affect the dispersion equation and the growth rate of the wave by virtue of their occurrence in the temperature anisotropy. The dispersion relation for the DCLC mode derived here using the particle aspect analysis approach and the general loss-cone distribution function considers the ion diamagnetic drift and also includes the effects of the parallel propagation and the ion temperature anisotropy. It is also found that the diamagnetic drift velocity due to the density gradient of the plasma ions in the presence of the general loss-cone distribution acts as a source of free energy for the wave and leads to the generation of the DCLC instability with enhanced growth rate. The particle aspect analysis approach used to study the EICI in inhomogeneous plasma gives a fairly good explanation for the particle energisation, wave emission by the wave–particle interaction and the results obtained using this particle aspect analysis approach are in agreement with the previous theoretical findings using the kinetic approach.

Double plasma resonance and fine spectral structure of solar radio bursts

The process of generation of upper-hybrid waves by electron beam with loss-cone distribution is considered. The necessary conditions of the double plasma resonance effect, which is considered to be one of the most probable formation mechanisms of the zebra patterns in the spectra of solar radio emission, are investigated. It is shown that this effect considerably affects excitation of waves by electrons with power-law energetic spectrum. Interpretation of observations and diagnostics of plasma for the April 21, 2002 event are performed. It is found that the zebra stripes consist of separate short pulses; there is a good correlation between the separate stripes (with a certain temporal shift). The conclusion about the impulsive mode of injection of energetic particles into the coronal loop is made.

Electromagnetic ion-cyclotron instability in the presence of a parallel electric field with general loss-cone distribution function - particle aspect analysis

Abstract. The effect of parallel electric field on the growth rate, parallel and perpendicular resonant energy and marginal stability of the electromagnetic ion-cyclotron (EMIC) wave with general loss-cone distribution function in a low β homogeneous plasma is investigated by particle aspect approach. The effect of the steepness of the loss-cone distribution is investigated on the electromagnetic ion-cyclotron wave. The whole plasma is considered to consist of resonant and non-resonant particles. It is assumed that resonant particles participate in the energy exchange with the wave, whereas non-resonant particles support the oscillatory motion of the wave. The wave is assumed to propagate parallel to the static magnetic field. The effect of the parallel electric field with the general distribution function is to control the growth rate of the EMIC waves, whereas the effect of steep loss-cone distribution is to enhance the growth rate and perpendicular heating of the ions. This study is relevant to the analysis of ion conics in the presence of an EMIC wave in the auroral acceleration region of the Earth's magnetoplasma.