General Loss-cone Distribution Function Research Articles

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.

Effect of general loss-cone distribution function on kinetic Alfvén wave in multi-ions plasma by kinetic approach

Kinetic Alfven waves with general loss-cone distribution function are investigated in multi-ions (H+, He+ and O+) plasma. Dispersion relation and damping rate for the wave are derived using Vlasov equation. Variations in frequency and damping rate versus $$ k_{ \bot } \rho_{i} $$ (where k⊥ is wave vector perpendicular to ambient magnetic field, ρi is ion Larmor radius and i denotes multi-ions) are investigated. Parameters relevant to plasma sheet boundary layer are used for graphical analysis. It is observed that wave frequency fluctuates with loss-cone distribution indices of ions. In comparison with Maxwellian plasma (J = 0), the wave frequency is enhanced for He+ and O+ and reduced for H+ with the increase in J indices and the wave existence limit shift towards lower $$ k_{ \bot } \rho_{i} $$ for lighter ions. This may be due to difference in penetration of multi-ions through the cone. H+ and He+ ions show damping at lower k⊥ρi only, whereas O+ ions exhibit damping over wide range of $$ k_{ \bot } \rho_{{O^{ + } }} $$ . The damping is reduced with the increase in loss-cone indices for all the ions which signify propagation of wave over long distances towards auroral ionosphere. The applications of these results are in understanding the effect of gyrating multi-ions in transfer of energy and in describing the generation of aurora.

Effects of temperature anisotropy on electrostatic ion-cyclotron (EIC) wave in multi-component plasma around polar cusp region-particle aspect approach

Particle aspect analysis is used to describe electrostatic ion-cyclotron (EIC) wave with multi-ion plasma (H+, He+ and O+) around polar cusp region. Variations of resonant energy and growth rate with general loss-cone distribution function and temperature anisotropy with perpendicular wave number are studied. The whole plasma is considered to consist of resonant and non-resonant particles. The resonant particles participate in energy exchange with wave, while non-resonant particles support the oscillatory motion of the wave. The wave is assumed to propagate obliquely to the static magnetic field. It is found that the temperature anisotropy enhances the transverse, parallel resonant energies of particles and growth rate of the wave. Distribution indices also enhance the growth rate and parallel resonant energy and reduce the perpendicular resonant energy. The study may explain the EIC waves observed in polar cusp region. The results are interpreted for the space plasma parameters appropriate to the polar cusp region in the earth’s magnetosphere.

Electromagnetic Ion Cyclotron Waves in Multi-Ions Hot Anisotropic Plasma in Auroral Acceleration Region-Particle Aspect Approach

Using particle aspect approach, the effect of multi-ions densities on the dispersion relation, growth rate, perpendicular resonant energy and growth length of electromagnetic ion cyclotron wave with general loss-cone distribution function in hot anisotropic multi-ion plasma is presented for auroral acceleration region. It is observed that higher He+ and O+ ions densities enhance the wave frequency closer to the H+ ion cyclotron frequency and growth rate of the wave. The differential heating of He+ ions perpendicular to the magnetic field is enhanced at higher densities of He+ ions. The waves require longer distances to achieve observable amplitude by wave-particle interactions mechanism as predicted by growth length. It is also found that electron thermal anisotropy of the background plasma enhances the growth rate and reduces the growth length of multi-ions plasma. These results are determined for auroral acceleration region.

Effect of parallel electric field on electromagnetic ion-cyclotron waves with hot anisotropic plasma

The effect of parallel electric field on the growth rate, parallel and perpendicular resonant energy of the electromagnetic ion-cyclotron (EMIC) waves with general loss-cone distribution function in hot anisotropic plasma in auroral acceleration region is investigated by particle aspect approach. The ion beam driven by parallel electric field is included in the analysis whereas electrons are assumed mixed with the back ground plasma. Plasma consisting of resonant and non-resonant particles has been considered. It is assumed that the resonant particle and ion beam participate in energy exchange with the wave, whereas non-resonant particles support the oscillatory motion of the wave. We observed that the parallel electric field is to control the growth rate of the EMIC wave, 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 analyse the broad scenario of EMIC waves in the auroral acceleration region of the earth’s magnetoplasma.

Kinetic Alfven wave in the presence of parallel electric field with general loss-cone distribution function: A kinetic approach

In past, kinetic Alfven waves are widely investigated regarding the transfer of energy from the magnetosphere to the ionosphere. These waves are supposed to be responsible for the acceleration of auroral electrons to exhibit auroral phenomena. The existence of parallel electric fields is always reported in association with the kinetic Alfven waves. In the present investigation, assuming parallel electric fields developed by different mechanism, the dispersion relation and growth/damping rate of the kinetic Alfven Wave (KAW) in the presence of parallel electric field are evaluated with general loss-cone distribution using the kinetic approach. The wave frequency w and growth/damping rate gL are obtained for two regimes of propagation k^ri 1, where k^ is perpendicular wave number andri is the ion-gyro radius. The results of the present study show that the frequency w and growth/damping rate of wave depend upon the distribution indices, parallel electric field and k^ri. The generation of kinetic Alfven wave by the combined effect of parallel electric field and loss-cone distribution indices (J), at a particular range of k^ri is noticed. Thus the propagation of kinetic Alfven wave and loss of the Poynting flux from plasma sheet boundary layer (PSBL) to the ionosphere can be explained more effectively on the basis of present investigation. The results of the present study show that the parallel electric field in the presence of loss-cone distribution index is an important parameter to study KAW in the PSBL. The finding of the present investigation is to report that auroral phenomena are suitably described by kinetic Alfven wave in the presence of parallel electric field and the general loss-cone distribution function. Key words: Kinetic Alfven wave, Plasma-sheet-boundary-layer, Parallel electric field, Kinetic theory, Loss-cone distribution function.

Effect of multi-ions on electromagnetic ion-cyclotron waves with a hot plasma around the polar cusp

Electromagnetic ion cyclotron (EMIC) instabilities with an isotropic ion beam and general loss-cone distribution of hot core plasmas are discussed. The growth rate of the wave, perpendicular heating of ions, parallel resonant energy and marginal instability of the EMIC waves in homogeneous plasmas are obtained using the dispersion relation for hot plasmas consisting of H+, He+,O+ ions and electrons. The wave is assumed to propagate parallel to the static magnetic field. The whole plasma is considered to consist of resonant and non-resonant particles permeated by the isotropic ion beam. It is assumed that the resonant particles and the ion beam participate in energy exchange with the wave, whereas the non-resonant particles support the oscillatory motion of the wave. We determined the variation in energies and growth rate in hot plasmas by the energy conservation method with a general loss-cone distribution function. We also discuss the effect of positive and negative ion beam velocity on the growth rate of the wave. The thermal anisotropy of the ions of the core plasma acts as a source of free energy for EMIC waves and enhances the growth rate. Heating of ions perpendicular to the magnetic field is discussed along with EMIC wave emission in the polar cusp region.

Effect of ion beam on electromagnetic ion cyclotron instability in hot anisotropic plasma-particle aspect analysis

Abstract. Using the general loss-cone distribution function electromagnetic ion cyclotron (EMIC) instability affected by up going ion beam has been studied by investigating the trajectories of charged particles. The 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 effect of ion beam velocity on the dispersion relation, growth rate, parallel and perpendicular resonant energy of the EMIC wave with general loss-cone distribution function in hot anisotropic plasma is described by particle aspect approach. The effect of beam anisotropy and beam density on electromagnetic ion cyclotron instabilities is investigated. Growth length is derived for EMIC waves in hot anisotropic plasma. It is found that the effect of the ion beam is to reduce the energy of transversely heated ions, whereas the thermal anisotropy of the background plasma acts as a source of free energy for the EMIC wave and enhances the growth rate. It is observed that ion beam velocity opposite to the wave propagation and its density reduces the growth rate and enhance the reduction in perpendicularly heated ions energy. The effect of ion beam anisotropy on EMIC wave is also discussed. These results are determined for auroral acceleration region. It is also found that the EMIC wave emissions occur by extracting energy of perpendicularly heated ions in the presence of an up flowing ion beam.

Comparative study between cold plasma and hot plasma with ion beam and loss-cone distribution function by particle aspect approach

The electromagnetic ion-cyclotron (EMIC) instabilities with isotropic ion beam and general loss-cone distribution of cold and hot core plasmas are discussed. The growth rate, parallel and perpendicular resonance energies of the electromagnetic ion-cyclotron waves in a low β (ratio of plasma pressure to magnetic pressure), homogeneous plasma have been obtained using the dispersion relation for cold and hot plasmas. The wave is assumed to propagate parallel to the static magnetic field. The whole plasma is considered to consist of resonant and non-resonant particles permeated by isotropic ion beam. It is assumed that resonant particles and ion beam participate in energy exchange with the wave whereas non-resonant particles support the oscillatory motion of the wave. We determined the variation in energies and growth rate in cold and hot plasmas by the energy conservation method with a general loss-cone distribution function. The thermal anisotropy of the core plasma acts as a source of free energy for EMIC wave and enhances the growth rate. It is noted that the EMIC wave emissions occur by extracting energy of perpendicularly heated ions in the presence of up flowing ion beam and steep loss-cone distribution in the anisotropic magnetosphere. The effect of the steep loss-cone distribution is to enhance the growth rate of the EMIC wave. The heating of ions perpendicular and parallel to the magnetic field is discussed along with EMIC wave emission in the auroral acceleration region. The results are interpreted for the space plasma parameters appropriate to the auroral acceleration region of the earth's magnetoplasma.

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.

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.

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.

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.

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.

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.

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.

Kinetic Alfve‘n wave in the inhomogeneous magnetosphere and general distribution function

Dispersion relation, associated current and growth-rate of the kinetic Alfve‘n wave with general loss-cone distribution function in a low β inhomogeneous plasma in the presence of an inhomogeneous magnetic field have been obtained by investigating the trajectories of the charged particles. The effects of steepness of loss-cone distribution and inhomogeneity of magnetic field are discussed. The treatment of the kinetic Alfve‘n wave instability is based on the assumption that the plasma consists of resonant and non-resonant particles. The excitation of the wave is treated by particle aspect analysis and the wave particle energy exchange method. The results are interpreted for the auroral acceleration region of the earth's magnetoplasma.