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.     

Effect of parallel electric field on electrostatic ion-cyclotron instability in anisotropic plasma in the presence of ion beam and general distribution function—Particle aspect analysis

Dispersion relation, resonant energy transferred, growth rate and marginal instability criteria for the electrostatic ion-cyclotron wave with general loss-cone distribution in low-β anisotropic, homogeneous plasma in the auroral acceleration region are discussed by investigating the trajectories of the charged particles. Effects of the parallel electric field, ion beam velocity, steepness of the loss-cone distribution and temperature anisotropy on resonant energy transferred and growth rate of the instability are discussed. It is found that the effect of the parallel electric field is to stabilize the wave and enhance the transverse acceleration of ions whereas the effect of steepness of loss-cone, ion beam velocity and the temperature anisotropy is to enhance the growth rate and decrease the transverse acceleration of ions. The steepness of the loss-cone also introduces a peak in the growth rate which shifts towards the lower side of the perpendicular wave number with the increasing steepness of the loss-cone.     

Kinetic Alfven waves in plasma sheet boundary layer—particle aspect analysis

The particle aspect approach is adopted to investigate the trajectories of charged particles in the electromagnetic field of kinetic Alfven wave. Expressions are found for the dispersion relation, damping rate and associated currents in homogenous plasma. Kinetic effects of electrons and ions are included to study kinetic Alfven wave because both are important in the transition region. It is found that the ratio β of electron thermal energy density to magnetic field energy density and the ratio of ion to electron thermal temperature (T_i/T_e) affect the dispersion relation, damping-rate and associated currents in both cases (warm and cold electron limits). The treatment of kinetic Alfven wave instability is based on the assumption that the plasma consists of resonant and non-resonant particles. The resonant particles participate in an energy exchange process, whereas the non-resonant particles support the oscillatory motion of the wave.     

Effects of density, temperature and velocity gradients on inertial Alfven wave in cusp region

The kinetic approach is used to evaluate the dispersion relation and growth/damping rate of inertial Alfven wave (IAW) with density, temperature and velocity gradients in an inhomogeneous plasma. The effects of gradient terms are studied for both the regions k_⊥ρ_i<1 and k_⊥ρ_i>1, where k_⊥ is the perpendicular wave number and ρ_i is the ion gyroradius. The relevance of theoretical results so obtained is predicted in accordance to the FAST observations in the cusp region. The results are interpreted for the space plasma parameters appropriate to the cusp region. This study elucidates a possible scenario to account for the particle acceleration and the wave dissipation in inhomogeneous plasmas. This model is also able to explain many features observed in plasma sheet boundary layer as well as to evaluate the dispersion relation, growth/damping rate and growth/damping length of inertial Alfven wave. It is found that density, temperature and velocity gradients control the wave frequency and effectively enhance the growth rate of inertial Alfven wave.     

On the magnetic structure and wind parameter profiles of Alfvén wave driven winds in late-type supergiant stars

Cool stars at giant and supergiant evolutionary phases present low-velocity and high-density winds, responsible for the observed high mass-loss rates. Although presenting high luminosities, radiation pressure on dust particles is not sufficient to explain the wind acceleration process. Among the possible solutions to this still unsolved problem, Alfvén waves are, probably, the most interesting for their high efficiency in transfering energy and momentum to the wind. Typically, models of Alfvén wave driven winds result in high-velocity winds if they are not highly damped. In this work, we determine self-consistently the magnetic field geometry and solve the momentum, energy and mass conservation equations, to demonstrate that even a low-damped Alfvén wave flux is able to reproduce the low-velocity wind. We show that the magnetic flux tubes expand with a super-radial factor of S > 30 near the stellar surface, larger than that used in previous semi-empirical models. The rapid expansion results in a strong spatial dilution of the wave flux. We obtained the wind parameter profiles for a typical supergiant star of  16 M_⊙  . The wind is accelerated in a narrow region, coincident with the region of high divergence of the magnetic field lines, up to 100 km s⁻¹. For the temperature, we obtained a slight decrease near the surface for low-damped waves, because the wave heating mechanism is less effective than the radiative losses. The peak temperature occurs at   r ≃ 1.5  r ₀  reaching 6000 K. Propagating outwards, the wind cools down mainly due to adiabatic expansion.