Study of inertial kinetic Alfven waves around cusp region

The effect of electron inertia on kinetic Alfven wave has been studied. The expressions for the dispersion relation, growth/damping rate and growth/damping length of the inertial kinetic Alfven wave (IKAW) are derived using the kinetic approach in cusp region. The Vlasov-kinetic theory has been adopted to evaluate the dispersion relation, growth/damping rate and growth/damping length with respect to the perpendicular wave number k⊥ρi (ρi is the ion gyroradius) at different plasma densities. The growth/damping rate and growth/damping length are evaluated for different me/βmi, where β is the ratio of electron pressure to the magnetic field pressure, mi, e are the mass of ion and electron, respectively, as I=me/βmi represent boundary between the kinetic and inertial regimes. It is observed that frequency of inertial kinetic Alfven wave (IKAW) ω is decreasing with k⊥ρi and plasma density. The polar cusp is an ideal laboratory for studies of nonlinear plasma processes important for understanding the basic plasma physics, as well as the magnetospheric and astrophysical applications of these processes.