Influence of trapped electrons on the dielectric properties of the Earth’s radiation belts

Abstract

The dielectric tensor of an axisymmetric magnetosphere is derived by solving the Vlasov equations for trapped particles for a two-dimensional plasma model with circular magnetic field lines. Because of the nonuniformity of the geomagnetic field any Fourier harmonic of the perturbed current density (after its Fourier expansion over the geomagnetic latitude) is proportional to the sum over all harmonics of the oscillating electric field; that leads to additional wave dissipation effects. The resonant conditions for wave–particle interactions are discussed taking into account the cyclotron and bounce resonances; these conditions in magnetospheric plasmas are entirely different from the Landau damping resonant factor in the uniform magnetic field. The numerical calculations of the longitudinal permeability in the Earth’s radiation belts (the equatorial distance of the magnetic field line is five Earth’s radii) are carried out for short-period oscillations with the frequency ω∼2 s−1 and longitudinal wave numbers n=1,...,15. The different energy levels of the trapped electrons, T∼40–4000 eV, are considered. It is shown that, in the low-frequency region, the imaginary part of the longitudinal permeability decreases as ∼T−2.5 whereas the electron temperature increases. This decrease is stronger than ∼T−1.5 for plasmas in a straight magnetic field. For a given wave frequency, the basic contribution of trapped electrons to the imaginary part of longitudinal permeability is associated with the low numbers of bounce resonances and the low longitudinal wave numbers.