Abstract
Abstract. In this paper, we derive the dispersion equations for field-aligned cyclotron waves in two-dimensional (2-D) magnetospheric plasmas with anisotropic temperature. Two magnetic field configurations are considered with dipole and circular magnetic field lines. The main contribution of the trapped particles to the transverse dielectric permittivity is estimated by solving the linearized Vlasov equation for their perturbed distribution functions, accounting for the cyclotron and bounce resonances, neglecting the drift effects, and assuming the weak connection of the left-hand and right-hand polarized waves. Both the bi-Maxwellian and bi-Lorentzian distribution functions are considered to model the ring current ions and electrons in the dipole magnetosphere. A numerical code has been developed to analyze the dispersion characteristics of electromagnetic ion-cyclotron waves in an electron-proton magnetospheric plasma with circular magnetic field lines, assuming that the steady-state distribution function of the energetic protons is bi-Maxwellian. As in the uniform magnetic field case, the growth rate of the proton-cyclotron instability (PCI) in the 2-D magnetospheric plasmas is defined by the contribution of the energetic ions/protons to the imaginary part of the transverse permittivity elements. We demonstrate that the PCI growth rate in the 2-D axisymmetric plasmasphere can be significantly smaller than that for the straight magnetic field case with the same macroscopic bulk parameters.
Highlights
Cyclotron waves are an important constituent of plasmas in solar corona, solar wind and planetary magnetospheres
To have some analogy with linear theory of cyclotron wave instabilities in the straight magnetic field (e.g. Kennel and Petschek, 1966), let us assume that the n-th harmonic of the electric field gives the main contribution to the n-th harmonic of the current density
As in the case of a uniform plasma confined in the straight magnetic field, the growth/damping rate of the cyclotron waves in a 2-D magnetosphere is defined by the contribution of the resonant particles to the imaginary part of the transverse dielectric permittivity elements
Summary
Cyclotron waves are an important constituent of plasmas in solar corona, solar wind and planetary magnetospheres. The main feature of 2-D magnetospheric plasmas is the fact that i) the parallel velocity of charged particles moving along the geomagnetic field lines is not constant (in contrast to a straight uniform magnetic field case), and ii) the ambient geomagnetic field is axisymmetric and has one minimum in the equatorial plane. All plasmaspheric particles are magnetically trapped, bouncing between the mirror points (where their parallel velocity is equal to zero), and the wave-particle resonance conditions should take into account the cyclotron and bounce resonances. The instabilities of the cyclotron waves in the Earth’s magnetosphere/plasmasphere should be analyzed by solving Maxwell’s equations with a correct “kinetic” dielectric tensor, which can be obtained by solving either the Vlasov or the drift-kinetic equation for trapped particles, taking into account a 2-D nonuniformity of the geomagnetic field and plasma parameters. The linearized Vlasov equation for (interesting us) harmonics f±s 1 can be rewritten in the form
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