[1] The polarization and field-aligned structure of drift-compressional modes and the corresponding plasma instability are studied in a gyrokinetic framework in the axisymmetric model of the magnetosphere with isotropic plasma. The plasma is assumed to be composed of core cold particles and an admixture of hot protons, with an inverted distribution of hot protons. Such plasma experiences a compressional resonance when the wave frequency is equal to an eigenfrequency of the drift-compressional mode. In this resonance, the wave is dominated by the field-aligned and azimuthal magnetic field components and is narrowly localized along the field line at the equator, the same as the plasma to magnetic pressure ratioˇ. The plasma instability occurs when the temperature diamagnetic drift velocity is less than the magnetic drift velocity or opposite in direction. Furthermore, the narrower the inverted distribution, the higher the instability growth rate and the smaller the value ofˇrequired for the instability to occur. The growth rate reaches its highest values when a positive radial temperature gradient and a negative radial density gradient occur simultaneously.

A mechanism for generation of the parallel electric field by Alfvén wave in the dipole model of the magnetosphere in full gyrokinetics is proposed. The parallel electric field of the Alfvén mode is caused by the coupling of the Alfvén and electrostatic modes due to the plasma inhomogeneity and field line curvature in presence of the trapped hot electrons. The parallel electric field is described by an inhomogeneous integral equation arising from the averaging of the bounce motion of hot electrons. It was found that the parallel electric field is localized near the ionosphere at the heights below 0.5 Earth's radius. For typical Alfvén wave amplitudes observed in space, the parallel electric field potential reaches the values of several kV, which can provide enough acceleration for the precipitating auroral electrons.

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The paper reviews the current state of the problem of interaction between long-period ultra-low-frequency (ULF) waves and high-energy particles. We consider elements of the theory of energy exchange between waves and particles, particle transport across magnetic shells under the influence of the electromagnetic field of a wave, the acceleration of radiation belt particles by both resonant and non-resonant mechanisms. We examine the mechanisms of generation of azimuthally-small-scale ULF waves due to instabilities arising from the wave–particle resonance. The cases of Alfvén, drift-compressional, and drift-mirror waves are analyzed. It is noted that due to the lack of a detailed theory of drift-mirror modes, the possibility of their existence in the magnetosphere cannot be taken as a proven fact. We summarize experimental data on the poloidal and compression ULF waves generated by unstable populations of high-energy particles. We investigate the mechanisms of modulation of energetic particle fluxes by ULF waves and possible observational manifestations of such modulation. Methods of studying the structure of waves across magnetic shells by recording fluxes of resonant particles with a finite Larmor radius are discussed.

Abstract. As shown within the gyrokinetic framework, drift-compressional waves can propagate in the magnetosphere in the direction of energetic electron drift. The plasma is assumed to be composed of cold particles with an admixture of hot protons with a Maxwell distribution and electrons with an inverted distribution. The conditions of existence of such waves and their intensification due to resonance interaction with energetic electrons (drift instability) have been determined. The results can be helpful in interpreting observation of wave phenomena in the magnetosphere with frequencies in the range of geomagnetic pulsations Pc5 and below.