On the possibility of the development of longitudinal wave instabilities on the background of the small-scale Bernstein turbulence in preflare chromosphere of a solar active region

The process of origination and development of instabilities of the longitudinal waves of two types, namely, low-frequency ion-acoustic and high-frequency (“electronic”) Langmuir waves, in the preflare atmosphere of an active solar region are studied. The area under study is located at the chromospheric part of the flare loop near its footpoint. A weak large-scale electric field of flaring loop is the main source of these instabilities. The velocity of an electronic flow in the preflare plasma is supposed to be much lower than thermal electron velocity. Instability development is considered against the background of small-scale Bernstein wave turbulence, which exists in the preflare plasma and has an extremely low threshold of excitation. The necessary conditions for the instability origination and development, as well as the boundary values of the main plasma and wave perturbation parameters, are calculated.     

Quasi-satellite orbits in the general context of dynamics in the 1:1 mean motion resonance: perturbative treatment

Our investigation is motivated by the recent discovery of asteroids orbiting the Sun and simultaneously staying near one of the Solar System planets for a long time. This regime of motion is usually called the quasi-satellite regime, since even at the times of the closest approaches the distance between the asteroid and the planet is significantly larger than the region of space (the Hill’s sphere) in which the planet can hold its satellites. We explore the properties of the quasi-satellite regimes in the context of the spatial restricted circular three-body problem “Sun–planet–asteroid”. Via double numerical averaging, we construct evolutionary equations which describe the long-term behaviour of the orbital elements of an asteroid. Special attention is paid to possible transitions between the motion in a quasi-satellite orbit and the one in another type of orbits available in the 1:1 resonance. A rough classification of the corresponding evolutionary paths is given for an asteroid’s motion with a sufficiently small eccentricity and inclination.