Relaxation oscillations in energy active zones

Boris Shevtsov,A Dmitriev,N Salikhov,Z Rakhmonov,G Vodinchar

doi:10.1051/e3sconf/202019602026

Abstract

Relaxation oscillations in energy active natural zones are considered as causes of sudden catastrophes. A general approach to the study of dynamical systems of a fast-slow type is proposed, the relaxation oscillations of which give an adequate description of catastrophic events. The general properties of such systems are discussed using the example of solar activity and geomagnetic dynamo. The analogies between magnetic dynamos, laser systems, charge particles precipitation in the ionosphere, lightning discharges and earthquakes are considered. It is shown that these analogies are based on the presentation of various natural phenomena using dynamic systems of a fast-slow type.

Highlights

The idea of this report arose from the need to understand what is common between many scientific areas that are involved in the study of natural disasters, and which have been constantly presented at our conference for many years
The object of our research is a system of geospheres, in which we call areas of intense motions energy active zones
It is very important that in the kinematic approximation, the dynamo numbers include convection, which was not in the early models of the magnetic dynamo and in their numerous generalizations [8, 9], it is precisely convection that pumps energy into the system. It is with convection in a spherical rotating layer [7] that it is necessary to begin studies of the mechanisms of generation of relaxation oscillations in energy active zones

Summary

Introduction

The idea of this report arose from the need to understand what is common between many scientific areas that are involved in the study of natural disasters, and which have been constantly presented at our conference for many years. The processes of accumulation and discharge of energy take place These cycles are known as relaxation oscillations. The form of this equation indicates that we have obtained a Van der Pol-like system [2,3,4], which is an example of a dynamic system of fast-slow type [5], if its nonlinearity parameter is large. Substituting (3) into (6), we obtain the equation of thermal diffusion with magnetic field feedback: tT (Gf , )(T T0) k (T T0)

Magnetopause

Kinematic coefficients

Three regimes of convection and oscillations

Reverse

Weak convection and kinematic approximation

Conclusion