The modes of magnetic field generation in a low-mode model of αΩ-dynamo with α-generator varying intensity regulated by a function with an alternating kernel

¹ Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, RU-684034, Paratunka, Elizovskiy district, Kamchatka region, Russian Federation
² Municipal budgetary institution of supplementary education «Center«Luch»», RU-684000, Yelizovo, Elizovskiy district, Kamchatka region, Russian Federation

^* e-mail: sheremeteva@ikir.ru
^** e-mail: anna_antonenko@mail.ru

Published online: 8 November 2021

Abstract

The low-mode model αΩ-dynamo is used in this paper to simulate the modes of magnetic field generation with insignificant changes in the velocity field of a viscous fluid. In the framework of those model the α-effect intensity is regulated by the process that is included in the magnetohydrodynamic system (MHD-system) as an additive correction as a functional Z(t) depended on the magnetic field energy. Function that determines damped oscillations with variable damping frequency and constant damping coefficient, taken equal to one, is selected as kernel J(t) of functional Z(t). The research of the behavior of the magnetic field is carried out on large time scales, therefore, a rescaled and dimensionless MHD-system with the unit of time iquel the time of the magnetic field dissipation (10⁴ years) for numerical calculations is used. The control parameters of the system are the Reynolds number and the amplitude of the α-effect, that include information about the large-scale and turbulent generators, respectively. Numerical simulation of the magnetic field generation modes was carried out for the values of the damping coefficient b = 1 and frequency a = 0.1, 0.5, 1, 5, 10. According to the results of numerical simulation, an increase in the values of the damping frequency, when the damping coefficient is equal to one, is characterized by a decrease in the inhibitory effect of the process Z(t) on the α-effect and an increase in the region of divergence of the magnetic field on the phase plane of the control parameters. In a comparative analysis with the results of the authors’ work, where the change of the α-effect intensity was determined by the function Z(t) with an exponential kernel and the same value of the damping coefficient, the following differences were noted: an increase in oscillations in both a magnetic and a velocity fields, the appearance of a chaotic regime of magnetic field generation at the value of the damping frequency equal to one, and also insignificant narrowing of the region of α-effect suppression at values of the damping frequency increasing to one.