Two-mode approximation with memory in the solar dynamo problem

This paper is devoted to the discussion of the results of modeling the two-mode hereditary model of the cosmic dynamo applied to a real space object, namely the solar dynamo. The magnetic field of the Sun is formed by the mechanism of the hydromagnetic dynamo. In this process, the moving conducting medium (plasma) in the convective zone generates a magnetic field, which then affects the flow through the Lorentz force, creating feedback. An important role in this mechanism is played by the memory of the system (hereditary). Memory in the system under study is implemented as feedback distributed over all past states of the system. The feedback is represented by an integral term of the convolution type of a quadratic form of phase variables with a kernel of a fairly general form. The quadratic form models the influence of the Lorentz force. This integral term describes the quenching of the turbulent generator. The presented model is based on the kinematic dynamo problem, where the large-scale velocity field is specified, its model representation of the field is constructed on the basis of helioseismological data. Free attenuation modes were chosen as components of the magnetic field. The work considered cases when the hereditary feedback with the system arose instantly and with a delay. The simulation results showed that the studied model reproduces the dynamic modes characteristic of the solar dynamo, in the presence of delays in the feedback. The work was supported by IKIR FEB RAS State Task (Reg. № NIOKTR 124012300245-2).