Magnetic Field Dynamical Regimes in a Large-Scale Low-Mode aO-Dynamo Model with Hereditary a-Quenching by Field Energy

The article considers a large-scale model of an a?-dynamo in the low-mode approximation. The intensity of the a-effect is regulated by a process that depends on the energy of the magnetic field and has hereditarity properties (finite memory). The regulation process is included in the MHD-system in the form of an additive correction. The action character of the process is defined by the alternating kernel with variable parameters: the damping frequency and the damping coefficient. The Reynolds number and the a-effect measure are the control parameters of the system. Information about the action of a large-scale generator is contained in the Reynolds number, and that about the action of a turbulent one is contained in the measure of the a-effect. The stability of the solution of the MHD-system is studied depending on the values of the control parameters and the parameters of the alternating kernel. Based on the results of numerical simulation of the dynamical regimes, limitations are determined for the values of the model parameters at which the regimes are reproduced against the background of small oscillations of the viscous liquid velocity field. The results of the study of the stability of solutions and numerical simulations of the dynamical regimes are represented on the phase plane of the control parameters. The paper investigates the question of changing the pattern on the phase plane depending on the values of the damping coefficient, the damping frequency, and the waiting time. A comparison is made with the results obtained earlier, when the a-effect intensity is a constant or is regulated by a process with an exponential kernel and the same values of the damping coefficient.

Automated summary

The article investigates a large-scale model of an a?-dynamo in the low-mode approximation. The intensity of the a-effect is regulated by a process with hereditarity properties. The stability of the MHD-system solution is studied based on the control parameters and the parameters of the alternating kernel. The results are represented on the phase plane, and the change in pattern depending on the damping coefficient, damping frequency, and waiting time is compared with previous studies.