Analysis of magnetic helicity generation in MHD-shell model

The mechanism of stellar large-scale magnetic field formation, including the eleven-year solar cycle, is currently generally understood. In particular, its linear mode, in which the reverse effect of the magnetic field on the velocity field can be neglected. However, the non-linear reverse influence, which stabilize the growing average magnetic field, is not completely clear. The most possible reason of the nonlinear stabilization of this process is assumed the hydrodynamic helicity, but the balance of hydrodynamic and magnetic helicity and its transport along the spectrum remains to be studied. The present report is devoted to this problem. An exponential growth of magnetic energy at sufficiently high magnetic Reynolds numbers can be observed in a random short-correlated plasma flow at small-scales relative the velocity correlation length. Magnetic helicity is generated in this case together with the small-scale energy of magnetic field. And despite the fact that this phenomenon is traditionally studied by using the Kazantsev’s approach, we are trying to recreate this process of small-scale generation by a mhd shell approach, which is more convenient for the subsequent study of the balance and energy/helicity transport from small scales to large ones. To do this, in the complex shell model we add a small magnetic field to the well-established Kolmogorov spectrum and, by observing the exponential growth of magnetic energy on small scales, we compare the generation process with the magnetic small-scale Kazantsev dynamo. We select the correlation time for the velocity field and the working spectral regions to show that, in general, both approaches describe the same process with the same generation rates and scales. Thus, we show that the shell approach can be used for the future study of small-scale energy/helicity transport along the spectrum and for the problems of large-scale stellar dynamo processes stabilization. This work was supported by the BASIS Foundation grant no. 21-1-3-63-1.