The emergence of contrast structures for galactic magnetic field: theoretical estimates and modeling on gpu

Magnetic field generation in galaxies turns out to be a significant problem both for cosmic magnetohydrodynamics and mathematical physics. It is based on dynamo mechanism characterising the transition between the energy of medium turbulent motions and the magnetic field energy. The evolution of the field is described with the help of mean field dynamo equations. For galaxies the solutions are commonly found using so-called “no-z” approximation, while the half-thickness of the galactic disc is considered negligible. In nonlinear case mentioned equations admit contrast structure formation, predicted by the singular perturbation theory, describing equations with small parameter at the elder derivative. From astronomical point of view some authors tend to connect such solutions with the spiral structure of the galaxies and the formation of magnetic field reversals (when in different parts of galaxy there are regions with opposite directions of magnetic, divided by a thin transition layer). From numerical point of view finding the solution of two-dimensional system of equations requires large computational resources, for this reason using GPU and parallel calculations turns out to be reasonable. One of the implementation methods is calculating using OpenCL, which allows one to increase the process efficiency several times. OpenCL is a perspective crossplatform standard for development of applications, particularly involving GPU, the efficiency of which is rapidly increasing as the drivers evolve. The present work presents basic theoretical assessments of magnetic field behaviour, which are further confirmed and clarified during the computations. It is shown that the formation of the transition layers is described by fundamentally different mechanisms in radial and azimuthal directions. While radial reversals of the field turn out to be rather stable, all of the azimuthal structures are rapidly blurred due to the nature of the interstellar medium motions. That also indicates the practical impossibility of non-axisymmetric distributions of the field.