Chaotic behavior of magnetic field lines near simplest current systems

In the context of studying the problem of simulation of magnetic fields on the Sun, the structure of the field in the vicinity of two circular current loops with different mutual arrangement in space is considered. When the symmetry in the arrangement is sufficient, a system of magnetic surfaces created by the closed field lines arises. With a reduction in symmetry, isolated closed lines may exist. For the case of two identical current loops coupled perpendicularly, it is shown that the subsystems of these lines may be ordered in space in a complex manner. At large distances, a system of loops is equivalent to a dipole with a high degree of accuracy, while an approximate winding of the lines on the deformed toroids, encircling each of the loops, occurs at small distances. At intermediate distances, there are regions of both ordered and chaotic behavior of field lines. Results were obtained with the use of the numerical simulation method.