Spontaneous magnetic field multipolar structure in toroidal plasmas based on 2D equilibrium

The multipolar magnetic field structure is investigated by the momentum conservation equation with self-consistent 3D sheared flows during transition of plasma properties from local paramagnetic to diamagnetic fields. Numerical results show that the traditional poloidal magnetic field ($B_P$) is one part of equilibrium magnetic fields. The non-zero-order quantities are originated from the higher-order terms of 2D equilibrium treatment based on a Fourier expansion of ψ (r, θ). The distributions of magnetic field vectors of the order of 1, 2, and 3 terms are presented respectively in two, four, and six polar fields with the local vortex structures (spontaneous magnetic connection). The excitation mechanisms of the magnetic vortices are the coupling effects of the magnetic fluid structure pattern and the toroidal effects. These results can help us understand the physical mechanism of the interaction between the external perturbation fields and control tearing modes, as well as the radial plasma flow and magnetic vortices. (paper)