不变流形生长公式及其在磁约束聚变中的应用

spiral ribbon-like pattern of heat deposition has been reported and investigated in the past, of which the field structure is essential to study how to expand the wet area of heat flux to reduce the tolerance-to-heat demand for materials at the divertor in a magnetically confined fusion device. The relevant notions concerning magnetic topology are formalized in this paper to utilize knowledge from dynamical system research. Of great importance to comprehending the topology of general 3D vector fields are cycles and the invariant manifolds grown from saddle cycles, which are analyzed in detail. How the Jacobian of Poincaré map evolves along a cycle is presented. Grown in the directions of the Jacobian eigenvectors at the beginning, the invariant manifolds of saddle cycles are essential to determine the chaotic field regions, which induce a mixing effect inside the plasma. With regard to three-dimensional continuous-time dynamical systems, the governing equation of invariant manifolds in cylindrical coordinates is deduced.