In this letter, the effect of full Hamiltonian approach to plasma particle dynamics, in the presence of magnetic islands in a tokamak, is discussed. Usually, for the estimation of the diffusion of particles, the stochasticity regime of magnetic field lines is considered as sufficient. We have found that for ions in Hamiltonian description, the diffusive character of their trajectories considerably differs from the diffusive character of magnetic field lines. This then could have, among others, an influence on the performance of the ergodic divertor.PACS: 52.65.Cc, 52.25.Gj
I n t r o d u c t i o nIn the pioneering period of the study of Hamiltonian deterministic chaos, the possibility of generation of chaos of static magnetic field lines was found [1]. This appeared due to the formal identity of equations, describing the geometry of magnetic field lines with the canonical Hamiltonian equations. Such possibility follows from the two following equations:Here, ~b(x) is a function which is constant on the magnetic surfaces (specifically, the toroidal flux inside a surface) and the second equation in (1) expresses the tangency of B to the magnetic surface r = const. The equilibrium magnetic field, which satisfies the condition (1), may be represented by the Clebsch form [2, 3]Here, F ( r is the dimensionless poloidal flux and 0* is the intrinsic coordinate standing for the poloidal angle. (The definition of 0* will be precised later.) Using the toroidal angle ( as a running parameter [2,4], field lines can be represented by the following equations: d e OF dO* OF d~ --0 0 ' ' d~ -0---r