Full hamiltonian description of the interaction of particles with magnetic islands in Tokamak

Abstract

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

Particle diffusion in a system of magnetic islands in tokamaks in fully Hamiltonian approach

“…The equations of motion can be obtained by differentiating the Hamiltonian. This has been done explicitly in [2].…”

“…In the previous paper [2], we also used a perturbation with only one Fourier component. It leads to an integrable Hamiltonian for the field lines, because a canonical transformation can transform it to a system equivalent to a pendulum.…”

“…First results of our study appeared in the paper [2]. There, we discussed the dynamics of particles, influenced in the tokamak magnetic field by one magnetic island.…”

“…For a non-homogeneous magnetic field, important drifts appear and force the particle to move far from the field line. (First informations appeared in [2]). Secondly, in a full Hamiltonian approach, the particle exhibits Larmor motion.…”

“…Our present paper can be considered as a continuation of [2]. The goal is to extend the study of the dynamics of particles in the tokamak magnetic field to the case two magnetic islands, which has important qualitative differences compared to the case of one island.…”