Magnetic Field Lines in Fusion Plasmas

Abstract

Study of mappings as a part of Hamiltonian dynamics of magnetic field lines in plasmas were initiated by the research in magnetically confined plasma devices in a quest for the controlled fusion¹. Actually, a fusion research in early sixties gave a huge impact on the development of Hamiltonian dynamics, particularly, on mapping methods. Since, particles predominantly follow magnetic field lines the determination of their structure is important to confine particles. In fusion devices, like tokamaks and stellarators the confinement of charged particles in a bounded area is achieved by specially created (by external coils and plasma current itself) magnetic fields whose field lines lie on nested (magnetic) surfaces (Wesson (2004)). In a study of field lines the most important was the fact that a divergence free magnetic field is equivalent to Hamiltonian system with 1 + 1/2 degrees of freedom (see, e.g., Cary and Littlejohn (1983); Boozer (1983); Morrison (2000)). The Hamiltonian formulation of magnetic field lines has been instrumental in early studies of the problems of stability and destruction of magnetic surfaces in tokamaks and stellarators due to the presence of magnetic perturbations (Kerst (1962); Rosenbluth et al. (1966); Filonenko et al. (1967); Freis et al. (1973); Hamzeh (1974); Finn (1975); Matsuda and Yoshikawa (1975)).