By Sadrilla Abdullaev
This is the 1st e-book to systematically think about the trendy facets of chaotic dynamics of magnetic box strains and charged debris in magnetically constrained fusion plasmas. The analytical versions describing the usual good points of equilibrium magnetic fields and magnetic perturbations in smooth fusion units are awarded. It describes mathematical and actual points of onset of chaos, universal homes of the constitution of stochastic magnetic fields, shipping of charged debris in tokamaks caused via magnetic perturbations, new facets of particle turbulent delivery, and so forth. The presentation relies at the classical and new specified mathematical instruments of Hamiltonian dynamics, just like the action--angle formalism, classical perturbation conception, canonical changes of variables, symplectic mappings, the Poincaré-Melnikov integrals. they're greatly used for analytical reviews in addition to for numerical simulations of magnetic box strains, particle dynamics, their spatial buildings and statistical houses. the various references to articles at the newest improvement within the zone are supplied. The booklet is meant for graduate scholars and researchers who drawn to the trendy difficulties of magnetic stochasticity in magnetically restrained fusion plasmas. it's also worthy for physicists and mathematicians drawn to new equipment of Hamiltonian dynamics and their applications.
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Extra resources for Magnetic Stochasticity in Magnetically Confined Fusion Plasmas: Chaos of Field Lines and Charged Particle Dynamics
Example text
6 Snowflake Divertor Configuration Up to now we have considered divertor tokamaks with the first order–null of the poloidal magnetic field at the X-point, where its first derivatives have finite values. By the appropriate choice of the divertor currents one can make the latter also vanish at the X-point. This case is called a second order null of the poloidal magnetic field. This kind of divertor tokamaks with the second order of null of the poloidal magnetic field have been recently proposed by Ryutov (2007); Ryutov et al.
Examples Poloidal divertor tokamaks are important concept to control the plasma edge. The magnetic configuration of these tokamaks contains a magnetic surface called magnetic separatrix which sharply separates closed field lines on nested magnetic surfaces from the open field lines hitting the walls of fusion devices. It has one (or two) Fig. 3 Elongated Plasmas: Analytical Solutions εδ Highest point 0 ε εκ 1 R/R0 singular point(s), X-point , on the poloidal plane (ϕ = const), where the poloidal magnetic field (B R , B Z ) has zero(es).
11 the barriers to a particle transport caused by a small scale turbulent field may be formed near the low–order rational values of q. 2 Magnetic Flux Coordinates 11 where G(ψ, ϑ, ϕ) is an arbitrary periodic function of (ϑ, ϕ), one can show that the ¯ ϕ). 27) also in the variables (ϑ, ¯ Beside of this the magnetic field B is not changed if we add to ϑ (or ϕ) any arbitrary function f (ψ) of ψ, Θ = ϑ + f (ψ). 36) We will use this property later to define the poloidal angle ϑ which would be convenient to treat the field lines in a tokamak plasma with a magnetic separatrix (see Sect.