Magnetic field line chaos, cantori, and turnstiles in toroidal plasmas

Abstract The mathematical concepts of chaos, cartori, and turnstiles underlie a number of areas of tokamak and stellarator physics. Nevertheless, these concepts have seldom explicitly appeared in publications on fusion plasmas. The absence of physical intuition about these concepts is responsible for misunderstandings and slows developments in a number of areas: magnetic reconnection, the most important electromagnetic correction to what are called electrostatic microinstabilities, non-resonant divertors in stellarators, disruptions and damage from runaway electrons in tokamaks. Physicists become interested in new mathematical concepts when they give insights into and solutions to practical problems. The importance of this review is not only in explaining chaos, cartori, and turnstiles as mathematical concepts but also in illustrating their significance through applications.