Abstract
Energetic particle populations in magnetic confinement systems are sensitive to symmetry-breaking effects due to their low collisionality and long confined path lengths. Broken symmetry is present to some extent in all toroidal devices. As such effects preclude the existence of an ignorable coordinate, a fully three-dimensional analysis is necessary, beginning with the lowest order (equilibrium) magnetic fields. Three-dimensional techniques that have been extensively developed for stellarator configurations are readily adapted to other devices such as rippled tokamaks and helical states in reversed field pinches. This paper will describe the methods and present an overview of recent examples that use these techniques for the modeling of energetic particle confinement, Alfvén mode structure and fast ion instabilities.
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