Benefits of Non-Axisymmetry in Tokamaks

Toroidal symmetry gives tokamaks excellent plasma confinement with engineering simplicity. A small breaking of the axisymmetry in the magnetic field by construction errors can unacceptably degrade confinement, but symmetry breaking can also allow undesirable effects, such as edge-localized-modes, to be avoided. Experiments show that careful design allows the benefits of non-axisymmetry to be obtained while robustly avoiding major degradations. The critical words are careful design. The stellarator concept of quasi-axisymmetry implies large departures from axisymmetry can be consistent with axisymmetric-type confinement even though departures from symmetry a hundred times smaller may not be. The careful design of three-dimensional magnetic fields requires the development of not only predictive computational tools but also of integrated optimization algorithms. The motion of passing particles is affected by the magnetic field becoming chaotic or developing islands in controllable regions. The motion of trapped particles is affected by non-axisymmetric variations in the magnetic field strength in magnetic surfaces. The multi-species motions creating electric fields and drifts can bifurcate non-axisymmetric magnetic topologies and modify key local profiles through convection, diffusion, and fluctuations. The motion of particles along open and stochastic field lines can significantly alter the power flux to plasma facing components, which should also be optimized for advanced tokamak operations in long pulse. The many advances that have been made in four areas will be reviewed: (1) understanding, (2) computational tools, (3) integration of optimization algorithms, and (4) empirical demonstrations on existing tokamaks. Areas in which further progress can be expected will also be discussed.