# What is a quasi-axisymmetric stellarator?

I know that a tokamak is a donut shape fusion confinement device with an axisymmetric magnetic field configuration. The stellarator is similar but its field configuration is non-axisymmetric.

I've heard about quasi-axisymmetric stellarators (QAS). I was told that the magnetic field strength of these devices is such that it's magnitude is axisymmetric.

Question: $$B\neq B(\varphi)$$ is the only condition needed to define a QAS? Shouldn't the magnetic surfaces of a QAS look axisymmetric as in the tokamak case?

The stellarator on the other hand generates the magnetic field only via magnetic field coils, such that there is no necessity for a strong plasma current. This requires, however, field coils which wind around the torus helically (to achieve the twist in the field lines). On modular stellarators this becomes more complicated as you use modular coils to mimic the helical winding. The increased number of coils (which can also be quite close to the plasma) generate a fully 3D magnetic field which has a strong modulation of $$|B|$$ in basically every direction.
The strong modulation of $$|B|$$ in a classical stellarator has a few consequences, mainly that transport losses are strongly increased (thus the confinement is decreased). This is what we call neoclassical transport (in contrast to classical transport which is due to collisions only).
Now we come back to your question (sorry for that lengthy introduction, but I have no idea about your background). Boozer [1] has developed the idea that those neoclassical transport losses depend on the variation of |B| within a flux surface, not on the vector components of B. These coordinates are nowadays referred to as Boozer coordinates. Nührenberg made use of this idea throughout the following years and proposed stellarator configurations that have a direction of quasi symmetry of $$|B|$$ in Boozer coordinates. Note that those configurations are still 3D in Cartesian coordinates (or more general in Euclidean space).