  Quasisymmetry is an unusual symmetry that can be present in toroidal magnetic
fields, enabling confinement of charged particles and plasma. Here it is shown
that both quasi-axisymmetry and quasi-helical symmetry can be achieved to a
much higher precision than previously thought over a significant volume,
resulting in exceptional confinement. For a 1 Tesla mean field far from
axisymmetry (vacuum rotational transform $>$ 0.4), symmetry-breaking mode
amplitudes throughout a volume of aspect ratio 6 can be made as small as the
typical $\sim 50$ $\mu$T geomagnetic field.

Plasma Physics