Omnigenity as generalized quasisymmetry

Any viable stellarator reactor will need to be nearly omnigenous, meaning the radial guiding-center drift velocity averages to zero over time for all particles. While omnigenity is easier to achieve than quasisymmetry, we show here that several properties of quasisymmetric plasmas also apply directly or with only minor modification to the larger class of omnigenous plasmas. For example, concise expressions exist for the flow and current, closely resembling those for a tokamak, and these expressions are explicit in that no magnetic differential equations remain. A helicity (M, N) can be defined for any omnigenous field, based on the topology by which B contours close on a flux surface, generalizing the helicity associated with quasisymmetric fields. For generalized quasi-poloidal symmetry (M = 0), the bootstrap current vanishes, which may yield desirable equilibrium and stability properties. A concise expression is derived for the radial electric field in any omnigenous plasma that is not quasisymmetric. The fact that the tokamak-like analytical calculations are possible in omnigenous plasmas despite their fully 3D magnetic spectrum makes these configurations useful for gaining insight and benchmarking codes. A construction is given to produce omnigenous $B(\theta ,\zeta )$ patterns with stellarator symmetry.