  In omnigeneous magnetic fields, charged particles are perfectly confined in
the absence of collisions and turbulence. For this reason, the magnetic
configuration is optimized to be close to omnigenity in any candidate for a
stellarator fusion reactor. However, approaching omnigenity imposes severe
constraints on the spatial variation of the magnetic field. In particular, the
topology of the contours of constant magnetic-field-strength on each magnetic
surface must be such that there are no particles transitioning between
different types of wells. This, in turn, usually leads to complicated plasma
shapes and coils. This Letter presents a new family of optimized fields that
display tokamak-like collisional energy transport while having transitioning
particles. This result radically broadens the space of accessible
reactor-relevant configurations.
