  Quasisymmetry and omnigeneity of an equilibrium magnetic field are two
distinct properties proposed to ensure radial localization of collisionless
trapped particles in any stellarator. These constraints are incompletely
explored, but have stringent restrictions on a magnetic geometry. This work
employs an analytic approach to understand the implications of the constraints.
The particles move in an intrinsically three dimensional equilibrium whose
representation is given by earlier work of Weitzner and its extension here. For
deeply trapped particles a local equilibrium expansion around a minimum of the
magnetic field strength along a magnetic line suffices. This analytical
non-symmetric equilibrium solution, enables explicit representation of the
constraints. The results show that it is far easier to satisfy the omnigeneity
condition than the quasisymmetry requirement. Correspondingly, there exists a
large class of equilibrium close to quasisymmetry that remain omnigeneous while
allowing inclusion of error fields, which may destroy quasisymmetry.
