For a multicomponent wave field propagating into a multidimensional conversion region, the rays are shown to be helical, in general. For a ray-based quantity to have a fundamental physical meaning, it must be invariant under the following two groups of transformations, which are used to construct solutions: congruence transformations (which involve linear combinations of components of the multicomponent wave field) and canonical transformations (which act on the ray phase space). It is shown that for conversion between two waves there is a new invariant not previously discussed: the intrinsic helicity of the ray.