  We present a theoretical description of charged particles with nonzero
projection of the orbital angular momentum (OAM) in a uniform magnetic field
with broken axial symmetry. The wave functions we find naturally account for
the asymmetry of the magnetic field at the entrance of the solenoid through the
continuous parameter and are a generalization of the Laguerre-Gauss states
commonly used to describe twisted charged particles. We analyze the asymmetric
Hamiltonian from an algebraic point of view and show how the OAM projection of
the twisted state is modified by symmetry breaking. We provide analytical
frameworks for properties of the asymmetric states, such as energy, RMS size,
and Cazimir invariant, and discuss advantages of the proposed description.
