  An analysis of single-electron orbits in combined coaxial wiggler and axial
guide magnetic fields is presented. Solutions of the equations of motion are
developed in a form convenient for computing orbital velocity components and
trajectories in the radially dependent wiggler. Simple analytical solutions are
obtained in the radially-uniform-wiggler approximation and a formula for the
derivative of the axial velocity $v_{\|}$ with respect to Lorentz factor
$\gamma$ is derived. Results of numerical computations are presented and the
characteristics of the equilibrium orbits are discussed. The third spatial
harmonic of the coaxial wiggler field gives rise to group $III$ orbits which
are characterized by a strong negative mass regime.
