Stable Orbits of Charged Particles in an Oscillating Electromagnetic Field

Orbits in a field of the cylindrical wave guide driven in the $T{E}_{01}$-mode have been studied. The radial components of the Lorentz force acting on the particle is never positive regardless of its charge; thus, it is attracted toward the axis of the wave guide around which it moves in a complicated path. Sufficient conditions are given under which the orbits are stable, that is, remain bounded for all times.