Adiabatic Invariants during Channeling in a Bent Crystal

We consider the channeling effect in a bent single crystal. In the accompanying reference frame moving along the plane or axis of channeling with the same velocity as the longitudinal component of the electron’s velocity, such motion essentially implements the model of a one-dimensional (1D) atom or a two-dimensional (2D) atom with controllable parameters. The depth and shape of the potential of the channeling plane or the ion channeling axis depend on the chemical composition, crystalline structure, and orientation of the crystal, as well as the energy of the electron moving in the planar or axial channel. The motion regime in the channel maintains stability even in a bent single crystal. By using expressions for adiabatic invariants of motion, the maximum bending angle of the single crystal is estimated at which motion in the plane or axial channeling regime retains stability. The maximum bending angle of the single crystal should not exceed the critical angle of Lindhard channeling, limiting the hypothetical possibility of using bent single crystals for deflecting beams of accelerated particles only to small angles.