  An investigation on stochastic deflection of high-energy negatively charged
particles in a bent crystal was carried out. On the basis of analytical
calculation and numerical simulation it was shown that it exists a maximum
angle at which most of the beam is deflected. The existence of a maximum, which
is taken in the correspondence of the optimal radius of curvature, is a novelty
with respect to the case of positively charged particles, for which the
deflection angle can be freely increased by increasing the crystal length. This
difference has to be ascribed to the stronger contribution of incoherent
scattering affecting the dynamics of negative particles that move closer to
atomic nuclei and electrons. We therefore identified the ideal parameters for
the exploitation of axial confinement for negatively charged particle beam
manipulation in future high-energy accelerators, e.g., ILC or muon colliders.
