  We develop a comprehensive quantitative description of the cross-section
mechanism discovered several years ago by Lazarian. This is one of the
processes that determine grain orientation in clouds of suprathermal cosmic
dust. The cross-section mechanism manifests itself when an ensemble of
suprathermal paramagnetic granules is placed in a magnetic field and is subject
to ultrasonic gas bombardment. The mechanism yields dust alignment whose
efficiency depends upon two factors: the geometric shape of the granules, and
the angle Phi between the magnetic line and the gas flow. We calculate the
quantitative measure of this alignment, and study its dependence upon the said
factors. It turns out that, irrelevant of the grain shape, the action of a flux
does not lead to alignment if Phi = arccos(1/sqrt{3}).
