  With a model for two-dimensional (2D) Brownian rotary ratchets being capable
of producing a net torque under athermal random forces, its optimization for
mean angular momentum ($L$), mean angular velocity ($\omega$), and efficiency
($\eta$) is considered. In the model, supposing that such a small ratchet
system is placed in a thermal bath, the motion of the rotor in the stator is
described by the Langevin dynamics of a particle in a 2D ratchet potential,
which consists of a static and a time-dependent interaction between rotor and
stator; for the latter, we examine a force [randomly directed d.c. field
(RDDF)] for which only the direction is instantaneously updated in a sequence
of events in a Poisson process. Because of the chirality of the static part of
the potential, it is found that the RDDF causes net rotation while coupling
with the thermal fluctuations. Then, to maximize the efficiency of the power
consumption of the net rotation, we consider optimizing the static part of the
ratchet potential. A crucial point is that the newly designed form of ratchet
potential enables us to capture the essential feature of 2D ratchet potentials
with two closed curves and allows us to systematically construct an
optimization strategy. In this paper, we show a method for maximizing $L$,
$\omega$, and $\eta$, its outcome in 2D two-tooth ratchet systems, and a
direction of optimization for a three-tooth ratchet system.
