The dynamo mechanism driven by weak plasma turbulence, called the p-om
ega dynamo, is studied. Under the assumption of the uniform rotation o
f a celestial body, a dynamo equation is derived from the magnetic ind
uction equation based on mean field electrodynamics. It is well known
that differential rotation is indispensable for an alpha-omega dynamo
to be operative. In contrast to the alpha-omega dynamo model, no matte
r if the rotation angular velocity is uniform or not, no matter in the
absence or the presence of the convection, the p-omega dynamo is oper
ative. Thp coupling between uniform rotation and plasma turbulence wav
es can also produce source terms in the dynamo equation which lead to
the generation of a poloidal and toroidal field. The existence of diff
erential rotation will evidently enhance the action of the p-omega dyn
amo. We present a complete uniform-rotational solution of the dynamo e
quation here, and dynamo solutions for several types of differential r
otation are given. Finally, we discuss the physical nature of these dy
namo solutions in Sect. 5.