  An exact solution of two fluid ideal classical plasma equations is presented
which shows that the jet-like outflow and magnetic field are generated
simultaneously by the density and temperature gradients of both electrons and
ions. Particular profiles of density function $\psi=\ln \bar{n}$ (where
$\bar{n}$ is normalized by some constant density $N_0$) and temperatures $T_j$
(for $j=e,i)$ are chosen which reduce the set of nonlinear partial differential
equations to two simple linear equations generating longitudinally uniform
axial outflow and magnetic field in cylindrical geometry in several
astrophysical objects. This mechanism also seems to be operative for producing
short scale plasma jets in the solar atmosphere in the form of spicules and
flares. The presented solution requires particular profiles of density and
temperatures, but it is a natural solution of the two fluid ideal classical
plasma equations. Similar jet-like outflows can be generated by the density and
temperature gradients in neutral fluids as well.
