  The plasma sheath sets a stage for a strongly nonlinear coupling of the
thermal, kinetic, and electric energies of plasma in a non-equilibrium, open
environment. The pressure, velocity, and electrostatic potential profiles
depend strongly on the boundary condition given on the internal side
(pre-sheath). By controlling the boundary values of the heat flux and the ion
Mach number, we solve a set of equations for the ion temperature and the
electrostatic potential. The boundary values of the ion velocity and the
electrostatic potential vary due to the change of the boundary ion temperature.
When the heat flux exceeds a threshold value (determined by the ion Mach
number), the temperature contrast is enhanced, resulting in a large entropy
production.
