Shadowing and the Plasma-Sheath Transition Layer

Summary.

This paper gives a rigorous derivation of the system μ ² d ² w ₀ \over dζ ² =w ² ₀ +ζ , w ₀ (ζ ₀ )=-(-ζ ₀ ) ^1/2 , dw ₀ \over dζ (ζ ₀ )= 1\over 2 (-ζ ₀ ) ^-1/2 , ζ ₀ <0 , governing the electric potential in the transition layer joining quasi-neutral plasma to space charge sheath in a weakly ionized plasma. The parameter μ represents the tolerance for ``shadowing,'' i.e., it measures the ``distance'' between the true solution of the full Euler-Poisson system and the solution of the reduced order limit equation for w ₀ (ζ) .