Asymptotic theory of double layer and shielding of electric field at the   edge of illuminated plasma
  The method of matched asymptotic expansions is applied to the problem of a collisionless plasma generated by UV illumination localized in a central part of the plasma in the limiting case of small Debye length ${\lambda}_D$. A second-approximation asymptotic solution is found for the double layer positioned at the boundary of the illuminated region and for the un-illuminated plasma for the plane geometry. Numerical calculations for different values of ${\lambda}_D$ are reported and found to confirm the asymptotic results. The net integral space charge of the double layer is asymptotically small, although in the plane geometry it is just sufficient to shield the ambipolar electric field existing in the illuminated region and thus to prevent it from penetrating into the un-illuminated region. The double layer has the same mathematical nature as the intermediate transition layer separating an active plasma and a collisionless sheath, and the underlying physics is also the same. In essence, the two layers represent the same physical object: a transonic layer. 
M. S. Benilov, D. M. Thomas
physics.plasm-ph