Abstract
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 λD. 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 λD 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.
Highlights
In the first part of this work,1 a collisionless plasma, generated by UV illumination localized in a central part of the plasma, was analyzed
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 kD
The four zones with different physics revealed by numerical calculations and shown in Fig. 1, that is, the illuminated plasma, the double layer, the un-illuminated plasma, and the near-wall space-charge sheath appear in a natural way in the course of application of the method of matched asymptotic expansions
Summary
In the first part of this work, a collisionless plasma, generated by UV illumination localized in a central part of the plasma, was analyzed. The ions continue to be accelerated in the un-illuminated region and enter the near-wall space-charge sheath with a speed significantly exceeding the Bohm speed. A very unusual, if not unique, feature that this simple system reveals in plane geometry is the coexistence of two quasi-neutral plasmas of the same size with the ambipolar electric field being confined in one of them (the illuminated plasma), while the other (the un-illuminated plasma) is to high accuracy electric field-free and uniform The latter is surprising since in all known models a near-wall space-charge sheath is bordered by a nonuniform quasineutral presheath where the ions going to the sheath are accelerated and the voltage drop is of the order of the electron temperature measured in volts. Mathematical details are placed in two Appendices in order not to overload the text
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