Shadowing and the Plasma-Sheath Transition Layer |
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Authors: | M Slemrod |
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Institution: | (1) Center for the Mathematical Sciences, University of Wisconsin-Madison, 1308 West Dayton Street, Madison, WI 53715-1149, USA e-mail: slemrod@math.wisc.edu, US |
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Abstract: | 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) .
Received February 22, 2001; accepted September 21, 2001 Online publication November 30, 2001 |
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Keywords: | |
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