BOUNDARY-CONDITION REFINEMENT OF THE CHILD-LANGMUIR LAW FOR COLLISIONLESS DC PLASMA SHEATHS

被引:32
作者
FAROUKI, RT [1 ]
DALVIE, M [1 ]
PAVARINO, LF [1 ]
机构
[1] NYU,COURANT INST MATH SCI,NEW YORK,NY 10012
关键词
D O I
10.1063/1.346898
中图分类号
O59 [应用物理学];
学科分类号
摘要
An exact solution to the problem of collisionless, space-charge-limited flow of cold ions across a one-dimensional (planar) dc plasma sheath of negligible electron density is derived for general values of the presheath ion velocity upsilon-0 and electric E0. For a given ion current density J and sheath thickness d, the exact solution reduces to the classical Child-Langmuir model in the case that epsilon-0 = 0 and E0 = 0. When either epsilon-0 or E0 is suifficiently large, however, the exact solution may differ appreciably from the Child-Langmuir law. The existence of a closed-form expression for the spatial variation of the sheath potential is shown to be contingent upon the satisfaction of a simple inequality relating epsilon-0 and E0 to J. When epsilon-0 obeys the Bohm criterion and the magnitude of E0 suggests that the Bohm energy is acquired over a distance not less than one Debye length, this inequality is indeed satisfied.
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页码:6106 / 6116
页数:11
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