We have derived an exact theoretical expression for the space‐charge limited current from the solid surfaces adjacent to plasmas that is applicable for an arbitrary sheath voltage. Our expression shows that the spacecharge limited current tends to saturate with the sheath voltage. This new formula is evaluated by 1‐D Particle in Cell (PIC) simulation and experiment, and is in a good agreement with the simulation and experimental results. We have also obtained an analytical equation fitted to the new formula based on conventional Child‐Langmuir formula by taking into account a more sophisticated dependence of the electrode potential and the plasma density through the effect of Debye shielding and a sheath expansion due to increased voltage across the sheath. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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Takamura et al. (2004) studied this question.
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