Limitations of the Heavy Species Transport Equations
Before continuing, some comments on the validity of the equations are necessary. Despite their relatively complicated form, the equations for transport of the heavy species are formulated under the following assumptions:
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The diffusion velocity must be much less than the thermal velocity; that is, Vk << vk. In the case of very low pressure CCP reactors, the ion drift velocity can approach or exceed the ion thermal velocity. In this case, the heavy species transport equations fail to fit the physics of the discharge.
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A single temperature is assumed for heavy species. In the case of reactors with high reduced electric fields, the ions can have a different temperature than the surrounding gas.