Abstract
It is shown that the local approximation for electron distribution function (EDF) determination at plasma periphery, where the ambipolar field is dominant, is not applicable even at high pressures when the characteristic plasma size exceeds the energy relaxation length of the electrons R > λε. Therefore, consistent results can be obtained only when solving the complete kinetic equation in both energy and spatial variables (i.e. it is necessary to solve nonlocal kinetic equation).
Highlights
Gas-discharge plasma properties are substantially determined by electron gas, much attention is paid in literary sources to finding its distribution function
Let us recall that at λε > L spatial diffusion occurs much faster than diffusion with respect to energy in electric field. In this case to use of local approximation for electron distribution function (EDF) is not physically justified and, as has been repeatedly demonstrated in literature, leads to errors
Such EDF is nonlocal, as it is determined by physical property values not at the given point, but in the region determined by energy relaxation length [2] λε ≫ λ - electron mean free path
Summary
Gas-discharge plasma properties are substantially determined by electron gas, much attention is paid in literary sources to finding its distribution function. Let us recall that at λε > L spatial diffusion occurs much faster than diffusion with respect to energy in electric field In this case to use of local approximation for EDF is not physically justified and, as has been repeatedly demonstrated in literature, leads to errors (for example, see refs). In this case to use of local approximation for EDF is not physically justified and, as has been repeatedly demonstrated in literature, leads to errors (for example, see refs1–7) Such EDF is nonlocal, as it is determined by physical property values (primarily by fields) not at the given point, but in the region determined by energy relaxation length [2] λε ≫ λ - electron mean free path. In order to find such EDF, it is necessary to solve a kinetic equation in variables of both energy and coordinates
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