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A one-dimensional model of electron multiplication in a gas is considered by using a system of equations of moments. An approximate expression for the first Townsend ionization coefficient is derived. It is shown that for a linearly decreasing electric field, the multiplication cannot be characterized by a local transport coefficient, such as Townsend's coefficient alpha . A method for the solution in this situation is suggested.
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Yu. Kagan (1991) studied this question.
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