ISSN 1063-7850, Technical Physics Letters, 2015, Vol. 41, No. 1, pp. 43–45. © Pleiades Publishing, Ltd., 2015. Original Russian Text © K.D. Kapustin, M.B. Krasil’nikov, A.A. Kudryavtsev, 2015, published in Pis’ma v Zhurnal Tekhnicheskoi Fiziki, 2015, Vol. 41, No. 1, pp. 87–93. 43 The electron distribution function (EDF) in plasma is usually determined with the use of the local approximation when in solving the kinetic equation the terms with spatial variables are excluded and the EDF is factorized in the form of the product of the electron density, which depend on spatial coordinates and time, and the EDF itself, which depends on the electron kinetic energy (1) In this approximation, the electron distribution by kinetic energy w at space point r depends on local val- ues of the reduced field E/p and other parameters (gas temperature, concentration of excited particles, etc.). The local distribution attracts researchers and is widely used mainly due to the considerably simplified computational procedure in solving the Boltzmann kinetic equation, which depends, in this case, on only one variable, kinetic energy w. The local approximation applicability criteria are obtained by a standard technique with regard to small- ness of the terms with coordinate derivatives as com- pared with the terms with energy derivatives in the kinetic equation for electrons. This yields the estima- tion in the form of the condition (2) i.e., characteristic diffusion length L of the plasma vol- ume should exceed electron energy relaxation length λ ε (see, e.g., [1, 2]). In expression (2), D r = Vλ/3 is the diffusivity of free electrons and the corre- sponding energy relaxation time (3) is determined by energy loss upon elastic and inelastic collisions (corresponding frequencies ν and ν*). Since at the elastic scattering the energy relaxation occurs at many collisions (the corresponding energy exchange factor is δ = < 10 –4 ), in the elastic energy range ε < ε 1 , where ε 1 is the first threshold of inelastic processes, the length (4) is significant and exceeds the free electron path by more than two orders of magnitude. For atomic gases, conditions (2) and (4) require relatively large values of the parameter pL > 5–10 cm Torr, where p is the gas pressure. It should be noted that when the local approxima- tion is used, the condition L > λ ε is implicitly assumed to be also the condition for negligibility of ambipolar field E amb as compared with current field E heat that heats electrons. Indeed, the simple estimations (5) show that the inequality L  λ ε is followed by the con- dition E heat  E amb . It can be seen from (5) that, in reality, the ambipo- lar field is small at the central plasma parts, where the plasma concentration is maximum, and grows toward the periphery, where it exceeds the longitudinal (heat) field. Since electrons react to the resulting electric fwrt ,, ( ) n e rt , ( ) f 0 wE / p , ( ) . = L  λ ε 2 D r τ ε , = τ ε 1 – δν ν * + = 2 m/ M λ s D r / δλ ( ) λ / δ 100 λ > ≅ ≅ E heat T e / λ ε , E amb ≅ T e ∇n e / n e – T e / L ≅ = The Role of the Ambipolar Field and the Local Approximation Inapplicability in Determination of the Electron Distribution Function at High Pressures K. D. Kapustin b , M. B. Krasil’nikov a , and A. A. Kudryavtsev a * a St. Petersburg State University, St. Petersburg, 199034 Russia b St. Petersburg State University of Information Technologies, Mechanics, and Optics, St. Petersburg, 197101 Russia *e-mail: akud@ak2138.spb.edu Received September 12, 2014 Abstract—It is demonstrated that the condition for applicability of the local approximation in solving the kinetic equation for electrons includes not only smallness of the electron kinetic relaxation length as com- pared with the characteristic plasma volume, but also smallness of the ambipolar filed as compared with the current (heating) field. Therefore, at the discharge periphery, where the ambipolar field exceeds the longitu- dinal one, the local approximation cannot be used for calculating the electron distribution function even at high gas pressures. DOI: 10.1134/S1063785015010071