Numerical resolution of the spatially dependent electron Boltzmann equation in cylindrical geometry
- Instituto Superior Tecnico, Lisboa (Portugal)
- Ruhr-Universitaet Bochum (Germany); and others
This paper presents a numerical resolution of the spatially dependent electron Boltzmann equation (EBE) in cylindrical geometry. An application is given for a helium HF discharge. The system under analysis is a cylindrical plasma column of radius R, under the action of a total electric field of the form {rvec E}(r, t) = E({sub {tau}})({tau}){rvec e}{sub {tau}} + {radical}2E{sub ef}cos({omega}t){rvec e}{sub z}, for a given gas density N (or pressure). The stationary component of {rvec E}(r, t) is identified with a radial space-charge field E{sub {tau}},(r) = -{Delta}{phi} ({phi} represents the space-charge potential), and its time-dependent component is associated with an axially applied HF electric field of angular frequency {omega}. We assume that the HF situation is characterized by the relation {omega} > {tau}{sub e}{sup -1}, where {tau}{sub e} is the characteristic time for electron energy relaxation by collisions with the gas atoms. In this case the EBE can be written using the classical two-term expansion in spherical harmonics together with the DC effective field approximation. With these assumptions the electron distribution function (EDF) is decoupled into a stationary isotropic component f(r, u) (which yields the macroscopic collision rate coefficients), a stationary anisotropic component f(r, u) (related to transport processes due to the space-charge field and the radial density gradients), and an alternate anisotropic component f{sub 1}{sup 1}(r, u) cos({omega}t) (related to the axial drift under the influence of E{sub ef}), which oscillates with the same frequency as the external field.
- OSTI ID:
- 213040
- Report Number(s):
- CONF-950749--
- Country of Publication:
- United States
- Language:
- English
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