Closed form analytic solutions describing glow discharge plasma

Abstract

On the basis of an analytic model developed previously [S. T. Pai, J. Appl. Phys. 71, 5820 (1992)], an improved version of the model for the description of dc glow discharge plasma was successfully developed. A set of closed form solutions was obtained from the governing equations. The two-dimensional, analytic solutions are functional and completely satisfy the governing equations, the actual boundary conditions, and Maxwell equations. They can be readily used to carry out numerical calculations without the necessity of employing any assumed boundary conditions. Results obtained from the model reveal that as the discharge gap spacing or pressure increases the maximum value in the electron density distribution moves toward the cathode. At a sufficiently large value of gap spacing, the positive column phenomenon begins to appear in the discharge region. The model has the capability of treating the positive column and negative glow as a continuous system without the necessity of studying them separately. The model also predicts a sharp rise of the positive ion density near the cathode and field reversal in the anode region. Variation of the electrode radius produces little effect on the axial spatial distribution of physical quantities studied.

DC Glow Discharge in Axial Magnetic Field at Low Pressures

“…In the above equations, except , , and , all other parameters can be regarded as constants in calculation. Equations (14), (15), and (16) are consistent with the model of the glow discharge without considering the axial magnetic field [18]. Their difference is only the difference in parameters.…”

“…Therefore, the same boundary conditions can be applied to the physical model without magnetic field [18]. …”

“…Next, we neglect the inertial terms { ⋅ ∇} in (2), as in the present case the average flow velocity in general is much smaller than the average speed of the random thermal motions [18]. Equation (2) becomes the following form:…”

“…Moreover, relationship between the various physical quantities is not readily apparent. In order to avoid these shortcomings, some of the early researchers sought analytic expression of the relevant parameters from the relevant classic discharge equation with applied analytic methods and actual boundary conditions and the theoretical model of glow discharge plasma under no magnetic field is established [15][16][17][18][19].…”