The transition from inertia-limited flow to mobility-limited flow of ions to the walls of the positive column of a planar gas discharge is analyzed from a hydrodynamic point of view. The analysis is based on the assumption that the electrons and ions in the positive column behave as inviscid fluids with different temperatures. The resultant formulation is valid for gas pressures from the free-fall limit to the continuum limit, including the high-field sheaths at the walls as well as the almost field-free plasma at the center of the discharge. Numerical results for the characteristic value, wall field, wall potential, and ion energy at the wall are given for many different pressures and central Debye lengths, and it is shown that the results are identical to those of Allis and Rose in the continuum limit and very close to those of Self in the free-fall limit.
The dc positive column is modeled with a system of balance equations based on moments of the radially dependent Boltzmann equation taken after the two-term Legendre expansion of the electron energy distribution function is made. The importance of the electron energy balance equation, which is frequently ignored in positive column analysis, is emphasized. A key assumption is that electron transport coefficients and collision frequencies in the nonequilibrium regime have the same relation to the average energy as in the equilibrium regime, according to a zero-dimensional Boltzmann solution for a particular value of average energy. Because of this assumption, the model makes a smooth transition to the traditional equilibrium model with radially constant average energy at sufficiently high pressure. Model results in the nonequilibrium regime agree closely with published results of a numerical solution of the one-dimensional Boltzmann equation, including results for radial heat flow in the electron gas with radially varying average energy. It is shown that three separate processes account for radial heat flow: convection, conduction, and diffusion. In the example chosen for illustration of the method, the convection component is small, while the conduction and diffusion components are large and opposite in direction, nearly canceling each other.
Improved positive column simulation techniques are needed because of
the non-local nature of typical low-pressure discharges used for lighting. In
a local model, the power balance between Joule heating and collisional
losses must hold for each volume element of the discharge separately while a
non-local model requires only a global power balance. The departure
from locality increases as either gas density ng or radius R is
decreased. Despite this, most current fluorescent lamp software is based on
the local concept. We present a non-local kinetic particle-in-cell Monte Carlo
collisions (PIC-MCC) code to simulate low-pressure, small-radius, positive
column discharges. This code is also compared to a non-local fluid code, a
non-local kinetic Monte Carlo code and to experimental data. The PIC-MCC code
made the least approximations and assumptions and was accurate and stable over
a wider parameter regime than the other codes. Also, 1d3v PIC-MCC simulation
speeds are quite competitive even on moderate workstations. Finally, we
analyse the PIC-MCC simulation results in detail, especially the power balance
and the radial electron kinetic energy flux Hr(r). We found that for low
ngR< 1×1015 cm-2, the electron kinetic energy flux is directed radially
outward while for higher ngR, it is directed radially inward except right
near the wall.
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