Radial structure of the constricted positive column: Modeling and experiment

We present a detailed self-consistent model of a positive column in argon glow discharge at moderate pressures and currents. This model describes the discharge transition between diffuse and constricted states. The model includes an extensive set of plasma chemical reactions and equation for inhomogeneous gas heating. The nonequilibrium behavior of an electron distribution function is also considered. One of the main features of the model is an accurate treatment of radiation trapping by solving the Holstein-Biberman equation directly. Influence of the radiation trapping on macroscopic parameters of the constricted positive column is studied. We propose a method for solving a boundary-value problem, including particle and energy balance equations for electrons, ground state atoms, atomic and molecular ions, and excited species. Unlike traditional solution approaches for similar systems, the method provides continuous Z- and S-shaped characteristics of discharge parameters, describing hysteresis in transition between diffuse and constricted discharge regimes. Performed experiments include measurements of volt-ampere characteristics and spectroscopic study of radial density profiles of excited atoms by measuring line emission and absorption, and electrons by measuring bremsstrahlung intensity. The role of resonance radiation trapping in spatial redistribution of $1s$ and $2p\mathrm{states}$ of argon is demonstrated. Results of modeling are compared to the experimental data.

Figure 1

Example of the field-current characteristic obtainable with different solution approaches. (a) The traditional time-dependent method; (b, c) the stationary boundary-value method.

Figure 2

Scheme of the self-consistent calculation.

Figure 3

Scheme of the experimental setup. Fragment of the constricted discharge (on the left).

Figure 4

(a) Measured density profile of the $2p$ state. (b) Instrument function of the experimental setup. (c) Calculated density profile of the $2p$ state (solid line), convolution of this profile with the instrument function (dashed line).

Figure 5

Examples of spatial profiles of ${\mathrm{\Phi }}_1,{\mathrm{\Phi }}_2,{\mathrm{\Phi }}_{1+2}$ measured in different spectral lines of Ar. Dashed vertical lines determine an area suitable for measurements (excluding the wall reflections).

Figure 6

(a) The measured emission spectrum of the argon glow discharge in the range of intensive continuum. (b) Measured radial profiles of the gas temperature [15], electron temperature, continuum intensity, and electron density.

Figure 7

Discharge characteristics as functions of a current computed in different approximations. (a) The relative current flow area, (b) the axial electron density, (c) the field-current characteristic, (d) test for the identity of expression (15).

Figure 8

Electron energy distribution function in case of the (a) diffuse discharge, (b) constricted discharge. The vertical dashed line is the excitation threshold ${\varepsilon }_{th}=11.55$ eV. (c) The radial distribution of fast electrons ($\varepsilon >11.55$ eV).

Figure 9

Influence of the radiation trapping on radial density distributions of the (a) $1s\mathrm{states}$, (b) $2p\mathrm{states}$ in the constricted discharge at 40 mA.

Figure 10

Influence of the radiation trapping on the density of (a) electrons, (b) $2p\mathrm{states}$, (c) metastable atoms in the $1s_5\mathrm{state},$ and (d) resonance atoms in the $1s_4\mathrm{state}$ in Ar at 15 mA (diffuse discharge) and 40 mA (constricted discharge). Dashed lines are profiles, calculated using effective lifetime approximation; solid lines are computed accounting for radiation transport.

Figure 11

Field-current characteristic in the Ar discharge at 42 Torr, comparison of the simulation with experimental data.

Figure 12

Radial profiles of excited atoms measured by various spectral lines in constricted Ar discharge at $p=42$ Torr, $i=40$ mA: (a) the various $2p$ states, (b) the metastable $1s_5$ state, and (c) the resonance $1s_4$ state.

Figure 13

Measured and calculated radial density profiles at $p=42$ Torr, $i=40$ mA. Points, experimental data averaged over lines; lines, convolution of the calculated profile with the instrument function. (a) The electron density, (b) $2p\mathrm{atoms}$, (c)–(f) $1s\mathrm{atoms}$.