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The positive-column plasma in low-pressure noble gas d.c. discharge as an integral plasma-field system
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Figures

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FIG. 1.

The universal form of the ionization equilibrium surface ( , (), ()) = 0 in the generalized space , , in the vicinity of the ‘wrinkle’. Portions 1 and 2 of the trajectory (, ) belong to the first sheet (I) of plasma states. Although the condition of ionization equilibrium is satisfied at portion 3 of the trajectory (, ), the plasma states are unstable and physically dormant there. Portions 4 and 5 of the trajectory (, ) belong to the second sheet (II) of plasma states.

Image of FIG. 2.

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FIG. 2.

Typical current-voltage characteristic of noble-gas discharges.

Image of FIG. 3.

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FIG. 3.

The classical ‘trident’, or ‘fork’, scheme for the roots ρ(), ρ(), and ρ() in the transition region of gas-discharge current-voltage characteristics.

Image of FIG. 4.

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FIG. 4.

Stages, or branches, of motion, and the self-deformation of ( (), ); (a) corresponding to ( (), ) in the initial stage of self- switching to the first branch of motion (change-over from (state 1) to (state 2), and (b) for the intervening stages; (c) corresponding to ( (), ) in the initial stage of self- switching to the second branch of motion (change-over from (state 2) to (state 1).

Image of FIG. 5.

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FIG. 5.

Intervening stages of motion of the local state of gas discharge plasma; (a) corresponding to the initial stage and (b), (c), (g), (f), (e), and (d) for the intervening stages.

Image of FIG. 6.

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FIG. 6.

Dynamic trajectories, or limit cycles, of the second class of solutions in the planes ( , ) and (*, ); (a) corresponding to the limit cycle () and (b) for the limit cycle *(). Curve 1(a) is the middle root () versus the control parameter . Curve 2(a) is the first root () and the second root () (respectively the upper and lower curve) versus the control parameter . Curve 3(a) is the first branch of the dynamic solution (). Curve 4(a) is the second branch of the dynamic solution (). Curve 1(b) is the first branch of the dynamic solution *(). Curve 2(b) is the second branch of the dynamic solution *().

Image of FIG. 7.

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FIG. 7.

Finding the value of μ from the Maxwell phase rule; (a) corresponding to the spatially homogeneous state and (b) for the stratified state.

Image of FIG. 8.

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FIG. 8.

The experimental amplitude of ionization versus the discharge-gap length .

Image of FIG. 9.

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FIG. 9.

Ranges of gas-discharge parameters in which artificial striations and self-excited striations appear in the plasma; (a) corresponding to the parameter () versus the electrical field and (b) for the value *().

Image of FIG. 10.

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FIG. 10.

Parameters of the diffuse ionization shock wave; (a) corresponding to parameters in the laboratory system of coordinates and (b) for the system of coordinates moving with the shock wave front.

Image of FIG. 11.

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FIG. 11.

The structure of the diffuse ionization shock wave; Sub picture (a) corresponding to = 1 and sub picture (b) for = 2.

Image of FIG. 12.

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FIG. 12.

The modification of the ionization potential ( , ) in close vicinity to the point of breakdown.

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/content/aip/journal/adva/1/2/10.1063/1.3592525
2011-05-10
2014-04-17

Abstract

A one-dimension model for positive-column plasma is analyzed. In the framework of this model, a complete, self-consistent set of equations for the plasma column is proposed and justified. Basic prerequisites for the model and the equations used in it are discussed at length to clarify the mathematics and physics that underlie the proposed generalized description of plasma states. A study of the equations has unveiled the existence of two structurally stable types of steady states and three integrals of motion in the plasma system. The first type of states corresponds to spatially homogeneous plasma, and the second type, to the self-forming plasma structure with striations. Analysis of spatio-temporal plasma structures (spatially homogeneous and stratified stationary plasma states) and their attendant phenomena is given in detail. It is shown that the equations offer a more penetrating insight into the physical states and properties of positive-column plasma in dc-driven gas discharges, and into the various phenomena proceeding in the discharge system. Such a behavior is intimately related to the influence which the electric field has on the rate of ionization reactions. The theoretical results are compared to experimental data and can be used for to place the great body of experimental data in their proper framework. The modern fluid bifurcation model proposed to describe the properties of non-isothermic positive-column plasma in dc-driven low-pressure noble-gas discharges proved to be rather realistic, capable of adequately reproducing the basic properties of real field-plasma systems.

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Scitation: The positive-column plasma in low-pressure noble gas d.c. discharge as an integral plasma-field system
http://aip.metastore.ingenta.com/content/aip/journal/adva/1/2/10.1063/1.3592525
10.1063/1.3592525
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