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Abstract
A onedimension model for positivecolumn plasma is analyzed. In the framework of this model, a complete, selfconsistent 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 selfforming plasma structure with striations. Analysis of spatiotemporal 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 positivecolumn plasma in dcdriven 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 nonisothermic positivecolumn plasma in dcdriven lowpressure noblegas discharges proved to be rather realistic, capable of adequately reproducing the basic properties of real fieldplasma systems.
The author would like to thank Profs. S.N. Bagayev and A.M. Tumaikin for valuable discussions and encouragement. The author also expresses his gratitude to Dr. Yu.P. Zakharov and Prof. A.G. Ponomarenko for fruitful discussions.
I. INTRODUCTION
II. BASIC EQUATIONS AND THEIR GENERAL CONSIDERATION
III. ANALYSIS OF COROLLARIES FROM EQUATIONS (1)–(5)
IV. GENERALIZED FUNCTIONAL FOKKERPLANCK EQUATION
V. QUALITATIVE ANALYSIS OF PLASMA STATES AND ATTENDANT PHENOMENA IN DETAIL
A. How do spatiotemporal plasma structures (spatially homogeneous and stratified stationary plasma states) and their attendant phenomena fit into the general scheme of things?
B. Striations
C. Jumps in current, shock waves and hysteresis phenomena
D. Structural self organization, plasma generation, and similarity laws.
VI. CONCLUSIONS
Key Topics
 Gas discharges
 77.0
 Ionization
 59.0
 Plasma ionization
 58.0
 Electric fields
 38.0
 Electrical properties
 35.0
Figures
The universal form of the ionization equilibrium surface K(N e , p(E), q(E)) = 0 in the generalized space N e , p, q in the vicinity of the ‘wrinkle’. Portions 1 and 2 of the trajectory (p, q) belong to the first sheet (I) of plasma states. Although the condition of ionization equilibrium is satisfied at portion 3 of the trajectory (p, q), the plasma states are unstable and physically dormant there. Portions 4 and 5 of the trajectory (p, q) belong to the second sheet (II) of plasma states.
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The universal form of the ionization equilibrium surface K(N e , p(E), q(E)) = 0 in the generalized space N e , p, q in the vicinity of the ‘wrinkle’. Portions 1 and 2 of the trajectory (p, q) belong to the first sheet (I) of plasma states. Although the condition of ionization equilibrium is satisfied at portion 3 of the trajectory (p, q), the plasma states are unstable and physically dormant there. Portions 4 and 5 of the trajectory (p, q) belong to the second sheet (II) of plasma states.
Typical currentvoltage characteristic of noblegas discharges.
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The classical ‘trident’, or ‘fork’, scheme for the roots ρ0(E), ρ1(E), and ρ2(E) in the transition region of gasdischarge currentvoltage characteristics.
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The classical ‘trident’, or ‘fork’, scheme for the roots ρ0(E), ρ1(E), and ρ2(E) in the transition region of gasdischarge currentvoltage characteristics.
Stages, or branches, of motion, and the selfdeformation of U(N e (E), E); (a) corresponding to U(N e (E), E) in the initial stage of self switching to the first branch of motion (changeover from N 1 (state 1) to N 2 (state 2), and (b) for the intervening stages; (c) corresponding to U(N e (E), E) in the initial stage of self switching to the second branch of motion (changeover from N 2 (state 2) to N 1 (state 1).
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Stages, or branches, of motion, and the selfdeformation of U(N e (E), E); (a) corresponding to U(N e (E), E) in the initial stage of self switching to the first branch of motion (changeover from N 1 (state 1) to N 2 (state 2), and (b) for the intervening stages; (c) corresponding to U(N e (E), E) in the initial stage of self switching to the second branch of motion (changeover from N 2 (state 2) to N 1 (state 1).
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.
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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.
Dynamic trajectories, or limit cycles, of the second class of solutions in the planes (N e , E) and (N*, E); (a) corresponding to the limit cycle N e (E) and (b) for the limit cycle N*(E). Curve 1(a) is the middle root N 0(E) versus the control parameter E. Curve 2(a) is the first root N 1(E) and the second root N 2(E) (respectively the upper and lower curve) versus the control parameter E. Curve 3(a) is the first branch of the dynamic solution N e (E). Curve 4(a) is the second branch of the dynamic solution N e (E). Curve 1(b) is the first branch of the dynamic solution N*(E). Curve 2(b) is the second branch of the dynamic solution N*(E).
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Dynamic trajectories, or limit cycles, of the second class of solutions in the planes (N e , E) and (N*, E); (a) corresponding to the limit cycle N e (E) and (b) for the limit cycle N*(E). Curve 1(a) is the middle root N 0(E) versus the control parameter E. Curve 2(a) is the first root N 1(E) and the second root N 2(E) (respectively the upper and lower curve) versus the control parameter E. Curve 3(a) is the first branch of the dynamic solution N e (E). Curve 4(a) is the second branch of the dynamic solution N e (E). Curve 1(b) is the first branch of the dynamic solution N*(E). Curve 2(b) is the second branch of the dynamic solution N*(E).
Finding the value of μ from the Maxwell phase rule; (a) corresponding to the spatially homogeneous state and (b) for the stratified state.
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Finding the value of μ from the Maxwell phase rule; (a) corresponding to the spatially homogeneous state and (b) for the stratified state.
The experimental amplitude of ionization N e versus the dischargegap length L.
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The experimental amplitude of ionization N e versus the dischargegap length L.
Ranges of gasdischarge parameters in which artificial striations and selfexcited striations appear in the plasma; (a) corresponding to the parameter J(E) versus the electrical field E and (b) for the value N*(E).
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Ranges of gasdischarge parameters in which artificial striations and selfexcited striations appear in the plasma; (a) corresponding to the parameter J(E) versus the electrical field E and (b) for the value N*(E).
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.
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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.
The structure of the diffuse ionization shock wave; Sub picture (a) corresponding to i = 1 and sub picture (b) for i = 2.
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The structure of the diffuse ionization shock wave; Sub picture (a) corresponding to i = 1 and sub picture (b) for i = 2.
The modification of the ionization potential U(N e , E) in close vicinity to the point of breakdown.
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The modification of the ionization potential U(N e , E) in close vicinity to the point of breakdown.
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Abstract
A onedimension model for positivecolumn plasma is analyzed. In the framework of this model, a complete, selfconsistent 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 selfforming plasma structure with striations. Analysis of spatiotemporal 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 positivecolumn plasma in dcdriven 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 nonisothermic positivecolumn plasma in dcdriven lowpressure noblegas discharges proved to be rather realistic, capable of adequately reproducing the basic properties of real fieldplasma systems.
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