Ionization Waves in Electrical Breakdown of Gases

In the years since the book of Lozanskii and Firsov "The Theory of Spark" [1975] was published, a number of experimental and theoretical studies in the physics of electric breakdown in gases were conducted. As a result of these studies, the concept of a wavelike nature of breakdown initiated by single high-voltage electric pulses or by a constant electric field was confirmed. Theoretical models in which the concept of breakdown in a constant external field was developed were first exposed in the above-named book in the chapter "Development of a streamer regarded as an ionization wave," written by Rodin and Starostin. This book treats the initial stage of electric breakdown as a wave pro cess. The wavelike nature of the phenomena under consideration is pre sented for streamers and sliding discharges, for electric breakdown develop ment in long discharge tubes as well as in gas-filled gaps. Chapter 1 gives a qualitative consideration of phenomena determin ing the electric breakdown of gases. The experimental data and theoretical results are exposed and discussed with application to streamers, plane ion ization waves, breakdown waves in long tubes, and propagation of sliding discharges. The subject of this chapter may be considered as an area of applications of different theoretical models, formulas, and estimates that are presented in other chapters of the book.

In the years since the book of Lozanskii and Firsov "The Theory of Spark" [1975] was published, a number of experimental and theoretical studies in the physics of electric breakdown in gases were conducted.

1. Wave Phenomena Determining Discharge Development in Gas Gaps.- 1 Dynamics of Streamers.- 1.1 Development of an Electron Avalanche.- 1.2 Propagation of Anode- and Cathode-Directed Streamers.- 2 Ionization Waves in Discharge Tubes and in a Sliding Discharge Formation System.- 2.1 Experimental Study of Ionization Waves in Discharge Tubes.- 2.2 Formation of a Sliding Discharge.- 2. Macroscopic and Kinetic Description of a Weakly Ionized Gas in an Electric Field.- 1 Basic Macroscopic Equations.- 2 Local Approach for the Frequency of Impact Ionization.- 2.1 The Townsend Ionization Coefficient and the Frequency of Ionization by an Electronic Impact.- 2.2 Conditions of Applicability of the Local Approach. Equation for the Electron Distribution Function over Energies in a Nonuniform, Nonstationary Plasma.- 3. Theory of Plane Ionization Waves.- 1 Stationary Plane Electric Breakdown Waves.- 1.1 Ionization-Drift Models of Anode- and Cathode-Directed Waves.- 1.2 Influence of Diffusion and Photoprocesses on the Plane Breakdown Waves.- 2 General Properties of Nonstationary Ionization Fronts.- 2.1 Integrals of Nonstationary Equations. Reduction of a General Problem to the Cauchy Problem for the Electric Field Distribution.- 2.2 Solution of the Cauchy Problem by the Method of Characteristics. Conditions for the Breaking of a Continuous Solution.- 2.3 Propagation of Strong and Weak Discontinuities of Electron Concentration.- 3 Dynamics of Formation of the Anode- and Cathode-Directed Waves from Initial Nonuniformities.- 3.1 Asymptotic Behavior of the Solution of the Cauchy Problem for a Finite Initial Distribution of Electron Concentration.- 3.2 Development of Ionization Waves from Infinitely Extended Distribution of Electron Concentration.- 4. Propagation of Ionizing Electric-Field Solitary Waves in Shielded Discharge Tubes with Preionization.- 1. Basic Equations and Assumptions.- 2 The Effect of the Surface Wave on the Formation of the Ionization Wave.- 3 Averaging Two-Dimensional Equations and Formulation of a Quasi-One-Dimensional Model.- 4 Numerical Simulation of Stationary Waves.- 5 Analytical Model of an Ionization Wave.- 6 Specialized Problems of the Theory of Breakdown Waves in Tubes with Preionization.- 6.1 Limiting Transition to a Nonlinear Model of the Electric Potential Diffusion. Conditions of Nonmonotonic Increase of Current in a Wave.- 6.2 Emergence of the Oscillating Structure of an Ionization Wave.- 6.3 The Effect of a Longitudinal Magnetic Field on the Structure of a Fast Ionization Wave.- 5. Propagation of Electric Breakdown Waves Along a Gas-Dielectric Boundary With No Preionization.- 1 Breakdown Waves in Shielded Tubes Without Preionization.- 1.1 Taking Account of Associative Ionization and Resonance Radiation Transfer.- 1.2 Results of Numerical Calculations of Breakdown Stationary Waves.- 1.3 Analytical Estimate of Breakdown Wave Velocity.- 2 Propagation of a Sliding Discharge Front as an Ionization Wave.- 2.1 Assumed Equations and Problem Statement.- 2.2 Formulating a Calculated Model of a Stationary Wave.- 2.3 Structure and Velocity of Front Propagation.- 3 Slow Breakdown Waves in Shielded Tubes.- 3.1 Features of a Quasi-One-Dimensional Solution Describing Slow Waves.- 3.2 Influence of a Longitudinal Magnetic Field on the Structure of Slow Waves.- 4 Solitary Wave of an Electric Field as a Source of Runaway Electrons.- References.