Shock Waves of Electric Field—Part 1: Theoretical Studies of Vysikaylo’s Jumps and Plasma Nozzles in Plasma With Current

In this work, we prove that the cumulation (self-focusing) of charged particles in a plasma (with current) is a universal property of cumulative-dissipative structures with characteristic sizes from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-15}$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{27}$ </tex-math></inline-formula> m. In this work, we theoretically (Part 1) and experimentally (Part 2) prove that shock waves of electric fields are focusing shells for plasma cumulative-dissipative positively charged plasma 3-D structures. In Part 1 of this work, we provide detailed theoretical justifications for the possibility of the existence of (locally self-focusing by ambipolar drift) Vysikaylo’s electric field shock waves caused by ambipolar diffusion due to a violation of the electrical neutrality of the plasma (in the presence of an electric current). Due to the greater mobility of electrons (ions are more massive), a structure with a positive space charge is formed in the electric field shock waves that self-form in the plasma (with current). Unlike Mach’s shock waves, in closed Vysikaylo’s shock waves transverse electric fields are generated due to space charge. This makes the problem (in the shock wave region of the electric field) 3-D (in particular, spherically symmetric in this region). In Part 1, we will limit ourselves to the study of stationary 1-D profiles: 1) parameters in shock waves of the electric field and 2) processes of ambipolar drift, leading to local cumulation of positive charge in the shock wave of the electric field. In Part 1, the author will limit himself to obvious remarks arising from the properties of 3-D structures with a positive space charge. Based on laboratory 3-D experiments (Part 2) and theoretical studies of gas-discharge plasma, we prove that ambipolar drift caused by different dependences of the mobility of electrons and positive ions in a simple plasma (with one type of ions) determines the dynamic processes of cumulation of plasma structures—4-D plasmoids in plasma (with current). Four-dimensional plasma structures are nonstationary 3-D structures. The author draws attention to self-formation in plasma structures (plasmoids) of stationary Vysikaylo’s plasma nozzles—analogs of Laval’s nozzles. A comparison of theoretical 1-D and experimental 3-D observations of discharge glow (this corresponds to changes in the main parameters) in gas discharge tubes will be presented in Part 2. In these experiments, a homogeneous plasma in a gas discharge tube is locally disturbed by a beam of fast electrons. This leads to the self-formation: 1) of electric field shock waves (a layer of positive volume charge) stopped by gas pumping and 2) of transition 3-D profiles and Vysikaylo’s plasma 3-D nozzles already in a quasi-neutral homogeneous plasma.