Non-stationary 3D Perturbation Theory for Describing Nonlinear Interaction of Electric Field with Matter in Inhomogeneous Plasma with Current. Vysikaylo’s Electric Field Shock Waves and Plasma Nozzles
Authors:   Plasma Chemistry Laboratory, Moscow Radiotechnical Institute RAS, 117519 Moscow, Russia, Vysikaylo Philipp I. 
Published: November 2024

In our works we theoretically prove that the cumulation (self-focusing) of charged particles in a inhomogeneous plasma (with
current) is a universal property of cumulative-dissipative structures with characteristic sizes from 10-15 to 1026 m. Electrical
phenomena are observed in non-uniform atmospheres and ionospheres of all planets of the Solar System. In this paper, the most
complete theory of perturbations to describe phenomena in gas discharge plasma is formulated and, based on this theory, the
most complete classification of ambipolar transfer processes in plasma with current and the classification of non-uniform plasma
parameter profiles are given. We compare our theoretical results with existing experiments and results obtained in other areas of
the natural sciences. In this work, we theoretically (Part 6.1) and experimentally (Part 6.2) we prove that shock waves of electric
fields are focusing shells for inhomogeneous plasma cumulative-dissipative positively charged 3D structures. In the Part 6.1 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 the space charge. This makes the problem
(in the electric field shock wave region) three-dimensional (in particular, spherically or cylindrical symmetric in this region). In
Part 6.1, we will limit ourselves to the study of stationary one-dimensional 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 6.1, the author will limit himself to obvious remarks arising from the properties of three-dimensional structures with a
positive space charge. Based on laboratory 3D experiments (Part 6.2) 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 – 4D plasmoids in plasma (with current).
4D plasma structures are non-stationary three-dimensional structures. The author draws attention to self-formation in plasma
structures (plasmoids) of stationary Vysikaylo’s plasma nozzles - analogues of Laval’s nozzles. A comparison of theoretical 1D and
experimental 3D observations of discharge glow (this corresponds to changes in the main parameters) in gas discharge tubes will
be presented in Part 6.2. 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 3D profiles and Vysikaylo’s plasma 3D nozzles already in a quasi-neutral inhomogeneous plasma.
In this work, we were the first to theoretically and experimentally study the processes of nonlinear ambipolar transport caused
by the violation of electrical neutrality and 3D interaction of electric fields with matter (charged particles) in an inhomogeneous
plasma with current. For the first time it has been proven that the coefficients of ambipolar diffusion due to the violation of
electroneutrality are vectors determined by the electric field vector.