  4D mathematical models of structurally related (conjugated, entangled, dual)
phenomena of dissipation and cumulation of electrical energy (an external
source in continuous media) are discussed, accompanied by the formation of
cumulative-dissipative structures and their ordering into a regular system - a
dynamic dissipative "crystal" with a long-range dynamic order. The excitation
of new degrees of freedom in such systems provides attractiveness or geometric
self-focusing of energy-mass-momentum flows (EMMF) for the entire regular
system. As a result of cumulation, EMMF structures acquire hyper-properties.
The cumulation of EMMF in rendered structures is a common property of media
activated to form 4D structures. The basis of such a dissipative structure is
an attractor, the end result of which is a cumulative jet from an attractor
with hyper-properties. Therefore, these structures are cumulative-dissipative.
We discuss a method for describing these structures and prove that cumulative
processes in plasmoids exist and can be described theoretically, although not
with the help of full-fledged mathematical 4D models. It has been theoretically
and experimentally proven that the cumulation of the electric field due to the
ambipolar drift of the plasma is an inherent property of the current carrying
gas-discharge plasma. The results obtained by modeling shock waves of the
electric field (E/N) can be useful to explain the cumulative formation in the
heliosphere, atmosphere and ionosphere of the Earth, since the Earth has a
negative charge of about 500,000 C, and the Sun positively charged at the level
of 1400 C. Based on the mathematical approach, a classification of shock waves
and types of cumulation in 4D space-time will be carried out.
