** **

**3.****
****The field in near and far zones. ****The vortexes interaction **

**
****through**** variable fields**

The understanding of a structure of
separate electromagnetic vortexes opens prospects
of studying collective processes. We know from a course
of electrical technology as constant charges can interact. Therefore here we shall
consider forces, which are caused only by variable fields. We shall begin with pair interaction.

The same is true to the same field of the right
vortex (dashed lines) with regard to the maximal density of the left vortex. If
the same situation has developed concerning the second field (**E** or** ****H**), then the total energy reaches its minimum. It is obvious that there
are at least several such minima of total energy, in view of periodical
dependence of the fields on the distance* **d*. Their general energy decreases with distance* **d*, as well as the squared cylindrical function of the half-integer
argument, describing the envelope turning around the fields in the linear range
(see Appendix 4 and 5). Except for distance* **d* such positions depend on
phases of oscillating processes in each vortex. And these phases, in turn, are
connected with spatial angles, made with each vortex. The types of waves in a
vortex, which depend on the corresponding attached Legander polynomials, define
the angles_{}. This phenomenon accounts for possible steady, i.e. stationary states of
system. Let's pay attention of the reader that vortexes can be the most
different and strongly differ among themselves in coefficients* **m* and* **n* of Legander polynomials.

Unstable intermediate positions (the
forbidden values of general energy) are bindingly located between such states,
for example at the distance_{ }*d _{2}*, as it is shown in the low part of Fig. 25. Thus, we can see a
fundamental property of vortexes: they have a multilevel system of interaction
with a set of the allowed and forbidden states. Further it can be easily
subjected to mathematical generalization, all the more so as the whole ideology
of calculations and their concrete technology have already been developed by an
outstanding Belgian scientist Ilia Romanovich Prigozhin [24, 25]. Even
Schrodinger equations are not necessary, for in this case all the
problems lead to Liouville

Basic properties of vortexes group transients from one
steady state to another state are very important. The elementary statistical
problem in this case should be formulated so: there is a system of vortexes,
which comprises, at least, two subsystems. The first subsystem contains
vortexes pairs which are being in the first steady state, the second - in the
second. Each of these subsystems is characterized by a fundamental oscillations
frequency of corresponding vortical pairs. Change of the state of system means change of proportions between
subsystems. All system is parametrical owing to nonlinear character of internal
interactions of all vortexes. Transitions of parametrical system from one state
in another are well investigated in 60^{th} years of the last century
(see, for example, [26, 27]) within the limits of the properties studying of
parametric amplifiers for needs of radio astronomy and of a radiolocation.

Distant interactions can be of interest too,
inasmuch as gravitation can be. It can also be easily calculated with the help
of Prigozhin's methods. The matter is that at greater distances average energy
is not set to zero, since forces of interaction are not rigid. In dynamic
electrodynamics, with which we are deal now (see Appendix 2), they are either
potential, or quasi-potential. I.e. we can observe elasticity, which causes field extension and field
squeeze with the general energy having a tendency to reach its minimum. This
leads to gravitation in accordance with Kulon's law. It is this law that
follows from the quadratic dependence of interaction forces according to the
amplitudes of the radial (Bessel) functions, which describe the dependence of
fields on the distance. We operate with these functions in Appendixes 4 and 5.

Thus, peripheral electromagnetic fields of a
set of vortexes are a source of a gravitational field, and not at all Mileva
Marich’s grandfather (see the preface) as the academician Okun thinks.