J. Mod. Phys., 2010, 1, 251-275
doi:10.4236/jmp.2010.14037 Published Online October 2010 (http://www.SciRP.org/journal/jmp)
Physics Base & Conceptual Views Complex of Ball
Lightning
Anton V. Pinchuk1, Vladimir A. Pinchuk2
1Scientific Technical Center “Protei”, Saint_Petersburg, Russia
2The Baltic state technical university, Saint_Petersburg, Russia
Received June 23, 2010; revised August 27, 2010; accepted September 16, 2010
Abstract
The complex of conceptual views about ball lightning (BL) as containing surplus electrical charge quasi-
stationary material foundation with distinctions between levels of translation temperature and exciting tem-
peratures of chemical bonds and electron energy states has been offered and is substantiated in the paper.
The being formed complex is grounded upon overstepping the limits of generally accepted physical base and
is aimed at all-round substantiation of jointly observed in nature manifestations of BL. Within the limits of
the being formed complex the possibility of localization of ball lightning in airspace is confirmed. The nature
of the one’s radiate capacity is substantiated. The role of environment as source that feeds BL with energy is
established. Power supply mechanisms, conditions and peculiarities of BL’s characteristics reproduction
through lifetime are specified. The formations channels of energy resources of BL are turned out. Levels of
BL’s energy potentialities, both permissibility proper and wide diapason of variation of the ones (multi-faces
of ball lightning) as well as the capability of BL to overcome any barriers from dielectric materials by means
of penetration through inanes in body of barriers and then to restore the one’s characteristic (octopus’s effect)
are substantiated. Adequacy of being formulated conceptual views as a whole is confirmed.
Keywords: Ball Lightning, Natural Anomaly
1. Introduction
In 1838 year Fransuar Arago-the member of French Sci-
ence Academy published the article with generalization
of several views of Ball Lightning (BL). Since then and
up till now the substantiation problem of BL’s nature is
in the attention centre of scientists of the all world. The
numerous works (Barry J., Dmitriev M. T., Elliott lo.,
Singer S., Silberg P., Shabanov G. D., Sokolovski B. Yu.
Smirnov B. M., Stakhanov I. P., …) directed onto both
the generalization of ball lightning observations and
making-up of a common ideas of the ones are known.
Among important results of their joint work the
portrait of Ball Lightning, having been formulated by
generalization of numerous observations of BL in the
nature, should be mentioned above all. The one can be
presented, for example, by the next means.
The ball lightning (BL) in itself is of nature origin,
being displaying with energy radiation into environment
a material formation, localized in airspace as rotation
ellipsoid or even in the similar to spherical shape, the
one being able to move, primary motion directions of
that aren’t determined, however, by gravitation and/or
air dynamic forces and lifetime of that, accordingly with
observations, is at least tens of second. Characteristics
of BL, being only insignificantly changed or even kept
practically constant in lifetime, don’t register seemingly
evident reduction of energy resources of ball lightning
during time of one’s existence in connection with radia-
tion energy to environment. What is more, the disap-
pearance (disintegration) proper of BL is accompanied
as a rule with an additional energy discharge into envi-
ronment (frequently considerably exceeds quasi-stationary
level of energy radiation). Multi-faces being manifested
first of all by energy levels differences being discharged
into environment with BLs at the disappearance period
under seemingly the same characteristics of the ones’
quasi-stationary state typical to BL.
At last “Octopus’s effect”, that is capability of BL to
overcome different barriers from dielectric materials
(window-frame, for example) by means of penetration
through inanes in the ones’ body (hollows, cracks, splits)

A. V. PINCHUK ET AL.
252
with essentially lesser sizes, concerning to dimensions of
BL and then to restore (reconstruct) in essence initial
shape and characteristics is peculiar to BL too.
However up to now, even after the lapse of about two
century, the generally accepted conception of both nature
and jointly fixed characteristics of BL on the base of
universally recognized physical views is not turned out
yet. What’s more the true sensation of pessimism in es-
timations of principal possibilities to interpret the BL
nature on this basis is felt.
It’s undoubtedly, that the being settled situation shows
first of all to exceptional complexity of BL as the invest-
tigation object. At the same time, it unquestionably notes
too towards the principal insufficiency of resolving
power of being used investigation methods formed in
these cases in the framework of traditional physical re-
strictions (i.e. towards imperfection of the physical basis
as itself).
It is interesting to note in this connection that the sci-
ence history is rich with examples when the one or other
problem, occurring itself interest for investigations and
being very important just as from practical so from sci-
ence standpoint, within of generally adopted physical
limits is kept unsolved and only going out of these limits
is way to solve the one. In other words there is reason so
to think that the Ball Lightning in the greatest degree is
in keeping with these features.
The attempts to work out the complex substantiation
of both the nature and manifestation of BL on the basis
of overstepping the limits of traditional physical restrict-
tions, earlier unknown Internal Energy Equilibrium Con-
ditions (IEEC–between energy states with different na-
ture) of material media are known too [1-13].
Admittedly, the developed views of BL so far do not
obtain of due expansion and of necessary public recogni-
tion (in that number owing to the being kept till now
doubts about substantiations of proper IEEC) and de-
mand so additional explanation and progress.
Having been formed situation and determined in es-
sence expediency and purposefulness of this work. The
paper is based upon materials of [1-13] and, at the same
time, is aimed onto generalization and further logical
progress of the ones.
2. Strategy Forming
2.1. Initial Views
On being formed of initial views of BL we will take into
account only common, beyond all doubt observed of ball
lightning’s characteristics.
It must be admitted so that BLs exist and are spring up
under conditions of developed electro-static fields. They
are moved somewhere else and are observed as localized
in the airspace material formations having form similar
to sphere. The prevailing transferences directions of ball
lightning in airspace are not determined by the both
gravitation and/or forces of aerodynamic origin1. BL’s
lifetime may achieve at least to several tens seconds.
The BL occurrence, as a rule, is accompanied by en-
ergy radiation into environment (thermodynamically
opened system) that is watched in the range of visible
spectrum part in that number. As this takes place, char-
acteristics of BL’s radiation are changed insignificantly
or even are kept practically an invariable. What is more,
disintegration of ball lightning often is accompanied with
extra energy escape into environment. The multi-faces,
revealed by considerable incompatibility of specific en-
ergy resources under seemingly equal or at least compa-
rable circumstances, else is peculiar to BL (see, for ex-
ample, [15,16]). Octopus’s effect-capability to overcome
different barriers from dielectric materials by means of
penetration through inanes in the body of barrier with
essentially lesser, concerning to dimensions of BL, sizes
and then to restore (reconstruct) in essence the ones’ ini-
tial shape and properties characteristic is characteristic of
Ball Lightning at last. The enumerated common proper-
ties with a great degree of trustworthiness are suited to
the real manifestations of balls lightning. However, up
till now the possibilities to realize the medium states with
noted characteristics intake, in the context of generally
accounted physics-chemistry views, are retained beyond
verge of explainable ones.
2.2. Basic Assumption
In evaluating of prospects for refinements of BL’s nature
in the framework of [1-13] the attention was being given
first of all to the established by observations fact that the
BL-medium contains surplus (uncompensated) electric
charge.
As an assumption, in connection with this, it was pre-
supposed that
“the observed characteristics of BL could be substan-
tiated, say, by the existence of traditionally not ac-
counted (earlier unknown) peculiarities of internal en-
ergy equilibrium conditions (IEEC-between energy states
with physical nature’s different kinds) for material for-
mations with surplus electric charge (AQN- or aquasi-
neutral formations) as determining, in that case by the
results of inevitably being exited relaxation of AQN-
formations on interacting with environment, and arising
and subsequent conservation in time (reproduction) of
1The marked indicates so that BL is subjected to force influences o
f
electric nature, i.e. keeps an uncompensated (surplus) electric charge.
The last is confirmed else by known theoretical investigations [14].

A. V. PINCHUK ET AL.
253
medium (in the AQN-formation’s composition) with
characteristics that differ from the environment and are
in keeping to BL”.
The possibilities to build on this base the physics-chemic
BL’s model will be estimate drawing away our attention
from both the composition and the nature of BL’s forma-
tion mechanisms as the subjects of specific interest as
itself.
3. The Internal Energy Equilibrium
Conditions (IEEC)
3.1. Ionization Equilibrium Conditions
Let’s estimate for the first time the possibly arising, in
connection with presence in medium’s composition of
surplus charge to fit the being expressed assumption, the
peculiarities of the medium’s inner ionization equilib-
rium.
3.1.1. Small Disturbances Method
As applied to p, T = Const let us separate out now some
volume of medium containing neutral (a), electron (e)
and ion (i) components. Let us account that the separated
so volume is bounded, for instance, by sphere of radius
bl
R and is thermodynamically opened system itself with
variable particles number and description of the one
conforms to three–liquid model ideas [17].
We’ll be take, as state parameters, the ionization degree
** *
*
(0) (0)(0)
ii i
aa a
pnkTn
pnkTn
   (1)
and relative content of uncompensated electron compo-
nent2

**
** **
** *
.
ei
ei ei
ii i
nnkT
pp nn
pnkTn



  (2)
Concentrations of components in medium’s composi-
tion in that case will be conform to relations
**()
;
o
ia
nn   ** (0) (1 );
ea
nn   *(0) (1 ) ;
aa
nn  
*(0)
[1(1 )].
a
nn 
 
Give up advantage to thermodynamic method as not
leaning upon any ideas of substance atomic-molecular
structure and being essentially phenomenological. As-
sume that by external in relation to sphere actions an
excess electric charge is inputted and at a later time is
retained in the composition of separated so medium
volume.
Accordingly generally adopted ideas inner equilibrium
of separated system should be in conformity with the
minimum of its thermodynamic isobaric-isothermal po-
tential “

” and, for ,pT Const, will be determined
in that case by equation
_
__ *
_
_
__ *
_
1,
*
*
11
,
*
*
1
0.
Jj
jpT
jj
jj
j
jpT
jj
j
N
N
NN
N
N






 




 


 





 
 



 



 










(3)
Here:
j


chemical potential of j-'s media compo-
nent (j = a, e, i).
Draw attention to the fact that under conditions when
the charge within the sphere is constant
**
()
qei
nnnConst  parameter

**
*
*(0)
q
ei
ia
n
nn f
nn






(4)
and first term of right part in equation (3) is identically
equal to zero. Equation (3) is transformed so to expres-
sion
_
*
*
11
0
jj
j
jjj
NN




 



(5)
and may be used for detecting of correlations between
states parameters of media plasma foundations corre-
sponding to inner energy equilibrium.
For the material system of examined composition the
equation (5) is rewrite in
0
iieea a
NN N







 (6)
and, with account of correlations between moles numbers
variations (0)
iia
Nnn

  ;
(0)
(1 )
ee a
Nn n



  ; (0)
aa a
Nnn

 
in accordance with (1). (2), is reduced to relationship


10
ie a
 

  (7)
For single-atom gas


3/2 5/2
3
0
2
ln ln
1, ,
,0,,
1, .
jj
jj
jjA j
gmkT
RT ph
ifj i
eZ NZifja
if je
















 



(8)
Expression (7) is converted into
2Here and below with «*» the parameters of media that contains surplus
charge are noted.

A. V. PINCHUK ET AL.
254


3/2 5/2
3
2
1, ,
exp,(1 ),,
1, .
j
j
c
j c
jj
jj
j
mkT
pgh
if ji
V
ec ifje
kT if ja









 

 






(9)
and, on the neglect of 2-order infinitesimal members,
corresponds to any from equations:
 
(1 )
3/2 5/2
**(1)
3
2
exp ,
e
ie i
e
aa
mkT
ppg g
pg h
V
ekT















(10)

(1 )
3/2
**(1)
3
2
exp
e
ie i
e
aa
mkT
nng g
ng h
V
ekT






 







(11)
or



 
(1 )
*(2 )
(1 )(1 )
**
(1 )
3/2 5/2
3
11
111
2exp
i
a
e
e
g
g P
mkT V
ge
kT h






















 

(12)
Here: V–media ionization potential determined in the
ordinary way;
–remote coulomb interaction potential (potentials
difference stipulating electrical action onto charge). More
detailed interpretation of its physical sense will be given
lower.
3.1.2. Ionization Equilibrium as Reaction onto
Disturbance
Assume as previously that some quantity of the same
charged particles are brought in (taken out from) the
considered volume owing to the system is moved up (and
at a later time exists) into the state with uncompensated
electric charge. It is obvious that charge introduction into
a system is equivalent to a work performance under the
one and causes so violation of inner energy equilibrium
of the system. With account of Le Сhatelier Principle
the last should being reestablished by inevitably arising
in these conditions system reaction, suppose in the
A
Ae

 kind.
If a work has been done under the system by external
actions is 1
1ee
LN   and a change of the system’s
thermodynamic potential was stipulated on the system
with external actions is iiee aa NN N

   
then being anew settled equilibrium must corresponds to
то condition
1.
ii ee aaee
NN NN

 

 (13)
It is obvious that ie a NN N

  and (13) is
presented in the kind
1.
e
iea e
i
N
N

 

 (14)
The ratio 11
ei ee
NNNN



determines the
molar part of excess charge carriers per ion component
mole and corresponds in being again settled gas medium
composition to system’s state parameter

according
(2). The equation (14) is truly kept to the relations (9)-
(12), which proves the statement.
3.2. Common Character of Inner Equilibrium
In deducing on (9)-(12) we assumed that inner equilib-
rium disturbance by carrying in system’s composition of
surplus charge is necessarily suppressed with reaction of
A
Ae


kind. However the noted is not having one.
Indeed, “from all possible steady states of thermody-
namic system being allowed with border conditions of
the law of mass transfer and conservation along with 2nd
law of thermodynamic the state with minimum produc-
tion of entropy is realized” [18], to say, that which is
priority one.
Let us assume that priority reaction formed in the sub-
system as response onto disturbance in connection with
carrying in medium composition of surplus charge is
reaction of
A
BAB

 shape. If the work was done in
the case under system by external actions is
1
1ee
LN



that being anew-formed equilibrium will
correspond to the condition
1.
ABABAA BBee
NNN N

 

 (15)
Take into account that the relation molar contribution
into a relaxation reaction of electron component
1/
eAB
NN    (that in full measure correlates with
physical interpretation of parameter according to expres-
sion (2)) and AB A B NNN



. By this means in
neglecting of 2-order infinitesimal quantities the expres-
sion (15) may be written in the form

exp ,
1, ,
,,
1,, .
cj
cjact
jj
jj
j
e
pKT kT
if jAB
cifje
ifjA B















(16)
Here: act


association reaction’s activation energy

A. V. PINCHUK ET AL.
255
(or any other one’s that in frame of specifically arising
conditions in the system is priority one) being deter-
mined in essence by generally accepted method.
3.3. Equilibrium Inner Peculiarities
The expressions (9)-(12), (16) determine so Inner Energy
Equilibrium Conditions (IEEC) in material media com-
positions in that number with account of possible pres-
ence of surplus electric charge in the ones composition.
From analogues of generally accepted form the lasts are
distinguished essentially with only presence in exponent
indexes of additional term e


.
Concrete character of IEEC accordingly (9)-(12), (16)
indicates so that, as applied to localized AQN-foundations
temperature Tas traditionally estimated parameter di-
rectly determines equilibrium populations of energy
states only with “mechanical” nature (translation, oscil-
lating, rotatory ones).
If in the framework of traditional description and with
account of (9)-(12), (18) *
exc
T-the excitation tempera-
tures of chemical bonds and electron energy states of
medium then their correlations with T-the excitation
temperature of mechanical energy states (after referred to
as translation one) to be determined by equation
*j
exc
j
TT e




 (17)
Corresponding to IEEC the function of population dis-
tribution of chemical bonds and electron energy states
will be correspond with relation
*exp
j
je
NkT

 




(18)
By IEEC, the population distribution function of
chemical bonds and electron energy states in medium of
AQN-foundations (directly since formation moment of
the ones) is necessarily transformed (or at least is put to
the deformation) to the form (18).
In other words IEEC in the form of (9)-(12), (16)
really point to existence of traditionally not accounted
(unknown) control channel over material media
states (chargeous control channel), where electrical
charge plays a role of control factor.
Draw attention that the transfer of the formed AQN-
formation in new corresponding to (9)-(12), (16)-(18)
state (one’s relaxation) is providedwith own energy-re-
sources of AQN-formation. The AQN-formation during
relaxation towards IEEC makes so some negative work.
If work done by the medium of AQN-formation in this
case is Lq, then ()() ()SignSignqSign

 
and ()0Sign

 .
The relations (9)-(12), (16) as well as (17), (18) jointly
point to reality of correlations *
exc
TT on
0
j
e



 , as well as *
exc
TT on .
j
e




The concrete corresponding to (17) dependence
*(),(0 2,14,
excj j
TfeeeV  300)TK

is presented with Figure 1.
Let us draw our attention to the fact that according to
(17) and regard to being expected character of
()eft


 during process of relaxation caused by
introduction/leading-out of surplus charge into/from me-
dium composition, for example, the population distribu-
tion function of excitation temperatures of medium’s
chemical bonds and electron energy states can be sub-
jected to discontinuity of the type (, )

 or
(, ).

 This fact among other things can be inter-
preted as an indirect indication of possibility of devel-
opment under these conditions of instability of medium’s
e


*
exc
T e

 *
exc
T
0 300 14,20 -21000,0
2 350 14,30 -14000,0
7 600 14,40 -10500,0
9 840 14,50 -8400,00
10 1050 14,70 -6000,0
12 2100 16 -2100
13,00 4200 17 -1400
13,50 8400 18 -1050
13,8 21000 19 -840
13,9* 42000* 22 -525
14,1* -42000* 28 -300
Figure 1. *, () 14
j
j
exc j
j
TT
f
eeV
e




 .

A. V. PINCHUK ET AL.
256
atom-molecular structure. The instability, as it might
expect, being acceptable to manifest itself, with losses of
electrons steadiness on the orbit and even with absorp-
tion of the ones by nuclei.
Common peculiarities of IEEC already at this stage
testify to real perspectives to form on the ones’ base of
conceptual views model of BL. Let us forestall however
the attempt with both clarification of favourable using
conditions of chargeous channel for controlling over
material media states AND additional confirmation of
validity of just IEEC themselves as base for the working
out of supposed model of BL.
4. Temperature Limitations of IEEC
Efficiency
Verification of temperature diapason that potentially not
excluding at least the ensuring possibility of significant
changes with chargeous influences of medium’s charac-
teristics, all other things being equal, is of special impor-
tance for validity to use IEEC as base in forming of true
notion of BL.
To make conditions for effective using of revealed
“E-channel” more precise, quasi equilibrious plasma’s
characteristics as applied to concrete parametric non-
uniformity in MGD-channel with sectioned electrodes
(Figure 2) were estimated versus temperature, all other
things being the equal, just as by traditional (generally
accepted) method, so by method with account of re-
vealed IEEC.
The values next were compared relative each other. It
was taken into account in this case that if a temperature
corresponds to diapason where using of ECC is effective
one so the differences in levels of being confronted
characteristics must be necessary displayed. In doing so
it was assumed that the work regime of MGD generator
is stationary and realized with constant pressure.
If the Hall’s component of electrical field in the MGD
channel **
00
(1)/()/
hqie
EuBEqenn

 
then **
0
()(1)/
ie
nnuBe   .
In view of (1), (2) *** *0 ()
ie ia
nn nn  
whence 0*
0
(1)/ ().
a
nuBe



 But 0
a
n(see (1), (2))
complies also with expression


0*
[1(1)]
a
nP kT 

 .
Figure 2. MGD channel.
Then
*
*
0
1(1)
(1 )
eP
uB kT

  


 what upon call-
ing
0
(1 )
eP C
uB kT  


 is transformed into form
*1[ (1) 1]C


. Potential  was evaluated with
()(1)()
hchch
EL xuBL x



 what is in keep-
ing with 0e


 (!!!).
The equation system



 
(1 )
*(2 )
(1 )(1 )
**
(1 )
32 52
3
11
111
2exp ;
i
a
e
e
g
g P
mkTV
ge
kT h






















 

0x
eP
CEkT


; *1
(1)1C
 

;
(1 ) ()
ch
uB Lx



 
under certain values of ,,,
ch
PTL x
, medium composi-
tion and regime of MGD generator is closed.
The system was used to estimate both the levels and
dependences character with temperature of ionization
parameters of medium that, in accordance with IEEC,
correspond to quasi-equilibrium conditions in MGD
channel. Related parameters of media in quasi neutral
states, all other things being same, were estimated too.
The presented below with Figure 3 results (along with
obtained as a whole) were being analyzed under assump-
tion that using of chargeous influences for controlling of
material media states will be the most effective in the
temperature ranges where, all other factors being the
same, just essential differences between estimations of
quasi equilibrium medium’s ionization parameters are
revealed depending on is accounted or no uncompen-
sated electric charge in the medium composition.
The results of Figure 3 correspond to conditions:
pressure 52 10 /PNm
, flow velocity 3
10 /ums,
Hall parameter 2


, load parameter 0

. Being
conditionally taken into account here media correspond
to K, Li, H, Ar (a, b, c, d correspondingly).
During investigations as a whole the following pa-
rameters were being modified over ranges: a conven-
tional medium composition (3.89,24.58)/VWA;
pressure 56 2 (10, 10)/PNm
; flow velocity
33
(10 . 210)/ums ; Hall’s parameter 1, 2, 4


;
load parameter of MGD generator 0, 0.5.


The taken into account range of temperature changes
was (300,3000)TK

. It was assumed that magnetic
induction 1.6BT

, channel length 1,0 .
ch
Lmxm
It was determined in this connection that significant
differences between of being so compared ionization

A. V. PINCHUK ET AL.
257
(a)
(b)
(c)
(d)
Figure 3. Characteristic comparison results (conditionally–
K, LI, H, Ar).
parameters are principally revealed only in field of rela-
tively low temperatures.
It is elucidated that differences of medium composi-
tion towards increase of ionization potential make to
extension of favorable temperature diapason where using
of chargeous influences might be effective for control-
ling of material media’s states.
By confrontational analysis it was revealed that, even
with account of wide variation of media compositions,
temperature diapason, where an essential differences of
the results are disclosed, is limited from the top and also
envelopes by itself only oblast of relatively low tem-
peratures.
Even after such seemingly optimistic generalization,
let draw our attention and up to basis of the work–IEEC
that was only recently pioneered by authors, till now
received no of sufficiency diffusion and in itself, in one
or other degree, is in need of some additional confirma-
tion.
The results of Figure 3 correspond to conditions: pres-
sure 52 10 /PNm
, flow velocity 3
10 /ums, Hall
parameter 2


, load parameter 0

. Being condi-
tionally taken into account here media correspond to K,
Li, H, Ar (a, b, c, d correspondingly).
During investigations as a whole the following pa-
rameters were being modified over ranges: a conven-
tional medium composition (3.89, 24.58)VWA;
pressure 56 2 (10 ,10 )PNm
; flow velocity
33
(10.210)ums ; Hall’s parameter 1,2,4

; load
parameter of MGD generator 0, 0.5.


The taken into account range of temperature changes
was (300,3000)TK

. It was assumed that magnetic
induction 1.6BT

, channel length 1,0.
ch
Lmxm
It was determined in this connection that significant
differences between of being so compared ionization
parameters are principally revealed only in field of rela-
tively low temperatures.
It is elucidated that differences of medium composi-
tion towards increase of ionization potential make to
extension of favorable temperature diapason where using
of chargeous influences might be effective for control-
ling of material media’s states.
By confrontational analysis it was revealed that, even
with account of wide variation of media compositions,
temperature diapason, where an essential differences of
the results are disclosed, is limited from the top and also
envelopes by itself only oblast of relatively low tem-
peratures.
Even after such seemingly optimistic generalization,
let draw our attention and up to basis of the work–IEEC
that was only recently pioneered by authors, till now
received no of sufficiency diffusion and in itself, in one or
other degree, is in need of some additional confirmation.

A. V. PINCHUK ET AL.
258
5. IEEC as Object of Investigation
5.1. Common Position
It was accounted that both character and meaningfulness
of waited manifestations of relaxation process being in-
evitably excited in medium composition at the forming
stage of AQN-formation and at the degradation stage of
the once alike are jointly conditioned by both up level of
e

 complex and changes character of the one in the
time of relaxation.
It should be waited in this connection that if
*()
exc
Tfe   function during the relaxation to (on the
stage of AQN-formation forming) or even against IEEC
(on the stage of one’s disintegration) undergoes discon-
tinuity (that is under conditions when instability of me-
dium’s atom-molecular structure becomes possible are
see Figure 1) then relaxation manifestation character
may be extremely complicated.
It may be suggested in particular that at this case re-
gardless of the composition, inevitably excited relaxation
to/against IEEC may be jointly accompanied by viola-
tions of chemical bonds of medium as well as flow out of
electrons from upper electron states (steadiness losses of
electrons on orbits, ones’ downfalls and even absorptions
by nuclei with origin of neutrons-analogue of phenomena
K
 or ecupture), that is by very complicated mani-
festations jointly not precluding in that number from
reactions excitation that produce energy of intra nucleus
origin. To substantiate the last (and, hence, IEEC in a
whole) the experimental researches results jointly with
materials of [9-13] in that number have been used.
5.2. Investigation Method and Installation
It was drawn attention to the fact, that according to
00
0
0
tt
аmmа
sura ie
t
cm mc
ce i
qdqef dt
ef dt



 






(19)
surplus charge in volume of some reactor (Figure 4)
could have be done, for example, by impulse of capacitor
discharge owing to differences between quantity of elec-
tricity being brought in reactor during time “t” (through
part of chain “positively charge cover of capacitor–elec-
trode-anode in rector”) and, opposite, being brought out
from reactor during the same time (through part of chain
“electrode-cathode in reactor–negatively charged cover
of capacitor).
In (19): ()
j
f
t , (,jei)–specific flow of carriers
of charge (electrons, ions) on boundaries of media division
parts of electrical chain am, cm (anode

medium, cathode

medium respectively).
By Figure 5 block-schema of experimental installa-
tion is shown.
In the one’s composition: reactor 1 fitted out with
electrodes “A”, “C” (basic ones), picking out reaction
zone and being used for formation of controlling influ-
ences onto medium in reactor and, sometimes (what isn’t
necessarily), with “SE” (subsidiary one) for any infor-
mation leading-out from reactor; system 2 of medium
storage and preparation of one’s wanted composition;
systems 3 of injection/ejection, additional preparation,
ensuring and regulation of barometric characteristics of
medium in reactor; power supply system 4; system 5 of
registration and measurements of optical, electromag-
netic and neutron radiation.
As reactor a vessel done from quartz glass was used
(see Figure 6).
Figure 4. Schema of set for forming and registration of sur-
plus charge.
Figure 5. Block-schema of experimental installation.

A. V. PINCHUK ET AL.
259
Figure 6. Some reactor variants.
On examinations the reactor was placed in capsule
from non-rusting stale (Figure 7) with hollow walls of
the one the reactor compartment was picked out.
For providing of controlling influences to medium
with energy 2.0-2.5 mF capacitor was used. The poten-
tial differences on the capacitor covers in diapason of
0,8-2,5 kV was varied. Measuring of neutron flow on
examinations was foreseen. As measure of neutron flow
power on examinations a number of events fixed per
discharge impulse was accounted.
Figure 7. Some sets of installation.
5.3. Common Results
Figure 8 illustrates typical experimental oscillograms of
tension and current between basic reactor electrodes on
examinations. Current–below curve, 227 A/div, tension–
upper curve, 500 V/div.
As applied to concrete conditions of receiving of
curves Figure 8, both the electrical field laying onto dis-
charge interval of the reactor and switching on of oscil-
lograph were carried at the same time with help of spe-
cial electron key being brought in feeding chain of dis-
charge zone of reactor.
As material of electrodes Mo, W and/ or Kovar (Fe, Ni,
Co)3 were used. Any dependence of results from elec-
trodes material was not revealed.
As applied to concrete conditions of the oscillograms
receiving the application of electrical field to the anode-
cathode gap and triggering of the oscillograph were being
at the same time with the help of electronic key, being
introduced into the feeding chain of the reactor.
The initial level of voltages on the capacitor’s plates
was supported in the frame of being took out diapason
and practically was not varied beyond the medium com-
position from number of being used ones (hydrogen,
helium, nitrogen, air, nitrogen-hydrogen mixture with
molar relation ~1:1).
Under conditions being typical ones for Figure 8,
from 100 to 200 events per discharge impulse were fixed
at distance 0,5 meter from reactor (in general neutron
radiation was able to be fixed up to 10 meter from reac-
tor). The trustworthiness of conclusion that being Regis-
tered radiation is really neutron one has been confirmed
with additional investigations [9,11-13].
For verification of radiation nature and exception so of
possibilities to distort results, in connection with influ-
ence to detector of one or other strays pick-up, the ex-
perimental tests have been done. So the additional analo-
gous block but with distant scintillating target was taken
up position side by side with detection block. This addi-
tional block detected no events during discharge. More-
over, the hollow walls of operating compartment with
hollow’s thickness ~250 mm were filled up with saturated
water-solution of boron acid and were used as a special
absorbent of neutrons. An introduction of this absorber
between reactor and detector was accompanied by sharp
weakening (by one order) of having been before registered,
all other being equal, neutron flow. In carry- ing out of
control experiments, when the hollow intra- walls was
empty or even filled up with distilled water, a weakening
of neutron flow was not observed. We can state so with
full assurance that fixed radiation is really neutron one.
3Change of material at that case was determined in essence only with
technological limitations, connecting with covering of side surfaces o
f
electrodes by glass.

A. V. PINCHUK ET AL.
260
(a)
(b)
Figure 8. Typical discharge on pressure: 0.5-1.5 Torr (H2,
He), 1.0-2.0 Torr (N2, air, N2 + H2, molar ratio ~ 1/1). Scan-
ning: (а) 1 ms/div; (b) 4 ms/div.
Let us note also that registration of neutron radiation
safely testifies to exciting under these conditions of en-
ergy producing reactions of intra nuclear origin too.
The pressure diapason corresponding to fixed neutron
radiation is set with experiment. To substantiate impor-
tance of arising so in reality of search stage in common
cycle of the work let us note that under the pressure
above 20 Torr, all other things being equal, discharge of
the capacitor takes of the classical shape (Figure 9).
Neutron radiation under such conditions is not found.
Let us draw an attention that by oscillograms of Figure
8 the overloading of capacitor’s covers with electrical
charge of opposite sign is fixed. The last testify to that
owing to chargeous influences to medium in that case an
untraditional source of energy in the reactor is formed.
The last shows so to principal possibilities to accompany
the chargeous influences onto medium with leading-out
of energy from reactor. Notice that presented with Figure
10 data testify to such conclusion.
Figure 9. Discharge characteristics under Р = 25 Torr
(1-current; 2–tension on capacitor covers).
(a)
(b)
Figure 10. The installation schema (a) and experimental
data; (b) 1-tension: 2-current on/from E-electrode, 0.022
V/A.
The received so experimental results is typical to all
investigations totality and, as it was assumed, in the
frame of used media nomenclature do not display any
once’ dependence from medium composition. In other
words, common rightfulness of IEEC themselves as well

A. V. PINCHUK ET AL.
261
as of attempts to form, on the ones’ base, model physics
views about BL received so experimental confirmation
too. By received results so not only the validity of waited
manifestations of chargeous influences to medium but
and additionally, on this time just with experimental way,
truth and fundamental character of IEEC itself as basis of
this work were confirmed too.
Let us further in consecutive order consider key prob-
lems of BL.
6. BL Model Views Forming
6.1. Sphericity
The sphericity substantiation of BL (as a foundation
with higher, in respect to the environment, temperature)
is traditionally considered as extremely complicated one
for solution (if not being defied explanation by ordinary
means at all [19]).
In the framework of the developed point of view (i.e..
when it is possible to assume that bl T-translation tem-
perature of BL and env T-a temperature of environment
are close to each other) the existence possibilities verify-
cation of material AQN-formations (after referred to as
BL-formations or BLs) localized in the space is taking
however some new tinge.
With the availability in medium of dipole molecules
with moment d and at a concentration d nn





bl
PkT 
 (

-the relative dipoles concentration) the
surface tension forces energy will be determined by
value
 
253
2
0
4
stsf dbl
d
QUrrSn Rn 


 (20)
If needed expenditures to retain the electric charge in
BL composition to be estimated by means of energy ac-
cumulated by the BL sphere being under consideration as
spherical condenser (bl env TT)
22
0
8
c
bl
qq
QCR

 (21)
then the greatest surplus charge being kept in the sphere
of BL may be determined with

56
32
42 ,
1, ;
1, .
jbl
j
qZdRn
if ji
Zifje







(22)
The excess electron concentration in BL medium
complying with q

56
32
32 .
j
q
bl bl
Zd n
q
neV eR


  (23)
Both physical meaning and level of potential

would be determined in that case by the greatest negative
work has been made by BL-medium itself when carrying
in of the surplus charge into BL sphere. So if the work
has been done with BL medium is 2/LqCq
then electrical potential will be determined as

56
12
0
2.
2
jbl
ZdR n
qC



  (24)
For a case when the sphere radius of BL-formation
0,075
bl
Rm

the absolute level of charge q held in
BL-medium (a), electric potential  (b) and energy ac-
cumulated by the BL sphere as a capacitor (c) versus
relative dipoles keeping are shown at the Figure 11.
The analogous characteristics, but versus BL’s sphere
radius and for case when relative dipoles keeping
0, 01


, are presented at the Figure 12.
Thus the possibilities for energy ensuring of BLs’
sphericity even in a case when relative dipoles keeping in
a medium corresponds to relatively low are confirmed by
presented results.
6.2. Energy Problem
6.2.1. Common Remark
BL origin in form of material formations with uncom-
pensated electric charge is made possible by only in
connection with manifestations of external disturbances
with one or another nature onto medium (the ones not
considered by us within this work). Similarly, the exis-
tence proper of BL itself likewise is realized under BL-
environment interactions.
In other words, the ball lightning presents by itself,
first of all, thermodynamically opened system the prop-
erties of the one are typical for significantly upset me-
dium formations and are necessary supported by especial
processes aggregate (complex) of heat and mass transfer
as between energy states of different physical nature of
BL medium, so between BL as a whole and environment.
Accounting significance of the noted let us underlines
once again that, in framework of the work, the revealed
Conditions of Inner Energy Equilibrium are wise to re-
gard, before all, not as the postulate directly indicating
the concrete characteristics of AQN formations but, to a
greater extent, only as the physical appropriateness
complex, justifying the excitation necessity of relaxation
in AQN-medium composition towards new conditions of
inner energy equilibrium (having been changed owing to
carrying in medium composition of surplus charge) dur-
ing of very that, with account of the concrete peculiari-
ties of both relaxation proper and interactions between
AQN-formations and environment, quasi-stationary
characteristics of the AQN-formations themselves are
being formed.

A. V. PINCHUK ET AL.
262
(a)
(b)
(c)
Figure 11. The holdable charge’s characteristics


,log
q
,
 
log c Qf

.
(a)
(b)
(c)
Figure 12. The holdable charge’s characteristics log(q), ,
log(Qc) = f(bl
R
)

A. V. PINCHUK ET AL.
263
6.2.2. Radiate Ability Problem
Within the formed ideas of BL as of material formation
with uncompensated electric charge the radiation capac-
ity is substantiated first of all by typical for aquasineutral
formations of excesses of chemical bonds and electron
energy states excitation temperatures (*
exc
T) over transla-
tion one (bl
T) (in that number and especially on the dis-
tant approaches to the equilibrium conditions, see (6.2.1)
and (17), (18))
In support of practical significance of the waited re-
flections in reference to the conditions that are similar to
Figures 11, 12 a quantitative estimations of
quasi-equilibrium parameters of different composition
media has been received.
The estimation was being conducted on the base of
system including both ionization parameters bonds equa-
tions of plasma medium within of three liquid model [17]
and expressions having been received in the work. Spe-
cifically the system was included following equilibriums:



(0) *
11
abl
nP kT 



;


;
bl
nPkT



56
32
42 jbl qZdRn 

; ;
d
nn 

 **(0) ;
ia
nn  

56
32
32 ;
jd
q
bl
Zd n
neR  *;
qi
nn  

56
12
0
2;
2
jbl d
ZdR n

  *j
exc
j
TTe







(1 )
*(2 )
(1 )(1 )
**
(1 )
32 52
3
11
111
2exp ;
i
a
e
e
g
Pg
mkTV
ge
hkT













 




 




Among unknowns in solution of the system ten following
parameters are accounted: (0) **
,,,,,,,,,
adqi
nn nnnq 

*.
exc
TThe parameters ,,,
bl j
R
VZ

were being varied. It
was assumed that 5
10
1.01325PPa
, 300TK, 1dD

.
The system so was being closed.
The revealed so ionization degrees *

of different
composition media (a) in common with the both excite
temperatures of electron energy states *
exc
T (b) and levels
corrections of ionization potentials being stipulated by
presence in media composition of surplus charge


(c) delivering the ionization degree versus relative dipole
keeping in media composition of BL with 0.075
bl
R
m

are presented at Figure 13.
The curves 1-6 conform to conventional media com-
position with 6,8,10,12,14,16 /VWA (curves 1-6 ac-
cordingly). Plots of Figure 14 present the dependences
(a)
(b)
(c)
Figure 13. The quasi-equilibrium characteristics
_*
log( )

,
__
,(log )
exc
Tf

 .
4In so doing will bear in mind that, under generally accepted views,
“any negative temperature *
exc
T is hotter relative any positive one”.

A. V. PINCHUK ET AL.
264
(a)
(b)
(c)
Figure 14. The quasi-equilibrium characteristics
_*,log( )

__
,()
exc bl
T
f
R  
of the same parameters but versus radius of BL founda-
tion sphere.
The plots conform to conventional media composition
with 4,6,8,10,12,14,16/VWA

(curves 1-7 accord-
ingly). Being taken into account the relative dipole
keeping in a composition of BL medium is 1%
(0,01)


.
Let us note that, as applied to no equilibrium aquasi-
neutral foundations state, reflecting best of specific
character of ones’ relaxation under conditions of energy
interchange with environment, the absolute values of
present-day parameter
_

  and levels
_
**
.
exc
TT
In other words, the obtained upper results indicate
convincingly as a whole that the natural air foundations
with uncompensated charge keeping in ones’ composi-
tion (BL) not only can exist themselves but also are
really able to radiate energy even under conditions, when
translation temperature of the foundations is correlated
with (or even less than) the environment temperature
()
bl env
TT

.
Let us bring into consideration an effective radiation
temperature rad T as parameter determining, on a basis
of the generally accepted propositions, radiating power
of BL into environment

4
2
0
4100
radbl radblgrad
QSq RCT   (25)
To concretize conditions for numerous estimations of
rad
Q will be assumed that rad T accordingly (25) at the
same time correlates with excitation temperature of
chemical bonds and electron energy states of some char-
acteristic for BL (within of the ideas about common fea-
tures along with a typical reactions relaxation composi-
tion and energy feeding mechanism) energy level *
j

5,
to say
*
*
j
rad bl
j
TT e


 (26)
In other words, the temperature rad T will be consid-
ered as a parameter determining, in traditional mind, the
radiating power of BL and, at the same time, as a factor
being functionally stipulated by peculiarities of excita-
tion temperature distribution of chemical bonds and
electron energy states peculiar to BL media.
It is possible so within of taken into account with (26)
bonds the degree of darkness
g

to be estimated by the
ionization degree of a media with *
j
eV

 as deter-
mining, in that case, the settlement density of energy
states with radiation transitions of electrons from one
5Admittedly, the accounted so character of bonds between rad
T and
energy states excitation temperatures is substantiated essentially,
within this work, by only the necessity to refinement conditions fo
r
following numerous estimations of rad
Q and in the future calls for a
more precise definition.

A. V. PINCHUK ET AL.
265
orbit to another in composition of BL media
qbl
g
nkT
P



 (27)
Here q n- surplus concentration of particles-charge
carriers.
6.3. Octopus’s Effect
The being noted by eyewitnesses capability of BL to
overcome different barriers from dielectric materials
(window-frame for example) by means of penetration
through inanes in the body of barrier (hollows, cracks,
splits) being essentially lesser, concerning to BL, sizes
and then to restore (reconstruct) in essence the ones’ ini-
tial shape and characteristic is substantiated too. The one
is substantiated, first of all, with susceptibleness of sur-
plus charge in composition of BL’s medium to influ-
ences of external electric fields and hence with one’s
obvious capability not only to overcome through barrier
(wall) from dielectric material along the channels in bar-
rier’s body in hollows (cracks, splits) form, but and then,
after penetration through channels, to form (to restore)
behind barrier in environment a new AQN-formation
with initially corresponding to BL characteristics.
6.4. The Energy Feeding Source
The way of attack untwisted in this work opens else real
prospects to solve the problem of nature substantiating of
the energy source for feeding of BL.
Indeed, as it has been readily apparent from observa-
tions, the keeping up (continuous reproduction) of
quasi-stationary states in process of BLs existence is
realized in that number (unless not always) under condi-
tions when the ones radiate energy into environment.
This seemingly that the radiation of energy into envi-
ronment must be accompanied by reduction of settlement
levels of energy states (relative to stationary settlement
level of the ones) with radiation transitions of electrons
from one orbit to another and so bring towards lowering
of radiating capacity of BL. As applied to stationary state
of BL the last however is practically kept constant one.
In the framework of the formed method of attack the
noted comes to be explicable.
Indeed, it is obviously that the settlements lowering of
chemical bonds and electron energy states, in connection
with radiation all other things being equal, to be neces-
sary accompanied by (stipulates) an additional excitation
(overheating) of “mechanical” energy states of BL me-
dium (bl
T) in relation to the being reduced so excitation
levels of the “no mechanical” energy states (*
exc
T).
The growth of misbalance in energy distribution over
states in connection with radiation is suppressed so by
the energy flow from mechanical energy states towards
the ones but being no mechanical nature. Let us draw
attention to the fact that the flow of energy from me-
chanical energy states leads to drop of BL’s translation
temperature (bl T) even to the levels below environment
temperature (en v T) and, in turn, stipulates origin of en-
ergy flow from environment to BL.
In other words the both existence and nature of source
to feed BL with energy is really substantiated. This
source feeding with energy of BL is so environment.
By this means in the framework of the formed model a
quasi-stationary state of BL is necessary consistent with
conditions when bl env TT

. Just that relation’s range
between the noted temperatures provides of BL with heat
absorption from environment as clearly indemnifies for
ball lightning’s energy escape by radiation and essen-
tially makes possible existing of BL in nature as itself.
The common picture of exchange energy-mass processes
in these conditions in full measure corresponds to both
Le Сhatelier Principle and the common character of ma-
terial systems reactions onto disturbances.
6.5. Energy Feeding Mechanisms
There can be no doubt that the feeding of BL with energy
from environment on a stationary existence stage is real-
ized by traditional mechanisms of energy-mass-exchange.
Both convective heat input and input of energy inside BL
in connection with mass-exchange between ball lightning
and environment are naturally enough to account in
components number of the energy supplying (energy
feeding) mechanism.
6.6. Energy Resource Components
Channels as and sources to form energy-resources of BL
along with needed conditions for supplying of the one’s
quasi-stationary characteristics are also substantiated
within the formed ideas model of BL as about localized
in the space containing uncompensated electric charge
material foundation with differences between transla-
tional temperature and excitation temperatures of both
chemical bonds and electron energy states.
In account with the revealed appropriateness in equi-
libriums and common conditions to localize material
foundatio9ns in the space, the common level of BL’s
energy resources is advantageous to estimate in that case
with discrete blocks. These are radiation flow energy
rad
Q, energy saved up by sphere of BL as capacitor c Q,
nergy Q

accumulated with BL media in account with
deformation of settlings distribution function of chemical
bonds and electron energy states under relaxation of

A. V. PINCHUK ET AL.
266
BL-media towards equilibrium conditions accounting of
availability of uncompensated electric charge in one’s
compositions.
6.7. The Multi-Faces Problem
Making longer discussion in the framework of the being
formed BL model let us attention draw to the fact that the
energy absorbed by BL from environment at the same
time can be used up at least in two directions. Firstly, it
is the one for indemnity of energy losses in connection
with radiation. For secondly, it is the one for putting
down settlings levels diminution of excited chemical
bonds and electron energy states (continuous reproduce-
tion of radiation capacity) stipulated by mass-exchange
processes between BL and environment.
It can be assumed that distribution character of feeding
energy flow between the noted directions determines the
total level of ball lightning’s energy resources and, in its
turn, is determined by common as well as being specifi-
cally established, as the existence conditions of BL re-
quire, peculiarities of energy feeding mechanism.
If this the case, the relative contribution of each from
energy feeding mechanism’s components (convective
heat exchange or/and mass transfer) must show essential
influence over quasi-stationary characteristics of BL. The
dependence of BL foundation’s energy resources upon of
concrete realized, at each single of occasion, energy
feeding mechanism can be considered so as the most
probable reason, from assumed ones, of being noted with
observations so called multi-faces of ball lightning.
By way of the first step for following consideration let
us more concrete formulate ideas upon waited, at each
separate case in connection with the noted, common pe-
culiarities of quasi-stationary states of balls lightning.
For better visualization of these peculiarities, the needed
consideration should be carry out with the supposition of
limit contribution into the BL’s energy feeding mecha-
nism either of one or another its component from the
accounted ones (only of convective heat exchange or, on
contrary, only of energy input inside BL from environ-
ment in mutual mass-exchange connection with).
Even not accounting of cognitive advisability, allow-
ance of the last is substantiated, among other factors, by
possible variations of real environment characteristics
and consequently of BL’s existence conditions.
6.7.1. Convective Heat Exchange
Overpowering contribution of convective heat exchange
into energy feeding mechanism of balls lightning with
stationary characteristics corresponds to conditions, when
BL-environment mass-exchange for the most part has
been put down. The quasi-stationary states of BL being
existed in the conditions must be characterized first of all
by constancy with time of both the radiation characteris-
tics and the settlements of chemical bonds and electron
energy states. The energy being supplied to BL from
environment must be expended in these conditions only
to compensate energy loses of ball lightning with radia-
tion (ideal case).
It should be emphasized that BL-media conforming to
quasi-stationarity conditions (and being exceptional so
with invariability of energy states and depression of
mass-exchange) must be characterized in the case by
essential deformation of distribution function of chemical
bonds and electron energy states towards internal energy
equilibrium with account of surplus electric charge in the
media composition.
Let us note that specificity of the being established so
distributions points to existence (and possibilities of ef-
fective displays) of nontraditional, in the framework of
generally accepted physical views, energy resources
formation channel of BL. Of the channel being substan-
tiated with obvious capacity of media with surplus elec-
tric charge to absorb energy of one or other source to
supply the deformation of media’s energy states settle-
ments and functioning, in principle, at any stage of ball
lighting’s vital cycle.
It is safe to assume also that the radiate characteristics
of BL in quasi-stationary state under energy feeding by
convective heat input (and hence when mass-exchange is
depressed) likewise are must be stood out with some
typical features.
By significant deformation of energy states settle-
ments, the BL’s radiation, in this case, must be mainly
realized by transitions in the diapason energy states hav-
ing been drawn (essentially!) to the internal equilibrium
conditions accounting presence of surplus charge in me-
dia composition
6.7.2. Mass-Exchange Energy Feeding
Contrary to the previous case the power supply of BL by
mass-exchange mechanisms necessary assumes that the
energy flow from environment to feed with energy of
quasi-stationary states of ball lightning is being neces-
sary expended at least towards two ways:
 Firstly, to supply radiation;
 To ensure with energy the continuous reproduction
of energy states settlements that determine the ra-
diate capacity of BL, secondly.
It is possible to assume also that radiate capacity of
BL-medium is substantially (most probably) manifested
in the field of distant approaches to equilibrium condi-
tions and is realized, in that case, by radiate transitions
between energy states with essentially higher levels of
excitation temperatures (the ones at the relaxation stage

A. V. PINCHUK ET AL.
267
undergo a rupture of (,)  kind). But the BL’s en-
ergy resources component conditioned by settlements
distribution function deformation of chemical bonds and
electron energy states with relaxation most likely in the
case is kept only partly filled up.
6.8. Preliminary Result
The preliminary examination materials testify that account
of revealed [1-13], earlier unknown peculiarities of inner
energy equilibrium conditions of media with surplus
(uncompensated) electric charge opens truly up new
prospects for adequate ideas model substantiation of BL.
The last however requires for addition confirmation
rather by numerous estimations.
7. BL’s Quasi-Stationary States
7.1. Common Positions
Will be considered that the BL quasi-stationary state is
manifested first of all with immutability in time of its
radiate characteristics.
Common conceptions about BL in this conditions will
be presided in connection with this by equations complex
jointly substantiating just as both the existence reality
and energy resources of the ball lightning in form of lo-
calized in space material foundation with uncompensated
electric charge so others characteristic parameters of the
BL versus media compositions and common specificity
of feeding energy mechanisms of its quasi-stationary
state.
With account of existence of differences channels for
keeping/radiation by BL from/into environment the en-
ergy resource of BL in quasi-stationary state will be es-
timated with separate components. Will be taken into
account specifically:
 radiation flow rad Q;
 energy c Qhaving been accumulated by sphere of
BL as electric capasitor;
 energy Q

having been accumulated under set-
tlements distribution function deformation of
chemical bonds and electron energy states of BL
medium when relaxing the one towards new equi-
librium conditions6.
7.2. Convective Energy Input
When convective heat input to be considered as the
mechanism feeding of quasi-stationary state of ball
lightning with energy that equation determining the
waited power input to BL from environment versus tem-
peratures as titled above is

2
4.
conv
hibl convblconvenvbl
QSqR TT    (28)
Here: conv

-heat transfer coefficient.
By the conditions of one-to-another equilibrium in
value of introducing (to BL from environment) and radi-
ated contrary (to environment from BL) energy flows
will be determined in that case the demands to supply
power mechanism feeding. In substantiated limitations so
(mass-exchange between the ball lightning and environ-
ment is depressed) through correlation of (25) and (28)
the conditions of BL’s quasi-stationary states supplying
with energy (of characteristics invariability) will be de-
termined as
4
0
*
100
conv
grad
convenv bl
conv
CT
TTT



 

(29)
As applied to a case of convective heat input the nu-
merous estimations of energy resources of balls lightning
under quasi-stationary states as well as feasibility of the
lasts by themselves were being conducted within equilib-
rium approximation (see 5.6.1).
As this take place, with account (26) the effective ra-
diate temperatures were taken equal to quasi-equilibrium
excitation temperatures exc Tof electron energy states
conforming to ionization energy
conv
radexc bl
V
TTT
V 

  (30)
As for relative blackness degrees
g

, the ones, all
other factors being the same, were set equal to quasi-
equilibrium ionization degree *

(estimations of *

along with of exc T

were presented above by Figures 13,
14). The equation
3
4
3
conv
bl
bl
P
QRe
kT




 (31)
was being used to estimate the energy resources compo-
nent conv Q

of ball lightning in that case.
The evaluations of both the radiate power conv
rad
Q (“a”)
according to (25) and the differences *
conv
T between
the ball lightning’s translation temperatures and envi-
ronment temperature (“b”) as well as of the BL’s energy
resources component conv Q

(“c”) versus the relative
dipoles content in BL’s media composition are represent
in Figure 15.
In during the estimations it was assumed that BL’s
sphere radius 0.075
bl
Rm

. The plots 1-6 correspond to
conventional media composition with
6,8,10,12,14,16 /VWA

respectively. As for the rest
6Existence of the energy resources’ component Q

corresponds to
inner energy equilibrium conditions with account of possible presence
of excess charge in media composition and in the framework of gener-
ally accepted till now views is not substantiated.

A. V. PINCHUK ET AL.
268
(a)
(b)
(c)
Figure 15. The graphics * ,,()
conv conv
rad conv
QTQf


(Quasi
-equilibrium approximation)
taken into account in calculations characteristics, then
ones correspond with analogues for results of Figure13.
Figure 16 gives the quasi-equilibrium levels of radiate
power conv
rad
Q (“a”), the differences *
conv
T between the
ball lightning’s translation temperatures and environment
temperature (“b”) as well as of the BL’s energy resources
component conv
Q

(“c”) but in the case, versus radius
sphere of BL. The levels of others taken into account in
calculations parameters correspond to conditions in cal-
culation of Figure 14 (0.01


,
4, 6,8,10,12,14,16/VWA

-plots 1-7 respectively).
The heat transfer coefficient from environment to BL
taken into account during forming of equations was de-
termined on the base of criterion equation
0.03 0.54
0.356 0.58
220.03Pr Re
0.35PrRe ,
conv bl
R
Nu



 

(32)
being used for description of transfer heat between a
sphere with radius bl
Rand flow running over with ve-
locity W [20]. With account of (32) and conformably
to standard parameters of air the value of conv

was
concrete estimated by equation

2
10
0.54 0.58
1
2.5812
20.02 Re0.3080 Re
conv
bl
R



 
(33)
Here:

5
10
Re 0.6802.
bl
WR (34)
7.3. Heat-Input with Mass-Exchange Mechanism
For case of heat-input for energy feeding of BL in quasi-
stationary state by mass-exchange mechanisms the en-
ergy input power was estimated by equation

2mt
hiblenv penvbl
QRWcTT   (35)
Here: , ,
p
env env
cT

-density, heat capacity and tem-
perature of environment accordingly;
W-velocity of environment flow relative of ball light-
ning.
It was taken into account that energy being inputted to
BL with environment flow, in that case in connection
with blowing off BL sphere by the environment flow, is
used up at least in two ways: to compensate a energy
loses of BL in connection with radiation, firstly, and to
suppress cutting of energy states settlements (reproduce-
tion of the ones) and practically to stabilize so, in condi-
tions of continuous mass-exchange between the ball
lightning and environment, the radiate capacity of BL as
a whole (relation radiate capacity
g

, effective radiate

A. V. PINCHUK ET AL.
269
(a)
(b)
(c)
Figure 16. Relations * ,,()
conv conv
rad convbl
QTQ
f
R

(Quasi-
equilibrium approximation).
temperature rad T and radiate power rad Q.
Taking into consideration the common dependences
specificity of excitation temperatures (see (5.6.2)) it is
assumed that the BL radiate capacity is realized in that
case by radiate transitions “on the distant approaches to
equilibrium of BL-medium” (**mt
rad excexc
TT T
).
With estimations of radiation flow mt
rad
Q by (25) and
expenditure power onto reproduction of energy states
settlements with
**2**rep
hiblj jblj j
bl
SW
QVnRWn
V
  (36)
the quasi-stationary conditions of BL were determined as

4
**
0
*4100
.
mt
jjgrad
mtenv bl
penv
Wn CT
TTTcW



 (37)
Here: *
j
n- the settlement of level *
j

suitable to en-
ergy states excitation temperature; bl
SW V-divisibility
of BL-media mass-exchange.
In Figure 17 are shown logarithmic relationships of
the power mt
rad
Q (“a”) radiated by ball lightning (with
sphere radius 0.075
bl
Rm

), temperatures differences
*
mt
T (“b”) conforming to the power levels as well as
the energy resources component mt
Q

(“c”) accumulated
of BL-media in that case with connection of continu-
ously reproduced deformation of energy states settle-
ments distribution function versus relational dipoles
keeping in BL-media composition.
The plots are built on the supposition that radiation is
realized by transitions on the distant approaches to equi-
librium of BL-media.
It was suggested that radiation temperature
5000
mt
rad
TK and, in that case, corresponds to repro-
duced with connection of feeding the excitation tem-
perature *
exc
T of BL-medium energy states with levels
*6,8,1 0,1 2,1 4,1 6
jeV
  (curves 1-6 accordingly).
Taken into account quantity of environment tempera-
ture 300 ,
bl
TK

of pressure-atmospheric one, of ve-
locity blowing-1/.Wms

To evaluate a quantity of

the dependence
*
1
jbl
mt
rad
T
eT






(38)
was used in that case.
It was taken into account that relational radiate degree
g

is determined with equation (27). At last, the mt Q

level was estimated by relationship
** 3*
4
3
q
mt
jj blblj
n
QnVR




 (39)
On Figure 18 the estimations relationships of the ra-
diated power mt
rad
Q (“a”) and the temperatures differences

A. V. PINCHUK ET AL.
270
(a)
(b)
(c)
Figure 17. Relationships * ,,()
mt mt
radmt
QTQ f


.
(a)
(b)
(c)
Figure 18. Relationships * ,,()
mt mt
radmtbl
QTQ
f
R

(Energy
feeding by mass-transfer).

A. V. PINCHUK ET AL.
271
*
mt
T (“b”) answering to being realized conditions
along with energy mt
Q

(“c”) accumulated by BL-me-
dium in connection with continuous reproduced defor-
mation of energy states settlement distribution function
versus sphere radius bl R of BL are presented.
The curves are being estimated by analogous kind in
assumption that energy radiation by BL into environment
is realized with radiate transitions on distant approaches
to equilibrium of BL-media.
It was assumed that the radiate temperature
5000
mt
rad
TK and corresponds to excitation tempera-
ture *
exc
T of energy states with levels *4, 6,8,10,12
j
 ,
14,16 eV (plots 1-7 accordingly) under atmospheric
pressure. Taken into account environment temperature
level 300
bl
TK.
The dipole molecules proportion 0.01

 (dipole
moment 1dD). It was assumed also that the relative
velocity of environment flow (BL blow-through)
1/Wms.
On Figure 19 the radiate power mt
rad
Q of BL with
sphere radius 0.075
bl
Rm and corresponding to levels
of the one the temperatures differences *
mt
T as well as
energy resources component mt
Q

versus radiate tem-
perature mt
rad
T of the ball lightning are presented.
The relationships are received by analogous with previ-
ous method and cover the diapason

5000,50000
mt
rad
TK.
Taken into account of the conventional BL-media com-
position corresponds to both relative dipoles content
0.001,0.005,0.01,0.05,

0.1,0.5,1 (the plots 1-7
correspondingly) and ionization potential 16 /VWA
(16
jeV

). As previous way it was assumed that
300
bl
TK, the pressure is atmospheric one, blow-
through velocity 1/Wms.
The analogous characteristics of BL with sphere radius
0.075
bl
Rmfor different composition media
(4,6,8,10,12,14,V16 /WA, the curves 1-7 accord-
ingly) with relative dipoles content 0.01

 are repre-
sented on Figure 20.
As in the above, the taken into account 300
bl
T

К,
pressure is the atmospheric one, blow velocity through
BL 1/.Wms Taken into account the radiate tem-
perature variation diapason in the case corresponds to

5000, 100000
mt
rad
TK.
Draw attention to the fact that levels of being esti-
mated BL’s energy characteristics (see Figures 11-20)
are in gratifying agreement with characteristics of BL
forecasted in the line of the notions about BL in the
frame of the one’s historically formed by observations
portrait (see [15,16,19,21-23], for example).
It should be especially emphasized, in that number,
that being formed so views about BL are whole consistent
with results of experimental valuation of one’s charac-
teristics having been received by research workers of
(c)
(c)
(c)
Figure 19. Relationships * ,,()
mtmtmt
radmtrad
QTQ fT

.

A. V. PINCHUK ET AL.
272
(a)
(b)
(c)
Figure 20. Relationships * ,,()
mtmtmt
radmtrad
QTQ fT

.
Nuclear Physics Institute (Saint-Petersburg, Russia) [22,
23].
7.4. Some Additional Words
It is obvious that common conditions of origin along
with existence of BL are characterized of electromag-
netic disturbances that influence an high effect on envi-
ronment. It can be said with confidence that, as one from
other factors, occasional in origin electro-magnetic in-
fluences on atmosphere not only determine origin possi-
bility of BL itself but in large degree substantiate move-
ment itself of the one through space and one’s common
characteristics as well.
8. Common Results
By investigations results totality, upon overstepping the
limits of generally accepted physical base, the conceptual
views complex of ball lightning as about of special shape
localized in the airspace material foundation with differ-
ences between one’s translation temperature and excita-
tion temperatures of one’s chemical bonds and electron
energy states have been formulated and is substantiated.
Adequacy and common rightfulness of the complex is
jointly established by inclusion to examination in totality
of all most significant characteristics and necessary exis-
tence conditions of BL, by revealed true of BL’s charac-
teristics being estimated on the complex base and of the
ones being prognosticated in the frame of historically
composed portrait of ball lightning and else by experi-
mental confirmation of trustworthiness of the IEEC as of
the physical base complex.
The complex is aimed to substantiation of jointly ob-
served manifestations of BL. In the context of views be-
ing determined complex composition the localization
possibility in airspace of ball lightning as material foun-
dation with noted temperature differences (sphericity of
BL) is confirmed. The nature of BL’s radiation ability is
based. The role of environment as source providing of
BL with energy was revealed. Energy feeding mecha-
nisms along with keeping conditions of quasi-stationary
characteristics of BL are determined.
Formation channels of BL’s energy resources (in that
number of untraditional character ones) is placed. By top
numerical estimations the energy resources levels are
confirmed, possibilities and variation diapason of the
ones (multi-faces of BL) are substantiated too.
Being received characteristics estimations of BL on
the formulated complex base is found in satisfactory
consent with characteristics of BL being prognosticated
in the frame of the one’s historically composed portrait.
Being revealed conformity like results of the work as a

A. V. PINCHUK ET AL.
273
whole testify to in all common rightfulness of being de-
veloped point of view, further progress expediency of the
one, possibilities to extend on the one’s base our knowl-
edge of nature.
Let us note else to independent scientific importance of
proper IEEC, the ones’ obvious fundamental character.
9. Conclusions
In the frame of an untraditional approach, upon over-
stepping the limits of generally accepted physical base
the conceptual views complex about ball lightning as of
quasi-stationary material foundation with differences
between one’s translation temperature and excitation
temperatures of chemical bonds and electron energy
states was formulated and are substantiated.
Every physical peculiarities of the base positions being
used in the work present independent scientific interest.
They note to existence of traditionally not accounted
control channel of material media states in what electri-
cal charge plays a role of control factor.
Jointly received result for the first time permits to for-
mulate the scientific substantiated model of BL in such a
way, for example.
Ball Lightning is containing of uncompensated (ex-
ceed) electrical charge atmospheric foundation with
quasi-stationary in time characteristics and sizes, life-
time duration reaching several tens second, being dis-
played with energy radiation into environment in visual
part specter too, manifesting else by an additional dis-
charge of energy under disappearance, differing with
capability to penetrate through inanes (hollows, cracks,
splits) with essentially lesser sizes in respect to the own,
to overcome so different barriers from dielectric materi-
als (window- frame for example) and then to restore
(reconstruct) in essence the ones’ initial shape and
characteristic, the foundations of properly forming, exis-
tence and charac- teristics of that under interaction with
environment jointly are provided with occasional in ori-
gin electro- magnetic disturbances of atmosphere, pres-
ence in the one’s composition of dipole components (of
components with unequal to zero dipole moment) along
with de- pendence of Internal Energy Equilibrium Con-
ditions of material media from presence or absence un-
compensated electrical charge in the ones’ composition.
Being developed in this work approach is of an uni-
versal character, is grounded upon overstepping the lim-
its of generally accepted physical base and presents itself
to be perspective for solving of not only of BL-problem
but and of wide circle of scientific and is applied prob-
lems. The last, however, demands of confirmation with
additional purposeful researches.
10. As Concluding Remarks
In the context of views, being jointly formed by [1-13]
and this work, definite interest presents a gaze to prob-
lem of combustion in detonation (DC) that, in connection
with having being multi-verified by experiment but not
interpreted just till now anomalously high heat release of
DC, draws to itself fixed, constantly increasing across-
the-board attention.
On being estimate an expedient decision way of this
problem an attention should be drawn to the fact that DC
as process is developed above all on background of ex-
ternal acoustic disturbances. With regard to [17] so,
combustion in detonation is realized in conditions that
are the most convenient for generation of macroscopic
AQN-formations in combustion products medium and,
hence, for excitement in the ones’ compound, at the re-
laxation stage to IEEC, of reactions, among them, may
be one or up intra-nuclear, energy producing (exothermic)
reactions too.
To put it differently, peculiar to DG high levels of heat
release reveal not only ones’ consistency to notions of
both [1-13,17] and this one, but even just with fact
proper of ones’ displaying (unquestionable having been
confirmed by numerous observations) testify to validity
of the IEEC in themselves as well as of conceptual no-
tions of being referred above works as a whole.
11. References
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Nomenclatures
e elementary charge (C);
g
statistical state weight;
h Plank’s constant (Js);
k Boltsman’s constant (J/K);
d dipole moment (Cm);
 thermodynamic potential (J/m3);

chemical potential (J/kmole);
q electrical charge, (C);
C electrical capacity (C/V);
p
c specific heat capacity (J/(kgK));
Q energy (J), power (J/s);
R radius (m), universal gas constant J/(moleK));
N molar concentration (mole/m3);
S area (m2);
n species concentration (m-3);

ionization degree, heat transmission coeffi-
cient (W/(m2K));

relative keeping of surplus electron compo-
nent;
,Pp
pressure (kg/(ms2));
T temperature (K);

density (kg/m3);

relative keeping of dipole component;
0

electrical constant (C/(Vm));
0
C radiate ability coefficient of absolute black
surface (W/(m2К4));
g

relative blackness degree;

electrical potential (V);
V volume (m3); ionization potential (V);
W velocity (m/s).
Symbol
0 undisturbed parameter;
a neutral;
e electron;
i ion;
c capacitor;
conv convection;
mt mass transfer;
s
f safe;
s
t safe tension;
rad radiation;
hi heat input;
bl ball lightning;
env environment;
exc excited parameter,
“-” true to equilibrium