THE HIGH-TEMPERATUHE PHYSICO-CKEMICAl PROCESSES IN THE LIGHTNING
(A Physico-Chemical Model of Ball Lightning)
Georgy P. Gladyshev
Institute of Chemical Physics USSR Acad. Sci., Moscow
Numerous research related to physico-chemical transformations in atmosphere
discuss specificity of the processes going under effect of the solar radiation,
electric discharges and other factors [1-12]. However, a range of phenomena
have not found a theoretical explanation based on exact calculations or
experimental data yet.
This work is focused on studies of the phenomena related to the high-temperature
chemical processes happening in the intensive atmospheric fields, i. e.,
basically, to the ball lightning phenomenon*. The key objective of this
study is to demonstrate that the ball lightning can be a diffusional flame
maintained by the atmospheric d. c. currents.
* An identified flying object observed by the author,
in March, 1980, 4p. m., at a site near Moscow in low continuous cloudiness
(temperature about 0oC). The object was observed over the forest,
at distance some 70-IOO m away, at altitude of 50-80 m. The object remained
motionless and was observed for over 15 minutes. It hardly looks like a
typical ball lightning. However, the object image resembles quite much
the ball lightning photograph taken by Charman W. N. (New Scientist, 56,
1972, p. 632).
The thermodynamic and kinetic analysis results [13-14] make it possible
to single out the basic chemical reactions going on in the lightning storm
atmosphere as well as the high-temperature ionization processes shaping
the ball lightning phenomenon.
Firstly, let's discuss the specific features of the physico-chemical
transformations of the lightning storm air in a wide temperature range.
In the lightning storm atmosphere nitrogen oxides, ozone and other "combustible"
components start to accumulate reaching concentrations in excess of the
normal levels (sometimes by several tent olds). Thus, nitrogen oxide is
synthesized through -the following process:
where: the reaction heat effect relates
to standard conditions. Having entered the low-temperature zone, is
"tempered" [15,16] and can react with oxygen and ozone as in the below
Under the lightning storm conditions the processes described by the
cumulative equation of the below type become significant too:
The created dissociates
in rain drops and fog particles in the following way:
It should be noted that ,
also a product of the cumulative process, is similarly unstable even at
low temperatures and in the liquid phase decomposes into and .
In addition, there are other known processes of the type:
increasing the liquid phase conductivity by several orders. The reactions
of and decomposition
in the gaseous phase under the appropriate conditions can generate some
amounts of ions as well.
Considering the ionization potentials and the values of affinity to
electron and proton of the particles identifiable in the atmosphere, one
can state that at temperatures of 300-500K the atmospheric air contains and
some other ions in relatively increased concentrations. However, it should
be noted, that due to the kinetic and thermodynamic limitations as well
as to the specificity of the nitrogen based oxygen compositions chemistry,
the ion composition in the atmospheric air under effect of temperature
changes can vary in the real environment in a complex manner (e.g. reaction
1 in the above range has some kinetic limitations; can
withstand temperatures practically up to 900K, whereas thermal decomposition
of is noticeable
at 800K and above, etc.).
The most significant role in the charged, particles generation in the
atmosphere is probably played, by the relatively advantageous, in terms
of thermodynamics, ionization processes involving electron transfer. Thus,
e. g. Interactions:
5.4 eV (8)
can intensively proceed, in the atmosphere including the lightning discharge
area, and roles of different reactions can vary depending on the temperatures
(at the right hand. side of equations 8-10 the upper possible values of
the processes' heat are indicated, whereas the lower limit values are given
The mentioned above ions are easily registered in the atmosphere and
ionospheres of planets [9-17]. However, it has been often mentioned that
the ion concentrations are significantly higher than those calculated by
the Saha-Boltzman equation [18-20]:
because the equation was obtained assuming that the thermal ionization
of atoms and molecules (A) in the system goes in the spontaneous way only
and the electric ionization and. other ionization processes on surfaces
of solid particles always present in the atmosphere are not accounted for.
In relation (1) the following symbols are used: -
concentrations of ions, electrons and neutral atoms or molecules; -
corresponding statistic weights; -
masses of the particles; -
For example, comparison of the experimental values of ion concentrations
in the lightning storm atmosphere (containing fivefold excess of )
at 1000K as well as those in the corresponding flame zones, against the
values calculated using the Saha equation assuming even the abnormally
low mean value of =
6 eV, shows that the experimental data exceed the calculated values by
On the other hand, the experimentally defined values of n. in the lightning
storm atmosphere correlate well with the estimates obtained by extrapolation
of the experimental data on transformation of the oxygen compositions of
nitrogen in liquid media with a low dielectric permittivity where effective
dissociation of the above compositions is observed with generation of ions
[21-23]. This is yet another evidence of the solvatational and other effects
role in dissociation in the real atmospheric environment.
Thus, we come to the conclusion that calculations by Saha assuming only
process (12) going on at temperatures about 1000K for the real atmosphere
give significantly underestimated values of .
However, the theoretical values of determined
using formula (I) for the air at temperatures 2000-2500K should have a
better correlation with the experimental data. The fact is that under such
temperature the type (12) processes become dominating, because under the
equilibrium conditions the air is practically a mixture of several gases: with
higher concentrations as compared to other components (e. g. ),
and the thermal ionization proceeds using only one component - (with
a relatively small ionization potential of 9.267 eV). In addition, under
such conditions the ionization involving solid particles in the real atmosphere
should be small.
Let's now discuss the ball lightning model in general. An electric lightning
discharge or a volumetric charge discharge in the atmosphere creates in
some point in space an elevated ion concentration and a high temperature,
i. e. the conditions required for the ball lightning flame initiation.
The flame is of ball (hollow sphere) shape and is maintained by dc atmospheric
Assume that in the relatively cold zones of the sphere the type (2-3)
processes are maintained by diffusion of the "fuel" and oxidants - and
It can be easily shown that even at the abnormally high concentrations
of the combustible admixtures (about 1 %) and the process mean heat of
35-40Kcal/mole the heat up can not raise temperature even to 600-700K.
The real content of the combustible products (including )
in the lightning storm atmosphere in no case can exceed 0.0003% (in volume).
Thus, the energy of the discussed chemical processes is by several levels
below the level required for the ball lightning heat up.
Moreover, consideration of a stationary diffusional burning of the fire
ball in a stable medium, which in a simplified model can be described by
a simple heat transfer and diffusion equations
with reasonable assumptions (on small areas of the on-surface transformation
zone, etc.) it easy to establish that this model is unstable against radial
excitations . In equations (II, III): -
concentration of combustible matter;
- chemical reaction rate; -
Thus, we understand that is hardly possible to create a purely "chemical"
model of the phenomenon without an external energy source.
If some burning gaseous sphere (a ball) containing ions of different
polarity is in the atmospheric electric field, there should be separation
of the on-surface (and volumetric) charges effected in the sphere by the
field (as well as by the thermo-diffusional and other effects though to
an insignificant degree). The charge of such a burning sphere (a ball)
and the field intensity on its surface can be estimated using the known
model of field, and model of charge distribution on a conductive sphere
in an external uniform electric field.
Assume, that a sphere of radius is
positioned in a uniform external electric field of intensity .
It is easy to show that the charges on the sphere's surface are distributed.
by the law
on-surface charge density; -
polar angle; -dielectric
constant. Such a distribution of charges is characterized by the dipole
element of area; -
radial coordinate; -
unit vector along z axis in the field
direction. The electric field beyond the sphere is defined as
It should be noted that the ball's own electrostatic field intensity,
the charge of which is uniformly distributed over the ball surface, coincides
beyond the ball limits with the point charge intensity, ,
positioned in the ball center. It is hard to say to what degree of approximation
the ball lightning can be treated as a burning sphere. It may well be closer
to burning ball charged uniformly over all volume. However, at the phenomenon
principle model creation it does not matter which of the cases is realized
in nature (it is not excluded that the both ones). So, let's estimate density
of the conductivity current, ,
for the "droplet" case
conductivities of the positive and negative ions; -
potential (С ).
Using relation (VII) let's estimate density of the conductivity current
for the realistically possible values of the ion concentrations, ,
potential gradient (С )in
the lightning storm atmosphere at temperature of 2500K. Selection of this
temperature value is fairly well substantiated because the ball lightning
temperature varies in a wide range and as a rule should reach this selected,
ion mobility =
We obtain =
7 103 s-1,
charge of electron (4.8Ч 10-10
CGSEq). Further, taking into consideration that in the pre-discharge instance
of the linear lightning can be equal to 104
V/cm2, the value of in
the "droplet" is 10-4 A/cm2.
Note, that the same density of current is obtained, at
n. = 1010 ion/crn3
and | |
= 103 V/cm, etc.
The obtained value of current is quite adequate to observe the diffusion-limited
endothermic synthesis (1) and to maintain the gaseous ball (sphere) at
a temperature of many hundred degrees. The obtained estimates correlate
well with the theoretical analysis and other calculation data. It can be
shown that the model of the diffusionally controlled reaction in the sphere
etc.) maintained by current
of power below the break down threshold is similar to "burning" of the
spherically symmetrical optical charge [14-20] and is stable against radial
Inflow of current heats up the sphere providing for synthesis
as it has been mentioned above. Additional quantities of nitrogen oxide
can be generated by the electric synthesis associated with the reactions
of the below type
Synthesis of and
other products  can go in the relatively cold areas of the sphere and
its adjacent environment.
Reaction (1) has been studied quite well; and of
the process are known. Hence, from equation
it is easy to calculate the reaction coefficient and.,
in the equilibrium mixture at the given temperature. Further, by putting
value into the Saha equation (1) it is possible to estimate ionization
level using relation 
E. g., using values of =
9.276 eV, =
3.60 10-3 =
7Ч 1016 particles/cm
(2.4 % by volume, by some other data - 2.0 %), we obtain 4.2Ч
Hence, it is evident that at 2500K the calculation gives a very high
value of ion concentration. The true ion concentration, as it has been
mentioned, above, can be even somewhat higher. Such an ion concentration,
as it has been discussed earlier, provides for flow of current adequate
to maintain endothermic burning and to heat up the ball of lightning. Note,
that for T = 2000K: =
which corresponds to the current some two orders lower as compared to the
current at 2500K.
The lightning heat is transferred into environment, and the temperature
inside the ball is distributed in the quasistationary way. let's consider
a simplified model of the gaseous ball ("droplet") in which the energy, ,
is emitted due to the electric current passage. The value of is
equal to the Joulean heat minus the reaction endothermic heat.
For the spherically symmetric problems the stationary equation of heat
conductivity at presence of a heat source with power density of is
given in the form of
heat conductivity; -
radius. Solution of equation (IX) for the ball interior has the form of
temperature at the ball-air boundary; -
the ball radius; -
temperature at distance
from the ball center.
Assuming that -
quantity of heat generated in the conductive medium of the lightning ball
and is determined by the Joule-Lenz law
current (ampere); -
voltage (volt); -
time (second). Given that =
4 10-5 A/cm2,Ѕ
= 104 V/cm, we get =
9.6.10-2 cal/cm3 s. Further, at =
sЧ K, and =
10 cm, we get the temperature value at the ball center equal to 2300K,
and the temperature 1 cm away from the ball surface 680K.
To present this in a more obvious way, estimation of the air molecules
diffusion time, ,
i. e. time for the air molecules diffusion into the sphere with =
10 cm at mean temperature of 2000K (,
diffusion coefficient), easily shows that the quantity of the heat absorbed
in the course of the diffusion-limited reaction (1) is a small fraction
(about 1 %) of the q value required for the sphere heat up. Thus, for the
model being discussed, is
consumed actually for the gaseous ball heat up only.
The quantitative evaluations listed above lead us to the conclusion
that under the real conditions the atmospheric volumetric charges pass
through the ball lightning and maintain it. Our approach in terms of the
phenomenon physics correlates with the findings discussed in some other
publications [4,26-29] considering the possibility of the transversal "compression"
of the cloud-to-ground current
(equation IV) in the high conductivity area., and noting that the
ball (sphere) positioning into a atmospheric
field intensity in the sphere. However, it should be noted that the above
mentioned and other studies have not paid the proper attention to the specific
role of the atmospheric volumetric charges (discharge between which in
no way can be connected neither to thunderclouds nor to the ground), and
have not offered a realistic physico-chemical mechanism of ion formation
and maintenance of high concentrations of charges in the ball lightning.
Disregard to the "chemistry of the phenomenon" has, probably, led a number
of authors to overestimation of the temperatures in the ball of lightning.
As it has been widely known, quite strong horizontal atmospheric currents
are able, to our estimates, to maintain the ball lightning. Those currents
are especially high when volumetric charges are generated at the lightning
storms, fogs, smogs, snow storms, dust storms. Those charges can maintain
burning of the ball lightning same as they can induce illumination of electric
Decrease of voltage and current in the atmosphere causes the ball lightning
death (disappearance). However, at the critical discharge values (in a
lightning storm) an explosion may happen or a linear lightning discharge
(sparkle, arch) with an enormous amount of energy release - the ball lightning
dies in the explosion. It is evident, that though the ball lightning has
a relatively small stock of interior energy, it can initiate high energy
discharges in the atmosphere. In principle, there is yet another possibility
of a ball lightning death - a local explosion of a "chemical nfature" with
no discharge of a significant power- the energy of such an explosion is
relatively small. It should be noted, that analysis of I, VI, X type equations
shows that a stable regime of burning in the lightning can be obtained
by variation of some parameters (,
etc. ) in a narrow range. The bulk of those parameters are interrelated.
It is clear now why the ball lightning is such a rare phenomenon with such
a short lifetime.
A more detailed theory of the phenomenon can be developed with regard
to the general approaches to the heat explosions and to the break down
of dielectrics [30,31] in the similar way as it has been applied to other
The model developed by us, though doesn't account for some factors (e.
g. convective transfer of matter, electric ionization degree, energy loss
at irradiation, side reactions in the cold zones, etc.), is basically substantiated
with reliable experimental data and is capable to explain many specific
features of creation, behaviour and death of both the ball lightning and.
the unidentified objects . The proposed model can be easily checked
experimentally. A number of concepts quoted in this study have been offered
by some researchers earlier. However, the existing theories, as a rule,
have not been substantiated with the real chemistry of the lightning storm
atmosphere and account for only individual aspects of the phenomenon being
discussed (either only physical or desciptional chemical ones, etc.). The
authors of the theories have not offered any physico-chemical mechanism
of ion formation and. maintenance of the required charge concentration
in the ball lightning. Our model explains a range of the known facts and.
concepts and actually presents a detailed physico-chemical model of the
The proposed, model doesn't in principle contradict to many well known
data and new findings as well as to calculations by various authors [35-38].
It is quite probable that the ball lightning phenomenon is associated with
the mechanisms of the processes that have not been discussed in this paper.
However, the author believes that the ball lightning is indeed a diffusional
flame fed by external energy source. The ball lightning may well be considered
as similar to the plasma flame created at combustion of nitrogen in industry
at the nitric acid. production.
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