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1. 6 November1995 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
PHYSICS LETTERS A
EI-SEVIER Physics Letters A 207 (1995) 281-288
Artificial ozone layer
A.V. Gurevich ‘, N.D. Borisov 2, S. Montecinos Geisse, P. Hartogs zyxwvutsrqponmlkji
Max-Plunck-Institut zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
fir
Aeronomie. 37191 Katlenburg-Lindau, German.v
Received 14 August 1995; accepted for publication 6 September 1995
Communicated by V.M. Agranovich
Abstract
The possibility of artificial ozone layer creation in the stratosphere by powerful microwaves is discussed theoretically.
Numerical calculations and analytical results for a simple oxygen model are presented.
1. Introduction
The decrease of ozone concentration in the stratosphere and the appearance of so-called “ozone holes” have
caused considerable anxiety in the last few years. Different approaches to the problem of ozone conservation
have been discussed. All these approaches require considerable energy expenditure. It seems that the most
promising approach is connected with the creation of an artificial ionized region in the atmosphere by
microwave discharges. The main advantages of this approach are the following:
(1) The energy can be transferred for considerable distances in the air almost without losses.
(2) The energy can be focused in the given region of the atmosphere to achieve the necessary effect.
(3) Different regimes of the microwave source can be used, which gives the opportunity to achieve the
necessary optimum conditions.
The problem of the creation of an artificially ionized region in the atmosphere at heights 20-50 km in
microwave discharges was formulated first by Gurevich [l]. Further the problem was investigated in detail
theoretically and experimentally in Refs. [2-S]. A considerable increase of ozone concentration up to lOI cmP3
in the ionized region was predicted theoretically in Ref. [3] and confirmed experimentally in Refs. [4,5].
So the possibility to increase the ozone concentration in the atmosphere can be considered generally speaking
as established. The aim of the present paper is to investigate the possibility of artificial ozone layer (AOL)
creation and to obtain preliminary information about its main properties.
’ On leave from the P.N. Lebedev Institute of Physics, 117942, Moscow, Russian Federation.
’ On leave from the Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (IZMIRAN), 142092 Troitsk, MOSCOW
Region, Russian Federation.
Elsevier Science B.V.
SSDf 0375-9601(95)00690-7

2. 282 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
A. V. Gurevich et ul. /
Physics Letters A 207 (1995) 281-288
2. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
Ozone creation and destruction
The main source of ozone creation and destruction is solar radiation. Under the action of solar radiation with
wavelengths A G 2400 A the dissociation of oxygen molecules occurs,
o,+hv+O+o.
Atomic oxygen is easily transformed into ozone in triple collisions,
(1)
O+O,+M+O,+M, (2)
where M is any molecule. The created ozone is very unstable. It is destroyed not only under the action of
ultraviolet WV) but also visible and even infrared radiation. The equilibrium ozone concentration in the
stratosphere is formed by photochemical processes of creation and destruction and also by dynamical processes
of horizontal and vertical transport.
The sun is a very powerful source of UV radiation. Indeed, the energy flux of radiation at the height of the
upper stratosphere with wavelengths h f 1200 A is of the order of I = 3-6 erg/cm’ s. But the flux responsible
for the process of oxygen dissociation diminishes rapidly with height and at the heights corresponding to the
maximum of the ozone layer, z = 20 km, it is approximately one order of magnitude smaller than at the height
7 = 35 km. Due to this circumstance the ozone lifetime rapidly increases with decreasing height. It achieves a
&
magnitude of the order of six months at the heights of the maximum of the ozone layer. The vertical transport in
this region is negligible. On the contrary, the horizontal transport is essential. It causes a global transfer of
ozone, which provides ozone layer formation for an extended period. On the other hand, it provides the
possibility of essentially influencing the weak vertical transfer and catalytic reactions with minor atmospheric
constituents on the ozone layer. Such phenomena cause in special conditions the formation of ozone holes -
considerable depletions in the integral thickness of the ozone layer. It should be mentioned that the long
characteristic time of ozone layer formation gives the possibility to influence the ozone concentration on global
scales by a gradual artificial increase of the ozone density in the local region.
In the present paper powerful microwave radiation is suggested as an artificial ozone source in the
stratosphere. Under the action of such pulsed radiation periodic microwave breakdown takes place. As a result
the concentration of free electrons in the discharge rapidly increases. During each breakdown pulse the averaged
electron energy achieves a value of E = 1-2 eV. But a considerable number of electrons acquire a higher energy
sufficient for the dissociation of molecular oxygen. So the appearance of a large amount of fast electrons in the
discharge causes a rapid increase of atomic oxygen.
Between the breakdown pulses the temperature of the electrons decreases. Meanwhile atomic oxygen is
transformed into ozone in triple collisions (2).
Ozone is pulled out of the discharge by atmospheric wind and gradually occupies some region. The
horizontal scales of the AOL grow with increasing lifetime at the heights where the discharge takes place. The
ozone lifetime connected with the photochemical processes of ozone destruction and turbulent vertical transport
grows with decreasing height. At the same time the microwave power necessary for breakdown and mainte-
nance of the discharge also grows rapidly with decreasing height. A compromise between these two factors
determines the height favorable for the creation of an artificial ozone layer.
3. Photochemical lifetime of ozone
The ozone kinetics in natural conditions is determined by several factors: the action of solar UV radiation,
reactions with different components of the air, horizontal and vertical transport. It seems reasonable to extract
and consider separately the role of the abovementioned factors. In the present section we concentrate mainly on

3. A. V. Gurevich et al. /Physics Letters A 207 (I 995) 281-288 283
the influence of UV radiation on the AOL. Because of that we consider the simplest oxygen model of the media
in which the following photochemical reactions are taken into account,
0,+/7v+o+o, (3a)
0~+hu+02+0, (3b)
o+o,+o,+o,+o,, (3c)
o+o,+o,+o,, (3d)
o+o+o,+o,+o,. (3e)
According to the set of reactions (3) the concentrations of atomic oxygen 0 and ozone 0, are determined by the
system of coupled equations
dNl zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
-=2J
,~N,+J
,N,-(K3N2N+K4N3+2KSN,N)N,,
dt
dN,
- = K,N,N,N- (J
o3 + K,N,)N.
dt
(4a)
Here N is the total concentration of molecules which is equal in our model to the concentration of molecular
oxygen 02, J
,, J
, are the coefficients of dissociation of 0, and 0,, K,, K,, K, are the reaction rates of the
processes (3c)-(3e). The coefficients of photodissociation depend on the sun zenith angle and due to this are
periodic functions with period T = 24 hours. So the stationary concentrations N,, N3 in natural conditions
should be also periodic functions N,(t) = N,(t + T), N3(t) = N&t + T). The concentration of O,, hence the
total concentration is assumed to be constant in time.
The system of differential equations (4) is nonautonomous due to the explicit time dependance of the
coefficients. Since no vertical transport is assumed we solve the system for each given altitude separately. The
reaction rates K,, K,, in Eq. (4) are given by the following expressions,
K, = 6.0 X 10-‘4(T/300 K)-2.3 (cm6 s-l),
K, = 8.0 X lo-” exp( -2060 K/T) (cmm3 s-l). (5)
Note that reaction rate K, is relevant only above 50 km. The temperature profile was kept constant during the
computations. The CIRA 86 mean temperature profiles were used. The initial profiles for 0 and 0, were taken
from Ref. [6].
The photolysis rate coefficients depend on the solar flux and are time and altitude dependent as well. They
are defined by the following integrals of the UV radiation wavelength A, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR
J;( z, x) = jh2u;P(h) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
““‘;:’‘) d*.
Al
Here x is the zenith angle, z is the height, sip is the dissociation cross section and dl/dz is the spectral
distribution of the solar flux. The integral is taken in the range of wavelengths where dissociation occurs.
We consider a sinusoidal parametrisation for J
i,
J
i(z, t) =0.5J;(z)[l -cos(nt/l2)], (7)
where t is in hours and J
F are taken as the photolysis rate constants for overhead sun conditions [7].
The numerical integration of the system (4) we perform in two stages. At the first stage we define the normal
initial conditions N,‘(z),
Nio=N,‘(t+T) (8)

4. 284 A.V.Gureuich et al. /
Physics Letters A 207 C19951281-288
Table 1
Nondistributed ozone profiles
; (km) Latitude 40”s Latitude 30%
October November December October November December zyxwvutsrqponml
20 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
4.le13 4.3e13 4.3e13 4.5e13 4.7e13 4.8el3
2.5 3.3eI 3 3.3e 13 3.2e 13 3.4e1.3 3.5e13 3.4el3
30 2.0e13 1.8e13 l&13 1.8el3 1.8e13 1.7el3
35 6.le12 5.Oe12 5.7e12 5.2e12 5.2el2 4.9e12
and integrate the whole system (4) starting from the initial conditions, taken from Ref. [6] until the normal
conditions are achieved. The normal values of ozone concentration NT obtained in this way for different heights
Z, months and latitudes C$= 3o”S, 40”s of the southern hemisphere are presented in Table 1. One can see from
Table 1 that the maximum values of Nt are reached at the heights z = 20 km.
At the second stage we add to the normal initial state NF an ozone perturbation caused by an artificial
source, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
SNf = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
CYN: exp[ - ( z - z0)‘/d2], (9)
where d = 2 km, z,, = 20, 25, 30, 35 km, (Y= 0.5, 1.0, 2.0. We investigate numerically the relaxation processes
to a normal state. The characteristic time in days of the decrease to one half of the initial ozone perturbation is
shown in Table 2. A very strong dependence of the ozone lifetime on the height in the stratosphere is seen.
Some diminishing of the lifetime with the growth of the amplitude of perturbation can be seen, but this
nonlinear effect is not too strong (for (Y= 2 the lifetime is 30% smaller than for cx= 1). Also a slight
diminishing of the lifetime with the month, changing from October to December (approximately on lo%), is
seen. There exists a noticable decrease of the lifetime with increasing latitude from 30”s to 40”s (approximately
20%-25%). The system (4) can be analysed also analytically. For this purpose let us average Eq. (4) in time.
We assume that at the heights z > 20-25 km the changes of ozone concentration are not strong: N,(t) = ( Nj)
+ 8N,(t>, 6N,/N, -=z 1. This assumption is proved by numerical calculations. As a result of averaging we
arrive at the following algebraic system of equations for concentrations (N,) and (N,), zyxwvutsrqponmlkjihgfedcba
2(J
o,)N,+(J
o1)(N,)-K,(N,)N,2--Kq(N,)(N3)=0,
K,(N,)N,‘-(J
oz)(N,)-K,(N,)(N,)=O. (10)
In deriving (IO) we omitted the last term in the right hand side of Eq. (4a), which is essential only for rather
large heights z >, 50 km. The solution of the system (10) takes the form
(J
o,)
ii zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
1
(Jo,) 2+SN, (J
o) “*
w =0.5N2 ( Jo,> + 0.5N2 ( Jo,> K, 2 (Jo,>
I
. (11)
The system of linear equations that determine deviations of concentrations sN,(t), sN,(t) can be obtained with
the help of (4) and (lo),
;SNj = -sJ
,l(t)(N& - 3 + 3,
711 712
(‘2a)
( 12b)

5. A. V. Gureuich et al. /Physics Letters A 207 (1995) 281-288 285
Table 2
Ozone relaxation time in days for cx= I
z(km) Latitude 40%
October November
20 257 276
25 36 36
30 9 8
35 3 2
December
287
34
7
2
Latitude 30”s
October November December
311 341 355
3-l 38 37
8 8 8
3 2 2
Here SJol<t>, sJo?(t> are deviations of coefficients of photodissociation from their averaged meanings (Jo,),
(Jo,), rij are the characteristic times of the process,
r;,’ = (Jo,) +K,(N,),
72,’ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
=(J
,,>-&(A’,),
7;; = K&= - K,(N,),
7;; = K,&= + K&h (‘3)
In the lower part of the stratosphere at heights z < 30-35 km, where the concentration of molecular oxygen is
very large, the times r,?, rZ2 are much smaller than T, ,, TV,. Due to this it is possible to determine
approximately the concentration c?N,(t> from Eq. (12b),
sNx(t) = 722[2~J
o?(44 + Wh]. (‘4)
Substituting (14) in Eq. (12a) we arrive at the following equation for the ozone concentration srl,(t>, zyxwvutsrqponm
;6N3 + 3 = 2%J
oI(r) N2 - SJ
,$N,),
7 712
(‘5)
where the ozone relaxation time T is determined by the expression
2
T11721
7=
721Tll - 722712
In the lower part of the stratosphere 722 = 7i2 and (16) takes the form
(‘6)
T= (2K,(N,))-‘. (17)
The time rapidly diminishes with height due to the growth of the air temperature (factor K4) and the averaged
concentration of atomic oxygen (N,). In Table 3 the photochemical times of ozone relaxation calculated with
the help of ( 17) are presented. One can see rather good agreement with numerical results.
Table 3
Averaged time of ozone relaxation for latitude 30’S
2 (km) N, (cm-‘)
20 2.0e7
2s 1.Oe8
30 4.0e8
35 8.Oe8
T (K) T (days)
213 573
222 77
232 13
243 4

6. 286 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
A.V. Gureuich et ul. /
Physics Lettem A 207 (1995) 281-288 zyxwvutsrqponmlkjihgfedcbaZYXWVUT
4. Formation of artificial ozone layer
Now we proceed to investigate the dynamics of the artificially created ozone perturbation SN3 and atomic
oxygen SN,. Suppose that a localized source of ozone and atomic oxygen operating continuously exists at a
given height z,,. We suppose also that atmospheric wind with velocity zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM
V, and horizontal turbulent diffusion
with coefficient zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
D are present. The dynamics of small perturbations SN,, 6N, in space and in time are
described by the following system of linearized equations obtained from (4)
[$+V;-D(-$+$)]aNa
= -J
o,6N, - K,N,aN3 f K,N,aN, + K3N$N, + zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCB
Q,,a( x)6( Y),
[$tY;a;-D($+$)]~N,
(184
=J
,$N,-K,N$N,-K,N$N,-K,N,6N,+Qol~(x)8(y). ( ‘8b)
Here zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
Qo,and Q,, are the sources of ozone and atomic oxygen production.
Atomic oxygen is rapidly transformed into ozone in accordance with reaction (2). Because of that it is
possible to neglect atmospheric wind and diffusion in Eq. (18b) and obtain for 6N,,
6N
I zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
Qo,GMY) + Joy Kd’, 6N
= K,N;+K4N3 K3N; + K,N, 3’
(19)
Substituting (19) in Eq. (18a) we arrive at an equation describing the dynamics of the artificially created ozone
perturbation,
Here zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
T is the photochemical ozone lifetime (see (16)) Qeff = Q,, + Q,, is the effective ozone source, which is
determined by the sum of two sources that produce atomic oxygen 0, and ozone 0,. Deriving Eq. (20) we
neglected small terms of the order of K, N,/K, Ni -=x1 in the right hand side. It should be mentioned that in
the general case the dynamics of ozone perturbation is described by Eq. (20) with lifetime zyxwvutsrqponmlkjihgf
T which is
determined not only by photochemical processes but also some others with minor atmospheric constituents, e.g.
catalytic reactions with nitric oxydes. We shall study the effect of admixture of minor constituents in a next
paper. The stationary solution of (19) can be represented in the form
64(x, Y) = ---&exp( Vx/2 D)/’ exp s + 4ii foci, (t-t,)-’ dt,,
--m eff
where 7Crf= 4Dr/(V2r+ 40).
Solution (21) can be rewritten in a more convenient form,
(21) zyxwvut
6N,(x, y) = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
&I( P>ev(Vx/2D)3 (22)

7. A. V. Gureuich et al. /Physics Letters A 207 Cl995) 26’1-288 287
where
I( zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
P> =/,
me v[-P( 5+ l/t>1 d5
5
, p= (gf)“*, s=t( ,,,c;:+y2J”2.
It is easy to find that for any wind velocity zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
V the total perturbation is conserved,
/
= aN,( x, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
Y) dx dy = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
Qefp.
-co
(23)
In the case when atmospheric wind exists solution (22) is asymmetric in the horizontal plane - it is stretched in
the direction of the wind velocity V. For
?
x=- 1, that is for large distances from the source x2 + y2 B- 407, or
for large wind velocity V z=- 2 D/ x2 + y* , it is possible to obtain from (22) an approximate analytical solution
~N,(x, Y) = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
Qeff +$
i
ev( Vx/2D - I(-)
/+y? .
(24)
For large wind velocity V z=- & one can see that the characteristic dimension of the artificial layer along the
x axis, L, N VT, is much larger than along the y axis, L, N &%. In this case the distribution of the
concentration for x > 0 takes the form
(25)
Distribution (22). (25) allows us to estimate the dimensions of the area occupied by the artificial layer for a
.,.
small velocity V-=x J2D7,
S = 41rDr,
and for a large velocity,
S = 2J;;VD’/2r3/2.
It is seen from (27) that the area of the artificial ozone layer
coefficient D, the wind velocity V, and the ozone lifetime r.
lifetime T and the wind velocity V should be mentioned.
5. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
Discussion and conclusion
(26)
(27)
becomes larger with the growth of the diffusion
Especially the strong dependence on the ozone
It follows from formulae (25) and (27) that the area occupied by the artificial ozone layer can be rather large.
Considering the layer created at the height z = 20 km we obtain from Table 2 for the lifetime T = 200 days. The
coefficient of turbulent diffusion D at such heights can be estimated as D = lo9 cm* s-l. For such parameters
even for the wind velocity V = 5 m/s the characteristic area is very large, S > IO* km2. Note that the creation
of a large AOL with the help of a localized source allows us to avoid the negative influence of powerful
microwave radiation by selecting for the generation zone a remote region. This is an important positive property
of the AOL created by the suggested method.
Of course, of special interest is the microwave power required for the creation in such an area of the AOL
with thickness N,, where NZ is total number of ozone atoms in an atmospheric column with unit square base,
NX = / N,$z) dz. The ozone thickness is measured in Dobson units: 1 D = 2.7 X 1016 cm-*. The averaged
concentration of ozone in the atmosphere is equal to Nz = 300 D. In the “ozone holes” the depletion is of the

8. 288 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
A. V. Gurevich et al. /Physics Letters A 207 I1995) 281-288
order of AN, = 50-100 D. SO for the maintenance of the natural ozone layer it is reasonable to consider an
AOL with thickness N, ‘- 50 D. For this purpose in a region of the order of the antarctic ozone hole the
generation of No, = 4 X 103’ molecules is required. According to Ref. [4] the averaged energy required for the
creation of one ozone molecule in air by pulsed microwave discharge at heights z = 20-25 km is E = 20-25
eV. Hence the total energy required for the creation of AOL is A = 1O37 eV. For the characteristic ozone
lifetime at heights z = 20 km, r= 200 days, we find the necessary power as
W = 15-20 GW. (28)
This power is extremely high. We note that the result (28) is a rather preliminary estimation of the energy
expenditure required for creation of an AOL. In a real situation catalytic reactions of nitrogen and hydrogen
cycles and noxious action of artificial admixtures in the atmosphere should be taken into account. The
peculiarity of the atmospheric wind dynamics in the polar regions also was not considered in our paper. On the
other hand, some factors can favour the diminishing of the required microwave power: a more careful estimation
of the energy cost of ozone creation in the microwave discharge, an investigation of the optimum conditions in
the discharge for ozone creation, the influence of the artificial ozone layer on the chemical composition of the
atmosphere (especially on noxious admixtures). It should be emphasized that the rather low temperatures in the
polar stratosphere at heights z = 15-20 km also favour ozone generation in the discharge.
So this preliminary analysis shows the possibility in principle and at the same time extreme difficulty of AOL
creation by powerful microwave radiation. Taking into account the current interest in the ozone problem it is
natural to expect future theoretical and experimental investigations to obtain exact answers regarding necessary
conditions and real possibilities of AOL creation.
References
[I] A.V. Gurevich, Sov. Phys. Usp. 23 (1980) 862.
[2] N.D. Borisov, A.V. Gurevich and G.M. Milikh, Artificial ionized region in the atmosphere (1986) [in Russian].
[3] N.D. Borisov, S.I. Kozlov and N.V. Smimova, Cosmic Res. 31 (1993) 63.
[4] A. Vikharev, A. Gorbachev, 0. Ivanov, A. Kolisko and A. Litvak, J. Geophys. Res. 99 (1994) 21097.
[5] A.V. Gurevich, N.D. Borisov, K.F. Sergeichev, N.V. Lukina, 1. Sychev, S.I. Kozlov and N.V. Smimova, Phys. Len. A 20 (1995) 234.
[6] G. Brasseur and S. Solomon, Aeronomy of the middle atmosphere (Reidel, Dordrecht, 1986).
[7] N. Nicolet, Aeronomic reactions of hydrogen and ozone, in: Mesospheric models and related experiments (Reidel, Dordrecht, 1971).