Artificial ozone layer

6 November 1995 PHYSICS

EI-SEVIER

LETTERS

A

Physics Letters A 207 (1995) 281-288

Artificial ozone layer A.V. Gurevich ‘, N.D. Borisov 2, S. Montecinos Geisse, P. Hartogs Max-Plunck-Institut firAeronomie. 37191 Katlenburg-Lindau, German.v Received 14 August 1995; accepted for publication 6 September Communicated by V.M. Agranovich

1995

Abstract The possibility of artificial ozone layer creation in the stratosphere by powerful microwaves Numerical calculations and analytical results for a simple oxygen model are presented.

is discussed

theoretically.

1. Introduction

The decrease of ozone concentration in the stratosphere and the appearance of so-called “ozone holes” have 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. caused

’ On leave from the P.N. Lebedev Institute of Physics, ’ On leave from the Institute of Terrestrial Magnetism, Region, Russian Federation. Elsevier Science B.V. SSDf 0375-9601(95)00690-7

117942, Moscow, Russian Federation. Ionosphere and Radio Wave Propagation

(IZMIRAN),

142092 Troitsk, MOSCOW

A. V. Gurevich et ul. /Physics

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Letters A 207 (1995) 281-288

2. Ozone creation and destruction The main source of ozone creation and destruction is solar radiation. Under the action of solar radiation wavelengths A G 2400 A the dissociation of oxygen molecules occurs, o,+hv+O+o.

with

(1)

Atomic oxygen is easily transformed O+O,+M+O,+M,

into ozone in triple collisions,

(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 maintenance 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

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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 system of coupled equations

of atomic oxygen 0 and ozone 0, are determined

dNl

-=2J,~N,+J,N,-(K3N2N+K4N3+2KSN,N)N,, dt

dN,

-

dt

= K,N,N,N-

by the

(4a)

(Jo3 + K,N,)N.

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, = 8.0 X lo-” Note that reaction computations. The from Ref. [6]. The photolysis are defined by the J;(

z,

x)

=

K)-2.3

exp( -2060

(cm6 s-l),

K/T)

(cmm3 s-l).

(5)

rate K, is relevant only above 50 km. The temperature profile was kept constant during the CIRA 86 mean temperature profiles were used. The initial profiles for 0 and 0, were taken rate coefficients depend on the solar flux and are time and altitude dependent following integrals of the UV radiation wavelength A,

as well. They

‘) d*.

jh2u;P(h) ““‘;:’ 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 Ji, Ji(z,

t) =0.5J;(z)[l

-cos(nt/l2)],

(7)

where t is in hours and JF 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)

284 Table

A. V. Gureuich et al. /Physics Letters A 207 C19951281-288

1

Nondistributed

ozone profiles Latitude

; (km)

40”s

Latitude

30%

October

November

December

October

November

December

4.3e13 3.3e 13

4.3e13

4.5e13

4.7e13

4.8el3

2.5

4.le13 3.3eI 3

3.2e 13

3.4e1.3

3.5e13

3.4el3

30

2.0e13

1.8e13

l&13

1.8el3

35

6.le12

5.Oe12

5.7e12

5.2e12

1.8e13 5.2el2

1.7el3 4.9e12

20

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, SNf = 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,),

2(Jo,)N,+(Jo1)(N,)-K,(N,)N,2--Kq(N,)(N3)=0, K,(N,)N,‘-(Joz)(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 large heights z >, 50 km. The solution of the system (10) takes the form

(Jo,) w

=0.5N2

( Jo,>

(Jo,) +

The system of linear equations the help of (4) and (lo), ;SNj

= -sJ,l(t)(N&

ii

0.5N2

( Jo,>

that determine

2+SN,

1

K,

deviations

- 3 + 3, 712 711

only for rather

“*

(Jo) 2 (Jo,>

(11)

. I

of concentrations

sN,(t),

sN,(t)

can be obtained

with

(‘2a) ( 12b)

A. V. Gureuich et al. /Physics Table 2 Ozone relaxation

time in days for cx =

z (km)

Latitude 40%

20 25 30 35

Letters A 207 (1995) 281-288

285

I Latitude 30”s

October

November

December

October

November

December

257 36 9 3

276 36 8 2

287 34 7 2

311 3-l 8 3

341 38 8 2

355 37 8 2

Here SJol, sJo?(t> are deviations of coefficients of photodissociation (Jo,), rij are the characteristic times of the process, r;,’ = (Jo,)

from their averaged meanings

(Jo,),

+K,(N,),

72,’ =(J,,>-&(A’,),

7;; = K&= - K,(N,), 7;; = K,&= + K&h

(‘3)

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), In

sNx(t) Substituting

=

722[2~Jo?(44 + Wh].

(‘4)

(14) in Eq. (12a) we arrive at the following

;6N3

+ 3

= 2%JoI(r)

7

equation

for the ozone concentration

N2 - SJ,$N,),

sr\l,(t>,

(‘5)

712

where the ozone relaxation

time T is determined

by the expression

2 T11721 7=

(‘6) 721Tll

-

722712

In the lower part of the stratosphere

722 = 7i2 and (16) takes the form

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-‘)

T (K)

T (days)

20 2s 30 35

2.0e7 1.Oe8 4.0e8 8.Oe8

213 222 232 243

573 77 13 4

286

A. V. Gureuich et ul. /Physics

4. Formation

of artificial

Lettem A 207 (1995) 281-288

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 V, and horizontal turbulent diffusion with coefficient 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

= -Jo,6N,

- K,N,aN3

f K,N,aN,

+ K3N$N,

+

Q,,a( x)6(

Y),

(184

[$tY;a;-D($+$)]~N, =J,$N,-K,N$N,-K,N$N,-K,N,6N,+Qol~(x)8(y).

( ‘8b)

Here 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 possible to neglect atmospheric wind and diffusion in Eq. (18b) and obtain for 6N,,

Qo,GMY)

6N I

+

= K,N;+K4N3

Joy

Kd’,

K3N; + K,N,

of that it is

6N (19)

3’

Substituting (19) in Eq. (18a) we arrive at an equation describing perturbation,

the dynamics

of the artificially

created ozone

Here 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 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)/’

where 7Crf= 4Dr/(V2r+ 40). Solution (21) can be rewritten 6N,(x,

y) =

&I(

exp --m

s

in a more convenient

P> ev(Vx/2D)3

+ 4ii eff

foci,

(t-t,)-’

dt,,

(21)

form,

(22)

A. V. Gureuich

et al. /Physics

287

Letters A 207 Cl 995) 26’1-288

where mev[-P(

I( P> =/,

5+

5

l/t>1 d5 ,

It is easy to find that for any wind velocity

/

= aN,( x, Y) dx dy =

-co

p= (gf)“*, V the total perturbation

s=t( ,,,c;:+y2J”2. is conserved,

Qefp.

(23)

In the case when atmospheric wind exists solution (22) is asymmetric in the horizontal plane - it is stretched in x=- 1, that is for large distances from the source x2 + y2 B- 407, or the direction of the wind velocity V. For for large wind velocity V z=- 2 D/ ? x2 + y* , it is possible to obtain from (22) an approximate analytical solution

~N,(x,

Y) =

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 In this case the distribution of the x axis, L, N VT, is much larger than along the y axis, L, N &%. concentration for x > 0 takes the form

(25) Distribution (22)..,. (25) allows us to estimate small velocity V-=x J2D7, S = 41rDr,

the dimensions

of the area occupied

by the artificial

layer for a

(26)

and for a large velocity, S = 2J;;VD’/2r3/2.

(27)

It is seen from (27) that the area of the artificial ozone layer becomes larger with the growth of the diffusion coefficient D, the wind velocity V, and the ozone lifetime r. Especially the strong dependence on the ozone lifetime T and the wind velocity V should be mentioned.

5. Discussion and conclusion 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

288

A. V. Gurevich et al. /Physics

Letters A 207 I1 995) 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] [2] [3] [4] [5] [6] [7]

A.V. Gurevich, Sov. Phys. Usp. 23 (1980) 862. N.D. Borisov, A.V. Gurevich and G.M. Milikh, Artificial ionized region in the atmosphere (1986) [in Russian]. N.D. Borisov, S.I. Kozlov and N.V. Smimova, Cosmic Res. 31 (1993) 63. A. Vikharev, A. Gorbachev, 0. Ivanov, A. Kolisko and A. Litvak, J. Geophys. Res. 99 (1994) 21097. 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. G. Brasseur and S. Solomon, Aeronomy of the middle atmosphere (Reidel, Dordrecht, 1986). N. Nicolet, Aeronomic reactions of hydrogen and ozone, in: Mesospheric models and related experiments (Reidel, Dordrecht, 1971).