LETTERE AL NUOVO CIMENTO VOL. 10, N. 17 24 Agosto 1974

Local Changes of the Atmospheric Electric Field by EAS Ionization.

G. BONINO and M. DARDO

Laboratorio di Cosmo-geo/isica del C N R - Tor ino

Is t i tu to di F i s i ca Generale dell' Univers i t~ - Tor ino

P. PAVESE and A. PIANO

Laboratorio di Cosmo-geo/isica del C N R - Tor ino

(ricevuto il 5 Giugno 1974)

I t has been suggested by WILSON (1) that local changes in the atmospheric electric field may be induced by the passage of an extensive air shower (EAS) in the atmosphere.

Possibilities of radio emission caused by the interaction of the electric field with the EAS have also been examined (2) in relation to charge separation caused by the field on the relativistic particles of the shower or considering the acceleration phase of the slow electrons (8) produced by the ionization process. These mechanisms refer to the fast component of the signal.

Recent experimental investigations performed by CUR~Y et al. (4) seem to indicate that the slow component, due to the motion of the molecular ions produced by EAS, may be detected. This fact revives the interest on this subject because of the possi- bil i ty of having new means of detecting large EAS.

We shall investigate in this paper the changes in the atmospheric electric field caused by the motion of the electrons and the molecular ions produced by EAS of different primary energies, paying at tent ion in particular to the radial dependence of pulse ampli- tude and temporal variations.

Our calculations are focused primarily on the electron component of the EAS since it gives the maximum contribution to the phenomenon.

During its development through the atmosphere the ultra-relativistic particles of the EAS collide with the air molecules producing pairs of slow electrons and positive molecular ions. The ionization electrons, detached from the molecular bonds, attach themselves principally to neutral molecules of oxygen with the formation of negative ions, and the duration of this a t tachment process is determined by the mean distance

(*) R. R. WILSON: Phys. Rev., 108, 155 (1957). (*) W.N. C~AR~.t~: Nature, 215, 497 (1967); ~VV. N. CHARMA~ and J. V..]-ELLEY: Can. Journ. Phys., 46, $216 (1968). (*) W. N. C]tARMAN: Journ. Arm. Terr. Phys., 30, 195 (1967). (*) A. CURRY, M. L. T. Kk~r~ANO~Rk and K. ]~. TURVER: Journ..Arm. Terr. Phys., 36, 215 (1974).

757

7 ~ O. BONINO, M. DARDO, P. PAVESE a n d A. P IANO

travelled by the electrons and their drift velocity. The molecular ions surround them- selves with a number of neutral molecules to form ~ small ions ,~. Successive recombina- tion of small ions of different signs or a t tachment of the same ions to suspended par- ticles with formation of (( large ions )~ may occur, terminating the chain of processes suffered by the products of the ionization.

The density of electrons and small ions created in the atmosphere by the EAS are determined by the longitudinal development of the electron component and by the lateral distribution of the particles with respect to the axis of the shower.

We consider showers init iated by protons of various energies in the range (10~+10 ~s) eV using data on the longitudinal development of the electron component calculated by simulation of EAS by the Monte Ca, rlo procedure by TUI~VER et al. (5).

The radial distribution of the shower particles from the axis follows the Nishimura- Kamata approximation (6) for the age parameter s:

(1) F(r) = C(N~(Ep, h)/R~)r~-~(1 -~ r) ~-4"5 ,

where r = B/R o is the distance from the axis of the shower in Moli~re units varying exponentially with the altitude, and N~(E~, h) is the total electron number at the height h in a shower generated by a proton of pr imary energy Ep. To produce an ion pair by a particle of the shower Vo ~ 30 eV are necessary; thus, the number of mo- lecular ions (electrons, small ions) generated in the interval h, h + dh by a shower electron is

(2) d N , = (e/Vo) ~o exp [-- h/ho] d h ,

where e ~ 2 MeV g-X cn1-2 is the total energy lost by the shower electron for collisions with the air molecules; ~ and ~o are the atmospheric densities at height h and at sea level respectively, and h o is the scale height of the atmosphere, varying with h (h o = 7.1 kin at sea level).

Introducing the lateral distribution (I) of EAS electrons we obtain the ion density

(3) qi(E~, h, r) = ( d N i / d h ) F ( r ) ( c m 3) .

Fig. 1 gives the variat ion of Oi wi th /~ for different Ep. For comparison we include also the mean concentration of the small ions in steady-state conditions (7).

Elec t r ica l s igna l s by the i o n i z a t i o n electrons. At the surface of the Earth, in normal fine weather conditions, a vertical electric field exists, with a sign which corresponds to a negative charge on the Ear th ' s surface. The values of this field range from --~ 10 Vm -1 at sea level, up to ~ 10 Vm -1 at ~-, 10 km altitude.

We use for the average field strength variation with height the empirical expres- 3

sion given by ISRAEL (8) Ea(h) = ~ A i exp [--Bib] (Vm-1), where the parameters have

the following values: A I = 81.8, A2= 38.6, A a = 10.27 (Vm-1), and B~= 4.52, B2= 0.375, B a ~ 0.121 (kin-l).

(') H.E. Dlxo~r, J. C. EAI~NSHAW, J. R. HOOK, G. J. SMIT~ and K. E. TIIRVER: Proceedings o] the X I I I International Cosmic Ray Con]erenee, Vol. 4, (1973), p. 2473. (6) K. GREISEBr: Progress o! Cosmic Ray Physics, edited by J. G. WlLSO~V, Vol. 3 (Amsterdam, 1956). (7) C.W. /kLLE~I: Astrophysical Quantities, II Edition (London, 1964), p. 128. (*) H. ISl~A~L: Atmospheric Electricity (Israel Program for Scientific Translations), Vol. 1 (1971), p. 75.

LECAL CHANGES OF THE ATMOSPHERIC ELECTRIC FIELD BY E A S IONIZATION 7 5 9

10

10

~E u

v

10'

tu "~

10 (

10-

. ~_ . . . . . __~:.+~y ~t.__t~ con,~it+on,

\ \

\

lo -Z l , , 0 20

\

\ ' \ -

\ -.

\

\ Ep=1016 eV "~

40 60 80 100 120 140 R(m)

Fig. 1. - Variation of the ion density ~ and of the atmospheric electric field AE a due to the ionization electrons attachment as a function of the distance R from the EAS core for different values of the primary eRergy Ep: ~ : . . . . . sea level; ~ E A : - - sea level, -- - -- 3000 m above sea level.

T h e s low i o n i z a t i o n e l e c t r o n s p r o d u c e d b y t h e E A S wil l e x p e r i e n c e an u p w a r d s

d r i f t m o t i o n a l o n g t h e a t m o s p h e r i c field l ines b e f o r e t h c i r a t t a c h m e n t t o t h e o x y g e n

molecu le s .

T h e w o r k done b y t h e e lec t r ic field d u r i n g t h e d r i f t d i s p l a c e m e n t dh on t h e ioniz-

a t i o n e l ec t rons c o n t a i n e d in t h e v o l u m e d V = 2zrdrdh a t a h e i g h t h a b o v e sea level

a n d a d i s t a n c e r f r o m t h e E A S ax i s is

(4) d W ( E p , h, r) = eEa(h)~dEp, h, r ) d h d V ,

w h e r e e is t h e e l e m e n t a r y cha rge .

7 ~ 0 G. BONINO, M. DARDO, P. PAVESE a n d A. P IANO

T h e e l ec t ro s t a t i c ene rgy dens i t y s to red in t h e a t m o s p h e r i c field will v a r y b y t h e a m o u n t

(5) du = eoE ~dE ~ ,

where e 0 is t h e d ie lec t r ic c o n s t a n t . The c h a n g e of t h e e lec t r ic field due to t h e i o n i z a t i o n e lec t rons a t t a c h m e n t so

o b t a i n e d is

(6) AE~(Ep, h, r) ~ (e/~o)e,(E ~, h, r ) ~ .

Here 2~ is t h e m e a n d i s t ance of t r a v e l of t h e slow e lec t rons before t h e a t t a c h m e n t ; we a s s u m e (1) ~r = 2 -10 - "E~ (era).

F i g u r e 1 shows t h e v a r i a t i o n of A E A as a f u n c t i o n of t h e d i s t ance f r o m t h e E A S axis for d i f fe ren t p r i m a r y energies.

I f we assume a d r i f t ve loc i t y % ~ 10~E~ (cm s -1) we m a y e s t i m a t e a d u r a t i o n of t h e e lec t r i ca l s igna l of t h e o rde r of some f r a c t i o n of ~s. T h e m a g n i t u d e a n d t h e d u r a t i o n of t h i s f a s t c o m p o n e n t seem to sugges t t h a t these s ignals cou ld be d e t e c t e d b y rad io t e c h n i q u e s in t h e l ow- f r equency range . R e c e n t m e a s u r e m e n t s of r ad io pulses a t 100 k H z f rom e x t e n s i v e a i r showers (8) a p p e a r to s u p p o r t t h i s suggest ion.

Slow signals by molecular ions. T h e r e c o m b i n a t i o n of t h e smal l ions g e n e r a t e d b y EAS a n d t h e s e t t l i ng of these on la rge cha r ged or n e u t r a l pa r t i c l e s are t h e m a i n pro- cesses to cons ider for t h e successive t e m p o r a l e v o l u t i o n of t h e i on i za t i on p roduc t s .

The d i f f e ren t i a l e q u a t i o n g o v e r n i n g t h e whole p rocess is of t h e f o r m

dn~ (7) d~- = q - - a ( n ~- ni) 2 - ~(n ~- n~)(N-~ No) ,

where n~ = n~+ = n~_ is t h e n u m b e r p e r em 3 a t t h e i n s t a n t t of pos i t i ve a n d n e g a t i v e smal l ions r e s u l t i n g b y t h e EAS i o n i z a t i o n o c c u r r e d a t t = 0; n = n+ = n_ (small ions), N = N + = N _ (large c h a r g e d ions) a n d N o ( large n e u t r a l ions) are t h e ion c o n c e n t r a t i o n s p r e s e n t in t h e a t m o s p h e r e in s t e a d y - s t a t e cond i t ions . T h e first t e r m q r e p r e s e n t s t h e c o n t i n u o u s source of new ion pa i r s p e r cm 3 a c t i v e in t h e a t m o s p h e r e . The r e c o m b i n a t i o n coefficient :r re fers to t h e process (n, n) a n d t h e c o r r e s p o n d i n g ~ to t h e processes (n, N) and (n, No). I n t h e e q u i l i b r i u m s t a t e (t < 0) we h a v e q = 2~r 2 + ~n (N § No) and , i f we p u t n i ( O ) = q~(E r, h, r) , t h e so lu t i on of (7) is

(8) n~(Ep, h, r, t) = Q~k exp [ - - k t ] ( ~ e ~ ( 1 - - e x p [ - - kt]) + k ) ,

w h e r e k = 2an ~- ~(N ~ No). A t sea leve l a n d a t ST P cond i t ions , a s s u m i n g n ~ 5-102 cm -3, )V ~ 2n, ~V o ~ 10n,

:r ~ 1 .6 .10 -6 cm 3 s -1 a n d ~ ~ 2a, we h a v e k ~ 2 .10 -2 s -1. E v a l u a t i n g t h e v a r i a t i o n AE~ caused b y t h e d r i f t m o t i o n of smal l ions in t h e same

w a y as for t h e e l ec t ron a t t a c h m e n t process , one o b t a i n s

e v i ~ e v i " i (9) AE~(Ep, h , r , t ) = - - | n ~ ( E p , h , r , t ' ) d t ' = - - l n ( c r e , ( 1 - - e x p [ - - k t ] ) + 1 ) ,

e o J 0

where v~ ~ 2 cm s -1 is t h e ion d r i f t ve loc i ty , a n d ~' = a/k ~ 8 ,10 -5 cm 3.

(') R.W. CLAY, P.C. CROUCH, A.G. GREGORY and J. R. PRESCOTt: ProccedingsoftheXIII International Cosmic Ray Conference, Vol. 4 (1973), la. 2420.

LOCAL CHANGES OF THE ATMOSPHERIC ELECTRIC FIELD BY ]~AS IONIZATION 761

The time for reaching l /m of the maximum value AEa~o is, 1/~' >>O/being in our range of values, T ~_, k - l l n ( m / ( m - 1))(s), and it is quite independent from the core distance and the primary energy. At sea level it is T(0.6 AE~= )~55 s, slowly decreasing with the altitude, because of the increased ion density in steady-state conditions.

Figure 2 illustrates the behaviour of the field variation AE~ at sea level as a function of the time for different values of R and Ep. Here it may be seen that the signals have amplitudes and slopes decreasing with the distance from the shower axis.

10 -2 -1

lO -3 / ~ R=]0m

, ! 10 . 4 !

' I ~ =100 I / / I ! I , /

10-~ -J a) I c)

T >E 10 . 6 , , L , , I ' ' ' ' '

uj~ 10 o <~ ~ R=10m R=10m

10 -1 . i _

10-3 b) 10-~

, L i ~0 -3 i ~ , i 10-40 2'0 4'0 60 0 2'0 4'0 60 t(s)

F i g . 2. - V a r i a t i o n o f t h e a t m o s p h e r i c e l e c t r i c f i e l d A E A d u e t o t h e s m a l l - i o n r e c o m b i n a t i o n as a f u n c - t i o n of the t ime for different va lues of the dis tance R f rom the EAS core. a) Ep =10 ~ cV, b) Ep =10 IT cV, c) E ~ = 1 0 ~ e V , d) E p = l O t S c V .

In conclusion, these quanti tat ive estimates indicate tha t this technique could offer useful possibilities in air shower research. We have in progress an experiment for studying this effect, with a system of antennas placed at some meters above ground level and their potential sensed by fast electrometric equipments.