The theoretical results of analysis of the expected spatial distributions of density, gradients and anisotropy of cosmic rays, obtained on the basis of the numerical solution of anisotropic diffusion equation in the presence of the disturbances of shock wave type in the interplanetary space are presented. The theoretical calculations on the definition of the energy spectrum and anisotropy of galactic cosmic rays during Forbush effect are compared with the experimental data

Alania, M. V.

Bakradze, T. S.

Bochikashvili, D. P.

Borchorishvili, T.

Despotashvili, M. A.

Nachkebia, N. A.

English

NASA Technical Reports Server

THE THEORETICAL AND EXPERIMENTAL INVESTIGATION OP 
COSlVIIC RAY FORBUSH-EFFECTS 
Alania MeV., Bakradze T.S., Bochor i shv i l i  T.V. 
Bochikashvi l i  D.P,, Despotashvi l i  M.A., Nachkebia N , A ,  
The I n s t i t u t e  of Geophysics, Georgian Academs of 
Science,  Z,Rukhadze a t r ,  1, 380093, T b i l i s i  
ABSTRACT 
The t h e o r e t i c a l  r e s u l t s  of a n a l y s i s  o f  t h e  expec- 
t e d  s p a t i a l  d i s t r i b u t i o n s  o f  dens i t y ,  g r a d i e n t s  
and an i so t ropy  of cosmic r a y s ,  obta ined on t h e  
b a s i s  o f  t h e  numerical s o l u t i o n  of a n i s o t r o p i c  
d i f f u s i o n  equat ion i n  t h e  presence o f  t h e  d i s t u r -  
bances o f  shock wave type i n  t he  i n t e r p l a n e t a r y  
space a r e  presented.  The t h e o r e t i c a l  c a l c u l a t i o n s  
on t h e  d e f i n i t i o n  of t h e  energy spectrum and ani-  
aotropy of g a l a c t i c  cosmic r a y s  dur ing Porbush - 
e f f e c t  a r e  compared wi th  t h e  experimental  da ta .  
The t h e o r e t i c a l  modal. Cosmic r ay  Forbuah-effects have 
a complex s t r u c t u r e  ana n a t u r e  /1,2/. They d i f f e r  fr80m each 
o t h e r  both by power and b~  energy spectrum i n d i c e s  e t  a l b  
However, t h e r e  e x i s t  t h e  l n d i c e t i o n s  such a s  t h e  recur rence  
and s p o r a d i c i t y  of Forbuah-effect o r i g i n  t h e  c h a r a c t e r  o f  
shock wave development causing   or bush-ehects, t h e  change 
o f  energy spectrum index i n  t ime e t  a l .  by wi th  t h e  d e f i n i t e  
c l a s s i f i c ~ t i o n  of Forbush-effects  can be c a r r i e d  ou t  /3-4/, 
I n  t h i s  paper  t h e  s tudy  of cosmic r a y  Forbush-effects  
on t h e  b a s i s  of  t h e  processes  occur r ing  i n  t h e  in terpl -aneta-  
r y  space I n  t h e  presence of t h e  d i s tu rbance  passage 11 i t e d  
by t h e  he l i o long i tudes ,  but  having no boundary i n  t h e  hl 
d i r e c t i o n  is c a r r i e d  ou t  i , e ,  the  type of r ecu r r en t  Forbush- 
- e f f ec t  i s  considered,  
The a n i s o t r o p i c  d i f fu s ion  equation/5/ i s  taken  a s  mo- 
d e l i n g  of  t h e  e lect romagnet ic  condi t ions  occur r ing  i n  t h e  
i n t e r p l a n e t a r y  space under t h e  fol lowing assumptions: a )  so- 
l a r  wind v e l o s i t y  U. and t h e  d i f f u s i o n  c o e f f i c i e n t  of  
c o m i c  r a y s  i n  t h e  d i s tu rbed  reg ion  changes n e a r l y  twice i n  
comparison w i t h  t h e  environment b )  t h e  d i s tu rbed  r eg ion  i s  
g iven  i n  a  cone form f o r  which !he he l ioequa tor  is  a aymmet- 
C 
r y  plane,  i , e .  a long  t h e  t r a j e c t o r y  of t he  Eur th  t h e  he l io -  
l a t i t u d i n a l  g r ad i en t  @n/d@ =0 , c )  i t  i s  considered 
* t h a t  s i n c e  t h e  d i s tu rbed  r eg ion  ac ros s  t h e  h e l i o l a t i t u d e  i s  
l i m i t e d  i n  t h e  range of  s eve ra l  e.u. and i n  t h e  r a d i a l  d i -  
r e c t i o n  t h e  p rocess  is  S ta t i ona ry ,  t h e  s t a t i o n a r y  approxima- 
E *' t i o n  is q u i t e  t r u e ,  i.e.;ab/at=0 . X-Ience, t h e  a n i s o t r o p i c  d i f f u s i o n  equa t ion  has t h e  fol lowing form: 
F .a (R3n). vi ui '0 vi (2eiKl&n) -T'i (n- Mi)+ ,,, ,, ( 1  
where wand 
-the dens i t y  and t h e  r i g i d i t y ' o f  oosmio r a y  
p a r t i c l e s ,  and U ;  t h e  s o l a r  wind ve loc i ty .  Taking i n t o  
https://ntrs.nasa.gov/search.jsp?R=19850026759 2020-03-20T16:51:33+00:00Z
account the above assumptions f o r  s o l a r  wind ve loc i ty  U 
and the  d i f fus ion  coe f f i c i en t  % u=uo(!+~, ,T)  (see Big .  
l a )  and ~=%(!-deP) (see ~ i g . i b ) ,  where = 3,4 ; 
4~~ 4175 and T = ~ c & ~ ~ ( ~ - ~ o ) ) - I w ~ : ~ ( ( Q - ? o ) ' ~ ) / ? ) J ~  
The equation (1) i s  solved by ne t  method under the  
following boundary conditions:  , 
. 
during Forbush-ebfect f o r  two r i g i d i t i e s  R =  20 GV end 
)2s 20 hl' i s  presented i n  Fig, 2, It i s  seen , t h a t  the  
change of s o l a r  wind ve loc i ty  LC and the d i f fus ion  coef- 
f i c i e n t  % (see ~ i g , l a , b )  induce a  gradual decrease end 
r e s t o r a t i o n  of c o m i c  ray i n t e n s i t y  t h a t  i s  c h a r a c t e r i s t i c  
o f  the  recurrent  Forbush-effeota, 
For the  case when t h e  approximation i s  given by 9 ( R ) -  ra , bhe energy spectrum index of Porbush-ef- 
f e e t  i s  equal f. 1,06 . 
The expec ed change of socmic ray  anisotropy before,  
during and a f t e r  the  cosmic r a y  Forbush-effect durat ion f o r  
the  r i g i d i t y  )?zIOC;L/ i s  presented i n  Fig, 3, It is seen 
t h a t  a f t e r  s t rong disturbances of anisotropy vec tors  near 
the  minimumof Forbush-effect the  monotone rea to ra t ion  t o  
the  i n i t i a l  pos i t ion  i s  observed, 
The change of i n t e n s i t y  of cos- 
covponeQ3 a t  a  l e v e l  0 and 
s t a t i o n  f o r  t h e  period 
i n  Fig,%, The change of 
the  energy spectrum of this Forbush-effect i n  time has been 
s tydied  by two independent methods. The first one i s  a well- 
known spectrographic method /5/ and the  second one - t he  
method of t h e  cou l i n g  c o e f f i c i e n t s  preaented by the  Ja- 
panese authors /6/fl The ens lya i s  by the  spectrographic me- 
thod has been c a r r i e d  out by the  i n t e n s i t y  of cosmic ray  
neutron and hard Jf -meson components a t  T b i l i s i  s t a t i o n  
and by method of the  coupling coe f f i c i en t s  - by the  data 
of T b i l i s i  s t a t i o n  and the  world network, The changes of t h e  
energy spectrum index , obtained by the spectrographic I 
method ( the dashed curve) and by the  coupling c o e f f i c i e n t s  ( the  s o l i d  curve) a r e  presented i n  Fig, 4b, It is seen t h a t  
the r e s u l t s  obtained by both methods ahow t he  same temporal I; 
changes however, the  values of the energy spectrum index 
obtained by the  spectrographic method a re  systematical ly  r( higher than the  values obtained by the  method of the  coup - 
l i n g  c o e f f i c i e n t s ,  In  the  P i g . 4 ~  t h e  changes of DSt varia- *. 
t i o n  of  the Earth 's  magnetic f i e l d  (dashed) and ' the  cutof f  ,8 
r i g i d i t y  threshold A Rc ( s o l i d )  a r e  presented, c 
Discusaidn and Conol$aion. The obtained r e s u l t  i s  ex- 
plaineci easily, Tne r a c t  i s  that  the  change of the  cutoff  
r i g i d i t y  threshold b R  i a  not taken i n t o  account i n  the  
process of ca lcu la t ing  the  energy spectrum index by the  me- 
287
Pig, 2 , Pig. 4
-0.2
Fig. 3
288
SH 5.1-20
thod of the coupling coefficients /6/, and is taken into
account in the spectrographic method.
Por the period considered the change of _ is oh -
served, in particular, its decrease and therefore the ampli-
tude absolute value of cosmic ray intensity decrease is
diminished, i.e. the energy spectrum calculated by the coup-
ling coefficients method will be more rigid, that is really
observed.
The rigid energy spectrum before reaching the minimum
of Forbush-effect must be connected with the predominant
cerring out of cosmic ray particles of re&mtively low ener-
ies with the high-velocity flux of the chromospheric flare
8/. In addition, the energy spectrum of magnetic inhomoge-
neity power of the medium frequencies which can induce cos-
mic ray particle modulation predominantly of relatively low
energies can be increased in front of the magnetic cushion
of the shock wave and in the cushion itself. Apparently,the
geometric factor, the size of the compressed cavity in the
front part of the shock wave plays an important role.
REFERNCES
I. Dorman L.I. "¥ariatsee Cosmicheskikh Luchei I Issledova-
nie Cosmosa". A_T SSSR, M.1963.
2. Krimski G.P. "Modulatsia Cosmlcheski_h Luchei V MeJplanet-
nom Prostranstve". "Nauka". M.I_69. '
3o Shah G.N. et el., Proc. 18th ICRC, Kyoto, Japan 8, 423,
I_9.
4. _lania _.V,, Bochikashvili D.P. 18th ICRC, Bangalore,
India, L;p, Vol.10, 168, 1988.
5. Dorman L.I. "AstroflzicheSkie Aspecti Cosmicheski_ Lu-
chei". "Nauka". _.6, I975.
6. Yasue S. et el., Coupling Coefficients of Cosmic Ray Dai-
ly Variations for Neutron _lonitor Stations. Nagoya, Ja-
pan, 1982.
7. Solar-Geophysical Data. _eb_. 1978. numb. 505, part I.
8. Alania M.V. Autoreferat of Doct. Dissertation, Kiev,
1981.
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The theoretical and experimental investigation of cosmic ray Forbush-effects

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