Results of the numerical solution of the anistoropic diffusion equation are presented. The modulation depth of galactic cosmic rays is defined by the degree of curvature of the neutral current sheet in the heliosphere. The effect of the regular interplanetary magnetic field (IMF) on cosmic ray anisotropy in the period of solar activity minimum (in 1976) is analyzed by the data of the neutron super-monitors of the world network, and the heliolatitudinal gradient and cosmic ray diffusion coefficient are defined

Alania, M. V.

Aslamazashvili, R. G.

Bochorishvili, T.

Djapiashvili, T. V.

Tkemaladze, V. S.

English

NASA Technical Reports Server

477
SH 4.2-18
THE EPFECT OF THE NEUTRAL SHEET STRUCTURE 0F THE
INTERPLANETARY mAGNETIC FIELD ON COSMIC RAY
DISTRIBUTION IN SPACE
Alania M.¥., Aslsmazashvili R.G.. Bochorishvili T.B.
Djapiashvili T.¥., Tkemala_ze V.S.
The Institute of Geophysics, Georgian Academy of
Science, Z.Rukhsdze str.1, 380093, Tbilisi
ABSTRACT
I.The results of the numerical solution of the
anisotropic diffusion equation are presented
in the paper. It is shown that the modulation
depth of galmctlc cosmic rays is defined by
degree of curvature of the neutral current
sheet in Heliosphere. 2.The effect of the re-
gular interplanetary magnetic f_eld (I_) on
cosmic ray anisotropy in the epoch of solar
activity minimum (in 1976) is analysed by the
data of the neutron super-monitors of the
world network and the heliolatitudinal gradient
and cosmic ray diffusion coefficient are defined.
The theoretical model. The recent investlgations/1,2/
show _ha_ t_e neutral current sheet changes its range sig-
nificantly for ll-year period of the Sun's cycle and can be
one of the reasons of cosmic ray modulation. Really, the
curvatures of the interplanetary magnetic field lines of
forces(I¾F) correspond to the waved structure of the neut-
ral sheet that is identical with the appearance of high-va-
lue zenithal component of I_F, Hz. The experimental obser-
vations in space show that Hz component of I¾_ is, in the
mean t a high value _ _0-_ _T /8/ and therefore, its ac-
count in solution of comic ray anisotropic diffuslon equa-
tion is of necessity.
The snisotropic diffusion equation /4/ for the statio-
nary case is used:
0
where _ -the tensor coefficients of diffusion, _ amd
-the density and the rigidity of the partlcle,an_ _-so-
lar wind velocity. It is suggested in equation solution
(1) t_st the radius of the modulation volume is 50 a.u.,
_-4.10_m/s, the diffusion coefficient along the magne-
tic field has the form
where _o =I022cm21se I. _I =0,05G¥, _,=3GV, _(0_ _ rchamged in the range I 5 from the helioequator to he a -
polar region, and _(_)= I+4 (_/To) , where _ =0,1, _o
-modulation region radius.
7 
 . - 8 
E F  F E E TRAL  RE O   
I ETARY MAGNETIC I   S I   
I I TI  I   
lania .V., sla azashvili R. . l ochorishvili T. ., japiashvili .V., Tke alattze .S. 
The I stit te of eophysics, eorgian cade y of 
cience, . ukhadze tr.l, 380093, bilisi 
S T 
I. e sults f t  umerical l ti  f t  
a is tr pic iff si  e uati n are resented 
i  t  aper. t i  s  t t t  odulation 
depth of alactic cos ic rays is defined by 
e ree f c r at re f t e eutral c rrent 
eet i  eli sphere. .  t f t  -
lar i t r l etary agnetic fi l  (IMF) on 
cos ic ray anisotropy i  the epoch f s lar 
ti it  i i  (i  I ) i  l   t  
t  f t  utr n er~ rs f t  
orl  t ork  t  li l ti inal r i nt 
a  c s ic r  iff i  effi i nt r  fi . 
e t retical odel. e r t i estigations/l,2/ 
 t t th  eutral rr t et es   -
ifi ntly f r II- r ri  f t  n's l     
one of the reasons of cos ic ray odulation. eally, the 
curvatures f the i ter la etary agnetic fiel  lines of 
forces(IMF) correspond to the aved structure of the neut-
l et t t  i ti al it  t  ear ce f i - a-
l  it l c ponent f IM , z. e eri ental ser-
vations i  space sho  that z co ponent of IMF is, i  the 
mean a high value rv Q 10-9 n r /3/ and therefore, its aC-
c nt i  s l ti  f co ic ra  is tr ic iff si  e a-
ti  i  f cessity. 
he a is tr ic iff si  e ati  / / f r the st ti -
nary case is used: 
VL(3eil<.Vt<.n)-Vi (n Ul}+ 3~~ ~(R3Y1)V; Ui =  (1) 
here Gei/( -the tensor coefficients of diffusion Yl and R 
-t  sit  and t e ri i it  f the rti le,anA Ui-SO-
lar ind velocity. It is suggested in equation solution 
(1) that the radius of the modulation volume is 50 a.u., 
, U =4.IObm/s, the diffusion coefficient along the magne-
ti  i l   t  f r  
ge /I = aeo EX P (Y< 4/ R ). (R 'l. + r< ) ~ <P (e)- cP ( rt ) (2) 
where CJeo _I022cm2/sec Ri :::0, 05GV, ~'l..c3GV, epee} is 
c aDged in the range 1-5 fro  the helioequator to the nea -
polar region, and <'P('t)=1+~(t"(/1.o) f where q=O,I,l(o 
~odul  re i  r i s. 
https://ntrs.nasa.gov/search.jsp?R=19850026542 2020-03-20T17:00:11+00:00Z
478
SH 4.2-18
The range of the waved structure of the neutral current
sheet is given in the form
(3)
and _ are chosen so that _he neural current sheet on
the Earth's orbit (_=1,5"I01_cm) i_ at the heliolatitude
IO° . In this case _ =5 and _ =lO_.
The equation (1) is solved by the net method for the two
dimensional case ( _, _ ) _=_ = 0 and the re-
sults are presented in Fig. la,b. The curve(a)shows the
change of the relative density of IO Gev energy cosmic rays,
when the curvature (8) is defined by the parameter _EO,5,
i.e. the maximum removal 6f the neutral sheet from the equa-
tor of the Sun on the Earth's orbit is _=2,5 "I0_ cm.The
curve(b) shows the case, when _=0 and L=0 . It is
seen that, really, with the increas_ of neutral current
sheet range, the significant cosmic ray modulation is expec-
ted, which by its value is compared with the amplitude of
ll-year variation in the energy region 10-20Gev.
The experimental data on cosmic ray anisotropy.
I_ _as been s_own in our previous paper /b/ _het the
particle drift effect at the expense of the gradient and the
curvature of the interplanetary magnetic field (IMP) is re-
vealed slnglevaluedly, especially in the epoch of solar ac-
tivity minimum. It is known that the particle drift effect
in distribution of cosmic ray density and anlsotropy can be
calculated with the antisymmetric part of the anisotropic
diffusion tensor /6/. but , in our opinion, this problem is
not always clear, and therefore, sometimes the incorrect
interpretation is made. _.g. as it has been done in the re-
port 77/ while reviewing paper /5/, where the epoch of solar
activity minimum I_65- has been considered.
Four neutron super-monitor stations: Kiel,Norikura.
Lomnitsky Stif and Khafelakar have been chosen for revealing
the effect of the particle drift in cosmic ray anisotropy
(I976). The data of these stations were free from the
trends with the periods more than 24 _urs and the harmonic
coefficients _ and _ for every day were defined.Then
they were averaged depending on the Earth's location in
"+" and "-" sectors of IMP.("+" corresponds to the direction
of the magnetic lines of forces from the Sun, and "-" to-
ward the Sun). Then, the values _ and _ have been de-
fined in cosmic space taking into account the drift into
the Earth's magnetic field and the coupling coefficients /8/
and the means by all four stations were found. The results
are presented in Fig._, where the solid vectors correspond
to the theoretical results, dud the dashed ones- the experi-
mental data of observation.
It can be seen that_ good accord is existed there.
Having the values _ and _ for "+" and "-"
sectors of IMP the algebraic equations have been constituted
of the form:
78 
  
  f  a e  t r   t  eutral r t 
s et i  i  i  t  f r  
'6 = II- Do (rt/rro) GO~ (16 fTrt/rtc) (3) 
Ir and 00 are chosen so t at the eutal current sheet on 
t e arth's r it ~ I,5·I013cm) iB t t e eli l tit e 
100 • I  t is Case A  5 and "0 =10 • 
The equation (1) is solved by tie net method for the two 
dimensional case ( 1(, e) ~,:. ~(f't :. 0 and the re-
sults are presented in Fig. la,b. The curve{a)sho s the 
change of the relati e density of 10 ev energy cos ic rays, 
hen the curvature (3) is defined by the para eter ~ =0,5, 
i. . the axi u  re oval of the neutral sheet fro  the equa-
tor of the Sun on the arth's orbit is ~ ::2,5 • 10~2. c . The 
r e( ) s s t  s , he  .JI= 0 a  ),,::.0 • It i  
seen that, really, ith the increase of neutral current 
s eet ra e, t e si ifi nt cos ic ra  odulation i  e ec-
ted, hich by its value is co pared ith the a plitude of 
- r Variati n    i  D-ZOGev. 
he ex eri ental data on cos ic ray a is tr  • 
s ee  s   r r  s er at t  
arti l  ri t t  t  s   t  r i nt  t  
curvature of the interplanetary agnetic field (IMF) is re-
vealed s~glevsluedly, especially i  the epoch of s lar ac-
ti it  ini u . It is kno n t at t e arti l  rift effect 
i  i t i ti   i   sit   $ i t y   
l l t  it  t  a tis metric art f t  is tr ic 
diffusion tensor /6/ t but, in our opinion, this problem is 
not always clear, ana therefore so eti es the incorrect 
i t retati n i  ade. B. .      i  t  
port 17/ hile revie ing paper /5/, where the epoch of solar 
ti it  i i  19 5- s  si ered. 
Four neutron super- onitor stations: iel, orikura 
omnitsky stif and hafelakar have been chosen f r re eali  
the effect of the particle drift in cos ic ray anisotropy 
(1 6). e t  f t s  st ti s ere fr  fro  t  
tr s it  t  ri s ore t   hours a  t  ar onic 
c efficients Ai and 8. f r every day ere defined. hen 
t  ere r d n~  t  arth's ~on i  
tt+,. and t1_,. sectors of I F.\"+" corresponds to the direction 
of the agnetic lines of forces fro  the Sun, and "_It to-
ward the Sun). Then, the values 11'( and A", have been de-
fi  i  s ic s  t i  i t  nt t  rift i t  
the arth's agnetic fiel  and t e coupling c efficients / / 
a  t  eans  ll f r st ti s ere f . e r s lts 
are presented i  ig.2, here the s li  vectors correspond 
to the theoretical results, and the dashed ones- the experi-
ental t  f servati n. 
It can be seen that p good accord is existed there. 
aving the values If~ and Jl tt for "+ II and It_" 
s t rs f I F t e al e raic e uati ns have ee  nstit t d 
f  : 
479
SH 4.2-18
-
Solving the system-of equations (4) the mean solar
wind velocity is found, and the retieus _=_Z/_ll and
_=3_,/_, lare estimated. ( _Lz , _ and 96,1 -the
transversal! Hall and parallel diffusion coefficients)
and the hellolatitudinal gradient and the diffusion coeffi-
cient are estimated.
Discussion and conclusion
I. T_e degree oi curva_u#e of the IMF neutral layer in-
fluences appreciably cosmic ray modulation. The modulation
depth is large during the extend of the waved neutron lay-
er and can be compared with the amplitude of ll-year varia-
tion in the energy region 10-20 Gev.
2.The particle drift effect st the expense of the gra-
dient and the curvature of IMF is revealed singlevaluedly
in Cosmic ray enisotropy in the epoch of solar activity mi-
nimum in 1976.
3. The inverse problem is solved by the equation (4).
The solar wind velocity . _=455km/s ( the direct observa-
tions by /9/ give _ =450) and ratio _ of the trans-
verse diffusion coefficient _ to the parallel one _Lu
( _ =0,3) are defined.
It is of interest to note that the same value has been
obtained for 1965 too.
4. The heliolatitudlnel gradient end the diffusion coe-
fficient have been estimated from (4) with the given
radial gradient of cosmic rays
constituting
respectively.
_EFRRENCES
I. Hoekseme _.T., Wilcox S.M. and Scherrer P,H., SUIPR,
Report _924, Stanford. California, 1982.
2. Thomas B.T. end Goldsteln B.E., Solar Wind Fi_e, NASA,
p.44.1982.
3, Slavin _oA. and Smith E,L., Solar Wind Five, NASA, p.3_,I982.
4. Rormen L.T. "AstrophlziCheskie aspekti cosmicheskikh
T,uchei". "Nauka ", M.I975.
5. Alania _.V. et el.. 18th IGRC, Bangalore, Indie,L.P.,
o I0 P 91, 36. _o_ipli _.E. L_$_ E.H. and Hubbard W.B., Astr.J. 213
864-868,1977'. ' '
7, Jones F.G., 18th IC_C. Bangalore, India.lnvited and Rap-
porteur P@e=s. Vol.12., p.379, 1988.
8. Nageshlma K. et al., Coup.Coef. of Oosmic Rays,Nagoya,
Japan,1982.
479 
SH 4.2-18 
Jl 1: ~ f)f) () n + ~ 
Jr If - (]{Cf'C fJ't - ae<f~ e;fJ 
(4) 
Solving the system-of equations ( ) the ean solar 
ind elocity is found, and the ::'eti0us c{ = de;./ dell and 
q1=O€u/d€" are esti ated. , 9t.l. , ~,,.,  'de-II -  
t sversal! a l s d para lel iff si n oe ficients) 
and the hel~olatitudinal gradient and the diffusion coeffi-
cient are esti ated. 
Discussion and conclusion 
t. Tfie degree of curvature of the I F neutral layer in-
fluences appreciably cos ic ray odulation. he odulation 
depth is large during the extend of the aved neutron lay-
er and Can be co pared ith the a plitude f II- ear varia-
tion in the energy region 10-20 Gev. 
2. he article rift ef-fect at the expense of the ra-
dient and the curvature of I F is revealed singlevaluedly 
i  os ic ray anisotropy i  the epoch of solar act-ivity i-
nimum in 1976. 
30 he inverse proble  is solved by the equation (4). 
he solar wind velocity U=4 5lon/s ( t e irect bserva-
tions by / / give U =450) and ratio c{ of the trans-
erse iff si n oefficient Gel t  t  arallel e '£/1 
( 0(  0 3) ar  efi ed. 
, It Is of interest to note that the same value has been 
obtained for 1965 too. 
4. he eliolatit dinal gradient and the diffusion coe-
ffi i t ave been esti ated fr  ( ) ith t  i en 
radial gradient of cos ic rays ~n=( 1-2) % / a.u. 
constituti g ~ . 
r spectively. 
~n==-(o,Q-O,4)%/C(U ) ge,,::;.(O,6-1,3) 1023 cm1./s 
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5 to 15 20 25 30 35' 'to lt5 50 I'(.. 
p 
O.j % 20 
t----t Oh l6 
~2 , 
6h 
"-
8 ~2h 
4 
27 9 6 
!i,!.2. 1"3' 3. 
d«f-> 


The effect of the neutral sheet structure of the interplanetary magnetic field on cosmic ray distribution in space

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