Aspects of the problem of galactic cosmic ray propagation, including inversion of the solar total magnetic field and an analysis of data related to the heliomagnetic cycle are discussed. It is noted that the global structure of the solar magnetic field results in an additional flux of galactic cosmic rays generated by curvature and gradient drifts. An analysis of heliomagnetic cycle data shows that the latitudinal gradient results in a N-S  asymmetry, with the amplitude of the effect growing with depth in the atmosphere. The inversion of the solar total magnetic field, drift effects, and other space distributions are found to contribute to a 22-year cycle of solar activity

Goncher, G. A.

Kolomeets, E. V.

Lyakhova, A. K.

Slyunyaeva, N. V.

Stekolnikov, N. V.

English

NASA Technical Reports Server

457 SH4.2-12
EFFECTSOF SOLARMAGNETICF£ELDON COSMIC RAYS
Gon_herG.A., KoqemeetsE.V.,
Lyskhova A.Kh.p Slyunyaeva N.V., Stekol'nlkov H.V.
Kazakh State Unlverslty, Tlmlryazeva St. 46,
Alme-Ata 480121,0SSR
The paper is devoted to sere @_pects of problem of
galactic ce_tic ray (gcr) propagation including inversion
of solar total m&ene_ic field (stmf,) and to analysis of
experlmental f_ct_ r_lated te hellomsgRetic cycle.
It is ksown't (Jokipii l.R.,et ai,,1977, Krainev
M.V.,1979,Erkhov V.I.,et ai..1983) that the global strecture
ef solar tot_l m_gne.ttc field ( Parker's field) results in
additional flux of gcr generated by curvature and gradient
drifts. Velocity of charged particles drift is
d
vhere_i_ _- antlsymmetric part of diffusion tensor. It can bewritten for atmf in the f_rm
where _'_'£ is reg,ular part and _a- s&nBular part Of velocity,
Delta function is cennected with the fact of existence of
boudary between inward and outward lines of force of magnetic
field of the S_n that is neut,ral cur_rent sheet.
The main equation including diffusion, convection,
energy changes end drifts in helioce_tric system of
coerdiaste is of the form: (_)
ehere_:_ _ Is density of galactic cosmic rays, _ -
kinetic eaergy -- Te analyse effects related to
redistribution of &alactic cosmic r_ys due to drift motion
let's consider the equation including only convection.
diffusion along lines of force of magnetic field and drift.
We obtain
Int_r_tion of equation (4) over _ within the limits
of _/R-_ and _/2._ and approaching _ to zero gives foll_wing
condition_
_herofl_(_)-density of 8_lactic cosmic _ays out of modulation
r$_ion t,hatia fo_ r_r o •
It sho_d be noted that on the basis of general
457 
EFFECTS OF SOLAR MAGNETIC FIELD O~ COSMIC RAYS 
Gon<Cftsr G.A.. KOllo.eets ·E. V •• 
Lyakhova A.Kh., Slyuoyeeva ~.V •• Stekoltnikov 
Kazakh State University, Ti'Jliryazeva St. 46, 
Alaa-Ata 480121,USSR 
SH 4.2-12 
N.V. 
The paper is devoted to some .&pects of problem of 
galactic cosaic ray (~cr) propegation including inversion 
of soler total .&gnet>ic field (ataf,) and to analysis of 
experillle·n·t-al f..-ct-e r.e-Iat.e4 to kelio_8gBetic cycle. 
It ia kaown'.. (Jokif)U I.R. ,e-t al., 1977. Krainev 
H.V.,1979,Erkhov V,I.,et 81.,1983) that tbe global struct~re 
of aolar tot-e-l lIlagnetic fie-Id ( Parker' s field) results in 
additional flux of gcr generated by curvature and gradient 
drifts. Velocity of charged particles drift ia 
~L= o~LiA) (1) 
(A) a)(J 
wh re ~li. - anti8y •• etric part of diffusion tensor. It can be 
wri tten for ittllf in the for. 
--... r --?;)=:l)J.. +o(9-!li/2)~2 (2) 
.here ~.L is re-i·ular part and ~z. - s.ingular part of velocity. 
Delta fUAction is cooRected with the f·act of existence of 
boudar, between inward and outward lines of force of magnetic 
field of tbe Su.n that is neut·ral cur·rent she-et. 
The lIlain &quatioB iBCludiR~ diffusion. cORvection, 
energy changes and drifts in heliocentric system of 
coordinate is of the for.: 
iI-M 'l'(~R-f1.JJ -~"hi"8le[si"9(ifto8e- -n9J.)]+ j~le(,W~) }! 
.here oL: rZ~~fI , n. is density of galactic 
kinetic energy. T0 analyse effects 
redistr1btlti.01l of g.alactic c0slltic rays due 
let's cGne14.r the equation including 
diffusion along lin~s of force of sagnetic 
We ebtain 
cos_ic rays, £ -
related to 
to drift .otion 
only convecti~n. 
field and drift. 
4Jt.[~~;t~-nu-n.1)'l)1-.~~[~6n.!DD] = 0 (4) 
Inte.1Jration of equation (4) over " 
of !/i/2. -E and $/2 -1-£ and approaching So to 
condition: 
/7..( 'l,E,(}=Ji/2)::' It,,(e) 
within the limits 
zero gives follGwing 
( 5) 
where l1o(t)-density af galactic COSII);i..c r.ays out of modulation 
r&&ian tlla t ie fe,r r~ro • 
It shOQd be noted that on the b.&is of general 
https://ntrs.nasa.gov/search.jsp?R=19850026537 2020-03-20T17:00:02+00:00Z
458
SH4.2-12
mathematical considerations (Nors F.M.,Feshbach C.,1958)
condition(5) has sense only for odd cycles of solar activity.
In order to solve parabolic equation (4) we used traditional
boundary conditions for this kind of the problems ( Ashirov
R.R. et al.,1979,Krylov V.I.,et a1.,1977)
where (- parameter, =
The set of boundary conditions (5) and (6) allows to
solve equation (4) correctly. Grid technique and Crank
Nicholson schemes (Krylov V.I.,B_bkov V.V**Nonastyrsky
V.I,,1977) were employed for solution. Equation (4) was
solved for the energy range 8>lGeV.Figure 1 shows radial
variation o£ _/f_o at the heliolatitude -7 for energies 1
and 10 GeV. Figure 2 illustrates latitudinal variations of
_/_or the energies. Following values of latitudinal
gradient of gcr were obtained st the orbit of the Earth:
Hence including iu the equation of gcr
propagation the term describing drift of particles results
in redistribution of density sappearance of latitudinal
gradient and reduction of modulation depth.
Letts consider and analyse exp_rimental data connected
with hell,magnetic cycle. As follows from abovementioned
facts latitudinal gradient results in N-S asymmetry (
Kolomeet$ E.V..et alo.1977) Let I
cosmic rays end solar activity, s eonsider asymmetry ofFigure 3 shows mplitude f
north-south asymmetry in the stra_osphere date of _irny end
Murmansk at the depths of 20 g/sm (a) and 480 g/s_ (b). One
can see that amplutude of the effect grows with the depth in
the atmosphere, this fact demonstrates rigid energy spectrum
of the effect.
The investigation of solar activity during the last
magnetic cycle reveals pronounced _-S asymmetry st ell
hell,latitudes. Figure 4 shows north-south asymmetry for the
ranges of heliolatitudes (20-30) (a); (30-40) (b); (40-5e)
(c). One can see 22-year wave in $-S asymmetry. The change
of the sign of north-south asymmetry occurs during the
periods of inversion of solar total magnetic field. Periods
of inversion are shaded.
In order to study nature of 22-year variation of
neutron component of. cosmic rays we analysed continuous set
of the data of neutron monitors of the worldwide network for
the last magnetic cycle. The wave averaged over two
eleven-year cycles was substructed from original data to
exclude ll-year variation. Figure 5(a) shows obtained 22-year
variation for Deep River station,
Taking into account 22-year wave in solar activity we
58 
5H .2-12 
a them tieal onsiderations (Mors .  •• Fe& baeh G.,1958) 
condition(5) has sense only for odd cycles f solar ctivity. 
In rder to solve arabolic equation (4) e used traditional 
boundary conditions for this kind of the problems ( shirov 
.R. t l.,1979,Krylov .I.,et l.,1977) 
n..(Z='lo,t,e)=nc(t); [6'n.+(1-6)f,}J(=O (6) 
where 6' _ parameter. '2.=0 
The set of boundary conditions (5) and (6) allows to 
solve equation (4) correctly. Grid technique and Craak 
ich lson schemes (Ir lov .I.,Babkov .V.,Monastyrsky 
.l.,1977) ere e ployed for solution. quation ( ) as 
solved for the energy range £>lGeV.Figure 1 shows radial 
variation of n.ino at the heliolatitude -7 for ener8i~s 1 
and 10 e . igure 2 illustrates latitudinal ariations f 
~/~or the enar-gies. Following values of latitudinal 
radient of gcr ere obtained at the orb~t of the arth: 
~ l/)(c = 1 GeV):::1.9%/()..u ~ ¥o(E =lOGeV)=D.16%/o...u 
ence including in the equation of gcr 
propagation the term escribing rift of articles results 
in r distribution f ensity . pe rance f latitudinal 
gradient and reduction of odulation depth. 
et's onsider and nalyse pxpprimental ata c nected 
ith eliomagnetic cycle. s f llows from abovementioned 
facts latitudinal radient r sults i  -S asymmetry ( 
olomeets g.  •• et a1 •• 1917). et's eonsider asymmetry of 
eos ic rays and solar activity. igure  ows a plitude of 
north-south asymmetry in the stratosphere data of MirnJ and 
urmansk at the depths of 20 g/sm1 (a) and 480 S/sJ ( ). ne 
can see that a plutude of the effect grows ith the depth in 
the atmosphere. this fact demonstrares rigid energy spectrum 
f t e fect. 
Tbe investigation of solar activity during the last 
magnetic cycle reveals pronounced I-S asvmm~try At ell 
beliolatitudes. igure 4 shows north-south asymmetry for the 
ranges of heliolatitudes (20-30) (a); (30-40) (b): (40-50) 
(c). One can see 22-year wave in N-S asy metry. The change 
of the sign of north-south asy metry occurs during tbe 
periods of inversion of solar total magnetic field. Periods 
f version re aded. 
In order to study nature of 22-year variation of 
neutron component of' cosmic rays we analysed continuous set 
f e ta f utron onitors f e rldwide twork r 
the last agnetic cycle. The ave averaged over t o 
eleveD-year cycles was substructed from original data to 
exclude II-year variation. Figure 5(a) shows obtained 22-year 
ariation f r eep iver station. 
Taking into account 22-year wave in solar activity we 
459
SH 4.2-12
i
11 \ i1 I I\
I\ i I/ I I\
I III / '_ I
2 I / I/ a.
i] ag82
-2 I 8
R.
2ll _:
IgSq 19_8 ICJG2 I_G6 IgI0
.o
t ,
"2 _/,0"
0..,_/o'
-_ X_._ ,"
o.o o'C
Fig.3. Temporal variation of amplitude of N-S asymmetry
stratosphere data of r41rny and _urmansk).
Fig.4. Temporal variation of N-S asymmetry of solar activity
at various hellolatltude regions.
Fig 5. 22-year variation of cosmic ray intensity, observed at
Deep River. (a) -22-year wave in cosmic rays expected due to
corresponding variation of solar activity. (b)- variation of
cosmic ray intensity due to drift effects,
459 
S  4. - 2 
JlN % r , ~ 
" \ 
'\ ~ \ '\ 
g \ , \ / \ \ I I I  6 \ , I ~ I I ~ I I ;'\ ~ I 4 \ \ I \ \ \ , t ,  \ \ , \ 
0 1982 
l \ \  
-AJ,% 
\ )(-)( 
\(/ 
ltD 
t 
D 19b'l ~8 1962 'SG6 1982 
-20-
2 
~% 6..), 0 
t o~~~~~~~~~~~~~~~~~~ 
'1./0>' -
/0" 
-4 -
y. , 
/ , 
0.;11 0' 
X_y..r : 
0'0 o:c 
Fig.3. Temporal variation of amplitude of N-S asymmetry 
stratosphere data of Mirny and Murmansk). 
Fig.4. Te poral variation of N-S asy etry of solar activity 
at various heliolatitude re2ions. 
Fig 5. 22-year variation of cos ic ray intensity, observed at 
Deep iver. (a) -22~year wave in cos ic rays expected due to 
corresponding variation of solar activity. (b)- variation of 
cos ic ra  i t sity due to rift eff ts. 
460 S-_ 4.2._ q2
determined contribution of the _ve to cosmic ray intensity.
22-year wave in cosmic rays expected due to 22-year variation
o£ solar activity was found on tile basis of empirical
relation between solar activity and cosmic ray intensity.
The result is given in figure 5 (b). One can see that
obtained change in cosmic rays due to solar activity is in
opposite phase with the observed variation of cosmic rays.
Substructing from obtained 22-year wave wave expected _ee to
corresponding variation of solar activity we obtained
variation of cosmic ray intensity produced by other
mechanisms and among them drift of particles in solar total
magnetic field. So corresponding variation o£ solar
activity, inversion of solar total magnetic £ield, drift
effects and other space distributions contribute to the
observed 22-year variation.
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n.h_o rt/_
IOGV iO
au / I Fq2 o
{Fig.1. Radial dependence of gcr density at heliolatitude
at energy_ 10 GeV.
Fig.2. Latitudinal dependence of gcr density at energies 1
and 10 GeV.
460 H 4.2fOt' 1  
etermined c ntribution f t e W&v~ t  cos~tc ra  i tensity. 
22-year ave i  cos ic ra s expected du~ t  -year ariation 
of s lar tivity as found on the asis f e pirical 
relation bet een s lar activity and cosmic ray i tensity. 
 sult  iven i  i ure  ).   e t at 
obtained change in cosmic rays due to solar activity is in 
opposite phase ith the observed ariation of cos ic ra s. 
bstructing fro  OBtained -year ave ave e pected ~tie t  
corresponding ariation of s lar activity e obtained 
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echanisms and a ong the  rift of articles i  s lar t tal 
agnetic ield.  rresponding riation f lar 
ctivity, i version f s lar t tal agnetic fi ld. rift 
fects  Uler ce ,distributions ntribute  e 
served -year riation. 
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rt[l1o 
l,OIl 
lOGe  
D94 
tt/no 
1.0~ ________ -I 
D.96 
a.9~ 
0.91 
D.S8 Fi{j .2 
J" 0 :1. 2 .3 I{ !j A
O 
6- 10 :1.6- fl t=!0~"!.--~--'::-.!:-' .-T:~' ~~'~;-' IF~g.l. Radial dependence of gcr density at heliolatitude 
t nergy 1 it.I1.d 0 e . i at energies 1 Fig.2. Latitudinal dependence of gcr dens ty 
nd 0 eV. 


Effects of solar magnetic field on cosmic rays

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