Beyond several AU, interactions among shocks and streams give rise to merged interaction regions in which the magnetic field is turbulent. The integral intensity of . 75 MeV/Nuc cosmic rays at Voyager is generally observed to decrease when a merged interaction region moves past the spacecraft and to increase during the passage of a rarefaction region. When the separation between interaction regions is relatively large, the cosmic ray intensity tends to increase on a scale of a few months. This was the case at Voyager 1 from July 1, 1983 to May 1, 1984, when the spacecraft moved from 16.7 to 19.6 AU. Changes in cosmic ray intensity were related to the magnetic field strength in a simple way. It is estimated that the diffusion coefficient in merged interaction regions at this distance is similar to 0.6 x 10 to the 22nd power sq cm/s

Burlaga, L. F.

Goldstein, M. L.

Mcdonald, F. B.

English

NASA Technical Reports Server

396
SH 4.1-11
COSMIC RAY MODULATION AND MERGED INTERACTION REGIONS
L. F. Burlaga, and M. L. Goldstein
NASA/Goddard Space Flight Center
Laboratory for Extraterrestrial Physics
Greenbelt, MD 20771
F. B. McDonald
NASA Headquarters, Washington, DC 20546
ABSTRACT
Beyond several AU, interactions among shocks and streams give
rise to "merged interaction regions" in which the magnetic field
is turbulent. The integral intensity of > 75 MeV/Nuc cosmic rays
at Voyager is generally observed to decrease when a "merged
interaction region" moves past the spacecraft and to increase
during the passage of a rarefaction region. When the separation
between interaction regions is relatively large, the cosmic ray
intensity tends to increase on a scale of a few months. This was
the case at Voyager I from July I, 1983 to May I, 1984, when the
spacecraft moved from 16.7 to 19.6 AU. Changes in cosmic ray
intensity were related to the magnetic field strength in a simple
way. It is estimated that the diffusion coefficient i_ merged
interaction regions at this distance is _0.6 × 10_- cm_/s.
I. Introduction. Variations in the intensity of galactic cosmic rays >
75 MeV/nucleon near 11AU on scales ranging from approxlmately a day to a
year were found to be related to the interplanetary magnetic field in
observations from Voyagers I and 2 from June, 1982 to August, 1983
(Burlaga et al., 1985a). The long-term variation of cosmic ray intensity
was related to the strength and separation of interaction regions. It
decreased or remained relatively low when interaction regions were strong
and closely spaced, and it increased when the interaction regions were
weaker and widely spaced. These results are consistent with the idea
that modulation is caused by diffusion in turbulent magnetic fields
(Morrlson, 1956) and the observation that modulation effects propagate
outward from the sun at the solar wind speed (McDonald et al., 1981). A
non-steady model of the 11-year variation which incorporates diffusion
and propagation of shells of disturbances has been constructed by Perko
and Fisk (1983).
The purpose of this paper is to extend the analysis of Burlaga et
al. (1985a) to examine the relation between cosmic ray intensity and the
interplanetary magnetic field from July I, 1983 to May I, 1984, using
Voyager I data. During this interval the spacecraft moved from a
heliocentric distance of 16.7 AU to 19.6 AU and from a heliographic
latitude of 2_ to 29.
/
//
/
i
396 
SH 4.1-11 
COSMIC RAY MODULATION AND MERGED INTERACTION REGIONS 
L. F. Burlaga, and M. L. Goldstein 
N SA/Goddard Space Flight Center 
Laboratory for Extraterrestrial Physics 
Greenbelt, MD 20771 
F. B. McDonald 
N SA Headquarters, Washington, DC 20546 
ABSTRACT 
Beyond several AU, interactions among shocks and streams give 
rise to "merged interaction regions" in which the magnetic field 
is turbulent. The integral intensity of > 75 MeV/Nuc cosmic rays 
at Voyager is g nerally observed to decrease when a "merged 
interaction region" moves past the spa ecraft and to increase 
during the passage of a rarefaction region. When the sep ration 
between interaction regions 1S relatively large, the cosmic ray 
intensity tends to increase on a scale of a few months. This was 
the case at Voyager 1 from July 1, 1983 to May 1, 1984, when the 
spa ecraft moved from 16.7 to 19.6 AU. Changes in cosmic ray 
intensity w re related to the magnetic field strength in a simple 
way. It is estimated that the diffusion coeffici2~t i~ merged 
1nteraction regions at this distance is "'0.6 x 10 cm Is. 
1. Introduction. Variations in the intensity of g lactic cosmic rays> 
75 MeV/nucleon near 11 AU on scales ranging from approx1mately a day to a 
year w re found to be related to the interplanetary magnetic field in 
observations from Voyagers 1 and 2 from June, 1982 to A gust, 1983 
(Burlaga et al., 1985a). The long-term variation of cosmic ray intensity 
was related to the strength and sep ration of lnteraction regions. It 
decreased or remained relatively low when interaction regions w re strong 
and closely spaced, and it increased when the interaction regions were 
weaker and widely spaced. Th se results are con istent with the idea 
that modulation is caused by diffusion in turbulent magnetic fields 
(Morrison, 1956) and the observation that modulation effects propagate 
outward from the sun at the solar wind speed (McDonald et al., 1981). A 
on-steady model of the 11-year variation which incorporates diffusion 
and prop gation of shells of disturbances has been constructed by Perko 
and Fisk (1983). 
The purpose of this paper is to extend the analy is of Burlaga et 
al. (1985a) to examine the relation between cosmic ray intensity and the 
interplanetary magnetic field from July 1, 1983 to May 1, 1984, using 
Voyager 1 d ta. During this interval the spa ecraft moved from a 
heliocentric distance of 16.7 AU to 19.6 AU and from a heliographic 
lati tude of 20° to 23° • 
/ 
/ 
/ 
https://ntrs.nasa.gov/search.jsp?R=19850026521 2020-03-20T17:00:39+00:00Z
897
SH 4.1-11
2.Observations.The intensityof cosmicrays> 75MeV/nucleon,measured
by the CalTeCh/Unzversityof New Hampshzre/GoddardSpaceFlightCenter
experiment is shown in Figure I, together with the strength of the
interplanetary magnetic field measured by the GSFC magnetometer (N. Ness,
Principal Investigator). The magnetic field strength _a_/_or_alized by
the spiral magnetic field strength, B = 4.75 x (I + r_) "" /r . Thus,
the magnetic field fluctuations in Figure I are perturbations on the
large-scale average magnetic field, which are produced by dynamical
interplanetary processes.
Figure _ shows a
correlation between VOYAGER I
B/B and the cosmic o_ ,
ray p intensity C: C INTEGRALRATE
24 HR AVG
generally decreases
during the passage of
an interaction region _o55
or merged interaction
region (B/B > I) and
it increases during
the passage of a rare-
faction region (B/B < o45
I). A similar _e-
lation was observed
near 11 AU by Burlaga
et al. The net effect
in the period shown in AUG! OCT] DEC] FEB! APR!
FigureI is an overall |98B 1984
increase in cosmic ray
intensity. The cosmic Fig. I Intensity of cosmic rays > 75
ray intensity profile MeV/nuclel versus tlme (top) and magnetic
is the result of a field strength relative to the spiral
competition between field strength versus time (bottom).
the effects of
interaction reglons and those of rarefaction regions. In this interval,
the interactionregionswere relativelyweak (B/B)ma _ 2.5 and the
corresponding decreases in C were relatively smal_, _ile the rarefaction
regions were large in extent, allowing more than enough time to recover
from the individual decreases.
3. Model. Burlaga et al. (1985a) modeled the variation of cosmic ray
intensity observed near 11AU from July, 1982 to August, 1983 with the
following set of equations:
dC = - D (B/B -I) when B/Bp > I (I)t p
dC
= R when B/B < I (2)
dt p -
where D and R are constants and B/B is the measured magnetic field
strength as a function of time. Using the 24-hour averages of B/B (t)
shown in Figure I, choosing D = 0.004 (counts/see/day) and R = 0.0_2
(counts/see/day) and taking the initial value of C at July I, 1983, these
397 
 .  
. bs rvations. e intensity f smlC ys  5 e / ucleon, e sured 
by the alTech/Unlversity of New a pshlre/Goddard Space Flight Center 
experi ent is sho n i  i re 1, t et er ith t e stre t  f t e 
i ter la etary agnetic fiel  easured by the SFC agnetometer ( . ess, 
Principal Investigator). The magnetic field strength ~a~/~or~alized by 
the spiral agnetic field strength, B = 4.75 x (1 + r) /r. Thus, 
the agnetic fiel  fluctuations ln iiure 1 are perturbatlons on the 
lar e-scale average agnetic fiel , hich are produced by dynamical 
interplanetary processes. 
i re s s  
relatlon et en 
/B   lC 
rayP intensity C: C 
generally decreases 
during the passage of 
 i t r ti n r i  
r erged l t ti  
r i  ( /   1) a  
1 t l creas~s ri g 
the passage of a rare-
f ti  re l  ( /   
1).  lar Pe-
t n as served 
ar    urlaga 
t e he t t 
i  t  riQ   i  
i re 1 i  I  r ll 
i r s  i  c s ic ra  
lntenslty. The cosmlC 
ray lntensi ty proflle 
is the result of a 
competitlon between 
 ff cts f 
~ 
.... 
II> 
065 
~ 0 5 
::;) 
o 
u 
.. 
III 
.... 
III 
045 
4 
3 
2 
, 
0 
GER 1 
INTEGRAL RATE 
24 HR AVG ~ /l ""ClEO ." .,,""' rJrrvti~~ 
,#1 
24 HR AVG 
~ III ~ V¥~~~ 
AUG 1 OCT 1 
1983 
DEC 1 FE81 
1984 
 1 
Fig. 1 t sit  f lC    
eV/nuclel versus tlme (top) and agnetic 
fleld strength relati e to the s lral 
 t   im  t ). 
i t r cti n r l s  t s  f r r f cti n r l s. I  t i  i t r al, 
the interaction regions were relatively weak (B/B )ma < 2.5 and the correspondl~g decreases ln  ere relatively smal~, w~i1e the rarefaction 
regions ere large in extent, allo ing ore than enough ti e to recover 
rom  i i ual reases. 
. odel. urlaga t ale (1985a) odeled t e ariati  f cos ic ra  
intensity observed near 11 AU fro  July, 1982 to ugust, 1983 ith the 
f llo i  t f uati ns: 
dC 
t = - D (B/B -1) P when B/B > 1  (1) 
 
dt = R 
here     nstants  
tr t  s  f ti  f tim . 
s  i  i re 1, si    
(counts/sec/day) and taking the 
 /   1  - 2  
/  i  t  easur  agnetic i l  
~  t  - r r es  / B(t) 
.  ( ts/ c/ y)    .   
initial value of C at July 1, 1983, these 
398
SH 4.1-11
equations were inte-
grated to obtain the VOYAGER 1
model cosmic ray in- 0.7 I
tensity profile shown I NUCLEI >75 MeV /in Figure 2. The ob- / 24 HR AVG _ _a-_VI
served 24-hour aver- _ O6 _ ""i_ _._._
ages of C(t) for > 75 m __ _ _4k C
MeV/nucleon eosmzc
rays are also plotted z
in Figure 2, for tom- _ 05 -OOS
parison. Note that
the model curve has u _ v -M _._-
been plotted with a I _ DAYS'-
constant offset of O4
0.03 (counts/see/day) JULY I,1983 MAY 1,1984
for the sake of elarl-
ty, but its initial
value can be ehosen to Fig. 2 The result of a model (see text)
be identical to the together with a plot of the observed
observed value for the oountlng rates.
integratlon of (I) and
(2). Between March 10 and March 20 there was a decrease in cosmic ray
intensity which is not predicted, because there was no large increase in
B/B at this time (see Figure I). Except for this anomaly, the model
pro_ides a very good approximation to the cosmic ray observations
throughout the 10-month interval.
A theoretical basis for the model given by (I) and (2) has recently
been given by Chih and Lee (1985). They found that under certain
assumptions
2
dC V V 6B
_-_=- _ (c-co) -_-Co_-, (3)
o
where K is the diffusion coefficient, V is the solar wind speed, _ is a
characteristic length and 6B is a measure of the fluctuations of B. It
has been observed th_36B{B _0.3 between I AU and 5 AU, varying slowly
wlth distance as _r (_urlaga et al., 1982), so it is reasonable to
take _B/B = 0.3 B/B in (3). In this case the second term on the BHB of
(3) has t_e same for_ as (I), and one can use our value of D to estimate
the diffusion coefficient K. With D = 0.004 (counts/see/day), Vg_ 4_0 1
km/s, C = 0.55 counts/see and 6B/B = 0.3 one finds K = 0.6 x 10-'cm-s-'.
This is°somewhat smaller than the value chosen by Chih and Lee (because
we used 6B/B = 0.3), but it is close to the value for the diffusion co-
efficient used by Perko and Fzsk (1983) to describe the 11-year varia-
tion. Identifying the first term on the RHS of (3) with R in (2), and
taking C-C^ = 0.03 counts/see, one finds that R = 0.002 (counts/see/day)
implies L _ 4 AU.
In Figure 3 we show spectra of the components of B (upper curve), the
magnitude of B (lower curve) and the magnetic helicit_ times frequency
(fHm) computed from one hour average Voyager I data from July I, 1983 to
May I, 1984, using the fast Fourier transform method with 26 degrees of
freedom, without detrending or filtering the data (Matthaeus and
equatlons were inte-
grated to obtaln the 
model cosmlC ray In-
tensi ty profile shown 
in Figure 2. The ob-
served 24-hour aver-
ages of C(t) for> 75 
MeV/nucleon cosmlC 
rays re also plotted 
ln Figure 2, for com-
parison. Note that 
the model curve has 
been plotted with a 
constant offset of 
0.03 (counts/sec/day) 
for the sake of clarl-
ty, but 1 ts inl tial 
value can be chosen to 
be identlcal to the 
observed value for the 
lntegrati n of (1) and 
398 
SH 4.1-11 
VOYAGER 0.7,...---------------, 
NUCLEI >75 MeV 
u 
~ 06 
24 HR AVG ~ 
..... 
r 
z 
::> 
o 
u 
u 
05 
......... MODEL C-0.03 
-t D~~S 14-04L-____ ___________________ ~ 
JULY 1,1983 MAY 1,1984 
Fig. 2 The result of a model (see text) 
together with a plot of the observed 
countlng rates. 
(2). Between March 10 and March 20 there 
lntensity which is not predicted, because B/B at this time (see Figure 1). Except pro~ides a very good approximation to the 
throughout the 10-month interval. 
was a decrease in cosmic ray 
there was no large increase in 
for this anomaly, the model 
cosmic ray observations 
A theoretical baS1S for the model given by (1) and (2) has recently been glven by Chih and Lee (1985). They found that under certain assumptlons 
2 
dC V V 0 B dt = - L (C-Co ) - K CO B' (3) 
o 
where K is the diffusion coefficient, V is the solar wind speed, 1 is a characteristic length and oB is a measure of the fluctuations of B. It has been observed t~'730B/B ~0.3 between 1 AU and 5 AU, varying slowly wlth distance as ~r (Burlaga et al., 1982), so it is reasonable to take oB/B = 0.3 B/B in (3). In this case the second term on the RHS of (3) has tRe same for~ as (1), and one can use our value of D to estimate the dlffusion coefficient K. With D = 0.004 (counts/sec/day), V22 4~0_1 km/s, C = 0.55 counts/sec and oB/B = 0.3 one finds K = 0.6 x 10 cm s • This isosomewhat smaller than the value chosen by Chih and Lee (because we used oB/B = 0.3), but lt is close to the value for the diffusion co-efficient used by Perko and F1Sk (1983) to describe the 11-year varia-tion. IdentifYlng the first term on the RHS of (3) with R in (2), and ~~~~~~SCLC~ ~ ~u~3 counts/sec, one finds that R = 0.002 (counts/sec/day) 
In Flgure 3 we show spectra of the components of ~ (upper curve), the magnitude of B (lower curve) and the magnetic helicity times frequency (fH
m
) computed from one hour average Voyager 1 data from July 1, 1983 to May 1, 1984, using the fast Fourier transform method with 26 degrees of freedom, without detrending or filtering the data (Matthaeus and 
399 SH 4.1-11
Goldstein, 1982). Posltive values of magnetlc helicity are denoted as
circles, negative values as triangles. Assuming that plasma is convected
past the spacecraft at the mean solar wind speed in the interval, _, the
frequency f corresponding to the correlation length L, is f = V/L, and
this is sho_n by the arrow in Figure 3. e
The spectrum of :05
power in the com-
ponents _3_ has thef rm f-_ expected 1°4
for homogeneous turbu-
• ..:_
lense in the range 4 _ :os _.
10-v Hz to 2 × 10-_ _
Hz, corresponding to 0 2
periods from 14 hours _ * :-_.'--__
to 3 days. This is _
consistent with ,o*
earlier results show- .._ ,
ing that the fluctua-
tions in interaction 1°°
regions are turbulent.
At periods between 4 10-I ........, ...._,..,........,
days and 15 days, the 1°-7 1°-6 1°-s 1°-4
spectrum of power in Frequency (Hz)
the components of 9 --
was el-', which is Fig. 3 Power spectra of the magnetic field (see
probably either a text).
remnant of the spec-
trum of fluctuationsintroduced at the source (Goldstein et al., 1984;
Burlaga et al., 1985b) or evidence of an inverse cascade of magnetic
helicity expected in fully developed MHD turbulence (Frlsch et al., 1975;
Montgomery and Matthaeus, 1981). If the former interpretatlonis cor-
rect, its presence is another indlcatlon that turbulence dld not develop
sufficientlyto modify the inltial spectrum in thls quasi-statlonaryflow
system, despite the long time available for evolution, viz. e18 AU/400
km/s . 78 days.
References
Burlaga, L., (1984), Space Sci. Rev., 39, 255.
Burlaga, L. F. and J. King, (1979),J. Geophys. Res., 84, 6633.
Burlaga,L.F. etal.,(1982),J.Geophys.Res.,87,4345.
Burlaga, L. F. et al., (1984), J. Geophys. Res., 89, 6579.
Burlaga, L. F. et al., (1985a), NASA/GSFC TM 86193.
Burlaga, L. F. et al., (1985b), NASA TM 86213.
Chih, P. P. and M. A. Lee, preprint, (1985), submltted to J. Geophys.
Res.
Frisch et al., (1975), J. Fluid Mech., 68, 769.
Goldsteln, M. L. et al., (1982), J. Geoph---ys.Res., 87, 6011.
Matthaeus, W. H. and M. L. Goldsteln, (1984), J. Geophys. Res., 89, 3747.
Matthaeus, W. H. and D. Montgomery, (1981)J. Plasma Phys., 25, 11.
McDonald, F. B. et al., (1981), Ap. J. (Letters),249, L71.
Morrlson, P., (1956), Phys. Rev., 101, 1397.
Perko, J. S. and L. A. Fisk, (1983), J. Geophys. Res., 88, 9033.
9 S  4.1- 1 
oldstein, 1982). osltive values of agnetlc elicit  are denoted as 
circles, negative values as triangles. Assu ing that plas a is convected 
past the spacecraft at the mean solar wind speed ln the lnterval, V, the 
frequency fc corresponding to the correlation length , is fc  / , and 
this is shown by the arro  in Figure 3. 
The spectru  of 
power i  t e co -
ponents -g73 ~ has the 
f r  f expected 
for ho ogeneous turbu-
le~ge in the range 4_~ 
10 Hz to 2 x 10 .' ,  , 
.. 
Hz, corresponding to 
periods from 14 hours 
to 3 days. his is 
nsistent it  
earlier results show-
ing that the fluctua-
t s  t ti  
regions are turbulent. 
t periods between 4 
days and 15 days, the 
spectrum of power in 
10 1 
10 0 
0-1~~~~w-~~~~ __ ~~~ 
10-7 10-6 10-5 10- 4 
the co~~onents of ~ 
was oI'f , which is Fig. 3 
probably either a 
re nant f t e s ec-
Frequency (Hz) 
 t a f t  agneti  eld ee 
t  • 
trum f luctuations l troduced t t  r e ( ol t in t l., ; 
urlaga et al., 1985b) or evidence of an inverse cascade of agnetic 
li ity expected i  f lly developed HD turbulence ( rlsch et l., 1975; 
ontgo ery and atthaeus, 1981). If the former lnterpretatlon is cor-
r t, it  resence is a t er i l tlon t t t rbulence l  t e elo  
sufficiently to odify the i ltial spectrum in thlS quasi-statlonary flow 
system, despite the long time available for evolution, viz. "'18 /400 
k /s + 78 days. 
ef s 
Burlaga, L., (1984), Space Sci. Rev., 39, 255. 
Burlaga, L. F. and J. King, (1979), J. Geophys. Res., 84, 6633. 
Burlaga, L. F. et al., (1982), J. Geophys. Res., 87, 4345. 
Burlaga, L. F. et al., (1984), J. Geophys. Res., 89, 6579. 
urlaga, L. F. et al., (1985a), NASA/GSFC TM 86193. 
urlaga, L. F. et al., (1985b), NASA TM 86213. 
hih, P. P. and . . ee, preprint, (1985), sub ltted to J. eophys. 
. 
Frisch et al., (1975), J. Fluid ech., 68, 769. 
oldstein, M. L. et al., (1982), J. eoPhys. es., 87, 6011. 
atthaeus, W. H. and M. L. oldsteln, (1984), J. Geophys. Res., 89, 3747. 
atthaeus, . . and . ontgo ery, (1981) J. Plasma hys., 25, 1 . 
cDonald, F. B. et al., (1981), Ap. J. (Letters), 249, L71. --
Morrlson, P., (1956), Phys. Rev., 101, 1397. ---
Perko, J. S. and L. A. Fisk, (1983), J. Geophys. Res., 88, 9033. 


Cosmic ray modulation and merged interaction regions

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