Radio Science, Volume 4, Number 9, pages 771-780, September 1969
Dynamo currents, winds, and electric fields
S. Matsushita
High Altitude Observatory, National Center [or Atmospheric Research
Boulder, Colorado 80302
(Received May 6, 1969.)
After a brief presentationof Sq and L electric current systemsdeduced from geomagnetic
data, electric conductivities and wind models in the dynamo region are discussed.It is then
shown that the solar negative-modethermal diurnal tide and the lunar semidiurnal gravitational tide having a phase shift with altitudes produce the best fit Sq and L current systems,
respectively. Distributions of electrostatic fields are computed, and electromagnetic drift
speedsin the ionosphericF region are also examined. These calculated values agree well
with
1. DEDUCED
observed
DYNAMO
results.
CURRENT
SYSTEMS
Methodsof deductionof dynamocurrentsand the
remainingproblems,particularlythe Se and L current systemsand the equatorial electrojet,were reviewed by Matsushita[1967a, b] and Onwumechilli
[1967]. Sincethe electricconductivity
in the dynamo
region (90-150 km altitude) is very low at night
on geomagnetically
quiet days, the dynamocurrents
on quiet nightsmay be almostzero. On the basisof
this idea, Matsushita [1968] obtained computerplotted Se and luni-solar current systemsfor three
seasonsand the yearly averagefrom his previously
obtained current systems[Matsushita, 1967b] by
shiftingthe baseline. Figure 1 showsSecurrentsystemsdeducedin thisway.
To obtain better luni-solar current systemsthan
thosededucedby usinga relativelysimpleadjustment
parameter[Matsushita,1968, Figure 11], more realistic parametersare estimatedfrom global ([oE)•
distributions
in equinoctialand solstitialmonthsduring moderatesunspotperiods.Figure2 presentsdistributionsof the parameterwith respectto the dip
latitude and the local time for the equinoctialand
the June solstitial months; a reversal of the hemispherefor the June solstitialmonths is assumedto
The deducedSq and L current systemsclearly
show the electrojet over the magnetic equatorial
zone. These equatorial electrojetsin the dynamo
regionwere furtherconfirmedby recentrocketobservations(Sq by Davis et al. [1967], Maynard
[1967], and Sastry[1968]; L by Maynard [1967]).
In section4, Sqand L currentsystemswith the electrojet, computedfrom estimatedelectricconductivities and wind models,are comparedwith thesededucedcurrentsystems.
2.
ELECTRIC
CONDUCTIVITY
MODEL
By assumingthat the physicalquantitiesof the
ionosphereare the same everywherealong the dip
equator except for the differencesarisingfrom the
asymmetryof the earth's permanentmagneticfield,
the cross-sectional
profilesof the effectiveconductivity (hence the electrojet), were determinedby Sugiura and Cain [1966] for differentlongitudes,particularly 80øE for India and 280øE for Peru. Price
[1968, 1969] examinedthe applicabilityof the layer
conductivities
in the two-dimensional
treatment
of
the dynamotheory of S•. Calculationswith a simple
three-dimensionalmodel suggestthat the currents
arising from wind-inducedelectromotiveforces are
be the distribution for the December solstitial
nearly horizontal throughoutthe dynamo layer, so
months.Multiplyingthe L currentsystems
of a mean that the two-dimensionalequationsinvolving the
lunarion [Matsushita,1967b] by these parameters layer conductivitiescan be used. However, the asproducesthe L current systemsfor a new moon or sumptionthat the horizontalcurrentdensityis nonthe luni-solarcurrentsystems
exhibitedin Figure 3. divergentand that consequently
a currentfunction
The total currentintensitiesare comparedin Table 1. can be foundhasbeenshownto be quiteuntrue.
For the purposeof obtainingtotal electricfield
Copyright ¸ 1969 by the American Geophysical Union.
distributions
calculated
from the deducedcurrentsys771
772
S. MATSUSHITA
D MONTHS
E MONTHS
90
. 90
ß',ßß,ßß,''•'',ßß,'ß,'ßt
-I1•.t
6O
'
.
30
60(•?
-15.5
0 i•(o
-17.7
•
,
.
80
!
t
05
i
i
f
06
,
,
i
09
,
.
i
!2
,
.
!
!$
,
.
i
!8
!
s
2!
•
24
980
05
06
09
t2
!$
!8
21
24
LOCAL TIME
Fig. 1. Computer-plottedexternal Sq current systemsfor December solstitial, equinoctial,and June solstitial
seasonsand the yearly average during the IGY (1958) when the current intensity at the midnight is zero.
The current intensity between two consecutivelines is 25 X l0 s amp, and the numbers near the cross marks
indicate the total current intensities of vortices in units of 10s amp [Matsushita, 1968].
tem and of computingcurrent systemswith wind for moderatesunspotperiodsare assumedto be
models,a simplebut reasonablemodel of the electric 1/1.3 of the valuesfor the IGY indicatedin Figure
conductivityis needed.From the COSPAR-1965 at- 4. These conductivities and the L current system
mospheremodel, collisionfrequencieswere computed by using the equationsderived by Nicolet
[1953] for the electron-ioncollisionfrequencyand
by Dalgarno [1961 ] for the electron-neutraland the
ion-neutralcollisionfrequencies.Obtainedheight-integrated anisotropic electric conductivity distributions for two seasonsduring the IGY are shownin
Figure 4. The conductivitydistributionfor December
solstitial months can be approximated by the reversalof the hemispherein the distributionfor June
solstitialmonths.The height-integratedconductivities
exhibitedin Figure 3 give the total electric field
(dynamo and electrostatic
fields) for the L; the Sq
currentsystemin Figure 1 and the conductivityin
Figure 4 presentthe total electricfield for the Sq.
These total field distributionsfor the Sq and L were
illustratedby Matsushitaand Reddy [1968]: the
total electric field in low latitudes is a few mvolt/m
for the Sq and a few tenthsof mvolt/m for the L.
The very smallvaluesof the field over the equator
indicate that the estimatedconductivityis probably
too largefor the equator.
DYNAMO
CURRENTS,
0.5
1,5
I
FIELDS
773
resultsof the current systemsusingthis conductivity
model are presentedin section4.
r•'ll"!JlJ•'•lJllllllllllll
60
'
WINDS, AND ELECTRIC
0.5
I
40
3.
• •o
:- -2o
-60
I•lll!•111llllllllllllll 12
18
24
1968; Kent and Wright, 1968]. Data from a new
L•TI•
CO:FFICIENTS FOR DAILY VARIATIONS
•l
i
i
i
i
i
i
i
i
i
i
i
meteor-windobservationsystemin France for 80-
d SFASON
i
i
i
i
I
MODEL
We haverecentlygaineda large amountof knowledgeaboutthe movements
of ionospheric
irregularities and upper atmospheric
windsby variousobservational techniques and extensive theoretical
estimations[e.g., Hines, 1966.; Woodrum and Justus,
.• o
O0
WIND
I
110 km altitudes(M. A. Spizzichino,privatecommunication)havebeenprocessed
by powerspectral
analysisto assessprevailingand tidal components
and to analyze the residualnontidal contributions.
• o
The major componentis semidiurnal,with a vertical
:- -20
wavelength
greaterthan 50 km and an amplitudeof
-•0
10-70 m/sec. A downwardphasevelocityof 5-10
-60
km/hr is largelydue to the semidiurnalcomponent.
O!•l• i I 111•
........... 8
;;'4
Similarresultsfor 90-130 km altitudesat nighthave
alsobeenobtainedby observations
of chemiluminous
Fig. 2. Adjustment parameter distributions in two
trails releasedby rocketsand gun-launched
projecseasons.
tiles [e.g., Wright et al., 1967; Bedingeret al., 1968].
A statisticalanalysisof seventymidlatitudevapor
To compute current systems,a slightly modified
trails
between 90 and 150 km altitude made by
conductivitymodel for equinoctialmonths during
Rosenberg
[ 196.8]showednot only a consistent
zonal
moderatesunspotperiodswas obtainedby Tarpley
60
40
'. \o.
iI
5'
LOCAL 'T
[1969]. The maximum value of ,a (Pedersen conductivity) in middle latitudesat noon is 3.1 x 10
emu at 127 km altitude and that of *,2 (Hall conductivity) is 4.5 x 10-• emu at 117 km. The tensor
components
of the height-integrated
conductivityat
noon are shownin Table 2. For the daily variation
of the conductivity
flow to the east below I00 km, but also mean values
of total velocityof 50 to 70 m/sec and mean shears
of 0.02 to 0.004 m/s/m, varying with height. One
full rotation occurs between 90 and 110 km and an-
other occursbetween105 and 150 km. The heightintegratedcurrent intensitycausedby the dynamo
actionof thistypeof rotatedwindwill be very small.
Those areas of wind measurements in which ade-
quate data are not yet available include vertical
• -- '• COS
]/2t
winds, daytime winds above 110 km, and horizonis adopted,and the conductivity
duringthe period tally spacedwindsto permit convergence
estimates.
1830 through 0530 LT is assumedto be constant Thus it is still difficult from observations to know a
and equalto 1/30 of the noon value.For detailsof detailedglobalpictureof the wind systemresponsible
temporal,latitudinal,and heightdistributionsof the for dynamo currents.Also estimationsof the wind
conductivity,refer to Tarpley [1969]. Computed patternsfrom dynamocurrentsand givenconductivnoon
TABLE 1. Totalcurrentintensities
of L currentsystems(X 10aamp)
Season'
Hemisphere:
Mean lunation
Luni-solar(before1200)
(after 1200)
D
E
J
Average
N
S
N
S
N
S
N
S
3.77
6.15
--9.00
--5.54
-10.74
10.82
5.09
10.24
-11.77
--5.09
--10.24
11.77
4.59
9.54
-8.90
--2.68
-4.03
6.89
4.16
8.34
-9.47
--4.11
-8.19
9.51
774
S. MATSUSHITA
D MONTHS
E MONTHS
ß
ß
'1
,
,
I
,
,
,
o•o.•
,
I
,
,
I
,
o'o
,
!
'
,
.
•
,
,
0.28
8O
-
,'n•/---.•oo
,.
O..x5
8
05
06
J MONTHS
09
YEARLY
90r'x
•
00
12
f5
f8
2•
AVERAGE
•
00
00
-0.73
0.x84
-60
LUNAR
TIME
Fig. 3. Estimated L current for a new moon (or luni-solar current system) during three seasonsand the
yearly average (moderate sunspotperiod). The current intensity between two consecutivelines is 103 amp.
ity modelsare an interestingpractice,but they are
not always very meaningfulbecauseof the phase
shift [e.g.,Maeda and Fujiwara, 1967]. One possible
way to attack the problemof explainingdynamocur-
eachof the wind systems.
Also,to explainthe S½and
solarflare currentsystems,
Greenfieldand Venkateswaran [1968] assumedvarious periodic and nonperiodicwind modelsand computedcurrent systems
rents is (1) to assume a reasonablewind model
for eachmodel. One commondifficultywith thesere-
basedon currentlyavailableknowledge
of the upper sultswasthat the computedcurrentfocusappeared
atmospheric
winds, (2) to calculatecurrentsystems at placesgreatlydifferentfrom the estimatedone.
from the wind model and a reasonableconductivity
To have theoreticalwind models,tidal theories
distribution,and (3) to comparethe obtainedcurrent systemswith the onesestimatedfrom geomagneticvariations.If the calculatedcurrentsystemsare
similar to the estimated ones, the assumedwind
modelmay givea hint asto the actualwindpattern.
On the basis of this idea, Maeda and Murata
[1968] and Maeda [1968] assumedmeridional and
need to be examined.The latitudinalstructureof a
tidal mode can be determinedby the solutionof
Laplace'stidal equation,whichhasthe Hough function O,n,8 and its associatedeigenvalue,namely, the
equivalentdepth h•, • for the tidal mode (m, s),
wherem denotesthe longitudinalwavenumber(m =
1 for diurnal and m = 2 for semidiurnaltides) and
zonalwindsystems
andobtained
currentsystems
for
Is]- rn is thenumberof modes
in theHoughfunc-
DYNAMO
CURRENTS,
WINDS,
AND
E MONTHS
SIG•
i
Xx
!
i
ELECTRIC
FIELDS
775
J MONTHS
E SEASON
!
i
,
i
i
!
i
i
i
I
I
i
!
i
i
!
!
!
i
i
60
4O
•
20
10-9
-40
-õ0
-o'o'' ' ' 'o; .....
SIGMA ¾¾
I
'• ........... 18
24
LOCAL TIME
E SEASON
60
40
40
,or.
•
,o"e
5 •o
io'•
•-yy
.•
• -20
-40
-40
-60
-60
.......
oo
SI GMAxY
60
40
,-. 20
•xy
.•
'6"'"•
o
.....
I
I
LOCAL T IPIE
;•.....
E SEASON
SI GHAxY
J SEASON
fIIIIII!I!IIiI1IiIII!I!!"'1 IIiiIIiIIIII!I!IIIII!IIi
Io'g ,•
,o'gi• Io•
40
.•
• •o
.
o
-60
-40
I I I I I ' J J , • • i • t , m,
O0
SIGMA XY
06
I I I I _
12
!8
LOCALtIME
i
i
,,,,,/:,/
,o-,
•o .
-• -10
-20 ...................
oo
O0
SIGMA xy
i
i
i
!
!
!
i
!
i
I
i
I
i
t
io.,•\
to'.\
06
/,o"
12
LOCAL TIME
• • , I • ,
18
06
! I I
12
!8
24
12
18
24
LOCAL.
tIME
J SEASON
i
IO'
lO
-60. I ! I I • ! I
24
E SEASON
i
'-'
-
x -20
-40
'"
24
24
,• -•o
•xy
o
• -20
lO
t '-o
a. -10
24
-20
00
06
LOCAL T IPIE
LOCAL TIME
Fig. 4. Distributions of height-integratedanisotropic electric conductivities2:•, 2:•, and 2:• with respect to tee dip
latitude and the local time for the IGY period. The unit is emu. The bottom two diagrams present 2:• distributions
enlarged for low latitudes.
776
S. MATSUSHITA
TABLE 2.
q,•(--• and q,•(-x), which are given with respectto 0
in Figure 5. The mathematicalforms of •I,•t-x) and
ß •(-x) refer to equations3.23-3.25 in Kato's paper
Height-integratedconductivitiesin
different latitudes at noon
Latitude,
deg
Z•, emu
0
1
2
3
6
9
12
15
21
30
45
1.07
1.03
2.83
1.28
3.24
1.45
8.28
5.40
2.89
1.55
8.14
X
X
X
X
X
X
X
X
X
X
X
10-4
10-*
10-6
10-6
10-7
10-7
10-8
10-8
10-s
10-8
10-9
60
75
90
5.41 X 10-9
4.27 X 10-9
4.05 X 10-9
z•,
emu
z•,
0
X
X
X
X
X
X
X
X
X
X
5.88
10-7
3.31
10-7
2.25
10-7
1.12
10-7
7.30
10-8
5.34
10-8
4.15
10-8
2.79
10-8
1.78
10-8
1.03
10-8
6.91 X 10-9
5.38 X 10-9
5.12 X 10-9
2.50
5.28
2.58
1.95
1.51
1.38
1.30
1.22
1.08
8.90
6.52
emu
X
X
X
X
X
X
X
X
X
X
X
10-?
10-8
10-8
10-8
10-8
10-8
10-8
10-8
10-8
10-9
10-9
4.99 X 10-9
4.19 X 10-9
4.05 X 10-9
[1966a].
A modified model for the solar (1, -1)
suggested
by Tarpley [1969] has the form
u = 0.25- cos
•'0
tide.
q-2 cot O1,_1(0)
ßsin(X+ '•) m/sec
(2)
cos
2 0 (2
130
cos
00_•
q_
cosec0)Ox._
• = 0.25-
ßsin(X +'•
+ 90ø)
m/sec
where y = 250 ø and o•._•(0) = 0.7767P•(0) +
0.5822PAX(0) + 0.0752P•(.0) + ß ß ß. HereP•'"(0)
are Schmidt
tion between the poles. The Hough function and
equivalentdepthsfor the importanttidal modeswere
calculatedby severalworkers:by Kato [1966a, b]
and Lindzen [1966, 1967] for the solar diurnal
modes,by Siebert[1961] for the solar semidiurnal
modes,and by Sawada [1954, 1956] for the lunar
mode
functions.
The
wind
distributions
of
thesetwo models,particularlythe latter one shown
in Figure 6, present a surprisingsimilarity to the
diurnal wind distributiondeducedfrom the dynamo
theory of Sq for the rotating earth model by Kato
[19561.
It must be noted that the solar (1, -1)
mode is
excitedby a hypothetical
E-regionheatsource,which
is assumed constant with altitude and confined to a
Tarpley [1969] has examinedvarious modes of layer one scaleheightin thickness[Kato, 1966b].
Detailed theoretical work on the lunar atmossolarandlunar tidestogetherwith nonperiodic
winds
for their effectson the productionof dynamo cur- pherictide was conductedby Sawada[1954, 1956].
rents. Among solar semidiurnaltides, (2, 2) and The lunar (2, 2) mode has the form
(2, 4) modes,and solardiurnal tides, ( 1, 3 ) and (1,
- 1) modes, the thermal-diurnal tide (1, - 1) producesthe best fit Sq current system.Since h,,, s of
O5
this mode showsa negativevalue (-12.25 km), it
1.0
is called a negativemode.When we useequationsof
0.4
the negative-modethermal-diurnaltide (1, -1)
shown by Kato [1966a], the adoptedwind speeds
O5
in the dynamoregionfor the equinoctialmonthsdur0.5
ing a moderate sunspotperiod are
02
Southward:
u = A(O) sin (X + ,/)
m/sec
(la)
0.1
Eastward:
0.0
0
v = B(O)sin(X+'•
q- 90ø)
m/sec
(lb)
where 0 is the colatitude,X is the longitude,and y =
70ø. The amplitudesA (0) and B(O) are shownby
A(O)= 100q•u•
(-•) m/sec
B(O)= 100q•o•
(-•) m/sec
Here q,•,.(-x) and q,•(-t)
are normalized values of
30
O3
90
Colotilude,degrees
Fig. 5.
,I,.(-• and (I)v(--1)with respectto
the colatitude given by Kato [1966a].
Read the right ordinate to find normalized values, ,I,,.v(-•' and ,I,,,s(-•.
DYNAMO
•0
I
I I '
. , I I I
....
0
II I •, .
CURRENTS,
•
0•
I
'
AND
ELECTRIC
FIELDS
777
•I I
' .....
I
WINDS,
ß '
3
6
9
t2
15
18
2•
24
LOCALll•
L• TI•
Fig. 6. Dist•bution of the wind vector by the negativemode the•al diurnal tide repre•nted by equation2, which
produces the •st fit S• current system.The len•hs equal
Fig. 8. Computer-plotted Sctype current system calculated
from the thermal tidal wind model shown by equation 2.
The tot• current intensityis 121,850 •p •d the position
of the focus is at 36ø latitude at 11.4 hour LT.
to 5 ø latitude co•espond to 50-m/sec wind speed.
A(z)(• 2cot0)•
where
risthe
lun•
fime
taken
tobe
zero
atthe
age of the moon • hours,X - r + v, and k is the
"= 0.93- cos"0 + •ff6 •,,0)
ßsin(2X- 2v+ kz+ •)
lower
transit,
vistheelongation
ofthemoon
orthe
(3) vertical
wave
number.
Here•,:(,0) - 3.4641Pe
•
•(z) (cos
00
)
(0)- 1.2987P4•(0)
+0.1736P•(0)
.... ,and
o = 0.93-- cos"0
k•6 00+ 2 cosec
0 •,,0)
ßs• (2•-
z istheveaical
height
above
thelower
boundary
of
the dynamo region, namely, 90 km in our model.
In Sawada'swind fields for the altitude 90
the phase constant• lies in the range 210ø-225 ø,
2v + kz • • • 90ø)
90•. t_.•__,'. , , • , • i • , i • • •" ; : I '
'
E
.
o
5
6
9
•2
15
t8
2t
24
LOCALT l•
•i•, 2. Computer-plotted
•-t• cu•rcmsystem
(top)
andelectrostatic
fielddistribution
(bottom)
calculated
from
thethe•al tidalwindmodel
shown
byequation
1.Thecurrent intensity between two consecutivelines is 104 amp, and
the circular current flow in the northern hemisphere is
counterclockwise.The vector of the static field is plotted
in 10• steps of latitude and lengitude.
J
J • • • .i • J • • • I • J • • • • • J
uoc• TIME
Fig. 9. Average S•-type electrostatic field distribution exp•ded in low latitudes •d plotted for each 10• step of
longitude and each 3 • step of latitude (also at 1• and 2 ø
latitude) for the wind model shown by equation 2.
778
S. MATSUSHITA
and the amplitude at latitude 30 ø lies in the range
2-8 m/sec, depending on the temperature profile of the lower atmosphere.Taking into consideration Sawada'stheory, Tarpley [1969] adoptedA(z)
= 7.5 m/sec, k - 4.25ø/km, and -/ - 228 ø. This
model of the lunar tide producesthe best fit L current system,as shown in the next section.
4.
OBTAINED
DYNAMO
ELECTROSTATIC
CURRENTS
AND
sunspotperiod.The phaseconstanty in equation2
can vary by -+45ø about the value of 250 ø without
greatly changingthe current pattern.
It is clearin Figure 9 that the N-S componentof
the electrostaticfield is very small in low latitudes,
whereasthe E-W field has a magnitudeof near 1
mvolt/m and is directedeastwardduring daylight
hoursandwestwardat night.The changeof direction
occurs around the sunrise and sunset times.
FIELDS
The electricconductivitymodel mentionedin section 2 and the wind model representedby equations
1 and 2 in section3 producethe currentsystemsand
electrostaticfield distributions shown in Figure 7
and Figures 8 and 9, respectively.The generalcurrent pattern, the total current intensity,and the location of the current focus of both current systems
presentvery reasonableresults,comparingthemwith
the deducedSq current systemshown in Figure 1
and bearingin mind that the currentsystemin Figure
1 is for the active sunspotperiod (hence, large current intensity), whereasthe currentsystemsin Figures7 and 8 are for the equinoxduringthe moderate
The vertical electromagnetic
drift speedsat 400
km altitudedue to the couplingof the earth'smain
northwardmagneticfield and the computedE-W
electrostatic
field were calculatedby Tarpley[1969].
The upwardspeedat noon is about 30 m/sec in
the equatorialregion and about 20 m?secin middle
latitudes,whereasthe downwardspeedaroundmidnightis about30 m/secin the equatorialregionand
about 15 m/sec in middlelatitudes.In general,the
results agree well with the observationsof drift mo-
tions and estimations
of the staticfield made by
radio wavesat Jicamarca,Peru [Balsley,1969], and
by barium release experimentsat Thumba, India
(R. Liist, private communication).
90
15
6O
•_45'
6O
- • d•
o
24
9
t2
15
24
Fig. 10. Computer-plottedL-type current systems(top) and electrostaticfield distributions(bottom) calculatedfrom
the semidiurnallunar (2, 2) tidal wind model.The moonis over the 0- or 12-hourmeridianin the left-handdiagrams,
and over the 3- or 15-hourmeridianin the right-handdiagrams.The currentintensitybetweentwo consecutive
linesis
10a amp, and the solid and dottedcircularlines indicatecounterclockwise
and clockwisecurrents,respectively.
The
vector of the static field is plotted for each 10ø step of latitude and longitude.
DYNAMO
CURRENTS, WINDS, AND ELECTRIC FIELDS
779
30
00
06
12
18
24
oo
06
12
LOCAL
LOCAL TIME
18
:)4
TIME
Fig. 11. AverageL-typeelectrostatic
field distribution
expanded
in low latitudes
and plottedfor each10ø stepof
longitude
andeach3ø stepof latitude(alsoat 1ø and2ø latitude).(Left) Themoonis overthe0- or 12-hour
meridian'
(right) the moon, over the 3- or 15-hourmeridian.
The currentsystems
and the electrostatic
field
Acknowledgments.
I wishto thankProfessor
S. Kato,
distributions
for twolunarphases
calculated
from Bribitzer
Dr.J. D.
Tarpley,
Mrs.MaryHilty,andMrs.Harriet
in my laboratory for their assistance.
the conductivityand lunar tidal wind modelsdiscussedin the precedingsectionsare presentedin
Figure 10. The currentsystemat the top left of
Figure 10 is very similarto the yearly averageL
currentpattern in Figure 3. The electrostatic
field
REFERENCES
Balsley, B. B. (1969), Nighttime electric fields and vertical
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