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AD-A0867998 NAVAL RESEARCH LAB WASHINGTON DlC F/G 4/1NONLINEAR EVOLUTION OF DIFFUSE AMRORAL F REGION IONOSPHERIC I RR--EflC (U)JUL 80 M J KESKINEN, S L OSSAKOW
UNCLASSIFIED NRL- R-42 5 B I-AD-EO O1NL
HEFT
30
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MfrROCOPY RI SOLUh (4 1W? (lARINA I (NA( 0(rfffAl il N ))t A
ECUflITYG IFICATION Of THIS PAGE (When Dais EnatereD)_________________
READ INITRUCTMOSrgjREPORT DOCUMENTATION PAGE BEFORE COMPLETDG FORM1. ma2. GOVT ACCESSION NO: T. RECIPIENT'S CATALOG NUMBER
4. TITL . TYPE OF REPORT & IO moCOVEREDInterim report on a
NONLNEA ZVOUTIN OFPIFUSE UROPAL contmumg NRL problem.SREGION IONOSPHERIC IRREGULARIffIES.- S. PERFORMING ORG. REPORT NUMBER
7. AUHOW~o6. CONTRACT OR GRANT NUNEER(q)
M.J. eeinen ' S1Lsao~~BE OWoal
9. -PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASKAREA A WORK UN IT NUMBERS
Naval Research Laboratory 61153N; RR0330244;Washington, D.C. 20375 67-0803-00; and 62704H;
67-0891-00I1. CONTROLLING OFFICE NAME AND ADDRESS
Defense Nuclear Agency Office of Naval Res i +'-.P GEWashington, D.C. 20305 Arlington, VA 22217 28
14. MONITORING AGENCY N!AME ALI .e~w CfltoIIu fIci) IS. SECURITY CLASS. (of this riport)
',Y~/~L-'1 K ~iA /'UNCLASSIFIED- f. .~/ 15a, DECLASSIFICATION/DOWNGRADING
III. SUPPLEMENTARY NOTES
*Present address: Berkeley Research Associates, Arlington, VA 22209This research was sponsored partially by the Defense Nuclear Agency under subtaskS99QAXHCO66, work unit title Magnetospheric and High Latitude Implications and workunit 13, and partially by the Offic of NalRearh
19. KEY WORDS (Continue on, reverse ide it necosimy and Ideattly' by block nubir)
Diffuse auroral F regionIrregularitiesCurrent convective instabilityNonlinear evolutionComputer simulation
20. ABSTRACT (Cmntinue an rev.es id lit neccoiomy and Identfy by block nuinber.)
-Numerical simulations of the nonlinear evolution of the current convectiveinstability in the diffuse aurora have been performed for conditions typical of thenighttime high latitude F region. Our results show nearly field aligned plasmairregularities developing in regions of well-defined northward gradients of total electroncontent (TEC) and field-aligned diffuse auroral particle precipitation. In addition, wefind equatorward movement of plasma enhancements and northward (poleward)
(Continues)
DD I A 1 1473 EDITION OF I NOV 65 IS OBSOLETES/N 002-LF.014-601 iSECURITY CLASSIFICATION OF THIS PAGE (Whon Data 54044
SECURITY CLASSIFICATION Of THIS PAGE (M~enl Date En'.'.0o
20. Abstzmct (Continued)
movement of plasma depletions (holes). Furthermore, one-dimensional spatial power spectraof the irregularities in both the north-south and east-west directions are well describedby inverse power laws.
ISECURITY CLASSIFICATION OPVHSS PAO9(fP DOM 41Mw
CONTENTS
1. INTRODUCTION.......................... .................... 1
II. MODEL................................ 9.....................2
III. RESULTS............................ o.......................4
IV. ACKNOWLEDGEMENTS..........................................7
V. REFERENCES.................................................8
VI. FIGURE CAPTIONS............................... o..........10
ACESSION for
INTIS White SectionDOC Buff secion 03UNAOUKO) C
jUSIFICATION
Dist. AVklL and Or E
NONLINEAR EVOLUTION OF DIFFUSEAURORAL F REGION IONOSPHERIC IRREGULARITIES
Introduction
Recently, new information has been acquired concerning the
phenomenology and structure of high latitude auroral F region iono-
spheric irregularities. After analyzing data from the Defense Nuclear
Agency's Wideband satellite, Rino and Owen [1980a] and Rino and
Matthews [1980b] have given additional evidence that the irregularities
causing high latitude scintillation enhancements observed in regions
with well-defined north-south TEC gradients and field-aligned diffuse
auroral particle precipitation are L-shell aligned localized sheetlike
structures [Fremouw et al., 1977; Rino et al., 1978) for wavelengths
X 1-10 km [C. L. Rino, private communication, 1980, less than the
ambient TEC gradient scale length. In addition, an equatorward moving
dynamic slab-like scintillation source region is observed. Furthermore,
depleted plasma zones (holes) have been recorded [Rich et al., 1980;
M. C. Kelley, private communication, 1980] in regions of strong field-
aligned currents and convection electric fields. Finally, using
simultaneous rocket probe, scintillation and incoherent scatter, Kelley
et al. £19803 have shown that the spatial power spectra of the irregu-
larities in the auroral F region can be described by inverse power laws
with spectral indices between 1.5 and 2.5.
The linear theory of the current convective instability in the
diffuse aurora has been proposed [Ossakow and Chaturvedi. 19793 to
account directly for large scale size irregularities in the diffuse
auroral F region. Chaturvedi and Ossakow £1979) have discussed the non-
linear stabilization of the current convective instability by isolating
Manucrpt submtted February 6, 1980.
I1
two Fourier components of plasma density and computing their self-
consistent evolution. Although these theoretical studies can show under
what conditions density fluctuations will grow and can give reasonable
growth rates, these studies are only valid locally and cannot determine
gross nonlinear effects such as relative movement of enhancements and
depletions and irregularity power spectra over a wide range of modes.
Numerical simulation studies are much richer in that many modes (waves)
can be kept with the result that nonlinear effects, both local and
global, can be delineated.
In this letter we reproduce several of the aforementioned
observations by performing the first numerical simulation of the non-
linear evolution of the current convective instability in the diffuse
aurora.
Model
We study the nonlinear evolution of large scale size plasma
density irregularities in the diffuse auroral F region by solving the
equations modelling the current convective instability [Ossakow and
Chaturvedi, 1979] in the following geometry: the total electron content
gradient is in the northward direction (y), the ambient electric field
E is westward (x), and the magnetic field is directed downward (z).
The basic equations can then be written:
;3n x V Y,*Vn - V n ( i V Y + i -) 0 ()at BB C1 I Vj
2LY' +. (L
where n(x,y,z,t) is the ion density, Vy 1 E with E(xyzt) the
total electric field, v is the ion-neutral collision frequency, V isi e
the electron-ion collision frequency, Q(Ge) is the ion (electron)
gyrofrequency, c is the speed of light, B is the ambient magnetic
field, - V - (Veo-Vioz) is the relative velocity of the electrons
and ions along the magnetic field, and 1. denotes perpendicular to the
magnetic field. Equations (1) and (2) are simply a restatement of the
ion-continuity equation written in a reference frame with velocity
V - E /B(j - v /aO ,) and quasi-neutrality V'J - 0, respectively. We
have neglected inertial and press.re effects since we will be interested
in modelling low-frequency long wavelength (greater than several km)
fluctuations. In addition, we have neglected the electron-neutral col-
lision frequency v compared with v and taken v /0 « 1 for c - i,een e O0
(F region approximation). Note that if one neglects the z-dependence
of density and potential (b/6z - 0) equations (1) and (2) are similar
to the equations modelling the long-wavelength collisional Rayleigh-
Taylor instability (without recombination damping) in the equatorial F
region ionosphere [Ossakow and Chaturvedi, 1978] and ExB gradient-drift
instability in F region plasma clouds [Ossakow and Chaturvedi, 1978).
Linearizing equations (1) and (2), taking n - n0 (y) + n! with
n,, , - exp[i(k x + kiz) + Ykt)] we find the growth rate Yk EOssakow
and Chaturvedi, 1979]
n y [Eo V- V
o3
(3)
We note that the linear growth rate Yk from (3) is independent of 1
but depends only on the angle made by k and B through the factor k[lIk x.
For total electron content plasma density increasing to the north
(an o/y > 0), unstable growth can be achieved if the field-aligned cur-
rent velocity Vd is such that Vd(kii/kx) > 0 and IVdkll > (kxcEo/B)
(Vi/ni). In the altitude range 350-400 km for typical ambient values
of E 0 -0 m/m, v/00L 10- , Vd = 500 msec, Lm n0 (n o/6y) - 50 km,
the maximum growth rate is Ymax 2.7 x l0- 3sec- 1 which occurs for
ki[/k x - 9.4 x 10 - 5 [Ossakow and Chaturvedi, 1979].
Results
In the following simulations we take advantage of the fact that the
fastest growing, most dangerous modes from linear theory are almost
field-aligned (kii/kI << 1). These modes are of most interest to us and,
as a result, we solve equations (1) and (2) in a plane containing these
modes which is nearly perpendicular to the magnetic field while fixing
the value of kii/k,. A similar approach has been adopted in numerical
studies of drift-wave [Lee and Okuda, 1976] and trapped-particle
[Matsuda and Okuda, 1976] instabilities in laboratory plasmas.
The simulation plane which is essentially horizontal at an
altitude of 350 km with a north-south extent of 410 km and an east-west
extent of 160 km is identical to the x'y' plane as shown in Figure 1.
The system of equations (1) and (2) was transformed to the x y z
coordinate system by a simple rotation about the y-axis by the angle
4 kLL/k x << 1. By solving the equations (1) and (2) in the x y' z
system a finite but small kii is effectively introduced into the model.
4
After neglecting the z'-dependence of all quantities, equations (1) and
(2) were then cast into dimensionless form and initialized with the pro-
file of the following type no(Y' )/N O M (l-A(l-tanh(y'-y 0 )/L (l + E(X' ,y'))
where N y0, and L are constant with A - 5/11. This gives a total den-
sity maximum to minimum ratio of approximately 10. The function
c(x',y') has a root-mean-square value of 3% and is generated from a ran-
domly phased Gaussian power spectrum. The computational mesh consisted
of 258 grid points in the y'-direction (north-south) with 102 points in
the x-direction (east-west). Periodic boundary conditions were imposed in
the xtdirection with Neumann (o/by'= 0) boundary conditions in the y"-
direction. We drop the prime notation for clarity.
Figures 2-5 show contour plots of n(x,y)/N at t 0, 900, 1400,
1900 sec. The following set of parameters were used: L = 50 km,
Yo 200 km, E0 = 10 mV/m, vi/02 = 10 - , e/0e = 10- . The value of
0 f 9.4 x 10- 5 is held fixed and is chosen so as to maximize the linear
growth rate (3). Fig. 2 shows the initial configuration which includes
the small random perturbation. Fig. 3 at t = 900 sec(Ykt 5) illus-
trates the linear stages of the simulation and shows unstable growth in
the region where bn /6y > 0 as predicted by linear theory. Fig. 40
exemplifies the early nonlinear regime where lower density plasma
(depletions) are moving in the positive y-direction (poleward) while
higher density plasma (enhancements) are convecting in the negative y-
direction (equatorward). The approximate velocities of the depletions
and enhancements are 270 m/sec and 30 m/sec, respectively. Finally,
well-developed steepened enhancements and depletions (of over 90%) are
seen in Fig. 5 at t = 1900 sec. This late-time configuration is
5
00
L
reminiscent of the motion of depletions (bubbles) moving vertically in
the equatorial F region [Scannapieco and Ossakow, 1976a3 and enhance-
ments (striations) in ionospheric F region plasma clouds [Scannapieco
and Ossakow, 1976b]. The length scales in Figures 2-5 are distorted with
the depletions and enhancements longer and narrower than is depicted.
Similar linear and nonlinear development is observed when L - 10 km,
but on a faster time scale.
Figures 6a-b give sample one-dimensional spatial power spectra at
t = 1900 sec both in the x-direction (east-west) and in the y-
direction (north-south). These spectra are obtained by first Fourier
analyzing 6n(x,y)/N and integrating over the direction in k-space cor-
responding to the north-south and east-west directions, respectively.
For both cases, these power spectra are well-fitted with an inverse
power law. Similar power law dependences were seen when L = 10 km.
The following physical picture of the evolution of current
convective instability in the diffuse aurora is supported by these
simulations. In the evening a westward electric field E begins to
form which convects plasma in the auroral region equatorward. In
regions where the northward gradient in total electron content becomes
well-defined nearly field-aligned fluctuations (kji/k << 1) will grow
unstable in regions where the field-aligned current velocities Vd9
ddi caused by precipitat~ng particles, are such that Vd(klL/k±) > 0 and
IVdkLiI> (k.cEo/B)(vl/RL). In the plane almost perpendicular to the
magnetic field by an angle e = k1l/k1 plasma depletions and enhancements
will move northward and southward, respectively, while steepening in
the process.
6
More detailed studies of the current-convective instability in the
auroral ionosphere are planned for a future report.
Acknowledgements
We wish to thank C. L. Rino of SRI International and M. C. Kelley
of Cornell University for useful discussions. This work was supported
by the Defense Nuclear Agency and the Office of Naval Research.
NOW"
References
Chaturvedi, P. K. and S. L. Ossakow, Nonlinear stabilization of the
current convective instability in the diffuse aurora, Geophys. Res.
Lett., 6, 957, 1979.
Fremouw, E. J., C. L. Rino, R. C. Livingston, and M. C. Cousins, A per-
sistent subauroral scintillation enhancement observed in Alaska,
Geophys. Res. Lett., 4, 539, 1977.
Kelley, M. C., K. D. Baker, J. C. Ulwick, C. L. Rino, and M. J. Baron,
Simultaneous rocket probe, scintillation and incoherent scatter
radar observations of irregularities in the auroral zone iono-
sphere, Radio Sci. (in press), 1980.
Lee, W. W. and H. Okuda, Anomalous transport and stabilization of col-
lisionless drift-wave instabilities, Phys. Rev. Lett., 36, 870,
1976.
Matsuda, Y. and H. Okuda, Simulation of dissipative trapped-electron
instability in linear geometry, Phys. Rev. Lett., 36, 474, 1976.
Ossakow, S. L. and P. K. Chaturvedi, Morphological studies of rising
equatorial spread F bubbles, J. Geophys. Res., 83, 2085, 1978.
Ossakow, S. L. and P. K. Chaturvedi, Current convective instability
in the diffuse aurora, Geophys. Res. Lett., 6, 332, 1979.
Rich, F. J., W. J. Burke, M. C. Kelley, M. Smiddy, Observations of field
aligned currents in association with strong convection electric
fields at sub-auroral latitudes, J. Geophys. Res. (in press), 1980.
Rino, C. L., R. C. Livingston, and S. J. Matthews, Evidence for
sheet-like auroral ionospheric irregularities, Geophys. Res. Lett.
5, 1039, 1978.
8
p.
:' ":.. .. .... .. i - :° " .. . . .I :-4- . ..-
Rino, C. L. and J. Owen, The structure of localized nighttime auroral-
zone scintillation enhancements, J. Geophys. Res. (in press), 1980a.
Rino, C. L. and S. J. Matthews, On the morphology of auroral-zone
radiowave scintillation, J. Geophys. Res. (communicated), 1980b.
Scannapieco, A. J. and S. L. Ossakow, Nonlinear equatorial spread F,
Geophys. Res. Lett., 3, 451, 1976a.
Scannapieco, A. J., S. L. Ossakow, S. R. Goldman, and J. M. Pierre,
Plasma cloud late time striation spectra, J. Geophys. Res., 81,
6037, 1976b.
9
AA
N.
zz
, e
VnO
y, y' (north)
(west) k E
x kz-k 11
Fig. 1 - Coordinate system used in simulations. The x'y' plane is thesimulation plane. The x',x,z',z axes are coplanar.
10
0 SEC410
--
-
Cr ---- - - - -- - - --------- ------------ --- -
Ln
ig
"~~~ ~ I KMIT - E S
] IFig. 2 - Real space isodensity contour plots of n(xyv)/n o for L fi 50 km
at t = 0 sec. Eight contours are plotted in equal increments from 1 to 10with the lower (higher) density contours denoted by solid (dashed) lines.The magnetic field B is directed into the page with the observer lookingdown the magnetic field lines toward the earth.
11
vj
900 SEC
4 10
- -- - - - - - - - - - - - - - - - --- - - - -
In
X 1K M I6WEST -EAST
Fig. 3 - Same as Fig. 2 but at t = 900 sec. Note wavelike configurationof solid contours in linearly unstable region (3n 0 /3y > 0).
12
14 00 SEC
410
X KM
WES -~ -s5
Fig. 4 -Same as Fig. 2 but at t - 1400 sec. Note movement of low-) densities (solid lines) into regions of higher relative densities (dashed lines).
j 13
19 00 SEC4 10
CMI
LnI
I-.X fKM
WES - EAS
Fi.5-Sm sFg u tt- 90sc oesuhadmvmn
I-A
10 -1
t :1900 sec
10-2_
kx-2.010 -3-.
0"
0 •0
io
10-6 -g
10-60
2 4 10 20 40 k/~II I If160 80 40 16 8 4 X (km)
(a)
10-2 t 1900 Sec
10-4-
0-5
lO - _o *
10-6-
2 4 10 2040 100 kx/kFyI I I I I I
410 205 102.5 41 20.5 10.25 4.1 k)(b)
Fig. 6 - Log-log plots of one dimensional (a) x power spectra P(kx) anld(b) y power spectra P(ky) for L -=50 km at A 1900 sec. P(kx) andP(k )are obtained by averaging I8n(k 1,k~)n over ky and kx, respec-I;Z .ie In (a) kp1 2ir/160 km*1 while in (b) kpyin 2*/410 km1l. Thedots represent the numerical simulation results while the solid line isobtained from a least squares fit.
15
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