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

1.25III~ 1. 6

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;

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Defense Nuclear Agency Office of Naval Res i +'-.P GEWashington, D.C. 20305 Arlington, VA 22217 28

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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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