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NRL Memorandum Report 5597In

A Simulation of High Latitude F-Layer InstabilitiesT in the Presence of Magnetosphere-Ionosphere Coupling

H. G. MITCHELL, JR.,* J. A. FEDDER, M. J. KESKINEN AND S. T. AEK

0 Geophysical and Plasma Dynamics BranchPlasma Physics Division

*Scence Applications International CorporationMcLean, VA 22102

July 8, 1985

This research was partially supported by the Defense Nuclear Agency under Subtask QIEQMXBB, workunit 00005, work unit title "Plasma Structure Evolution," and by the National Aeronautics and SpaceAdministration and the Office of the Naval Research.

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NAVAL RESEARCH LABORATORYWashington, D.C.

Approved for public release; distribution unlimited.

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I I TITLE (include Security Classification)

A Simulation of High Latitude F-Layer Instabilities in the Presence of Magnetosphere-Ionosphere Coupling

2. PERSONAL AUTHOR(S)Mitchell, MG., Jr.,* Fedder, J.A., Keskinen, M4. and Zalesak. S.T.

13a. TYPE OF REPORT 13b, TIME COVERED 14 DATE OF REPORT (Year MonthDay) S. PAGE COUNTInterim FROM _ ___TO ____ 1985 July 8 30

16 SUPPLEMENTARY NOTATION*Science Applications International Corporation, McLean, VA 22102 (Continues) '

17 COSATI CODES 18 SUBJECT TERMS (Continue on reverse if necessary and identify by block number) 'FIELD IGROUP ISUB-GROUP Ionospheric structi-e, Magnetosphere-ionosphere coupling;

Hfigh latitude ionosphere, Interchange instabilities rI 4A c-.

19 ABSTRACT (Continue on reverse if necessary and identify by block number)

A magnetic-field-line-integrated model of plasma interchange instabilities is developed for the high lati-tude ionosphere including magnetospheric coupling effects. We show that the primary magnetosphere-ionosphere coupling effect is to incorporate the inertia of the magnetospheric plasma in the analysis. As aspecific example, we present the first simulation of the gx B instability in the inertial regime, i.e., yj*< cwhere vi is the ion-neutral collision frequency and tP fhe wlave frequency. We find that the inertial E x BNinstability develops in a fundamentally different manner than in the collisional ease &' k). Our'risultshow that striations produced in the inertial regime are spread and retarded by ion inertial effects, and resultin more isotropic ireuaiisthan those seen in the collisional case.

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J. D. Hub. 1 202) 767-3630 Code 4780DD FORM 1473.04 MAR 83 APR edition may be used until exhausted

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16. SUPPLEMENTARY NOTATION (Continued)

-~ This research was partially supported by the Defense Nuclear Agency under Subtask QIEQMXBB,work unit 00005, work unit title "Plasma Structure Evolution," and by the National Aeronauticsand Space Administration and the Office of Naval Research.

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CONTENTS

I. INTROD UCTION ....................................................................................................................... 1

II. M OD EL ....................................................................................................................................... 2

I R T. RESULTS .................................................................................................................................... 5

IV . CONCLUD ING REM ARKS ....................................................................................................... 6

ACKNOWLEDGMENTS ....................................................... 9

REFERENCES .................................................................................................................................... 10

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A SIMULATION OF HIGH LATITUDE F-LAYER INSTABILITIESIN THE PRESENCE OF MAGNETOSPHERE-IONOSPHERE COUPLING

I. INTRODUCTION

Recent experimental ground-based, rocket, and satellite (HILAT,

DYNAMICS EXPLORER, AUREOL-3) observations in the auroral zone and polar cap

ionosphere have indicated the existence of both large [Weber et al., 1984;

Basu et al., 1984; Bythrow et al., 1984; Cerisier et al., 1984; Vickrey et

al., 1980] and small [Hanuise et al., 1981; Baker et al., 1983] scale

density structures and irregularities. Different mechanisms, have been

proposed to account for high latitude ionospheric irregularities, e.g.,

particle precipitation, plasma instabilities, and neutral fluid turbulence

[Keskinen and Ossakow, 1983]. Considerable quantitative progress has been

made in explaining ionospheric structure using plasma interchange

instabilities, e.g., the Rayleigh-Taylor instability [Balsley et al., 1972;

Ossakow, 1981] in equatorial spread F, and the E x B and current-convective

instabilities in the high latitude ionosphere [Ossakow and Chaturvedi,

1979; Keskinen and Ossakow, 1983]. Recently, Weber et al. (1984) and

Cerisier et al. (1984) have invoked the E x B instability to explain large

scale density fluctuations in the high latitude ionosphere.

A shortcoming of most past research on the nonlinear theory of

the E x B instability as it applies to ionospheric structure is that it hasbeen restricted to the collisional (or non-inertial) regime, i.e., vi >> W

where v is the ion-neutral collision frequency and w is the wave

frequency. One exception is the recent work of Huba et al. (1985) who

studied the nonlinear evolution of interchange instabilities in both the

inertial and non-inertial regimes. However, their work was limited to

short wavelength turbulence, i.e., kL >> 1 where k is the wavenumber and Lis the density gradient scale length, which is not applicable to large

scale ionospheric structures.

In this letter, we present the first simulation of inertial high

latitude ionospheric interchange instabilities (e.g., the E x B

instability) with inclusion of magnetospheric coupling effects. The basic

conclusions of this study are (1) magnetospheric coupling effects reduce

the growth rate of the E x B instability, (2) striations produced by the

inertial E x B instability develop in a different manner than in the non-

Manuscript approved April 17, 1985.I

inertial (vi >> w) regime, (3) in configuration space, the striations in

the inertial regime are more isotropic and spread out resulting in

irregularities oriented perpendicular to those produced in the non-inertial

case.

I. MODEL

The physical configuration and assumptions of our model are described

as follows. We only consider structure in the plane transverse to the

ambient magnetic field, i.e., the xy plane. The F-layer is initially

characterized by a 6 to 1 density enhancement with a Gaussian profile of

scale size 12 km in the x-direction and uniform in the y-direction, a

uniform magnetic field in the z-direction (Bz = 0.5 G), and a background

electric field in the y-direction (Ey . .025 V/m). The entire enhance-

ment E x Bdrifts in the x-direction at a velocity vx - 0.5 km/sec. A

uniform horizontal magnetosphere is assumed above the F-layer linked by the

vertical magnetic field lines. The back edge of the F-layer enhancement,

relative to the drift, is unstable to the E x B instability, which drives

ion Pedersen currents in the F-layer and ion polarization drift currents in

the magnetosphere due to the perpendicular electric field mapping along the

geomagnetic field. These currents close along the magnetic field via

parallel electron currents. Assuming that all ion drifts associated with

the perpendicular currents are negligible compared to the E x B drift and

that - -V_$, the equations describing this system are

an + Vl • nv -0 (1)

at -iLcV±.

v -v - - -- z (2)-eL -ij B

cnev

IF"- (= )Vo- - a V.0 (3)

IM- 4j v2 at "LV

2

". %

where n is the ion (and electron) density, Ye(i)± is the perpendicular

electron (ion) velocity, JF and JM.L are the F-layer Pedersen 4and the

magnetospheric polarization drift current densities, respectively, ap is

the F-layer Pedersen conductivity, VA- B/(41nmi) 1/2 is the Alfven velocity,

and vi and Qi are the ion-neutral collision frequency and ion gyrofre-

quency, respectively. Using (2)-(4) in (5) yields the potential equation,

':: [ cV±€

0 • Y + CM [ - Z) V] jVLO (6)p M at B

where the field-line integrated F-layer Pedersen conductivity is

.p f Fdz up$ (7)

and the field-line integrated magnetospheric inertial capacitance is

CM I dz (c2/v2). (8)

M w":"" M

Since the magnetospheric layer is uniform and the ion flow given by (2) is

incompressible, the magnetosphere remains uniform and the continuity

* equation for this layer may be neglected. The F-layer continuity equation

for n may be written as a continuity equation for E

Zp + V* (ZpV .) , 0. (9)

Therefore, the system is completely described by (2), (6) and (9) in the

variables E and 0,. with CM a constant capacitance describing the magnitudep

of magnetosphere-ionosphere coupling.

The numerical methods used to simulate the model equations are

described in Zalesak et al. [1982]. The continuity equation (9) is solved

numerically using the multi-dimensional flux-corrected techniques of

Zalesak [1979], while the potential equation (6) is solved with the

" incomplete Cholesky conjugate gradient algorithm of Hain [1980]. The

simulations are performed on an 100 x 80 cell grid (x,y) with a cell size

of 1.0 km x .25 km which is drifting with the enhancement at the Ey x B

velocity. Periodic boundary conditions are assumed in the y-direction, and

the grid is initialized with a random 1% density fluctuation.

* 3

If Ep has scale length L-1 = (1/Ep)3Ep/ax, the non-inertial (CM = 0)

growth rate for a wave with wave vector k parallel to y is Y 0 cE y/BL in

the regime kL >> 1. For the parameters of our simulation, the maximum (non-

inertial) growth rate is YO - 0.05 sec The e-folding distance

of E_ parallel to B for this wave is about X| (a|/aj)I/ 2 k - [Volk and

Haerendel, 1971], implying that a wave with kl - = 1 km has an e-folding

distance of 103 km parallel to the field and that E L maps well up into the

magnetosphere where the e-folding distance is much greater due to the rapid

decrease in a . The Alfven speed is VA - 103 km/sec so that electric

fields of a wave with a growth time of 20 sec map upwards on the order of

104 km into the magnetosphere, and CM has a value of roughly 1013 cm

(or - 10 farad).

The effect of ion inertia on the E x B instability has previously been

studied by Ossakow et al. [1978] in the linear regime. Although their

results were for Pedersen and polarization drifts at the same altitude, the

linear growth rates are effectively the same for our model equations. A

non-zero inertia implies the existence of an inertial relaxation rate,

"Yi Zp/CM, The growth rate in the presence of inertia for the short

wavelength approximation has two regions of interest, the non-inertial

regime

Y YO for 4YO << Yi (10)

and the inertial regime

Y (YOY )112 for 4IY >> Y (11)010 i* (1

Assuming a E for the F-layer of 8 x 1010 cm/sec (-0.1 mho), a typicalJ. p

value of Y for the simulation is .008 sec -1, which is in the inertial

regime and which reduces the growth rate of the instability from .05 se -1

to .02 sec 1. For our simulation, two cases were run: a non-inertial case

for which Y 1.00 sec - , and an inertial case for which 'Y 0.01 sec 1 .

4r .. *.,."**

III. RESULTS

The results of the two simulations are shown in Figures 1 and 2. The

four panels in each simulation show approximately equal times relative to

the linear growth time of the instability. Figure 1 shows the results for

the non-inertial x 5 instability, while Figure 2 shows the results for

the inertial case. It is clear that the results of the two cases are very

different at later times.

The behavior of the plasma in Figure 1 is typical of that observed inprevious E x § instability simulations [Keskinen and Ossakow, 1982]. In

panel 2, at 104 seconds, we see that early in the nonlinear stage a set of

"fingers" has clearly formed. The high density fingers grow outward into

the low density plasma while the low density fingers penetrate into the

high density cloud. Subsequent nonlinear evolution involves the continued

elongation of these fingers with very little apparent change in the size of

the structures perpendicular to their long dimension as seen in panels 3

and 4. The original density enhancement has effectively been sliced into a

group of sheets parallel to the initial density gradient.

The behavior of plasma and structure formation in Figure 2, the

inertial case, is very different. During the time period between panel 1

and panel 2, before 300 seconds, the growth of the instability closely

resembles that in Figure 1. There is nonlinear development of long narrow

high and low density fingers which move in opposite directions. However,

after 300 seconds, the behavior changes radically. In panels 3 and 4, we

see that the fingers form mushroom-like heads and tend to thicken. No

longer are there long thin interpenetrating fingers, rather they are fat

interpenetrating blobs. Any narrow fingers which begin to form quickly go

to a mushroom shape and then spread out. In a number of simulations we

have noted a tendency for the structure in the y direction to undergo an

inverse cascade to the longest mode which will fit in the system. This

feature can clearly be seen in panel 4, where the structured state

throughout most of the simulation region shows two blobs; one of high

density, the other of low density.

The non-inertial simulation, shown in Figure 1, is characterized by

striations with a large value of ky, which grow in the x-direction without

hindrance, completely destroying the initial orientation of the density

-. .--

. ... * X" :,_ .- _ . ,f.%. . - . .. .- - - ,- - -. .. . . . . - - . , . . . - - . ,. • ,

enhancement in the y-direction. The inertial simulation, shown in Figure

2, is characterized initially by striations with a large value of ky, which

are hindered in their growth in the x-direction. The plasma at the leading

edge of the striation finger is swept to either side and around the

striation forming the characteristic mushroom shape. Further evolution

involves an inverse cascade in k to the minimum value allowed on they

numerical grid while simultaneously, the typical value of kx increases.

Consequently, individual enhancements tend to an orientation similar to the

original x-directed orientation. Furthermore, the individual enhancements

appear to be stabilized to further B x 5 structuring owing to velocity

shear along their apparently unstable faces (Perkins and Doles, 1975; Huba

et al., 1983).

Interestingly, Rino et al. (1979), Livingston et al. (1982), and Rino

and Vickrey (1982) have reported sheet-like structures in the night side

auroral region which are aligned perpendicular to the large scale F region

ionospheric density gradient. This alignment perpendicular to the density

gradient is not easily explained by the traditional instability theory.

However, the alignment is similar to the final alignment observed in the

inertial simulations.

IV. CONCLUDING REMARKS

Several conclusions can be drawn from our simulations. First,

-*.. instability-generated electric fields in the high-latitude F-layer may map

well up into the magnetosphere, resulting in a much reduced linear growth

rate due to the effectively increased ion inertia. Second, the nonlinear

development of the instability is fundamentally different in the presence

of this coupling; the striations produced are spread and retarded by ion-

V'. inertial effects resulting in more isotropic irregularities than in the--°

non-inertial case. The inertial effects may even tend to stabilize the

final nonlinear state by producing a velocity shear across normally

unstable gradients. The simulation results demonstrate some interesting

features which may have been observed in the high latitude nighttime

ionosphere.

6

W. .

'.L .

-. . - . - ~,- -- -- - -

:"'.0 s e c l

y- 1.00 sec - 0 e

.E 10 4 sect

ExB 10 km

201 sec

300 sec

Fig. 1. A plot of density for four times for the case of Y 1 .00

sec- 1(the non-inertial ease). The shaded region represents those

areas whose density is greater than 2.5 times the background

density. The simulation grid is periodic in the direction of E

and is moving with the E x B velocity.

7

4i!i

-1 0 sec= 0.01 sec

E 302 sec

ExB 10 Ian

601 sec

899 sec!

Fig. 2. A plot of density for four times for the case of Y.= 0.01 sec

(the inertial case). The shaded region and the simulation grid

are the same as in Fig. 1. The times shown in the two figures are

roughly equal multiples of the linear growth time for the

instability in the two cases.

8

Z,

Acknowledgments

We thank Dr. J.D. Huba for helpful discussions and a critical reading

of the manuscript. This research was supported by the Defense Nuclear

Agency, the National Aeronautics and Space Administration, and the Office

of Naval Research.

:i% %

References

Baker, K.B., R.A. Greenwald, and R.T. Tsunoda, Very high latitude F-region

irregularities observed by HF-radar backscatter, Geophs. Res. Lett.,,

10, 904, 1983.

Balsley, B.B., G. Haerendel, and R.A. Greenwald, Equatorial spread F:

recent observations and a new intepretation, J. Geophys. Res., 77,

5625, 1972.

Basu, S., S. Basu, E. MacKenzie, W.R. Coley, W.B. Hanson, and C.S. Lin, F

-. region electron density irregularity spectra near auroral acceleration

and shear regions, J. Geophys. Res., 89, 5554, 1984.

Bythrow, P.F., T.A. Potemra, W.B. Hanson, L.J. Zanetti, C.-I. Meng, R.E.

Huffman, F.J. Rich, and D.A. Hardy, Earthward directed high-density

Birkeland currents observed by HILAT, J. Geophys. Res., 89, 9114,

1984.

Cerisier, J.C., J.J. Berthelier, and C. Beghin, Unstable density gradients

in the high latitude ionosphere, Radio Sci., 1985, in press.

Hain, K., A non-recursive incomplete Cholesky decomposition method for the

solution of linear equations with a sparse matrix, NRL Memorandum

Report 4264, Naval Research Laboratory, Washington, D.C. 1980. ADA087005

Hanuise, C., J.P. Villain, and M. Crochet, Spectral studies of F regionirregularities in the auroral zone, Geophys. Res. Lett., 8, 1083,

1981.

Huba, J.D., S.L. Ossakow, P. Satyanarayana, and P.N. Guzdar, Linear theory

of the E x B instability with an inhomogeneous electric field, J.

Geophys. Res., 88, 425, 1983.

Huba, J.D., A.B. Hassam, I.B. Schwartz, and M.J. Keskinen, Ionospheric

turbulence: Interchange instabilities and chaotic fluid behavior,

Geophys. Res. Lett., 12, 65, 1985.

Keskinen, M.J. and S.L. Ossakow, Nonlinear evolution of plasma enhancements

in the auroral ionosphere, 1, Long wavelength irregularities, J.

GeoPhys. Res., 87, 144, 1982.

Keskinen, M.J. and S.L. Ossakow, Theories of high-latitude Ionospheric

irregularities: a review, Radio Sci., 18, 1077, 1983.

10

4 4

Livingston, R.C., C.L. Rino, J. Owen, and R.T. Tsunoda, The anisotropy of

high-latitude nighttime F region irregularities, J. Geophys. Res., 87,

10519, 1982.

Ossakow, S.L., Spread-F theories - a review, J. Atm. Terr. Phys., 43, 437,

1981.

Ossakow, S.L. and P.K. Chaturvedi, Current convective instability in the

diffuse aurora, Geophys. Res. Lett., 6, 332, 1979.

Ossakow, S.L., P.K. Chaturvedi, and J.B. Workman, High-altitude limit of

the gradient drift instability, J. Geophys. Res., 83, 2691, 1978.

Perkins, F.W. and J.H. Doles, III, Velocity shear and the E x B

instability, J. Geophys. Res., 80, 211, 1975.

Rino, C.L., R.C. Livingston, and S.J. Matthews, Evidence for sheet-like

auroral ionospheric irregularities, Geophys. Res. Lett., 5, 1038, 1978

Rino, C.L and J.F. Vickrey, Recent results in auroral-zone scintillation

studies, J. Atmos. Terr. Phys.," 44 875, 1982.

Vickrey, J.F., C.L. Rino, and T.A. Potemra, Chatanika/Triad observations of

unstable ionization enhancements in the auroral F-region, Geophys. Res.

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Volk, H.J. and G. Haerendel, Striations in ionospheric ion clouds, 1, J.

Geophys. Res., 76, 4541, 1971.

Weber, E.J., J. Buchau, J.G. Moore, J.R. Sharber, R.C. Livingston, J.D.

Winningham, and B.W. Reinisch, F layer ionization patches in the polar

cap, J. Geophys. Res., 89, 1683, 1984.

Zalesak, S.T., Fully multidimensional flux-corrected transport algorithms

for fluids, J. Comp. Phys., 31, 335, 1979.

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conductivity, J. Geophys. Res., 87, 151, 1982.

N,

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