parametric excitation and suppression of convective i ... · instabilities in the high latitude...
TRANSCRIPT
flD-8Ai30 652 PARAMETRIC EXCITATION AND SUPPRESSION OF CONVECTIVE i/
30 ARSHINGTON DC MJ KESKINEN ET AL. 14 JULPSA 83II E U ALRSAC A
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SgCUmAVv CLASSIFICATION Of ThIS PAGE I'llbe e ____________________
REPOR DOCUMENTATION PAGE BEFORECOPEIGFRI. REPORT HUMgER ji GOVT ACCESSION 0NO 7. RE1CIPIENT'S CATALOG NUMDER
.4 NRL Memotnduni Report 5134TITLE (and iubflhI) S. TYPE OF REPORT It PERIO0 COVERED
IPARMWM EXITATON M SPPRESIO GFInterim report on a continuing.4PRITU XIAI~NADSPRSINO NRL problem.
CONVECTIVE PLASN" NSTABILITIES IN THEs EFOMN ~.REOTM~EHIGH LATITUDE F-REGION IONOSPHERE
7. AUTNORW. S. CONTRACT OR GRANT NUMOER-76J
M.J. Keskinen, P.L Oiaturvd, and SLL Ouakow
9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASKAREA & WORK UNIT NUM9ERS
-, Naval Research Laboratory15 61153N; 6271511; RR0330244;
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Approved for public relems; distrbution unlimited.
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Is, SUIPPLEMENTARV MOTES
*Present address: Science Applications, Inc., McLean, VA 22102This research ws sponsored by the Defense Nuclear Agency under Subtask S99QMXBC,work unit 00067, work unit titde "Plasma Structure Evolution," and the Office of Naval Research.
I9. iciy WORDS (ContA. 410 feere old* it neeswm and IdsetI&by w~ lofeeS.,~)
Convectve plasma instabilities High latitude F regionhriametrlc excitation Linear theory
2111 STIACTrctmm en revee.,e &I noeeowp mnd fod#&l 1W b leck Iade)
Paaerccoupling proeseeS of a large amplitude electromagnetic pump wave with convectiveplamn fluid instabilities (R X B gradient drift and current convective) in the high latitude F regionIonospher have been studied. We find that a pump wave, with frequency near the upper hybridfroqueney and with electric field component perpendicular to the ambient magnetic field, can
% stbilize or destabilize the R X B gradfient-drift and/or current convective Instability. For parmeterstypical of the nighttim hih latitude F region Ionosphere we find stabilization or destab~la~j Witha vfrtically Incident 0 mode carrying a hoee space incident power density on the order o f,10=Wm 2
DD I ljrAN78 1473 EDITION of, I NovIt is ob"LETE .
SECURITY CLASSIFICATION Of TIS P7 9 (Wig. ne os 0evE)
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101 *!,.** -. . .. . . . . . .
CONTENTS
INTRODUCTION .............................................. 1
THEO RY .................................................... 2
SUM M ARY .................................................... 8
APPENDIX I .................................................. 10
ACKNOWLEDGMENTS .......................................... 11
REFERENCES ................................................ 12
Accession For
NTIS GRA&IDTIC TAB LIUnannounced ElJustificatioDTIC 0 10, Dsriuin
ELECTE S Availability Codes
JUL2O 193Ds Ava il a nd/orDist Special
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::..- ..... ........ ....... ...................................... .............. .. ... ..... . . . . . . . . . . . . . . . . . ...... . . *
.- ,: .. ' -, ~ e -' . .• ".- ."°. "." ".",.. , . o5..' 9 ". o *, " S" , S. %". . .• ' - " -
PARAMETRIC EXCITATION AND SUPPRESSION OF CONVEC1IVE PLASMAINSTABILITIES IN THE HIGH LATITUDE F-REGION IONOSPHERE
1. INTRODUCTION
Using a variety of experimental techniques, e.g., satellites [Dyson,
1969; Dyson et al., 1974; Sagalyn et al., 1974; Clark and Raitt, 1976;
Phelps and Sagalyn, 1976; Rodriguez et al., 1981], rockets [Olesen et al.,
1976; Ogawa et al., 1976; Kelley et al., 1980], scintillations [Aarons et
al., 1973; Fremouw et al., 1977; Erukhimov et al., 1981], and radar
backscatter [Weaver. 1965; Greenwald. 1974; Hower et al., 1966; Vickrey et
al., 1980; Hanuise et al., 1981], it is now known that the high latitude
ionosphere, from the auroral zone into the polar cap, is a highly
structured and nonequilibrium medium containing irregularities (plasma
density fluctuations and structures) with scale sizes ranging from hundreds
of kilometers to meters. Aside from being an interesting scientific
phenomenon, ionospheric irregularities are of practical interest since they
can disrupt transionospheric radio wave communications channels (see recent
review by Davies [1981] and references therein).
Several theories, e.g., particle precipitation, plasma instabilities
and processes, and neutral fluid dynamics have been proposed to account for
high latitude ionospheric irregularities (see recent review by Keskinen and
Ossakow [1983a] and references therein). Recently, considerable
quantitative progress has been made, especially in the area of ionospheric
plasma instabilities, in identifying the physical processes that can lead
to high latitude irregularities. In particular, convective plasma
instabilities such as the E x B gradient drift instability [Simon, 1963;
* Linson and Workman, 1970; Keskinen and Ossakow, 1982, 1983b] and current
convective instability [Lehnert 1958; Kadomtsev and Nedospasov, 1960;
Ossakow and Chaturvedi, 1979; Chaturvedi and Ossakow, 1979; Keskinen et
±1.p 1980; Chaturvedi and Ossakow 1981] have been invoked to explain high
latitude density irregularities in and near large scale convecting auroral
plasma enhancements [Vickrey et al., 1980].
However, it is well known [Silin, 1965; Dubois and Goldman, 1965;
Nishikawa, 1968] that under the influence of high-frequency long wavelength
elentromagnetic fields electrostatic modes of oscillation in a plasma may
become parametrically coupled and may grow exponentially in time or space
Manunufpt approved May 13, 1983.
V.2
d, .
• .. ..-: : . ........ .: . : > > .- : .....> : ...: ...-.., : --. ....: > .: . :. :. 1 ~
"44 * * , ' € " ',/ -" ' ."= ' .' " . . . . ." ' ' " i " ""' " " " " ' " " " J '
before saturating at large amplitudes. These results have been used by
many investigators [see reviews by Perkins et al., 1974, Fejer 1979 and
references therein] to study the role of parametric instabilities, induced
by high power ground based radars, in ionospheric modification. In jaddition, parametric effects have been used to study the possible
stabilization or destabilization of plasma instabilities, e.g., drift waves
[Fainbers and Shapiro, 1967; Sundaram and Kaw, 1973] by high frequency
electric fields. Lee et al. [1972] have shown that high frequency
electromagnetic waves launched from ground based heaters might lead to
stabilization or destabilization of the Farley-Buneman and gradient-drift
instabilities in the equatorial electrojet E region ionosphere. In this
paper we show that the E x B gradient drift and current convective
instabilities in the high latitude i region ionosphere can be stabilized or
destabilized by high power radio waves. In section 2 we outline the theory
of the E x B gradient drift and current convective instabilities in thepresence of a high frequency electromagnetic pump wave with frequency near
the local upper hybrid frequency. We calculate the incident power density
required to stabilize or destabilize these instabilities. Finally, in
section 3 we summarize and discuss our results.
2. THEORY
For wavelengths greater than the ion mean free path we use fluid
equations to describe the ion and electron plasma. The following geometry
is used: the y-axis is in the north-south direction, the x-axis points
west, and the z-axis is along the magnetic field. The set of equations, in
.4 the frame of reference in which the neutrals are at rest, become
BNat e + V(N & V 0
'V VP. VxB
+' ( ) e (I + '- - vV (n2 -)
. V (N V 0e (3)
at v(i_)
.I + (4)at (!') 1 m-mNi m, V -4
V.E -4we(N i N Ne) (5)
2
Here Nala - i or e) is the species density, K- + cos Wot -V is thea =
total electric field which includes the ambient electric field E.o, pump
field I cos wot, and self-consistent field V.. In addition, Re - -
mV ( - VI ), a - NTG vi is the electron-ion collision frequency,
Van is the electron or ion neutral collision frequency, c is the speed of
light, and T the species temperature. Production and loss terms have beena
neglected. Since we will be considering perturbations with scale sizes
mch less than the wavelength of the pump wave we take Ep to be spatially
uniform. Since pump frequencies of a few M z corresponds to free space~.4pump wavelengths of several hundred meters, we restrict ourselves to
maximizing irregularity scale sizes on the order of tens of meters.
In equilibrium 0 0) we have
VO o + v U 0 (6)
V x B0n -E(o-+ - ) -0 V V (7)
V xd V -+5 e ,+u (8)dt--up -ma ±p J c!a-p
where a - i,e and V o, V op refer to the drifts induced by the ambient and
pump electric fields, respectively. Linearizing equations (l)-(5) by
assuming N - N + 6n , n << N ,V - v + V, E - +E cos wot +a 00 a a ao _U -nio - - ~ -SE we obtain
a n + + V ).-Vn + 6V.VN + N.-v6 -o 9)
S3V 6V x B- + (Vo + V ).vsV - + ) -L +
m- , 6V - 6R (10)
V.8E - 4e( ti - 6ne) (11)
The equations (9)-(11) can be reduced to a single equation (dispersion
relation) for one scalar function in six different ways: one may work in
either the lab or oscillating frame; and one may eliminate the electron
density, eliminate the ion density, or (using Poisson's equation) eliminate
3d
_R -
"% -, • *.• . • - - . * . , . , . . . • . . . . . . " |
both densities in favor of the electrostatic potential. We will work in
the oscillating frame [Silin. 1965; Arnush et al., 1973; Lee et al., 1972]
to find the density perturbations, eliminate the electron density, and
finally transform back to the laboratory frame to use Poisson's equation.
The oscillating frame (denoted by tildes) is defined by
- r - R (t), with (d/dt) R (t) - V (t), 6n (r,t) - 6n ( ,t),- a - Up a a a
6v (rt) =6, v( ,t), 6E(r,t) - 6E(r ,t). Equations (9) and (10) in thea I a -
oscillating frame are identical to those in the lab frame except for the
substitutions V + V + V , 6n + 6n, v + 6v , 6E + 6E, r r-- MO -ap a a -a a01 -a
Assuming 6v, Sn , E a exp[i(k.r - mt)] with k - kx j.+ ky + kzW r + iy, kL >> 1, L N ;(VNo), one can then define susceptibilities
Xi and Xe by Xni - (-ikxi/e)6E- and Xne - (ikXe/e) E giving
wP2 i ai2L k 2 x k .VNL vn - + - + o- -(]12)"-Xi 4w " " I
i i19 k2 Vink2 N k2
and
W2 - k2 S1 k2 2 z xk.VNi 1 r e e z+ 1 e -(3)
e" -e Re [l+ ek 2 e k
2 1 + -2 Nok 2
wherew 2 = 4wNe 2/ S E x z-k + k-V + i(Dk 2 +Dk 2 ),OL 0 Q wi B-- i - -oiz I1I I ID = M=VA ( C/l) , C/ l eB/m c
D (vin/ i)(Ti/mini) + (vei/e)(C2/Ri) D1 = C2/8i n' a e 'a E x zek + key , Z - n- iW, and k2 - k2 + k2 .
We Bol -- ez e e vei' ei 'ei I X yIn deriving the above susceptibilities we have used ae/v > fi/v >> 1 (F-
eei - S i iregion approximation). In addition, we have modeled weak cold diffuse
auroral field aligned currents as a relative drift, between electrons and
ions, with velocity Vd - Vd " z- oez - Voiz)
Having found the susceptibilities in the oscillating frame we must now
transform back to the laboratory frame to use Poisson's eqn. (5). (Since
we will be considering high frequency pump waves with w > > W one can
neglect the effect of the pump on the ions.) This transformation and
resultant dispersion relation can be found in Arnush et al. [1973] and Lee
et al. [1972] and can be written:
[1 + 4 w(Xi + Xe)] - - J2(4)4w Xi(1 + 4w Xe) x+ Xe)] 1 e) 1
1 + 1 (14)
4
-. • . .-.- .. .- ... ... .
-n e coswhere Jn(¢) -C -- f e co n 8 dO is the Bessel function of integral
order n, C is defined by k.R - 4 sin (wot + B), and He -(4w Xe)-
(1 + 4w ye). In deriving (14), the approximation C << 1 has been made,
i.e., the electron excursion length is small compared to the perturbation
wavelength.
In the absence of the pump Ep M 0, for low frequency modes,
6n a 6ni. This gives
V k2 a k 2 zxkVN V k2 a k2 x k. VNo-i I z Z1W I e z -
ieg k2 Vin k2 N k2 e k2 Vei k2 N k2o 0
(15)
L Lwith solution w r iyk given by the linear growth rate [Keskinen and
Ossakow, 19821
L c A-- E xzek (16a)a r B-oJ---
- k2 z x k u-zkVNL + Vin Ve ) - e " -i xV' S kEk"VoLk - (z- in -1 eiic-
V2 "i ne i) i I io -- z kd k2 NI 10
- D k2 - D k2 (16b)
'in T vei C2
with D I - -.+--s nd D =-"i mi i ge "i in
For finite E we havep
k tO V zxkk 2 k2 zxk.VNin I + iz + - I1- e) [i Z e 1[-- -(WWi) Z; -- -L+ i VN°
"t k2 vin k2 Ne k2 Vei k2 N k200
0 °2 w2 k2 ixkVN
- - J~(~)(arweY - e. L.a 4 ... + i~
"- o k2i i i 2 Nin k 2pi ixk, o
wx. 1 e k 0k2 +i)
5
% * .' ,' . -,,. ,- e .s *'.-. . , . ..- o .",,, " ' , .-. , -*. . _--- - - -,- -.- , , - ' ... .. . ..- . . ..-.. - - . . .
x 1 + (17)
Defnin e et +R 0,~ 6 a measure of the frequency
mismatch, 60 "' ( 2 -2W2 ), we find from (17) (see Appendix 1) the00
modified growth rate
Lk 2 vivi (z xk .VN 2 V2, W2 6
Y ik + 22(!+ p e (18)- k2 n i e k2N Vei p2 2+,2 pe
10 e 0
where C2 - k2 E 2E2 + -S.(k2 E2 + k2 E2 )(X p ypy 2 Y~p X py
+ 2E E [k k coa *(I e.. k2 sinp1 py x y W2 C% 0
0
e k E [k E - k E sin + k E Cosul (19)W2 Z pz x px W K px y Py
0
Here we have taken [Lee et al., 1972]
E exp(-iwot) x +p exp(i t i*~)y + Ez t'p(- + c.c.-p -21 -21 (i 0t -21~ e 0~w_
(20)
and included E since we are considering modes for which k *0.pII
When 6 > 0, i. e. , when w 0 the pump induced term produces a
destabilizing effect whereas when 6 < 0 it produces a stabilizinginfluence. We assume that the length of the irregularities along the
magnetic field (k << k )exceeds the length of regions in which
destabilization (6 > 0) or stabilization (6 < 0) occurs. The pump induced
-'term in eq. (18) contains terms proportional to wpe, an increasing5ie
(decreasing) function of altitude on the bottomside (topside) ionosphere,e.g., w2 (z) = w2(1 + z/LN) with LN constant, in local bottomside
regions. In addition, Das and Fejer (1979] have shown that the altitude
6
.1N
dependence of the pump wave electric field near the resonance region must
also be considered. As a result, a net destabilization (stabilization)
will occur in bottomside regions if the pump electric field increases
(decreases) with height in the resonance region. For topside regions, the
opposite is true. For simplicity, in this discussion, we have neglected
the effects of spatial dispersion. Spatial dispersion will cause a
resonance at a somewhat lower height than when w° -(W2 + 12)1/2 Thepe e
physical mechanism responsible for stabilization or destabilization of
these convective instabilities can be understood as follows. A nonlinear
interaction between E x B and current convective perturbation electric
fields 6K and the pump field E gives a new field E. The combined beating
of the fields E' and E can produce a low frpquency force with component of
the form exp[i !.LLxwt + 8)], k - + k p, wL - w' + p, with phase
determined by the sign of 8, which can in turn affect 6E and modify the
dispersion relation. This force will be pondermotive if kLj > 1.55/x c
whereas the partial pressure force will dominate if k! < 1.55/Xc [Fejer,
*1979]. Here A is the electron mean free path and kL the component ofc a
parallel to the magnetic field. We take k - kxx + kzz, an ambient
electric field Eox, and N - No(y), i.e., a configuration unstable to the E
x B and current convective instabilities. The growth rate in (18) is
maximized for x a - + 80 + (ve/Wo) (w2 - 2w2 ). Inserting this-a o t(ei o pe 0
value for 6, eq. (18) can be written as
k2 e -lVin2+ 'n 'e')-' ve (kxL) [_ c kE - kzV (kLQ
k2 9 x i1 x o zd-4 x
x pe) pe D k2 - Dflk2 (21)
fe Vei o" pe I
Here the upper (plus) sign refers to the case when 6 > 0 (destabilization)
while the lower (minus) sign applies when 6 < 0 (stabilization). Eq. (21)
gives the approximate minimum required power density for destabilization or
stabilization
C32 (kQ 2u -N vei vi ek EITZ ' x -0 [(kL) j-I j 0- kzVd)-(Dlk2 + DIk2)
..
4 97
*~hi
k2 V inV ei B2(cj g2)
x (- ei 0 e (22)k 2 i Pe ck2
where we have assumed a circularly polarized 0 mode with t f - n12 in eq.
(19).IFor typical ionospheric F region parameters at diffuse auroral
latitudes in the 300-400 km altitude range, which give linear unstable8.5 6 06e- , 7pe-1 32 -1
growth ( 8.5 x 10 sec 1 Wpe 3 x 10 7sec - 1 Vei 5 x 10 2sec
Vin/ i = 10-4 , E 0 l0 mV/m,T = T1 1000K, Jn = neVd = I VA/m 2,
kL = 2 x 10, k - 30 m, kz/k ! 10 we find from (22) the
approximate power density for stabilization to be cE2 /8w t 6 x 10 2W/mpThis is an overestimate since we have not considered electric field
enhancements near the reflection point [Ginzburg 19641. For an linearly
damped mode k-1 - 5m, we find, using eq. (22) the approximate power densitynecessary for destabilization (6 > 0) to be cE2/8w 3.2 x 10-4W/m 2
pThis power density corresponds to a pump electric field amplitude of
E p= 1.5 x l0-2V/m. This electric field amplitude is comparable to that
required by the thermal coupling mechanism of Vaskov and Gurevich [1975,m1977] and Das and Fejer [1979] to destabilize field-aligned density
irregularities with scale lengths on the order of 0.5 - 5m. In reality,
both the mechanism discussed in this paper and thermal mechanisms are
probably acting simultaneously. From the coupling parameter as given by
(19) we see that there must be a component of E perpendicular to B
since k /k<< 1. At high latitudes this can be accomplished using a
vertically incident pump wave. An 0-mode pump wave is preferred since the
X-mode will be reflected at the right hand cutoff before it ever reaches
the coupling region near the local upper hybrid frequency.
3. SUMMARY
The parametric effects of a large amplitude electromagnetic pump wave
on convective plasma fluid instabilities (E x B gradient drift and current
convective) in the high latitude F region ionosphere have been studied
analytically. These convective instabilities have been invoked (Keskinen
and Ossakow- 1982] to explain naturally occurring density irregularities in
8
and near large scale convecting auroral plasma enhancements [Vickrey et
±a.., 1980]. We find that parametric coupling effects associated with a
pump wave oscillating with approximately the upper hybrid frequency can
stabilize or destabilize the E x B gradient drift and/or the current-
convective instability. For parameters typical of the nighttime high
latitude F region ionosphere, we find that these modes can be
stabilized/destabilized with a free space incident power density on the
order of 10-Wm 2 Since the pump wave should have a component of its
* electric field vector perpendicular to the magnetic field, a vertically
propagating 0 mode is suggested. In addition, we note that these power
density levels needed could be achieved using current ionospheric heaters
* located in Norway [Stubbe et al., 19811 and Alaska [Wong et al.. 19811.
In our development we have made several approximations. We have
assumed that *the pump electric fields are spatially uniform (dipole
approximation). We have ignored pump induced temperature and density
changes. The time scale for these changes, to a firit approximation, is
longer than the parametric time scales of the instabilities studied here.
- In addition, we have neglected lower altitude absorption effects. Finally,
we have assumed that the instabilities studied here are at or near marginal
stability. We reserve these topics for a future report.
9
%I
Appendix I
In solving eq. (17) for the growth rate V we must first evaluate the
quantity H ( + W ) + H (W- W) where H () = - x e (01e 0 e o e ewI[1 + 4w X(M)] and xe(w) is given by eq. (13). We have
e -2 zxk I
1 k2 e I + e oH e(w) - -- 2p. [_I z+I V
e-we ei k2 "e l+e 2 1+ 2e N k2
e o2
k2 k2 zxk VNO+ ne 1e z i e -- oe Ve k 2 k2 1+ 2 k2 ' e 1+ N k2
ww e e 0
{l-[i [-.. ii,
.2 e e
pe e
W-e fl-(w+ivi )2S-[ + weI 2 (Al)
[1 W+l*Vi l
pe
where we have neglected the small k and VN effects on the sidebandsz0
H e(U+w ) and He (w-wo). As a result we can write, with w + w+w -we
ee e e ei 1o
.-z.+% . l + "+ 2-( .+= +iv )e (W+w) [+ e + I-
pe
"w++we+Vei.2[++e e 1+ [na2-(-j++we~ +Ve )2
e+ew++wev i 1 i++ e e ei
- l+iVi (++wel
pe o
6e +- p 10
.10
. .., . -..-.. .. ..- -. • . , -W '.,:-,'..-.-,.., . ._, , -v ..'<.- .., _, ,,', .: . . . .' _ ., . ...-,-. ,Z.le tt-, r.. n t.,. , t ..
where we have assumed that w~~,w. ,v /W << 1, and 6 iw 2 ++44eo' c+o-'i 0 pe(+ V2-w2. Similarly,e e o
6i *,2-(w2 -2w 2)
As a result 0 e
Hej .0 + H-'(,..) X 6(62+62)1 (li
where 60 -(Vei/wo)(w 2 -2w2). Inserting Eq. (A0) into eq. (17) it is
straightforward to solve for I w =y as given by eq. (18).
Acknowledgments
This work was supported by the Defense Nuclear Agency and the Of fice
of Naval Research.
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14
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15t
V.
.44
p!
-4"
. 1
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