Copyright by the American Geophysical Union. Scales, W. A., P. A. Bernhardt, and G. Ganguli (1994), Early time evolution of
negative ion clouds and electron density depletions produced during electron attachment chemical release experiments, J.
Geophys. Res., 99(A1), 373–381, doi:10.1029/93JA02752.
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 99, NO. A1, PAGES 373-381, JANUARY 1, 1994
Early time evolutionof negativeion cloudsand electron density
depletionsproducedduring electron attachmentchemical
releaseexperiments
W. A. Scales
Bradley Department of Electrical Engineering,Virginia Tech, Blacksburg,Virginia
P. A. Bernhardt and G. Ganguli
SpacePlasma Branch, Plasma PhysicsDivision, Naval ResearchLaboratory, Washington D.C.
Abstract. Two-dimensionalelectrostatic particle-in-cell simulations are used
to study the early time evolution of electron depletionsand negativeion clouds
producedduring electron attachment chemicalreleasesin the ionosphere. The
simulationmodel considersthe evolutionin the plane perpendicularto the magnetic
field •nd • three-speciespl•sm• that containselectrons,positive ions, •nd also
heavy negativeions that result as a by-productof the electronattachment reaction.
The earlytime evolution(lessthan the negativeion cyclotronperiod)of the system
showsthat a negative chargesurplusinitially developsoutsideof the depletion
boundary as the heavy negative ions move acrossthe boundary. The electrons
are initially restricted from movinginto the depletiondue to the magneticfield.
An inhomogenouselectric field developsacrossthe boundary layer due to this
chargeseparation.A highly shearedelectronflow velocitydevelopsin the depletion
boundary due to E x B and VN x B drifts that result from electron density
gradientsand this inhomogenous
electricfield. Structureeventuallydevelopsin the
depletionboundarylayer due to low-frequencyelectrostaticwavesthat havegrowth
times shorter than the negativeion cyclotronperiod. It is proposedthat these
wavesare most likely producedby the electron-ionhybrid instability that results
from sufficientlylarge shearsin the electronflow velocity.
1. Introduction
in the ionosphericplasma density is created. Calcula-
A problem that is similar in many respectsto the
release of neutral chemicals that photoionize in the
Earth's ionosphere,such as barium, cesium, sodium,
europium, and lithium, is the releaseof electronattachment chemicals. Initially, when releasedinto the Fregion, these chemicalsattach electronsand produce
electrondensity depletions. Heavy negativeion clouds
are created as a by-product of the electron attachment
reaction. At later times, the backgroundpositive ion
electron attachment chemicalsproducefaster, larger,
and longerlasting perturbationsto the ionospherethan
typical photoionization chemicals. This is becauseof
the larger reaction rate constantsof the electron attachmentmaterials. The largestelectrondensitygradients, ion fluxes, and polarization electric fields should
be produced by electron attachment chemical releases.
Important usesfor the electronattachmentreleasemay
tions by Bernhardtet al. [1991]havepredictedthat
density(composed
primarilyof O+ at the altitudesof be the perturbationof auroralcurrentsystems[Berninterest)will be reducedby mutualneutralizationwith hardt et al., 1991],focusingof high-powerradio waves
the heavy negative ions. The mutual neutralization re- [Bernhardtand Duncan,1987a],and the studyof the
actionprovidesa usefulground-basedoptical diagnostic physicsof negativeion plasmasin space[Gangullet
tool sincethe reaction productsare left in electronically al., 1993]. Typical chemicalsusedduring recentex(SF6), trifioromethly
excitedstates[Bernhardtet al., 1986].Two important perimentsare sulfurhexafiuoride
(Ni(CO)4).The
advantagesof the electron attachment chemicalrelease bromide(CFsBr),andnickelcarbonyl
overthe photoionization
chemicalreleaseis that (1) no
sunlight is requiredfor the chemicalreactionsto take
dissociative electron attachment
terials are as follows:
reactions for these ma-
placeand (2) a depletionratherthan an enhancement
SF6+ e- -• SF• + F
Copyright 1994 by the American GeophysicalUnion.
CF3Br + e- --• Br- + CF3
Paper number 93JA02752.
Ni(CO)4+ e- • Ni(CO)• + CO
0148-0227/94/93JA-02752505.00
373
374
SCALES ET AL.: EVOLUTION
OF CHEMICAL
RELEASES
In each case, heavy negative ions are created whose tector was near the depletion boundary layer, waves
massis muchlarger than the background
O+ mass. near 200 Hz were observed. This comparesto a lower
hybrid frequencyof several kilohertz. At later times,
The studiesby Bernhardt[1987b]and Bernhardtet
[1991]
haveshown
thatNi(CO)4, CF3Br,andSF6arein when the detectorwas further insidethe negativeion
many wayssuperior to chemicalsthat have been histor- plasma,wavesat frequenciesbetween2 and 10 Hz were
ically usedto create electrondepletionsby ion-molecule observed.These waveswere possiblynear the Br- and
reactions such as H2 and H20. This is because of the
Ni(CO)• cyclotronfrequencies
whichwereroughly9
large reactionrate constantsof the electronattachment and 5 Hz, respectively.
materials.
These new observationsduring NICARE have motiIn the past decade,there havebeenseveraltheoretical vated us to develop a numerical simulation model to
and numericalstudiesof processesassociatedwith elec- study the very early time microscopicprocessesobtron attachment chemical releases. Theoretical studies
servedduringthe releases.In this paperwereport on an
have considered electron attachment and neutralization
initial attempt at modelingthe early time evolutionof
chemistry,airglow production,ambipolarelectricfields the electrondepletionand negativeion cloudas well as
alongthe geomagneticfield, and macroscopic
plasmain- the developmentof low-frequencyelectrostaticwaves.
stabilities[MendilloandForbes,1982;Bernhardt,1984, Section 2 describes the simulation model in detail. Sec1986, 1987b]. The first nonlinearnumericalsimula- tion 3 describesresultsfrom a representativesimulation
tion of the electron
attachment
release was the two-
run. The initial evolutionof the electrondepletionand
dimensional
workof Bernhardt[1988].This workused negativeion cloud and the developmentof electrostatic
an electrostatic fluid mode] to study the macroscopic plasma wavesin the depletionboundary layer are emprocessesassociated with the motion of the electron phasized. A summary of the results and a discussion
depletion and negative ion cloud acrossthe geomag- are presentedin section 4.
netic field when under the influence of a neutral
wind-
generatedelectric field. This work predictedthe struc- 2. Simulation
Model
turing of the plasma depletionby the E x B interchange
To model the e•rly time behavior of the electron
instability. Recent simulationworksby Bernhardt et al.
density
depletion,negative ion cloud, •nd electrostatic
[1991]and ScalesandBernhardt[1991]haveconsidered
w•ves
observed
during the NICARE experiments,we
the electrodynamicsof the re]easesalong the geomagnetic field lines and structuringof the depletiondue to h•ve developed• two-sp•ce •nd three-velocitydimenhigh-speedre]easeof the chemicalsat satellitevelocities sionperiodic electrostaticp•rticle-in-cell simulationcode
acrossthe geomagneticfield. Theseworks,like the work by usingstandardtechniques[Hockheyand Eastwood,
1991]. Our
of Bernhardt[1988],usedmacroscopic
fluid simulation 1988;Tajima, 1989;Birdsalland œangdon,
modelsand consideredthe evolutionon largespaceand simulation model considersthe evolution in the plane
perpendicularto the geomagneticfield •nd • low bet•
A recently conductedseriesof soundingrocket ex- plasma. The simulation model •11owsus to study proon timescalesof the order of or lessth•n the negperiments called the Nickel Carbony] Re]easeExper- cesses
iments(NICARE) have been able to study the very ative ion cyclotron period which correspondsto • few
early time microscopicprocessesassociatedwith the one-tenthsof secondsduring the experiments.Our tworelease of electron attachment
chemicals for the first
dimensional•pproxim•tion is v•lid on this timescale
timesca]es.
time [Bernhardtet al., 1991,1993;Gangullet al., 1993]. sincethe work of Bernhardtet al. [1991]showsthat
Theseexperiments
released
CFsBrandNi(CO)4at al- the electrondepletionlifetime •long the m•gnetic field
titudes of 300-400 km at midlatitudes
and were success-
fu] at creatingelectrondensitydepletions.A Langmuir
probe and VLF plasma wave receiverwere used to obtain the first in situ measurementsof electron density
and electricfield fluctuationsduring an electronattachment chemical release.
Results of the NICARE
1 ex-
periment[Bernhardtet al., 1991;Ganguliet al., 1993]
is •t least • few tens of seconds.L•rge •mbipol•r electric fieldssustainthe steepfield-•lignedelectrondensity
gradient•nd preventelectronsfrom filling the depletion
in during this time period. Of course,the electrondensity gradientin the plane perpendicularto the m•gnetic
field is sustained by the cyclotron motion of the electrons. Therefore
the electron hole c•n be considered in
showedthat during the releaseof 30 kg of CFsBr, the • plane perpendicularto the m•gnetic field. The sp•-
electrondensitywasreducedfrom105cm-3 to 15 cm-3
till
scales to be considered
•re hundreds of meters in
in ]essthan 0.1 s. Large electrondensitygradientswere •ccord•nce with the steep e•rly time densitygradients
observedthat initially had scalelengthslessthan 100 observedduring the NICARE experiment.
We consider• three-speciesm•gnetizedplasm• that
m whichcompares
to an O+ Larmorradiusof the order
of heavynegativeions,X-, positiveions,O+,
of 10 m. Therefore the modified ionospherecould be consists
considered
asanambient
ionospheric
plasma(e--O +) •nd electrons,e-. The massr•tios •re rnx/rne = 400
massr•tio betweenthe
separated
froma negativeionplasma(Br- -O +) by a •nd rno/me = 50. The choosen
relatively thin boundary layer. The NICARE 1 plasma positiveions •nd electronsis sufficientto separatethe
wave receiver detected VLF
waves that were coincident
with the formation of the electron depletion and neg-
ion •nd electron timescales •nd •11ows the simulation
to be run with • reasonable •mount of CPU time while
ative ion cloud. At early times(< 5 s), whenthe de- following the full electron dynamics. The mass r•tio
SCALES
ET AL.'
EVOLUTION
of the negativeion speciesdiscussed
earlier(SF•, Br-,
OF CHEMICAL
RELEASES
375
ADe).All particlesare loadedwith standardMaxwellian
andNi(CO)•) andO+ isapproximately
8, 5, and9, re- velocity distributions and have zero-directedvelocity.
spectively.The massratio of the negativeand positive After initialization, the particles are allowed to freely
ionsin the simulationis rex/too - 8 whichis represen- move acrossthe boundary becauseof their initial thertative of these values. The chemical reactions that occur
mal energy. For the simulationresultsthat we discuss,
duringthe releasedirectly determinethe densitygradi- the ratio of the ambient electron plasma frequencyto
Wpe/•ce,is 0.5. The
ent scalelengthsin the boundarylayer and indirectly the electroncyclotronfrequency,
determine the dc electric field that results from charge temperature of the three speciesis taken to be equal,
imbalance near the boundary. In our present model, that is, Te=Tx=To. With the chosenvalues of partiwe neglectthe complexitiesof the chemicalreactions, cle temperaturesand cyclotronfrequencies,the Larmor
in particular, the electronattachment,and assumethat radii of the electrons,negative and positiveions moving
electronshave been attached prior to the initialization at the thermal velocity are p• = 0.5ADe,Px - 10AD•,
of the simulation. Note that this does not necessarily and Po - 3.5ADe,respectively.In this case,the radius
imply that all of the neutralshave attachedelectrons of the electrondepletionis 3.2px. As we stated earlier,
prior to initialization. On the early timescaleswe con- the results of one simulation run with the parameters
sider, only a small fraction of the total number of neu- previouslystated will be presentedand discussedin detrals have attached electrons. However, becauseof the
high neutral densityon this timescale,this small fraction of neutrals may be enough to totally deplete the
electron density in a sufficientlysmall localizedregion.
We have developeda more sophisticatedmodel that incorporateselectron attachment and the results of how
chemistry affects plasma processeswill be reported on
in the near future.
Figure 1 showsa crosssectionof the densitiesof the
three particle speciesin our simulation at initialization.
The simulation box is 128 x 128 grid cells, where the
grid cell size is equal to the ambient electron Debye
length ADe. We use 20 simulationparticlesper grid cell
for each species. The electrons are initialized with a
density depletion in which there are no electronswithin
a circular disk region at the center of the simulation
box. The negative ions populate this circular disk region, while the positiveion densityis constantthroughout the simulation box. This configurationguarantees
chargeneutrality and zero electrostaticenergy at initialization. The importanceof the mutual neutralization of the negativeand positiveionsmay be neglected
as a result of the short timescaleswe are considering.
The electrondepletionhas a radiusof 32 grid cells(or
tail. The ratiosm•/mo, rex/too, Wp•/•, andT•/Tx
and the depletion radius have been varied in a number
of other simulation runs producing qualitatively similar results. The important effectsof varying severalof
these parameters will be briefly discussedafterward.
3. Results
The simulation model just described was used to
study the nonlinear early time evolution of the electron depletion and negative ion cloud producedby an
electron attachment
chemical release.
The simulation
wasrun to the time Wpet- 1000 whichis roughly0.8
negativeion cyclotronperiodsor 20 ambient lower hybrid periodswhere the ambient lowerhybrid frequency
•LH, is
WI2'H
--1+(Wp•/f•c•)
2
with ;vo the ambient0 + plasmafrequency.Note that
the lowerhybrid frequencyin the boundarylayer, where
bothion species
are present,
will be givenby ;V•H=
(w• + w•)/(1 + (Wpe/•c•)2),
wherewx is thenegative
ion plasma frequency. Since mx >> mo and therefore
w• >> w•, the lowerhybridfrequency
in the boundary layer is approximatelyequalto that in the ambient
plasma. First, we describethe initial dynamicsof the
system and afterward the developmentof electrostatic
wavesin the depletion boundary layer.
DENSITY
w•t = 0
ELECTRONS
3.1. Initial Dynamics
0
The early evolution in the simulationshowsthat the
heavy
negative ions move acrossthe depletionbound•v(,)
IONS
ary due to their initial thermal energy since they are
essentiallyunmagnetizedon the simulation timescales.
The electronsare strongly magnetized,and the magPOSITIVE
netic field restricts their motion acrossthe boundary.
IONS
This producesan excessof negative chargeoutside of
the boundary and an outward electricfield, Er, devel0
128
ops in the radial, •, direction. This field is localized
X/•D•
Figure 1. A cross- sectionof the initial particle den- at the depletion boundary. Figure 2 showsthe angle
sities in the simulation model. Units of the density are averaged densitiesof the three particle speciesat two
particlesper grid cell. Note that the electrondensityis times during the simulation run. At the early time,
zero inside the depletion.
Wpel= 300, the electronshave been unable to move
40
NEGATIVE
376
SCALES ET AL.' EVOLUTION
OF CHEMICAL
ELECTRON
DENSITY
4O
,%t '300' '
20
RELEASES
[
NEGATIVE
ION
POSITIVE
ION
FLUX
FLUX
FLUX
N•ga/No¬,•
Nxgx•/No¬,•
Nogo•/No¬,•
.2O
a• et
ELECTRONS
0
4o
-.20
NEGATIVE
20
,
.20
,
,
I
'
,
a
•
i
w•et ' 100....
IONS
0
'
- •
0
4o
20 .
POSITIVE
2o
.20
[ .
i
!
,
i
-
,
I
•
-
!
Wpet= lOOO
I
i
i
iONS
0
64 0
64
o
64 o
64 o
64
Figure 2. Particle densityprofilesin the simulation
run at Wpet- 300 andWpet- 1000. Light line indicates Figure 3. Azimuthalfluxes(N•) of the threespecies
the densities
at Wpet- 0. Notethe negativeionsdiffuse at wp•t = 0, 100, and 1000. The fluxes are normalacrossthe boundary at early times and the electrons
izedto N0•he whereN0 is the ambientparticledensity
diffuseinto the depletion at late times.
and •he is the electronthermal velocity.Note that the
electronflux is muchlargerthan that of the ionsand is
acrossthe boundaryinto the depletiondue to the mag- sheared
at Wpet= 100.At theendof therun(wp•t=
netic field. The negative ions have moved acrossthe 1000)the electron
flux h• decrededsignific•tly.
boundaryto createa surplusof negativechargeoutside
the depletion.Also, note that the positiveion density
where e is the unit chargeand e0 is the permittivity
exhibits a depressionnear the boundary. This is due
constant. Since the particle densitiesdependon the
to accelerationof the positiveionsacrossthe depletion radial distance, r, both the E x B and VN x B flow
by the radial ambipolarelectricfield beforethey begin velocities will be sheared. Also note that the E x B
their cyclotron
motion. At later times,a•pet-- 1000, and diamagneticdrifts will be in the samedirectionfor
the electronshave diffusedinto the depletion due to
the electronsandin oppositedirections
for the negative
anomalousprocesses
causedby the developmentof elec- ions.
trostatic wavesin the depletion boundary layer. This
Figure3 showsthe azimuthalflux (N•) of the three
will be discussed
in more detail shortly.
particle speciesat three times during the simulation
Anazimuthally
directed,
•, E x B flowvelocity
may run. (Note that theseprofileshavebeenaveraged
in
developin eachparticle speciesdue to the radial electric
field. Also,because
of the radialdensitygradients
at the
boundary,azimuthaldiamagnetic
drifts(VN x B) may
result. The total azimuthalflow velocityof a particular particlespecies,•, will be madeup of thesetwo
the azimuthaldirection.)At Wpet= 100,the electron
flux can be seento be muchlargerthan the ion fluxes.
The electronflux is also highly shearedand localized
nearthe depletionboundary(r/Ape = 32). By the end
of the run, the electronflux profileis seento significomponentsand is given by
cantly broaden. There is also a shift of the maximum
flux to a radiuslargerthan the initial depletionradius.
Throughoutthe run, the fluxes of the ion speciesremain small in comparisonto the electronflux sincethe
ions
are weakly magnetized. The negativeion flux is
Here the particlespeciescharge,density,and temperobserved
to be in the oppositedirectionto the postive
ature are denotedby q,, N,, and T, respectively.The
T, i ONe(r) (2)
ø(r)- E(r)
s qoS
first term in (2) is the E x B drift, Vz(r), andit may ion and electron flux.
be relatedto the particledensitiesthroughPoisson's The temporal evolution of the electrostaticfield enequation as
ergy and averageazimuthalflowvelocityof eachspecies
OVz(r)
Figure 4. The total electricfield is composedof the ra-
Or
i OE•(r)
-
B
Or
(averaged
overall particles
of that species)
is shownin
e(No(r) - (Nx(r) + Ne(r)))/eo
dial component,
Er, that resultsfromthe radialcharge
(3) separationand an azimuthal component,E•, that ulti-
SCALES
ET AL.'
EVOLUTION
OF CHEMICAL
RELEASES
377
kinetic energy lossby the negativeions goesinto the
densityand flow velocitygradients.The energyin these electrostaticenergyand the accelerationof the positive
two components
of the field (normalizedto the initial ions acrossthe boundary. The total electron kinetic ennegativeion kineticenergy)is shownseparately.The ergy change(not shown)is negliblysmall duringthe
radial electrostaticenergy growsabove the noiselevel run.
and reachesa maximumaroundWpef----300 and then
3.2. Wave Development
slowly decreases.The azimuthal field energy,which is
smallerthan the radial energy,growsrelativelyrapidly
As we discussedearlier, electrostaticwavesassociated
during the time the radial energy grows. A slow in- with the azimuthal electricfield developin the depletion
creasein the azimuthal energy is observedafter that boundary layer and propagate azimuthally around the
time. The averageazimuthal flow velocitiesmaximize depletion boundary. These waveswhich begin to demately results from plasma instabilities driven by the
around
the same time
that
the radial
electrostatic
en-
ergy doesand begin to decreaseby the end of the run.
The averageazimuthal flow velocityfor the electronsis
larger than that for the ion species.Again, we seethat
the averagenegativeion flow velocityis in the opposite
direction to the electronsand positive ions. Note that
the averageflow velocitiesare small in comparisonto
the electron thermal velocity Vtheand also smaller than
the negativeion thermal velocityin this case.The maximum value for the electronflow shownin Figure 4 is
roughly 0.6VthX.
The energyfor the electrostaticfieldsshownin Figure
4 ultimately comesfrom the motionof the negativeions
as they moveacrossthe depletionboundary due to their
initial kinetic energy.Figure 5 showsthe kineticenergy
velopearlyin the run, caninitiallybe seenaroundWpef
= 100and continueto growuntil roughlyWpet- 400.
Figure 6 showsthe radial and azimuthalelectricfieldsat
Wpet- 300whichis nearthe time the total electrostatic
energy maximizes in Figure 4. We see that the radial
electricfield is highly localizednear the boundaryof the
depletion(r/ADe -- 32). The azimuthalelectricfieldat
the boundary in Figure 6 exhibits coherentstructure
with the wavelengthroughly 9ADewhich is less than
the negativeion Larmor radius.
To considerthe effectof developmentof the waveson
the densityof the plasmaspecies,we showin Figures7
and 8 the electrostaticpotential and the densityof each
plasma speciesin two-dimensionalspace. These quan-
tities are shownat three times,Wpet- 100, 400, and
of the ion species
(normalizedto the initial negativeion 1000. At Wpet- 100, Figure 7 showsthe potentialis
kineticenergy)duringthe simulationrun. The negative localizednearthe depletionboundary.At Wpet- 400,
ions initially decelerateas they move acrossthe bound- the potential exhibits structure as a result of the develary and their total kineticenergyminimizesat the same opmentof the wavesand has increasedin magnitudeby
time the total electrostaticenergymaximizes. Because roughly a factor of 2. At the end of the run, the poof the developmentof the radial electric field, the posi- tential has broadenedin space,and its magnitudehas
tive ions are acceleratedacrossthe boundary, and their reduced
to a valueneartothatat Wpet
- 100.Figure
8
total kinetic energyinitially increasesas can be seenin showsthe initial developmentof the wavesin the elec-
Figure 4. At later times,the positiveion kineticenergy tron densityat Wpet- 100. Later, at Wpef- 400 and
decreasesand the negativeion kinetic energyincreases 1000, the structure is more pronounced,and closeinas the total electrostaticenergy decreases.The total spection showsthe developmentof vortices. Becauseof
anomalousdiffusionof the electronsinto the depletion
0.02
KINETIC
ENERGY
1.00
ELECTROSTATIC
ENERGY
azimuthal
NEGATIVE
IONS
0.00
.03
0.85
5.22•
•
0
•
O+
-.03
0
1000
i•
5.0s I ............
Figure 4. Radial and azimuthal electrostaticfield en-
0
IONS
]POSIT
1000
•pe t
ergy(normalized
to the initialtotal negativeionkinetic
energynxTx) andthe averageazimuthalflowvelocities Figure 5. Kineticenergyof the positiveand negative
(averagedoverall particlesof the species)of the three ions(normalizedto the initial total negativeion kinetic
particlesspeciesduring the simulation.
energy,nxTx) duringthe run.
378
SCALES
ET AL.: EVOLUTION
OF CHEMICAL
RELEASES
POTENTIAL
?j.".'.'•'-..:'::2:.:,.::'.".'i
'•..
•j::?.--:
:.':::'"c.:'
'.::.:.:...F.•,
..•Y::•..':.:'•
-4:.-.'
....
:•??:'i"!"-::'.... •':•'•:i??:?-i
'• wp•t= 100
-.5
0..............
.5
E•
64
-.:""•"'"
'••:••..."4!:...:'f
"' "•
'
':-'i:•..•,-
ß
.::,•..'.';:!;:':;"•".-c.•":•':;•?:
!'a;':'
..... "'•.'.;-':/
ß; •.• '.-•.:•::
-:.:."."', '.'.',:,'-:'E:•..
•;:... :..
'.•"::
:.•.:
.'_..'.',%',.:.:'.",:::_'i-,:.;:•;'
• ß
0
w•t = 300
0
y/AD
.p,t = 400
-.5
o
o
Figure 6. Radialandazimuthalelectricfieldsat wpet
- 300 (normalized
to meVtheWpe/q).
Notethe radial
fieldis localizednearthe depletionboundary(r/,•De -3•).
128
"::".::F•?::"t•::.•.'::•.•-•.:'•?'(
•
' :'....[•' .4.¾2%.:.:",::':.:
'?""•':"'•
.....
'"'"'?::'
wp•t- 1000
causedby the development
of waves,the initial sharp
electrondensitygradientrelaxessignificantlyby the end
of the run. This canbe seenclearlyin Figure2 aswell.
The diffusionof the negativechargeinto the depletion
0
128
ultimatelyreducesthe radial componentof the electric
x/Xr
fieldasshownin Figure4. The structurein thenegative
run
and positiveion densitiesis lesspronouncedthan the Figure 7. Potential(eq•/Te)duringthe simulation
levelsrun from-1.0to 2.6 by 0.144).Dotted
structurein the electrondensity. However,we find that (contour
the structureis morepronouncedin the lighterpositive contours indicate •b ( 0. Note the structure in the
potential due to wavedevelopment.
ionsthan the heavynegativeions.
Figure 9 showsa power spectrum of the azimuthal
electricfield E•, taken at a singlegrid point on the argued to be the sourceof the wavesobservedin the
electrondepletionboundary(r/Aoe = 32). Thesewaves simulation work of Galvez et al. Galvez et al. found
are driven by plasma instabilitieswhosepossiblefree that there was relatively good agreementbetweenthe
energysourceswe will discussshortly. The spectrumis wavelengthof maximumgrowthobtainedby solvingthe
takenoverthe timeperiodfromWpet- 200to 1000and electrostaticdispersionrelationfor the LHD instability
representsthe wavesin a nonlinear saturated state. The and the simulationresults.The scalingof the instabilwave power is low frequencywith the power existing ity wavelength
with magnetic
fieldstrength
between0.1 to 0.3WLS.Spectralanalysisof the radial predictedby the LHD instability showedsimilar trends
field, Er, showsthat it is essentiallya zero-frequency with the simulations. However, they found that the
(dc) field.
frequencyand wavelengthpredictedby the LHD instaWave growth similar to the casestudied here was ob- bility did not agreewith the observations
madeduring
servedin numericalsimulationsby Sydoraet al. [1983] the AMPTE barium releaseexperiments. In general,
and Galvezet al. [1988]of barium cloudreleasesin the predictedwavelengthswere too short, and the prewhichthe barium cloudswereallowedto expandacross dicted frequencieswere too high. There was also disa static magneticfield. The primary differencein these agreementbetweenthe frequencyof the unstablewaves
two studieswas the fact that the work of Sydoraet al. and phase velocitiespredictedby the LHD instability
consideredthe caseof a nonzeroradial expansionveloc- and the results observed in the simulations. Galvez et
ity of the ions and electrons.Sydoraet al. attributed al. alluded to the fact that thesediscrepanciescouldbe
thesewavesto the Kelvin-Helmholtzinstabilitythat re- due to their model's exclusion of the effect of shears in
sultsfromthe shearin the azimuthalflowvelocityat the the electron flow velocity.
cloudboundarylayer.The lowerhybriddrift (LHD) inAnother instability processthat showsmuchpromise
stability resultingfrom E x B and VN x B drifts was in explainingthe wavesin the electrondepletionbound-
SCALES
ELECTRON
NEGATIVE
DENSITY
ET AL.'
ION
DENSITY
128
EVOLUTION
OF CHEMICAL
RELEASES
POSITIVE ION
DENSITY
POWER
.01
379
SPECTRUM
..................
'w•,t
='10
0
Io()l =
0
,%,t , 400
128
ß
.
V/Ave
o
2
02/ 02LH
Figure 9. Power spectrumof the azimuthalelectric
field Es, taken on the electrondepletionboundaryfor
200 < Wp•t< 1000.
o
ß 'w•,t'=1000• ' '
128
1
ELECTRON
FLOW VELOCITY
0
128 0
128 0
128
1.0
w•et = 100
x/Ave
Figure 8. Densitiesof the threeparticlespecies
during
the run (contourlevelsrun from0.0 to 24.0by 2.0).
Note that pronouncedstructuredevelopsin the electron
density.
0.0
ary layer in our numerical simulationsis the electron-
ion-hybrid
(EIH) instabilityof Ganguliet al. [1988].
This instability results from the shear in the electron
flow velocity V•. A nonlocal linear electrostaticfluid
dispersion
relationfor wavespropagating
perpendicular Figure 10. Azimuthalelectronflowvelocityprofileat
to the magneticfield in a plasmawith a perpendicular Wpet'- 100, showinglargeinitial velocityshearsat the
electronflow velocityand perpendicular
flow velocity depletionboundary.
and densitygradientsis givenby [Ganguliet al. 1988,
1993;Romeroet al., 1992a]
instabilitiespredictlinear wavegrowthwith w ,,, WLH.
However,the EIH instabilityhasthe advantagein that
vs()
,.
it
predictslonger wavelengthswith ka.L• ,,, 1 where
=
=0
k• is the wavenumberperpendicularto the magnetic
(4) field and L• is the scalelengthof the electronflowvewhere
G(w)= •2/(• + 1)(1- (WLH/W)2),
$ = Wpe/flce,locityprofile(p, < L• < fo). This is comparedto
- +
=
and =
-
hy- k.l.pe"' (Te/•) 1/2fortheLHDinstability.
In general,
brid frequencyWLHis the valuein the boundarylayer
whereboth ion speciesare present• discussed
earlier,
and the first-orderperturbationelectrostaticpotential
is denotedby 4•(z). Notethat in oursimulationgeometry,theradialvariabler corresponds
to z in (4), which
is the directionof densityand flow velocitygradients.
The azimuthal variable 0 correspondsto •, which is
the directionof the flowvelocityandwavepropagation.
Thethirdtermin (4) represents
thefreeenergyforwave
growth. The two free energysourcesare shearedelectronflow(V•(z) and V•(z)) andelectrondensitygr•
both free energysourcesin (4) may exist. However,
the workof Romeroet al. [1992b]hasshownthat if the
shearfrequency,
w, = Vm•x/L•, whereVm•xis the maximumvalueof the electronflowvelocity,is largerthan
the lowerhybridfrequency,WLH,then the EIH instability drivenby the electronflowvelocityshearsdominates
the LHD instability.
To considerthe role of the EIH instability in more
detail, we showin Figure 10 the electronflow velocity
profileearlyin the simulation
(Wpet
= 100)at the time
wavesinitially beginto be observed
in Figure8. Figure
dients(en).If thevelocity
shearcontributions,
V•• and 10 showsvery large velocityshearsnear the depletion
V•, arezero,thenthe dispersion
relationin (4) reduces boundary. The maximum flow velocityis observedto
to the form for the LHD instability[Krall and Liewet be --0.9Vtheand the scalelength over which the elec1971].On the otherhand,if theelectrondensitygradi- tron flow is localizedis roughly2Aoe. This impliesa
ent contributionen is zero,then the dispersionrelation shearfrequency
of 0.45Wpe.
The lowerhybridfrequency
reduces
to that for the EIH instability[Ganguliet al., fromthe parameters
of section2 is 0.134Wpe.
There1988;Romeroet al., 1992a,b].Both the LHD and EIH forew,/WLH= 3.4 > 1, and the EIH instabilityshould
380
be the dominant
SCALES
ET AL.:
EVOLUTION
source of the waves in our simulation
run. The condition kxLz ~ i for EIH instabilitydriven wavespredicts a wavelengthof roughly 12.6ADe
which is in reasonableagreementwith the value 9ADe
that is observedearly during the simulation. Another
important piece of evidencethat supportsthe EIH instability is the nonlinear evolution of the system. As
we discussedearlier, vortex formation is observedin the
electrondepletionboundarylayer in the nonlinearstage
of the developmentof the waves.This is the dominant
OF CHEMICAL
RELEASES
in the boundary layer. Becauseof anomalousdiffusion
causedby these waves, the electronsmay diffuseback
into the depletion. This ultimately causesthe density
gradient and flow velocity profile to relax as well as a
reduction
in the electric field.
We find that the wave-
lengths of these waves are less than the negative ion
Larmor radius and that the frequencyin the nonlinear
regimeto be muchlessthan the lowerhybridfrequency.
The most likely candidate for this wave development
is the EIH instability that results from shearsin the
nonlinearsignatureof the EIH instability(wa/WLH
> 1), electronflow velocity[Ganguliet al., 1988]. Shearsin
wherethe dominant nonlinearsignatureof the LHD in-
the electron flow velocity in the simulation runs were
stability (wa/WLH< 1) is the development
of kinksin shownto be sufficientlylarge to excite the EIH instathe electrondensity[Romeroet al., 1992b]. Because bility. Also, the fact that vorticeswere observedin the
of the broadeningof the electron flow velocity profile nonlinearregimesupportthe EIH mechanism.
by the EIH instability, the dynamical evolutionof the
systemin time shouldexhibit a cascadefrom high fre-
Finally, we may briefly compare our results with
wavesobservedduring the NICARE i experiment.Our
quencies
(• ~ •LH) andshortwavelengths
to lowerfre- simulationsdescribethe evolution on time periods of
quencies
(•v<<•VLH)andlongerwavelengths
[Ganguliet the order of or less than the negative ion cyclotron
aL, 1993].This is consistent
with Figure9 whichshows period. This correspondsto timescalesof 0.2 seconds
that the power spectrum of the saturated state of the or lessassuming
Br- and Ni(CO)• cyclotron
frequensystemis dominated by waveswith frequenciesthat are cies of 9 and 5 Hz, respectively. Waves near 200 Hz
much lessthan the lower hybrid frequency.
were observedon this timescaleas the diagnosticpayWe have performed other simulation runs varying load initially passedthrough the steep densitygradiTe/Tx, •pe/•ce, and me/mo. Theseshowqualita- entsat the negativeion cloudboundary[Ganguliet al.,
tively similar results. We note that in varying 0.5 •
1993].Assumingan ambientlowerhybridfrequencyin
Wpe/•½e
• 2, wefind that for strongermagneticfields, the kilohertz range, our powerspectrumresultswould
the electron flow velocity profile scale length Lz is scaleto frequenciesin the hundredsof hertz whichis in
shorterin the simulationruns. (The thicknessof the agreementwith the observations.More detailedanalynegative charge surplus layer becomesthinner as the sisof the electrondensityand wavesobservedduringthe
magneticfieldstrengthincreases
as well.) We alsofind NICARE seriesof experiments
is nowunderinvestigathat the wavelengthof the wavesin the boundarylayer tion. Future work will make more detailedcomparisons
are shorter in an absolutesenseas the magneticfield with the experimentaldata.
strength increases.This is keepingwith the fact that
Our ongoingwork is to incorporate and study the
kxLz ~ i for the EIH instability.
effectsof electron attachment chemistryin our model.
This study will provide a more realistic descriptionof
the attachmentof the electronsand creationof neg4. Summary and Conclusions
ative ions by the releasedneutrals. A more accurate
Numerical simulations have been used to study the descriptionof the initial formation of the electronand
early-timeevolutionof electrondensitydepletionsand negative ion density gradients as well as the flow venegativeion cloudsproducedduring electronattach- locitiesin the boundary layer can be obtainedfrom this
ment chemicalreleasesin the ionosphere.We have con- modelaswell. Extendingour simulationmodelto study
wavesat the negativeion cyclotronfresideredthe dynamicsin a plane perpendicularto the lower-frequency
magneticfield and focusedon timescaleslessthan the quencyis alsounder investigationto considerthe waves
negative ion cyclotronperiod. This is in contrast to at thesefrequenciesobservedat later times during the
previoussimulation work that consideredmacroscopic experiments.
fluid processes
[Bernhardt,1988;Scalesand Bernhardt,
1991].We find that a negativechargesurplusdevelops
Acknowledgments.
This work was supported at Va.
outsidethe depletioninitially as the negativeionsmove Tech by ONR grants N00014-92-J-1498 and N00014-92-Jacrossthe boundary,sincethey are unmagnetizedon 1484. The work was supported at NRL by the Office of
Naval TechnologyPostdoctoralFellowshipProgram(WAS)
this timescale. The electrons remain bound to the field
lines and are restrictedfrom movingback into the depletion initially. This chargeseparationat the boundary producesa inhomogenous
electricfield acrossthe
boundarylayer. A highlyshearedelectronflow velocity
developsat the depletionboundarydueto the E x B and
X7N x B drifts that result from this inhomogenous
electric field and electrondensitygradients. We find that
electrostaticwavesbeginto developin the boundaryafter severallowerhybrid periodsand producestructuring
and NASA.
The Editor thanks a refereefor his assistance
in evaluating
this paper.
References
Bernhardt, P. A., Chemistry and dynamicsof SF6 injections
into the F region, J. Geophys.Res., 89, 3929, 1984.
Bernhardt, P. A., E. J. Weber, J. G. Moore, J. Baumgardher, and M. Mendillo, Excitation of oxygenpermitted line
SCALES ET AL.: EVOLUTION
emissionsby SFs injection into the F region, J. Geophys.
Res., 91, 8937, 1986.
Bernhardt, P. A., and L. M. Duncan, Ionosphericfocused
heating- A hybrid modification experiment, J. Atmos.
Terr. Phys., •9, 1107, 1987a.
Bernhaxdt, P. A., A critical comparisonof ionosphericdepletion chemicals, J. Geophys.Res., 9œ,4617, 1987b.
Bernhardt, P. A., Cross-B convectionof artificially created,
negative-ion clouds and plasma depressions:Low-speed
flow, J. Geophys.Res., 93, 8696, 1988.
Bernhardt, P. A., P. Rodriquez, C. L. Siegering,and C. S.
Lin, Field-aligneddynamicsof chemicallyinducedperturbations to the ionosphere,J. Geophys. Res., 96, 13,887,
1991.
OF CHEMICAL
RELEASES
381
Hockhey,R. W., and J. W. Eastwood,ComputerSimulation
Using Particles, Adam Hilger, New York, 1988.
Krall, N. A., and P. C. Liewet, Low-frequencyinstabilities
in magnetic pulses, Phys. Rev. A: Gen. Phys., 4, 2094,
1971.
Mendillo, M., and D. Forbes, Theory and observationsof
a dynamically evolvingnegativeion plasma, J. Geophys.
Res., 87, 8273, 1982.
Romero, H., G. Ganguli, Y. C. Lee, and P. J. Palmadesso,
Electron-ionhybrid instabilitiesdriven by velocity shear
in a magnetizedplasma, Phys. Fluids B, 4, 1708, 1992a.
Romero, H., G. Ganguli, and Y. C. Lee, Ion acceleration
and coherentstructuresgeneratedby lower hybrid sheardriven instabilities, Phys. Rev. Lett., 69, 3503, 1992b.
Scales,W. A., and P. A. Bernhardt, Simulation of high.
Bernhaxdt, P. A., J. D. Huba, J. A. Fulford, P. A. Forsyth,
D. N. Anderson, and S. T. Zalesak, Analysis of rocket
speed(orbital) releasesof electronattachmentmaterials
in the ionosphere,J. Geophys.Res., 96, 13,815, 1991.
beacontransmissionsto reconstructionosphericdensities,
Sydora, R. D., J. S. Wagner, L. C. Lee, and E. M. Wescott,
Radio Sci., •8, 613, 1993.
ElectrostaticKelvin-Helmholtzinstability in a radially inBirdsall, C. K., and A. B. Langdon, Plasma Physics Via
jected plasma cloud, Phys. Fluids, •6, 2986, 1983.
Computer Simulation, Adam Hilger, New York, 1991.
Galvez, M., S. P. Gary, C. Barnes,and D. Winske, Computer Tajima, T., ComputationalPlasma Physics: With Applications to Fusion and Astrophysics,Addison Wesley, New
simulationsof plasma expansionacrossa magneticfield,
York, 1989.
Phys. Fluids, 31, 1554, 1988.
Ganguli, G., Y. C. Lee, and P. Palmadesso,Electron-ionhyP. A. Bernhardt and G. Ganguli, SpacePlasma Branch,
brid mode due to transversevelocity shear, Phys. Fluids,
Plasma PhysicsDivision, Naval ResearchLaboratory,Wash31, 2753, 1988.
mil)
Ganguli, G., P. A. Bernhardt, W. Scales,P. Rodriquez,C. L. ington,D.C. 20375.(e-mail:bern•ppd.nrl.navy.
W. A. Scales,Bradley Department of Electrical EngiSiegering,and H. Romero, Physicsof negativeion plasmas
created by chemicalreleasesin space,in Physicsof Space neering,Virginia Tech, Blacksburg,VA 24061. (e-mail:
ee.vt.edu)
Plasmas(199œ),ScientificPublishers.Conf. Proc. Repr. wayne• staxchild.
Set., vol. 1•, ScientificPublishers,Cambridge, MA, p. (ReceivedApril 22, 1993;revisedAugust18, 1993;
161, 1993.
acceptedSeptember17, 1993.)