Simulation studies of parametric decay processes associated with ...

Radio Science,Volume 32, Number 5, Pages2099-2107, September-October1997

Simulation studies of parametric decay processesassociated with ionospheric stimulated radiation A. A. Hussein

and W. A. Scales

BradleyDepartmentof Electricaland ComputerEngineering,Virginia PolytechnicInstitute and State University Blacksburg

Abstract. Parametricinstabilityprocessesare thoughtto producestimulated electromagneticemissionsduring ionosphericheatingexperiments.The phenomenonis primarily attributed to plasmaturbulenceexcitedby the high-frequencyheater in the altitude regionwhere the pump frequency•o0 is near the plasmaupper hybrid frequency OOuh. In this study,parametricinstabilityprocessesthoughtto produceionospheric stimulatedradiation are studiedusingelectrostaticparticle-in-cellsimulationmodels.The emphasisin this work will be to considerthe excitationand interactionsbetween electrostaticwavesgeneratedby the pump wave. The simulationplasmais driven with a uniform oscillatingelectricfield directednearly perpendicularto the background geomagneticfield B to considerinteractionswhen OOuh is near electroncyclotron harmonicsn•ce. The pump frequencyand amplitudeare varied to considerthe effectson the simulationelectricfield power spectrum.Also, the effect of varyingthe electronto ion temperatureratio Te/T i is discussedand evaluated.The simulationresultsshowrichly structuredsidebandsupshiftedand downshiftedaboveand below the pump frequency, which are attributedto parametricinstabilityprocesses. The relationshipbetweenthe simulationresults,the theoreticalmodels,and the experimentalspectrumare discussed. Introduction

Many phenomenaattributedto wave-waveinteractions have been observedduring ionosphericheating experiments. Stimulated electromagneticemission (SEE) is a wave-waveprocessthoughtto be produced by parametricprocesses. The SEE spectrumexhibits sidebandsupshiftedand downshiftedfrom the pump wave within roughlyabout 100-KHz bandwidth. Since the discoveryof SEE [Thid• et al., 1982], interest has been rapidly growingbecauseit may be usedas a diagnostictool for the ionosphereand also becauseit is a fundamentalplasmaphenomenon.A classificationof SEE spectral features and the descriptionof their generationthroughparametricdecayinstabilityprocesses were first providedby Stubbe et al. [1984].The SEE spectralsidebandswere found to dependon a numberof ionosphericparametersin additionto the pumpwave.It wasalsopostulatedthat the sidebandsin the SEE spectrumshoulddevelopin the altituderegionwhere •o0 is near the plasmaupper hybridfrequencyOOuh. This spectrumis dependenton the proximityof •o0 to the harmonicsof the electron Copyright1997 by the American GeophysicalUnion. Paper number97RS01349. 0048-6604/97/97RS-01349511.00

cyclotronfrequencyn•ce. It was noted that important featuresin the spectrumare suppressed when •o0 is equal to n•ce. One of the prominentSEE spectralfeaturesis the downshiftedmaximum (DM). This sidebandin the SEE spectrumhas a frequencyshift below the pump frequency approximatelyequal to the local plasma lowerhybridfrequencyOOlh. Theoreticalstudiesof the DM have considered the generation through the parametricdecayof the electromagneticpump wave into upper hybrid waves. The upper hybrid waves either decayinto a lower hybridwave and an O-mode wave [Murtazaand Shukla,1984;Stenfioand Shukla, 1992;Leyseret al., 1994] or decayinto a lower hybrid waveand an electrostaticupperhybrid/electronBernstein wave which is scatteredby field-alignedirregularities into electromagneticwavesthat are observed on the ground[Zhou et al., 1994]. Another SEE spectral feature is the downshifted peak (DP). The DP is usually observedwhen the pump frequencyis very closeto the third harmonicof the electron cyclotron frequency 3•ce. Its offset frequency from the pump is about 2 KHz. It was postulatedby Huang and Kuo [1995] that the generation mechanismfor the DP feature is throughparametricdecayof an electronBernsteinpumpwaveinto

2099

2100

HUSSEIN

AND

SCALES:

IONOSPHERIC

STIMULATED

RADIATION

an electronBernsteinsidebandwave and a nearly Theory perpendicularlypropagatingion acousticor electro-

staticioncyclotron decay wave. Porkolab [1972] hasdiscussed thecoupling between Themostimportant upshifted featurein theSEE low-frequency andhigh-frequency electrostatic waves spectrum is thebroadupshifted maximum (BUM),' byparametric instabilities. Themodelmaybe used only seen when 6oo is above nlOce. It was noted by Leyseret al. [1989] that the BUM feature could be generated through a four-wave interaction process involvingtwo pump photonsor upper hybrid plasmons, a decay mode at nløce, and the stimulated radiation at 6oBUm-Whenthe heater frequency6o0 is abovean electroncyclotronharmonichiøce,frequency-upshifted upper hybrid waves and frequencydownshifted

electron

Bernstein

waves can be excited

abovethe upper hybrid resonancelayer via the considered four-wave process.Huang and Kuo [1994] developeda rigoroustheory based on the idea of Leyseret al. [1989].They proposedthat the BUM is producedin the regionwhere the pump frequencyis about the mean of the upper hybrid wave frequency and the electron Bernstein wave frequency.A lowfrequency electrostaticoscillation in the frequency regime of 6olhis also generatedvia this process. Although numerical simulationsmay provide important contributionsto the understandingof nonlinear processes that are thoughtto produceSEE, there havebeen only a few studiesin the past [Scaleset al., 1996, and referencestherein]. In this work we study some of these proposed processesassociatedwith SEE generationusing particle-in-cell(PIC) simulation models. The PIC simulation

model was used in

this study since it includes kinetic modes such as Bernsteinmodes,which are thought to play an important role in producing SEE. It also allows for detailed studyof nonlinear evolution. The emphasis in this investigationis on electrostaticparametric decayprocessesthat have been proposedto produce the DM, DP, and BUM sidebandfeatures.We primarily concentrateon the casewhere 6oo > hiøce in thiswork. As mentionedearlier,we will onlyconsider the excitation

and interactions

for analyzingdownshiftedsidebandssuchas the DM and DP through parametric decay. The parametric couplingprocessfor the decayof a pumpwave (600, k0) into a sideband(6ol, kl) along with a lowfrequencydecaymode(6os,ks) hasthe frequencyand wave vector matching conditions 6oo = 6o• + 6os, k o = k• + k s. The dispersionrelation for this three-waveinteractionis givenby

between

electrostatic

•:(tOs) q--•-Xi(tOs)

--2': 0

(1)

where •e = 2kvosc/(6oo + •'e), Vosc= qEo/me6oO is the electronoscillatingvelocity,k is the wavenumber, m e the electron mass,E 0 is the electric field pump strength,and q is the electron charge.Also, •:(tO)= 1 q- Xe(tO)q- Xi(to)

(2)

•:e(tO): 1 q-Xe(tO)

(3)

where Xe and Xi are the ion and electronsusceptibility, respectively.The susceptibilityof the jth species

Xj is givenby

xj(to, k) =

{1+ •'jo•

k2A2Dj

n=-•

rn(bj)Z(•jn)}

(4)

where bj - k2zpj/2; •jn= (to- nglj)/k vtj;Fn(bj) = I n(bj) exp(-bj); Z istheFriedContefunction; I n is the modified

Bessel function

of the first kind of order

n; ;tr)jistheDebyelength; kll(kñ) isthecomponent of k parallel(perpendicular) to B; pj is the gyroradius;andvtjisthethermalvelocity. Zhouetal. [1994] have developeda more complete treatment of the three-wavedecayto interpret SEE. Our future work will make comparisons with this more detailedtheory. The Porkolab [1972] model was found to be more than adequatefor guidingthe simulationwork and, in general,wasin closeagreementwith simulationresults. Since we considerprocessesnearly perpendicular to the magnetic field, the relevant low-frequency decaymodesin this caseare the lower hybrid and the electrostatic ion cyclotron modes. The dispersion relation for the lower hybridwave,in the regime 0