Whistler Waves in Space and Laboratory Plasmas

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. A7, PAGES 14,379-14,395, JULY 1, 1999

Whistlerwaves in spaceand laboratoryplasmas

R. L. Stenzel Department of Physicsand Astronomy,University of California, Los Angeles

Abstract. An overviewof whistler wave phenomenain space and laboratory plasmasis given. Common features and different approachesbetween laboratory and spaceplasma researchare pointed out. Both researchactivities have discovered a rich variety of whistler wave effects. Many useful applicationshave emerged. Open researchtopics and interactions between lab and spaceresearch on whistlers are pointed out.

1. Introduction called "helicons." Thus a reader from the space sci- Whistler waves are possiblyone of the first plasma ence community should simply interpret a laboratory waves observed. These waves have been studied for whistler as any wave propagating in the whistler mode more than 100 years. A vast body of literature exists irrespective of its excitation mechanism. on whistlers and related phenomena in at least three ar- Historically, whistler wave researchstarted with pas- eas: spaceplasmas, laboratory plasmas, and solid state sive ground observationsof low-frequency radio waves physics. It is impossibleto present a comprehensive from the ionosphere. Space plasma researchblossomed review on this field in a short article. Instead of an in the era of spacecraftexploration. A wealth of whistler in-depth review in any particular area, this article at- wave phenomena has been collected. Remote observa- tempts to convey the large variety of whistler wave ef- tions from ground, point measurementsfrom space,and fects discoveredby complementarymethods in space lack of parameter control have sometimes caused diffi- and laboratory plasmas. In the spirit of the conference culties in explaining the observations uniquely. This where this material was presented[Interrelationships lead to the desire to study whistlers in a controlled Between Plasma Experimentsin the Laboratory and laboratory plasma. After the developmentof suitably Space(IPELS), Maui, Hawaii,June 23-27, 1997], this is large and collisionlesslaboratory plasmas and advanced an "interdisciplinary"review article which does not only plasma diagnostics many contributions on linear and focus on whistler phenomenain space plasmas. The nonlinear whistler waveswere made in laboratory plas- latter hasbeen thoroughly done in classicalbooks [Hel- mas. Phenomena like resonance cones, beam-driven liwell,1965], long review articles [Al'pert, 1980], and an VLF hiss, filamentation instabilities, antenna proper- abundanceof topicalreviews [Helliwell, 1988; Sazhin et ties, whistler wings, etc., added to the knowledge of al., 1992;Hayakawa, 1992; $azhin and Hayakawa,1992; whistler waves. The purpose of the present paper is $ingh, 1993; $azhin et al., 1993; $azhin and Hayakawa, to describethe major findings in both areas of whistler 1994; Hayakawa, 1995; Sonwalkar, 1995; Johnstone, researchso as to possiblystimulate new investigations. 1996; Singhet al., 1998]. After a brief historicbackground, the followingsections There exist different terminologiesfor whistler waves presentwhistler properties, major findingsin spaceand in the space and laboratory communities. In space laboratory plasmas, a sectionof emergingapplications science, a "whistle" is specifically defined as an elec- of whistler waves,and presently open questionsfor further research on whistlers. tromagnetic wave excited by lightning and dispersed whilepropagating through the ionosphereand magnetosphere. All other excitation mechanisms lead to "whis- 2. Brief History tler-mode wave." Depending on their sound and spec- More than 100 yearsago, Preece [1894] reported that trogramsthey are given many exotic namessuch as hiss, operators on the Liverpool-Hamburg telephone lines roar, saucers,chorus, risers, hooks, triggered emissions, heard strange rumbling soundsnot produced by man. etc.. In laboratory plasma physicsany wave propagat- No explanation was given for these "Earth currents." ing in the whistler mode is simply called a "whistler Following the developmentof vacuum tube amplifiers, wave." However, in bounded laboratory plasmas, in Barkhausen[1919] describes observations of "Pfeift6ne" particular solid state plasmas, these waves are often (whistlingtones) on longwire antennasand relatestheir occurrenceto lightning, auroral activities, and wave dis- Copyright 1999 by the American GeophysicalUnion. persion. Such whistlersconsist of electromagneticsig- Paper number 1998JA900120. nals which, after conversionto sound, produce falling 0148-0227/99/1998JA900120509.00 tones from a few kHz downward, lasting up to several

14,379 14,380 STENZEL:WHISTLER-MODE WAVES IN SPACEAND THE LABORATORY seconds.In the 1920sand 30s Eckersley[1935] pursued over long distancesalong B0. All groundobservations the researchon "musical atmospherics," quantified the of whistlers,in particular the multiply reflectedwhis- dispersion, and related the phenomenon to radiowave tlers, involve ducting. Even narrow density troughs propagationin the ionosphere. The evolution of the (d < All),requiring an eigenmodeanalysis [Sodha and magnetoionictheory [Appleton, 1932] produced a quan- Tripathi,1977], exhibit remarkablygood ducting prop- titative understandingfor the dispersionof plane whis- erties[Stenzel, 1976b]. tler wavesin coldplasmas [Storey, 1953; Ratcliffe, 1959]. Plane whistler waves can decay because of electron After World War II a nearly explosivegrowth started collisionswith neutrals and ions, becauseof collisionless in whistlerwave research. It was stimulatedby (1) the electroncyclotron damping (•- • = k-ve), and be- era of satellites, enabling in situ observationsin space, causeof Landaudamping for obliquemodes (• = k-v•). (2) the developmentof plasma sources,enabling con- The latter two mechanismscan also give rise to insta- trolled laboratory experiments,and (3) advancedthe- bilities when the distribution function at the resonant ory and numerical simulations for whistler instabilities velocity has a positive slope. The stability of whistlers and nonlinearities. A vast body of knowledgeon whis- in plasmas with non-Maxwellian distribution functions tler modes has been accumulated and is continuing to has been studiedtheoretically in detail [Lee and Craw- grow because of ongoing basic research in all areas. n ford, 1970]. Nonlinearwhistler phenomena will be de- parallel, many interesting applicationsof whistler-mode scribed below in connection with observations. waves are arising such as imaging subterranean structures[Thiel et al., 1996],predictions of earthquakesand volcaniceruptions [Hayakawa et al., 1993;Molchanov et 4. Observations of Magnetospheric al., 1993],electron cyclotron and heliconplasma sources Whistlers and Whistler-Mode Waves for industrial applications[Stevens and Cecchi,1993; 4.1. Ground-Based Measurements Chen, 1996], high power plasma switches[Weber et al., 1996],directional whistler antennas, etc., to be de- The earliest and most common observations of whis- scribed below. tlers are performedwith long-wire antennas,amplifiers, and conversionto sound. The signalsmay be recorded and displayed as spectrogramssuch as the one shown 3. Properties of Linear Whistler Modes in Figure i [Potter, 1951]. The observedwhistlers are Whistler waves are electromagnetic waves in magne- excited by natural lightning, couplethrough the Earth- tized plasmas at frequencies below the electron Lar- ionosphericwaveguide into an ionosphericduct, and un- mot frequency, • _< •ce, for electron plasma frequen- dergo singleor multiple reflectionsat conjugatepoints cies, OJpe• OJceand OJpe• OJce.The low frequency [Smith,1961]. Ducted whistlersare observablefor fre- limit of "electron" whistlers is the lower hybrid fre- quenciesbelow half the minimum gyrofrequencyalong quency,•lh • (•ceo:•i)•/2 There are also "hydro- the L shelldetermined by the observer'slatitude [Car- magnetic" whistler modes in the range of the ion cy- penter, 1968]. Rarely, unductedwhistlers are observed clotron frequency,o:•i [Russell et al., 1971; Albert, on the ground[Sonwalkar, 1995; Ohta et al., 1997]. 1980]. Whistler modesare dispersivewaves (group and Although whistler wave propagation is firmly based phase velocitiesare frequencydependent), which can on the theory of ducting, direct measurementsof wave propagate oblique to the static magnetic field B0 up to propagation in ducts cannot be performed from the a limiting "resonancecone" angle, given for electrons by Ophase,,•ax= cos-•(•/•). Near the obliqueres- Signal onance the group and phase velocities are essentially 10 orthogonal, and the wave energy is dominated by the electricfield. For frequencies• < •e/2 there existsan obliquemode at Op•as•- cos-• (2•/•c•) with parallel groupvelocity called the Gendrinmode [Gendrin, 1961]. Frequency Along the directionof wave propagation(k) the wave (kHz) magnetic field is right-hand circularly polarized. The electric field of oblique whistlers has both spacecharge and inductive contributions,E - -V•- OA/Ot. At an oblique density discontinuity the reflection of whistlers produces two reflected and one transmitted mode 0 Time (s) • [Lee, 1969]. Refractionof whistlersin densitynonuni- Figure 1. Typical spectrogramof ionosphericwhis- formitieshas been studiedcarefully [Smith, 1961; Hel- tler waves observedon the ground. The (top) re- liwell, 1965; Walker,1976] since it explainsthe remark- ceived waveform is Fourier an&lyzedand (bottom) able ducting properties of whistlers. Ducting confines displayed as an intensity plot vs frequency and the wave energy in a field-aligned density crest or trough real time. (CourtesyS. P. McGreevy, http://www- and allows oblique whistlers to propagate undamped pw'physics'uiøwa'edu/mcgreevy/' 1998). STENZEL: WHISTLER-MODE WAVES IN SPACE AND THE LABORATORY 14,381 ground. Properties of ducts have been indirectly ob- and cyclotron instabilities [Gurnett and Frank, 1972; tained from optical emissions[Hansen and Scourfield, Maggs, 1989], and recently reviewedby $azhin et al. 1989]or from spacecraftdata [Sonwalkaret al., 1994c; [1993]. VLF emissionscan also propagateto and be Strangeways,1986]. studiedon the ground [$azhin and Hayakawa,1994]. Passive observations of whistlers have been success- Whistler-mode emissionsare also produced in the bow- fully used to obtain plasma parameters in the mag- shockregion of Earth [Hayashi et al., 1994] and of netosphere such as density, large-scale electric fields, variousother planets [Orlowskiand Russell,1995], in and electrontemperature [Carpenter,1988; Sazhin et the solar wind [Gary et al., 1994], in radiation belts al., 1992; Singh et al., 1998]. Ion compositionsare [Coroniti et al., 1987], by proton beams [Wong and obtained from hydromagneticwhistlers (ion cyclotron Goldstein,1987], and by pick-upions [Tsurutaniet al., waves)[Russell et al., 1971; Al'pert, 1980; Boskovaand 199]. Whistler emissionsare alsotriggered by lightning- Jiricek, 1986]. Whistler-modewaves have also been generatedwhistlers [Nakamura and Ohdoh,1989; Son- used to diagnose magnetic fields and particles in solar walkar and Inan, 1989] and man-madewhistler-mode physics[Mann and BaumgSrtel,1989; Chernov,1990]. waves [Helliwell and Katsufrakis, 1974; Mielke et al., Whistler wave-particle interactions are important pro- 1992]. Other sourcesof natural and man-madewhis- cesseswhich can lead to wave amplification and par- tler-mode waves detected in space are emissionslinked ticle precipitation [Kennel and Petschek,1966; Mel- to seismicactivity [Molchanovet al., 1993;Parrot, 1995; rose,1986]. Precipitationof energeticelectrons into the Chmyrev et al., 1997], nuclear explosions[Helliwell, lower ionosphere/atmosphereresults in optical emis- 1965], powerline harmonicradiation [Helliwell et al., sions[Hansen and Scourfield,1989] and ionizationphe- 1975; Bullough,1995; Parrot and Zaslavski,1996], and nomena which cause phase changesin subionospheric active wave injection experiments discussedbelow. VLF waves[Helliwell et al., 1973; Inan et al., 1985; 4.3. Active Experiments With Whistler-Mode Burgessand Inan, 1993; Strangeways,1996]. Ground Waves observationsare complemented by measurements from low-altitudesatellites [Voss et al., 1998]. Electronpre- Man-made excitation of whistler-mode waves in the cipitations can also be triggered by active stimulation ionospherehave been performed with high-power VLF experimentswith ground-basedhigh-power VLF (3- transmittersfrom ground stations [Helliwell et al., 1964]. 30kHz) transmittersdiscussed below. In transmission experiments between conjugate points, not only the applied wave is observed but also triggered emissionswith larger intensities and different fre- 4.2. Observations From Satellites quencies[Mielkeet al., 1992]. Freeenergy in anisotropic Whistlers are readily detectedwith electric and mag- electron distributions is thought to be released by the netic antennas on spacecraft. As on the ground, only injected wave in the form of VLF emissions and elec- frequency spectra are recorded while wave vectors are tron precipitation[Kennel and Petschek,1966; Winglee, inferred[Sakamoto et al., 1995], radiation sourcesare 1985; Molvig et al., 1988; Johnstone,1996]. The in- extrapolatedfrom direction-findingtechniques [Haya- jected wave signals observed on satellites have shown kawa et al., 1990] and ray-tracingmodels [Nagano et spectral broadeningand sidebands[Bell et al., 1983; al., 1998]. In situ measurementsare sensitiveto the en- Tanaka et al., 1987]. These have been explainedby tire spectrumof obliquewhistlers (•: < •:cecos O), hence both linear [Bell and Ngo, 1990] and nonlinearwave- most of the observedwhistlers are oblique, unducted, wave interactions, for example, parametric instabilities magnetosphericallyreflected (MR) waves.Ducted whis- [Chian,1996] and trappedparticle instabilities [Denavit tlers are rarely observedon satellites [Thomson and and Sudan,1975]. Dowden,1977; Sonwalkaret al., 1994c]. Few whistlers With strong HF transmitters on the ground, VLF are observedin the outer magnetosphere[Koons, 1985; waveshave been generatedduring ionosphericmodifica- Nagano et al., 1998]. Lightningexcites whistlers not tion experiments[Belyaev et al., 1987; Rowland et al., only in Earth's magnetospherebut alsoon Jupiter [Ho- 1996; Bart and Stubbe,1997]. The principleis based baraet al., 1995],Neptune [ Curherr et al., 1990; Curherr on a controlled modulation of the electrojet current and Kurth, 1995],and on Venus[Scarf, 1985], although by changing the plasma conductivity through electron the latter observationsare still beingdebated [Cole and heating with a modulated HF wave. The more efficient Hoegy,1997; Strangeway, 1997]. direct excitation of VLF waves from spacecraft has not The ionosphere/magnetosphereproduces various plas- yet been successfulbecause of difficulties of deploying ma instabilities which lead to the emission of waves large loop antennas[Sonwalkar et al., 1994a] or long propagating in the whistler branch. Most of these tethersin space[Stone and Bonifazi, 1998]. Earlier ex- instabilities are due to anisotropic electron distribu- periments with powerful HF topside sounders showed tions such as beams, loss cones, rings, and temper- the nonlinearexcitation of lower-hybridwaves [Benson ature anisotropies. In the auroral zone, VLF hiss is and Vinas, 1988]. generatedby energeticelectrons [Cornilleau-Wehrlin et Whistler-mode waveshave been generatedduring the al., 1993],explained by mechanismssuch as Cherenkov injection of electronbeams from rockets[Winckler et 14,382 STENZEL: WHISTLER-MODE WAVES IN SPACEAND THE LABORATORY al., 1984; Gringuazet al., 1985;Kellogg et al., 1986]and (a) B = 0.6 mG spacecraft[Reeves et a/.,1990],as reviewedby Neubert and Banks[1992]. Analysis[Farrell et al., 1988; Wong *:•i'•i-.'•. and Lin, 1990]and numericalsimulations [Nishikawa et al., 1989]indicate that the wavesare mainly generated by coherent Cherenkov instabilities as earlier demon- stratedin the laboratory[Stenzel, 1977].

5. Laboratory Experiments on I Whistlers G)

5.1. Early Experiments One of the first identifications of whistler waves in laboratory plasmas was reported on ZETA, a toroidal t= 0.35ps pinchplasma for early fusionexperiments [Caller et al., (b) kz• Bo 1960]. The transmissionof microwavesignals (• < ! B(k,m)= •ce • •pc) betweentwo fixed antennaswas shownto • 2.7pGcm 3 s be field-aligned, as predicted for parallel whistlers. Fur- 0.8cm-' • ./ ther transmission experiments were performed in linear discharge plasmas including phase measurements to infer the dispersionrelation [Mahaffey,1963; Dellis and Weaver,1964; Bachynskiand Gibbs,1966]. Sim- ilar phase shift measurementswere employed in solid state physics to demonstrated the existence of helicon wavesin semiconductors[Furdyna, 1965]. How- ever, in contrast to solids,the receiving antennas can be moved through a gaseousplasmas so as to record the local phase and amplitude. Interferometry with movable antennas was developed, which allowed direct mea- kx k surementsof wavelengths,hence the dispersionrelation Theory Y c)(k)/c)c= O.11 •(k). Wave damping due to collisionsand cyclotron dampingwere investigated[Mc Vey and Scharer,1974; Figure 2. Whistler wave pulse excited with a loop Ohkuboand Tanaka, 1976; Barrett, 1986]. Propaga- antenna in a uniform laboratory plasma. (a) Instan- tion of wave packetsyielded the group velocity [Baker taneous amplitude distribution of the wave magnetic and Hall, 1974]. Sinceantenna-launched waves are not fieldin threedimensional real space,(Bx • + By2 + plane wavesand the plasmaswere not infinite and uni- Bz•)l/2(x,y,z, t - const). (b) Fouriercomponents of form, corrections for finite-sized geometries were re- the wavefield in 3-D k space,B(kx, ky,kz,• = const). quired[Lee, 1969; Ohkubo et al., 1971;Uhm et al., 1988]. The grid representsthe theoreticaldispersion surface Early interferometry was performed by moving a re- of whistlers. These data illustrate present multipoint ceiving antenna along a line, for example, parallel to (• 104)measurements in laboratory plasmas [Rousculp B0. Subsequently,the measurementswere extended to et al., 1995]. two dimensionsby scanning over a plane and finally were extended to a three-dimensional(3-D) volume. An example of such 3-D data is displayed in Figure 2 from electric and magnetic field measurementsassum- [Rousculpet al., 1995]. The spatial amplitudedistri- ing plane wavesand the validity of the dispersionrela- bution of the magneticfield, B(x, y, z, t -- const), of tion [Sonwalkarand Inan, 1986; Ladreiter et al., 1995; a whistler wave packet excited by a current pulse in a Sakamotoet al., 1995]. Vice versa, whistler spectro- magnetic loop antenna is shown in Figure 24. In time, gramsare not commonin laboratory plasmasalthough the wave packet propagatesdispersively along B0. Fig- the waveform of a nose whistler can be readily demon- ure 2b shows a 3-D Fourier transform of the wave field strated [Stenzel,19764]. in k spaceat a givenfrequency, B(kx, ky, kz,o: - const). The eigenmodesof the wavepacketlie closeto the theo- 5.2. Resonance Cones, Antennas, and Ducting retical whistlerdispersion surface c•(k) indicatedby a 3- At a given frequency, the whistler wave dispersion D grid. The loop antenna with its axis along B0 excites predictsa continuumof modeswith wavevectors kll • only oblique whistlers. Since multipoint measurements k < oc. These can be excited by antennas where the have not been performed, such 3-D data is unavailable amplitude and phase of the eigenmodesdepend on the for space plasmas. In space, k vectors are calculated shape of the antenna. For a "point radiator," both STENZEL:WHISTLER-MODE WAVES IN SPACEAND THE LABORATORY 14,383 theory and observationsshow that the field amplitude 10-9 assumesa maximum along a resonancecone of angle Argon,Pn - 1.5x10 -4 Torr 9group,max= 7r/2 -- 9pnase,max--•sin -•(a;/a;ce) [Fisher kTe= 1.5 eV and Gould,1971]. Thesecones have been observedfor ne - 2x 10! 1 cm-$ short electric and magnetic dipoles in both the near ta = lOOps Af = 350 kHz zoneand the far zone (r > A) [Boswelland Gonfalone, o• - 0.94 1975;$tenzel, 1976c]. Resonance cones also exist in the 10-1o -- frequencyregime a;c• < a;< (a;p2•+ a;c• 2 )1/2 , whichis of interest for density diagnostics. Fine structure due to warm plasma modes can be used to obtain the electron G - temperature [Muldrew and Gonfalone,1974]. These laboratory observationshave stimulated diagnosticap- _ plicationsin ionosphericplasmas [Gonfalone, 1974; Ro- hde et al., 1993]. 10-11 _ _ Since antennas in plasmas are essential for wave excitation and detection, their properties have been ex- _ tensivelystudied in laboratoryand spaceplasmas [Bal- main, 1972]. Radiationpatterns of VLF antennashave 2x10-12 been calculated[GiaRusso and Bergeson,1970; Wang 1 10 100 500 and Bell, 1972]. Impedancemeasurements have been f (MHz) performedin space[Koons and McPherson,1974], but Figure 3. Thermal magneticnoise in a Maxwellian af- in the absenceof multipoint measurementsin space, ra- terglowplasma in the rangeof whistlerwaves. The 1/f diation patterns of loops are only obtained in large lab- spectrum consistsof Cherenkov-excited oblique whis- oratory plasmas[$tenzel, 1976a]. Recentexperiments tlers. The fiat spectrum above a;c• is due to shot noise. with loop antennas in a uniform plasma obtain the Note the high sensitivity of magnetic measurements whistler wave fields, B(r,t), in three dimensionsand (• 10-13T) [Golubyatnikovand $tenzel, 1993]. time [Rousculpet al., 1995]. SubsequentFourier transformation in spaceand time, B(k,a;), revealsa spectrum of oblique eigenmodessatisfying the theoretical 1994]. For magneticloop antennas,nonlinearities arise dispersionrelation for planewhistler modes, a;(k). The from the v(B) x B term, whichgenerates harmonics and frequency-dependentradiation resistancehas been de- dc magneticfields [$tenzeland Urrutia, 1998a]. Non- termined from the Poyntings vector and antenna cur- linear whistlers with wave magnetic fields comparable rent, a method prefertable over measurements of the to the ambient field have been generated in high-beta driving point impedance since the latter includes non- laboratory plasmas, a topic of interest to the study of radiative absorption processes. whistlerson Venus[Cole and Hoegy,1997]. With receiving loop antennas, the thermal noise of Becauseof the difficulty of deployinglong wire anten- whistlerwaves has been measured in a Maxwellianplas- nas (tethers, loops) in space,it has been suggestedto ma [Golubyatnikovand $tenzel,1993]. The observed usemodulated particle beams as antennas[Harker and 1/f spectrum,shown in Figure 3, consistsof oblique Banks,1985; Kotsarenko et al., 1988]. Suchideas have whistlers produced by incoherent Cherenkov radiation beentested both in laboratoryand spaceplasmas [Neu- of tail electrons. In the presenceof energetic,high bert and Banks,1992]. In a laboratoryplasma a field- pitch angleelectrons the magneticfluctuation spectrum aligned,modulated (a; < a;ce),resonant (Vbeam = a;/kll) peaksat harmonicsof the electroncyclotron frequency, electron beam is observed to linearly excite whistler [$tenzeland Golubyatnikov,1993], which has also been waves[Krafft et al., 1994; Kostrov et, 1998a]. Per- observedin activeexperiments in space[Gough et al., pendicular injection of an energeticmodulated electron 1998]. beam excites whistlers like a magnetic loop antenna Laboratory experiments have demonstrated that the [Griskeyet al., 1997]. However,the coherenceof these sign of the magnetichelicity in whistler wave packets "beam antennas" is limited by velocity spread caused dependson the directionof wavepropagation with re- by rapidly growing high frequencybeam-plasma insta- spect to the dc field. Novel directional antennas based bilities. on helicityinjection have been developed [Rousculp and With the developmentof large-diameter(up to I m) $tenzel,1997] as will be discussedfurther below. cathodes[$tenzel and Daley, 1980] it was possibleto Sheaths surrounding electric antennas are a well- generate large, dense, uniform, magnetized discharge knownsource for nonlineareffects, which can give rise plasmas of high quality. With antennas movable in to rectification[Takayama et al., 1960],parametric in- three dimensions through the plasma, it became pos- stabilities[$tenzel et al., 1975],transit-time instabilities sible to do ray-tracing measurements.The propagation [$tenzel,1989], and frequencymixing, a topic relevant of antenna-launched whistlers in uniform and nonuni- to but rarely discussedin spaceplasmas [Boehm et al., form plasmas has been measured, demonstrating lin- 14,384 STENZEL:WHISTLER-MODE WAVES IN SPACEAND THE LABORATORY ear ducting [Stenzel,1976a; Sugai and Takeda,1980], mode conversion[Bamber et al., 1995; Rosenbergand Gekelman,1998], the Gendrin mode [$tenzel,1976a], I and efficient ducting in density troughs narrower than a parallel wavelength[Stenzel, 1976b; Sugai et al., 1979]. Since wave propagation in ducts cannot be mapped with a spacecraft, these laboratory experiments should be of great interest to the space community interested Ar=4 cm Az(cm) V in the leakageof whistlersfrom narrowducts [Strange- (b) Ar m/2•c = 150 MHz ways,1986; Kaufman, 1986;Karpman, 1997],duct size m/inc= 0.71 [Hansenand Scourfield,1989; Sonwalkaret al., 1994c], ) and duct formation[Rodger et al., 1998]. Vp 5.3. Whistler Instabilities (Velocity Space, Beamø•ø%,, 4 Parametric, and Modulational) ro l Whistler waves can be driven unstable by wave-par- Z,o,', ticle interactions involving Cherenkov and cyclotron 10m) resonances. The former has been demonstrated in a Point / ,,F-2 large beam-plasmalaboratory device [Stenzcl,1977]. Source The beam generates broadband whistler wave noise, -4 o which,by two-dimensional(2-D) correlationtechniques, •MIN is found to consist of oblique whistlers near the reso- o 6 • •MA)• nance cone whose parallel phase velocity matches the o\ beamvelocity (w/kll _ vbca•) ß The Cherenkovin- o/ I I I stability is further clarified by amplifying a test whis- z•r tler wave launched from a small antenna. The one- I•¾fl dimensional (l-D) interferometer trace of Figure 4a (c) (cm) 100150.• w showsthe growth of the test wave along the beam, sat- isfyingwave-particle resonance, w/kll = vbca,•. Two 20 46 304050 • g dimensionalinterferometry shows the phasefronts (Fig- ure 4b) and amplitudecontours (Figure 4c). Thesemea- 2 surementsshow that in the half space along the beam the wave grows in the direction of the group velocity cone,sin Ogroup - w/wc•,nearly orthogonal to the phase velocitycone of anglecos Oph•s• - •/•. In the opposite hemisphere, the wave decays along the resonance cone as without a beam. The instability saturates by beam broadening. Suchlaboratory experimentsdemon- strate clearly the physics of the Cherenkov instability which is discussedbut not experimentally proven for 20 30 50 VLF hiss and electron beam injection experiments. I I I I I I I I Loss cone distributions and temperature anisotropies -6 '4 -2 0 2 4 6 8 10 (T:_> Tii) canproduce whistler instabilities [Litwin and Axial PositionAz (cm) Sudan,1986] , whichhave beenobserved in a magnetic mirror device with RF heating at the electron cyclotron Figure 4. Cherenkovinstability of whistlersin a large beam-plasmasystem: (a) 1-D interferometertrace of frequency[Garner et al., 1987]. In a high-betaplas- a test wave from a point sourceshowing wave growth ma an anisotropic tail of electrons creates a new unsta- alongthe beamand a resonancecone peak opposite to ble electromagneticmode [Urrutia and Stenzel,1984], the beam,(b) 2-D phasefronts showing oblique phase which has been explained theoretically and related to velocityof unstablewhistlers close to the limitingangle spaceplasmas [Goldman and Newman,1987]. of propagation,COS(?phase • W/Wce, and (c) 2-D ampli- Parametric instabilities of whistlers have probably re- tude contoursshowing oblique wave growth close to the ceived more attention in theory [Trakhtengerts,1973; groupvelocity resonance cone angle, sin Oa•ou p •_ •/•c• Berger and Perkins, 1976; Lee and Kuo, 1984; Chian [Stenzel,1977]. et al., 1994] than in experiments[Boswell and Giles, 1976]. Boswelland Giles[1976] observed the trapping and kinetic Alfv6n waveshas been analyzed[Yukhimuk of whistler decay wavesalong the resonancecone where and Roussel-Dupree,1997] so as to explainobservations convectivelosses are at a minimum(Vgroup -• 0). In the of lightning-excitedwave spectra[Kelley et al., 1990; ionospherethe decayof whistler wavesinto lowerhybrid Bell et al., 1994]. Three-waveinteractions between an STENZEL: WHISTLER-MODE WAVES IN SPACEAND THE LABORATORY 14,385

electromagneticpump and decaywhistler and lowerhy- ing occurred in density depressionsas narrow as the brid waveshave also been investigatedin laser-plasma wavelength. Later experiments found that the density interactions[Mourenas, 1997]. The interactionof Lang- trough was produced by electron heating in the antenna muir waves and whistlers can produce the observedfil- near-zone[$ugai et al., 1978]and that the efficientwave amentary fine structure of solar type IV radio bursts trapping involvedreflections of quasi-electrostaticwhis- [Fomichevand Fainshtein, 1988]. tlers in the duct [Golubyatnikov et al., 1989;Kostrov et Modulational instabilities arise when a whistler wave al., 1998b]. These nonlinearphenomena studied in the modifies those plasma parameters which affect its dis- laboratory have stimulated new ideas for more efficient persionand thereby modifiesits propagation and am- VLF antennason spacecraft[Zaboronkova et al., 1996]. plitude. Most common are density modifications via Density modifications by the ponderomotive force the ponderomotiveforce, thermal pressure, and ion- have been investigated for oblique whistlers above the ization, which can lead to self-focusingand filamenta- lower hybrid frequency[Stenzel and Cekelman,1977]. tion instabilities[Washimi, 1973; Sodhaand Tripathi, Using a circular line source,a convergingresonance cone 1977; Karpm.an, 1992]. Initial observationsof ther- produced at its focus a wave pressurefar in excessof the mal self-focusingof whistlerswere reported by Litvak particle pressure. Time-resolved measurements of the [1974].Channeling by self-ionizationhas been reported pulsed experiment showedthe formation of a deep den- by Vdovichenkoet al. [1986]. A detailed experiment sity depressionat the focus, the deformation of the res- on "self-ducting"of whistlerswas performed in a large onancecone fields, a partial density recovery,and repe- uniformlaboratory plasma [Stenzel, 1976b]. A large- tition of the nonlinear interaction. Ion acceleration via amplitude whistler wave was observedto generate a space charge fields dominated over parallel electron ac- field-aligned density depressionin which the wave be- celeration. These observationsare related to the physics cameducted. As shownin Figure 5, nearly perfectduct- of lower hybrid solitons[Seyler, 1994] and presentno questionsabout particle conservation[Robinson et al., (a) 1996]. Brf Unducted Whistler In collisional plasmas, a modulational instability can arise from the temperature dependence of the plas- _ ma conductivity. Fast electron heating and parallel heat conduction is observed to form a field-aligned channel of high Spitzer conductivity in a cold uniform Brf magnetoplasma[Urrutia and $tenzel, 1991]. The intense whistler wave propagates predominantly in its self-generatedcollisionless channel while low-amplitude •"•• ne DuctedWhistlerwhistlers are collisionally damped. No ducting by density gradients is involved in this filamentation process. I I Kr,Pn i = 3x10 -4 Torr tOAOce= O.73 5.4. Whistlers in Electron MHD (Transient Currents, Helicity, and Whistler Wings) j• O•pe/O)(o72• --= 22 I • J• Prf=2 W ta=3ps 150 MHz While many wave phenomenaare thought of in terms r=O_ of plane monochromatic eigenmodes, a vast class of whistler phenomena arise in the form of temporal tran- sients and spatially bounded phenomena, i.e., wave packets. Such transient phenomena are common in electron magnetohydrodynamicss(EMHD) physics[King- sep et al., 1990]. In contrastto ordinary MHD where the plasma behaves like a single magnetized fluid, in EMHD only the electrons are magnetized while the ions

are not' This ariseson timescalesfc-• 1 < t • f-1ci and spatialscales rce - I • r • rci.-• The transition 0 40 60 80 100 regimehas been called Hall MHD [Huba,1995]. A ba- z (cm) sic initial and boundary value problem is the penetra- Figure 5. Filamentation of whistlersin a laboratory tion of transient currents or magnetic fields into ideal plasma. (a) Schematicdiagram showingthat a small- plasmas, which is a solution to the differential equa- amplitude antenna-launched whistler exhibits an am- tion describingfrozen-in fields, OB/Ot- V x (v x B). plitude decay becauseof geometricwave spread while a In MHD, the transient processes can be decomposed strong whistler producesa field-aligned density trough in which it becomestrapped. The duct can be narrower into Alfv6n eigenmodes;in EMHD they can be decom- than the parallel wavelength. (b) Measured ducted posed into low-frequency whistler modes. For propa- and unductedwhistlers in a laboratory plasma [Sten- gation along the ambient field, Fourier analysis of the zel, 1976b]. differential equation yields the whistler dispersion re- 14,386 STENZEL: WHISTLER-MODE WAVES IN SPACE AND THE LABORATORY lation,• -- a•ce(kC/a•pe)2. In EMHD the fluid velocity is given by the Hall effect, v - ve- -J/ne • E x Bo/B•. For smallperturbations, B << B0, propagating along B0, the evolution equation predicts that the current density is parallel to the wave magnetic field,J - i•HVll B, wherean -- ne/Bo - J/E is the Hall "conductivity"and vii - E/B is the propagation velocity. Fields with J ]l B I] A exhibit helicity, de- finedas H - f A. (V x A)dV, whichimplies vortex topologies with linked, knotted, or twisted field lines [Moffat, 1978; Berger and Field, 1984; Isichenkoand Marnachev,1987]. Conservationof helicityand energy '"••i•?".":::'!".":i...'Y'•.., . .... "• are of interestin both MHD and EMHD [Taylor,1974]. Force-freeelectromagnetic fields exist in EMHD [¸s- Figure 6. Measured current density lines, J(r,t - herorichand Gliner, 1988;Stenzel and Urrutia, 1990a]. const), and surfaceof a current tube (I = const) for a When the electron inertia is retained in Ohm's law, the pulsed current from an electrode in a magnetoplasma. generalizedvorticity, • - V x ve-eB/m•, rather than The flux-rope topology arisesfrom the superpositionof the magnetic field B is frozen into the electron fuid, an electron Hall current and the field-aligned current. In electron MHD the current front propagates at the O•/Ot z- V x (v• x •) [Yankov,1995; Urrutia and speedof a whistlerwave[Urrutia and Stenzel,1997]. Stenzel,1996]. Near magnetic null points, MHD changesto EMHD as the ion Larmor radius becomeslarger than the magnetic field gradient scale length. Reconnectionof thin persioncauses a sphericalvortex to elongateinto a con- currentsheets (½/•dpe • r < rci) is governedby EMHD ical shape. Weaker secondaryvortices of oppositeJ, B physics[Bulanov et al., 1992; Drake et al., 1994; Bis- but same helicity are induced. kamp et al., 1997; Avinashet al., 1998]. The motion The helicity properties of whistler wave packets are of small conductingbodies and magnetsthrough space not only of scientific interest but can lead to new ap- plasmasgenerates magnetic perturbations in the form plications such as directional antennas. As schemati- of a Cherenkovcone, named "whistlerwing" [Stenzel cally shown in Figure 8, a simple magnetic or electric and Urrutia, 1989; Kivelson et al., 1993; Gurnett, 1995; dipole antenna excites wave packets of opposite helic- Wang and Kivelson,1996; Thomsonet al., 1996]. Hall ity propagating in iB0 direction. Since no helicity is and electron MHD physicsalso apply to the rapid pen- injected, no net helicity is found in the plasma, which etration of magnetic fields during barium releasesin is consistentwith helicity conservation. Helicity injec- space[Huba et al., 1992],plasma beams /Armale and tion with linked or knotted antennas implies asymmet- Rostoker,1996], and plasma-openingswitches in the ric radiation [Rousculpand $tenzel,1997]. The signof laboratory[Weberet al., 1995]. the injectedhelicity determinesthe directionof wave Detailed laboratory experimentshave shownthat un- propagation. A positive-helicity antenna excites vor- der EMHD conditions, pulsed currents are transported tices along B0 but receivesthem from the opposite di- in the whistler mode [Urrutia and Stenzel, 1988 and rection; hence transmission is nonreciprocal. A linked 1997]. Typically, a step functionor pulsedvoltage is torus-loop antenna has been found to have excellent di- applied to an electrode, and the perturbed magnetic rectionality(• 20 dB). Measurementsof its wavefields field is measuredin three-dimensionalspace and time. are shown in Figure 9. Figures 9a and b show the vor- Fourier analysis showsthat the eigenmodesfall on the tex topology as displayed by the linked fields B0 and dispersionsurface of oblique whistlers,•(k) - const. Bz. Figure 9c demonstrates that the wave amplitude The current density is obtained from AmpSre's law, is much larger for propagation along B0 than opposite J(r, t) - V x B/y0. The currentlines are usuallyheli- to B0. Wave propagationof Bz(z,t) is shownin Fig- cal becauseof the linkageof field-alignedand Hall cur- ure 10 for a sinusoidalantenna current, I(t). The wave rents. At the current front, the current density lines amplitudes in +z direction differ by almost an order of spiral back to the return electrode, satisfyingcurrent magnitude. The direction of preferred radiation is re- closureat all times. As shownin Figure 6, an applied versedby a simple sign changeof either the toroidal or current step evolvesinto a long flux rope. Figure 7 solenoidal current. demonstratesthat a short current pulse detaches from The motion of a conductingand/or magnetic ob- the electrodeand propagatesas nearly sphericalvortex ject in a magnetoplasmainduces time-dependent plas- along B0. Its helicity is positive(negative) for propa- ma currents. These may fall into the EMHD regime gation along (against)B0. Reflectionsreverse the sign when the transit time acrossthe field is short compared of the helicity. Collisionaldamping decreasesmagnetic to an ion cyclotron period. Examples in spaceare elec- helicity and energyat the samerate; however,the topo- trodynamictethers in the ionosphere[Dobrowolny and logical property, A I] B ]l J, remainsunchanged. Dis- Melchioni,1993; Stone and Bonifazi, 1998] and aster- STENZEL: WHISTLER-MODE WAVES IN SPACE AND THE LABORATORY 14,387

strength in the plasma. These are manifestations of the dispersion of a whistler wave packet. In time, as the tether current is switched off, all current loops close within the plasma as they propagate away from the ex- citer in the whistler mode. In order to obtain the fields of a moving dc source,many delayed current pulses, excited from displaced tether positions, are superimposed as by Huygen's principle to form a wavefront. Similar to a ship's wake, a coherent electromagneticperturba- tion, termed a whistlerwing, wasobserved [$tenzel and Urrutia, 1989]. Both the tether wire and the two end electrodes,i.e., the entire dipole, radiate coherent whistler wave packets when they move acrossB0. Because of the whistler dispersionand oblique propagation, the wings are broadening with distance from the source. Thus the current path (J II doesnot form a simple field-alignedloop into the ionosphereas predicted by earlier MHD models[Banks et al., 1981]. Subsequent theories and numerical simulations have confirmed the relevanceof whistler wings to tethers and ionospheric current modulations[Wilson et al., 1996; Zhou et al., 1996;;Papadopoulos et al., 1994]. The results of whistler wings from an electric dipole Plasma havebeen extended to that of a magneticdipole [Urru- tia et al., 1994b]. Measuringthe pulseresponse from a loop antenna, the whistler wake of a dc dipole moving acrossand along B0 have been constructed. Figure 12 showsan example of a whistler wing from a dc magnetic dipole moving across B0 or, vice versa, a stationary

Wavepacket Figure 7. The excitation of a short current pulse Loop antenna in a magnetoplasmaproduces a magnetic field of vortex topology: (a) measurement,and (b) model of a

spherical vortex. The vortex propagates in the whis- Vwhistler tler mode,is force-free,and haspositive/negative helicity for propagationalong/opposite to B0 [Stenzeland Urrutia, 1990a]. HO

Loop-Torus

Bo oidsin the solarwind [Kivelsonet al., 1993;BaumgSrtel No wave • et al., 1994; Gurnett,1995; Wangand Kivelson,1996]. The current path and closure of tethered satellites has beenaddressed in a laboratoryexperiment [$tenzel and H>O H>O Urrutia, 1990b; Urrutia et al., 1994a; $tenzel and Urru- tia, 1998b]. An electron-emittingelectrode has been Reception Directionafity Transmission tethered across B0 to an electron collector and ener- Figure 8. Schematicdiagram explaining antenna di- gized by a current pulse of duration given by veloc- rectionality by helicity conservation. A simple field- ity and electrodedimension, At •_ d/vñ. The space- aligned loop antenna possessingno hellcity excites two time dependenceof the transient current pulsehas been equal whistler vorticesof oppositehelicity propagating measured. A snapshot of the observed current den- in +B0 direction; hence zero helicity is maintained. An sity lines is presentedin Figure 11. One can identify antenna consistingof a loop along the axis of a torus a primary current loop consistingof the tether current, produceshelical fields. For positive-helicityinjection a vortex of positive helicity, i.e., propagatingin +B0 di- two field-alignedcurrent channelsfrom the electrodes, rection, is excited. Its directionality is reversedas a re- and a cross-fieldHall current induced by the insulated ceiving antenna, its directionality is reversed. Transmis- tether wire. The primary loop induces a multitude sion between two identical antennas is unidirectional, of secondaryloops of oppositepolarity and decreasing i.e., nonreciprocal. 14,388 STENZEL:WHISTLER-MODE WAVES IN SPACEAND THE LABORATORY

Earth, they have important applications for communi- i I i cation with submarines[Vego, 1987] and subterranean imagingof mines and man-madestructures [Thiel et al., 1996]. Direct excitationof VLF signalsfrom satel- liteshave encountered setbacks [Sonwalkar et al., 1994b; Stone and Bonifazi, 1998]but hold potential for many interestingapplications [Penzo and Ammann,1989]. The detection of seismogenicVLF emissionsfrom space is an important activity which holds a poten-

-10 0 10 tial for predicting earthquakes and volcanic eruptions x (cm) [Hayakawaet al., 1993; Molchanovet al., 1993]. How- (c) Loop-TorusAntenna ever, as with most new results, they are not without controversy[Rodger et al., 1996]. 10B-z ••-:•..- - • ' There are many applications of whistler wave phenomena in laboratory plasmas. Helicon plasma sources YO are used in the fabrication of microelectronic devices (cm) suchas large-scaleintegrated circuits usedin every com- puter. Whistlers waves couple RF power efficiently -10 into the electrons and produce dense uniform plasmas -20 - 10 0 10 20 for high-qualityplasma processing [Mieno et al., 1992; z (cm) Ellingboeand Boswell, 1996; Chen, 1996]. Whistlers are also useful to heat electrons and drive dc currents - 1O0 0 1O0 in toroidalfusion devices [de Assisand Busnardo-Neto, 1988]. Figure 9. Snapshotof the magnetic field components Pulsedpower technology produces short (20 ns), high- excited by a current pulse to a loop-torus antenna of positivehelicity: (a) transversefields dominatedby Bo power(1012 W) pulsesto accelerateparticle beams for due to the torus, (b) axial field Bz due to the linked inertial fusion[Weber et al., 1995]. Inductivelystored loop, and (c) axial field Bz in the central y - z plane energy is transferred to a load via a plasma opening showinga large amplitude asymmetry along B0 associ- switch whose transient EMHD current propagates at ated with hellcity conservation. the whistler speed. The electrons are magnetized by the wave magnetic field hence the current penetration is nonlinear[Fruchtman, 1991]. dipole in a streaming magnetoplasma. The results are relevant to observationsof magnetic signaturesnear as- 20 teroidsin the solarwind [Kivelsonet al., 1993]. Several recent theoretical and numerical investigationsof whistler wingshave supported the observations[Baumgiirtel et al., 1994; Gurnett, 1995; Wang and Kivelson, 1996; lO Thomsonet al., 1996].

6. Applications of Whistlers Ever since the basic theory for whistlers was devel- (cm) oped, the potential for remote diagnosticsof the ionosphere has been obvious. The average electron density -10 can be obtained from the dispersion of low-frequency whistlers or, more accurately, from "nose whistlers" [Helliwell,1965]. Electrontemperature, large-scale electric fields, ion composition, and fractional densitieshave -20 beenmeasured [Russell et al., 1971; Sazhinand Haya- 0 0.5 t (ps) 1.0 1.5 kawa, 1992]. Magnetic fields in solar and laser plas- Bz(G) mas have been estimated, and the presence of non- -O.2 0 O.2 Maxwellian electron distributions can be inferred from whistler emissions. Figure 10. Axial field component,Bz(z,t), excited Ground-based ionospheric modification experiments by a positive-helicity loop-torus antenna located at z = 0 and driven by a sinusoidalcurrent I(t) (cen- are pursuedto generateELF/VLF signalsin a con- tral trace). Becauseof helicity conservation,a predom- trolled way [Rowlandet al., 1996; Bart and Stubbe, inantly positive-helicity whistler wave is excited along 1997]. Since these signalscan penetrate deep into STENZEL: WHISTLER-MODE WAVES IN SPACE AND THE LABORATORY 14,389

presentlyof great interest [Biskampet al., 1997; Ya- mada et al., 1997]. Fundamentalquestions of helicity and energy transport during reconnectionare also the focusof presentresearch [Canfield and Pevtsov,1998]. Novel methods of wave excitation with beams and antennas are successfullyexplored in the laboratory prior to possibleapplications in space[Griskey et al., 1997; Rousculpet al., 1997;Kostrov et al., 1998a]. The mechanisms for electron acceleration in the near-zone of antennas could be resolved experimentally since it is of broadinterest in variousfields [Karpman, 1985; Kolobov and Economou,1997; Chen,1996]. The capability of measuringcurrent systemsin threedimensional space and time opens up many useful investigations such as currents carried by pulsed beams [Nakamuraet al., 1989]or thermal currentsgenerated by heat pulses,which, in EMHD, form flux ropes[Sten- Figure 11. Snapshot of measured current density zel and Urrutia, 1996]. The high sensitivityof mag- linesJ (r) excitedby tetheredelectrodes in a laboratory netic measurementsallows one to study whistler ther- magnetoplasma.An appliedcurrent pulse (At •_ 70 ns) generates helical plasma currents at each electrode, mal noise in I eV plasmas or to resolve temperature which are closed by electron Hall currents induced by changesof AkTe -• 10-3 eV for detailedheat transport the insulated tether wire. Multiple current loops are ex- studies. cited which propagate in the whistler mode along B0. Active experiments in spaceor ground-basedwave in- A secondcurrent system(not shownhere) propagates jection experiments form a bridge between laboratory in the-B0 direction. and observational space research. The applied signals can be controlled, the plasma parameters are set by nature, the effects are usually detected remotely, and for 7. Forefront and Open Topics in most experiments the plasma is unbounded although Whistler Wave Research not uniform. Precipitation of energetic electrons by whistlers is an important topic of energy transfer from Although whistler phenomenahave been studied for the magnetosphereto the atmosphere. Controlled pre- 100 years, there are still many interesting questions cipitation by VLF injection may be of interest for com- left. Some problems are better suited for experiments munication and aeronomy. Active whistler wave injec- in space;others are better suited for experiment in the tion experiments from space deserve more attention. laboratory. The low collisionalityand large scale-length Free-flying or tethered diagnostic packagesare needed of space plasmas is ideal for observing wave-particle to measure spatial wave properties. and wave-wave interactions. The former require time- Basic research in laboratory and space plasmas have resolved measurements of the electron distribution func- fundamentally the same scientificgoals, i.e., to observe tion combined with complete wave measurements;the and understand new plasma phenomena. In the labora- latter require multipoint data for correlation and bis- pectral wave analyses. Such measurements could ad- vance the knowledgeof phase spaceinstabilities, transport processesin velocity space, particle acceleration processesinvolving whistlers, and nonlinearly coupled modes. Laboratory experiments are highly suited for per- ...... >...... • ..... :...... •...v.:.. forming multipoint measurements,excitation of large- .... :.'"'"'%'%.ß...... ':':i•'.;:.'...... '...... •i•i:iiii•i•i•i;;;?;•.•?::!!•::•i•i;;i:•i•.•?•;•;•;ii•;•;;•::•::..::...... •.- ' "•--•:.•-.....::._....i:• j:..'::-'. :'.'.-.:::' '...... ::• amplitude waves, and controlled parameter variations...... ;<;;;;:"-'"'"'"""'•"--"''"'••-•-•-•,i,,,,:::!' A basic linear problem which could be measured in ...... :..-...... ::?...•:....:-..;.-...... :?!•:.:?:;::!. :!:.::..'!!-:-:.. a large laboratory plasma is the coupling of whistlers into the Earth-ionosphericwaveguide. The propertiesof 0 B (mG) 750 Antenna nonlinear whistlers whose wave amplitude exceedsthe ambient field are just beginning to be studied. These Figure 12. Whistler wings in the perturbed magnetic waves can create magnetic null points, reverse the he- field of a current loop moving with velocity v A_ B0. The wing is constructedby Huygensprinciple from a su- licity density, and propagate at a speed which depends perposition of delayed whistler wavelets from displaced on amplitude and field direction. looppositions [Urrutia et al., 1994b].Similar structures The role of the whistler mode in magnetic recon- have been observedbehind magnetized asteroidsin the nection and the dynamics of narrow current sheets is solarwind [Kivelsonet al., 1993]. 14,390 STENZEL:WHISTLER-MODE WAVES IN SPACEAND THE LABORATORY tory the goal is to isolate a physicalprocess and study Belyaev,P. P., D. S. Kotik, S. N. Mityakov,S. V. Polyakov, it in detail under controlled conditions. In space this V. O. Rapoport,and V. Y. Trakhtengerts,Generation of electromagneticsignals at combinationfrequencies in the is usually not possible, and one has to understand a ionosphere,Radiophys. Quant. Electr., 30, 189-206,1987. complex coupled system from a limited set of passive Benson,R. F., and A. F. Vinas, Plasmainstabilities stimu- observations. While the approaches,methods, and ap- latedby HF transmittersin space,Radio Sci., 23, 585-590, plicationsoften vary, eachactivity canonly benefitfrom 1988. learningabout the differentaspects of whistler wavere- Berger,M. A., and G. B. Field, The topologicalproperties search. of magnetichelicity, J. Fluid Mech., ld7, 133-148,1984. Berger,R. L., and F. W. Perkins,Threshold of parametric instabilities near the lower-hybridfrequency, Phys. Flu- Acknowledgments. The author acknowledgesmany ids, 19, 406-411, 1976. researchcontributions made by J. M. Urrutia. His assistance Biskamp,D., E. Schwarz,and J. F. Drake, Two-fluid theory in the presentation and evaluation of the data is greatly ap- of collisionlessmagnetic reconnection,Phys. Plasmas, d, preciated. This work was supportedby the National Science 1002-1009, 1997. Foundation grant PHY 93-03821. Janet G. Luhmann thanks Vikas S. Sonwalkar and an- Boehm,M. H., C. W. Carlson,J.P. McFadden,J. H. Clem- other referee for their assistancein evaluating this paper. mons,J. H., R. E. Ergun, and F. S. Mozer,Wave rectification in plasmasheaths surrounding electric field antennas, J. Geophys. Res., 99, 21,361-21,374, 1994. References Boskova,J., and F. Jiricek, Deuteron whistlersin the outer ionosphere,Studia Geophys.et Geod., 30, 196-205, 1986. Al'pert, Y., 40 years of whistlers, J. Atmos. Terr. Phys., Boswell, R. W., and M. Giles, Trapping of decay waves in 42, 1-20, 1980. whistler resonancecones, Phys. Rev. Lett., 36, 1142-1144, Appleton, E. V., Wireless studies of the ionosphere, J. Inst. 1976. Electr. Eng., 71, 642, 1932. Boswell,R. W., and A. Gonfalone,Interference structure in Avinash, K., S. V. Bulanov, T. Esirkepov, P. Kaw, F. Pego- the far field of the resonancecone, Phys. Lett. A, 51, raro, P. V. Sasarov, and A. Sen, Forced magnetic field line 485-486, 1975. reconnection in electron magnetohydrodynamicss, Phys. Bulanov, S. V., F. Pegoraro, and A. S. Sakharov, Magnetic Plasmas, 5, 2849-2860, 1998. reconnectionin electron magnetohydrodynamicss,Phys. Armale, R., and N. Rostoker, Fast magnetic field penetra- Fluids B, d, 2499-2508, 1992. tion into a plasma beam, Phys. Plasmas, 3, 2742-2752, Bullough, K., Power line harmonic radiation: Sourcesand 1996. environmental effects, in Handbookof Atmospheric Elec- Bachynski, M.P., and B. W. Gibbs, Propagation in plasmas trodynamics,vol. 2, edited by H. Volland, pp. 291-332, along the magnetic field, Phys. Fluids, 9, 520-538, 1966. CRC, Boca Raton, Fla., 1995. Baker, D. R., and T. A. Hall, Direct measurement of the Burgess,W. C., and U.S. Inan, The role of ductedwhistlers propagation of whistler wave packets, Plasma Phys., 16, in the precipitation loss and equilibrium flux of radiation 901-907, 1974. belt electrons, J. Geophys. Res., 98, 15,643-15,665, 1993. Balmain, K. G., Antennas in plasmas: Characteristics as a Canfield, R. C., and A. Pevtsov, (Eds.), Proceedingsof the function of frequency, Radio Sci., 7, 771-775, 1972. Uhapman Uonferenceon Magnetic Helicity in Spaceand Bamber, J. F., J. E. Maggs, and W. Gekelman, Whistler LaboratoryPlasmas, Nat. Cent. for Atmos. Res., Boul- wave interaction with a density striation: A laboratory der, Colo., 1998. investigation of an auroral process,J. Geophys.Res., 100, Carpenter, D. L., Ducted whistler mode propagationin the 23,795-23,810, 1995. magnetosphere:A half-gyrofrequencyupper intensity cut- Banks, P.M., P. R. Williamson, and K.-I. Oyama, Electri- off and someassociated wave growth phenomena,J. Geo- cal behavior of a shuttle electrodynamic tether system phys. Res., 73, 2919-2928, 1968. (SETS), Planet. SpaceSci., 29, 139-147, 1981. Carpenter, D. L., Remote sensingof magnetosphericplas- Barkhausen, H., Zwei reit Hilfe der neuen Verst/irker ent- ma by meansof whistler mode signals,Rev. Geophys.,26, deckte Erscheinungen, Phys. Z. 20, 401-403, 1919. 535-549, 1988. Barr, R., and P. Stubbe, ELF and VLF wave generation by Chen, F. F., Physics of helicon discharges,Phys. Plasmas, HF heating: A comparisonof AM and CW techniques, J. 3, 1783-1793, 1996. Atmos. Solar Terr. Phys., 59, 2265-2279, 1997. Chernov, G. P., Whistlers in the solar corona and their rel- Barrett, P. J., Measurements on whistler waves in a colli- evanceto fine structures of type IV radio emission,Solar sional plasma column, S. Afr. J. Phys., 9, 147-151, 1986. Phys., 130, 75-82, 1990. Baumg/irtel, K., K. Sauer, and A. Bogdanov,A magnetohy- Chian, A. C.-L., S. R. Lopes, and M. V. Alves, Nonlin- drodynamics model of solar wind interactions with aster- ear excitation of Langmuir and Alfven waves by auroral oid Gaspra, Science, 263, 653-656, 1993. whistler waves in the planetary magnetosphere,Astron. Bell, T. F., and H. D. Ngo, Electrostatic lower hybrid waves Astrophys., 288, 981-984, 1994. excited by electromagnetic whistler mode wavesscattering Chmyrev, V. M., N. V. Isaev, O. N. Serebryakova, V. M. from planar magnetic-field-aligneddensity irregularities, Sorokin, and Y. P. Sobolev, Small-scaleplasma inhomo- J. Geophys. Res., 95, 149-172, 1990. geneitiesand correlatedELF emissionsin the ionosphere Bell, T. F., H. G. James, U.S. Inan, and J.P. Katsufrakis, over an earthquake region, J. Atmos. Solar Terr. Phys., The apparent spectral broadening of VLF transmitter 59, 967-974, 1997. signals during transionospheric propagation, J. Geophys. Cole, K. D., and W. R. Hoegy, Nonlinear whistlers: Impli- Res., 88, 4813-4840, 1983. cations for 100 Hz electric fields observed in the Venus Bell, T. F., U.S. Inan, D. Lauben, V. S. Sonwalkar, R. A. ionosphere, J. Geophys. Res., 102, 14,615-14,623, 1997. Helliwell, Y. P. Sobolev, V. M. Chmyrev, and S. Gonzalez, Cornilleau-Wehrlin, N., J. Solomon,A. Korth, and G. Krem- DE-1 and COSMOS 1809 observations of lower hybrid ser, Generation mechanismof plasmasphericELF/VLF waves excited VLF whistler modes, Geophys. Res. Lett., hiss: A statistical study from GEOS 1 data, J. Geophys. 21, 653-656, 1994. Res., 98, 21,471-21,479, 1993. STENZEL: WHISTLER-MODE WAVES IN SPACEAND THE LABORATORY 14,391

Coroniti, F. V., W. S. Kurth, F. L. Scarf, S. M. Krimigis, C. D.C. Thompson, and W. J. Raitt, Megahertz electron F. Kennel, and D. A. Gurnett, Whistler mode emissionsin modulations during TSS 1R, Geophys. Res. Lett., 25, the Uranian radiation belts, J. Geophys.Res., 92, 15,234- 441-444, 1998. 15,248, 1987. Gringuaz, K. I., N. I. Izhovkina, S. A. Pulinets, and N.M. de Assis, A. S., and J. Busnardo-Neto, Current drive with Shyutte, Mechanisms of emission and transformation of whistler waves, Phys. Fluids, 31, 943-945, 1988. whistler-frequencywaves observed in the experiment with Dellis,A. N., and J. M. Weaver,Whistler mode propagation injectionof electronpulsers into the ionosphere(ARAKS), in a laboratory plasma, Proc. Phys. $oc., 83, 473-489, Cosmic Res., 23, 391-394, 1985. 1964. Griskey, M., J. M. Urrutia, and R. L. Stenzel, A novel Denavit, J., and R. N. Sudan, Whistler sidebandinstability, magnetic loop antenna consistingof an electron beam or- Phys. Fluids, 18, 575-584, 1975. bit acrossB0 (abstract), Eos Trans., 78 (46), Fall Meet. Dobrowolny,M., and E. Melchioni,Electrodynamic aspects Suppl., F566, 1997. of the first tethered satellite mission,J. Geophys.Res., Gurnett, D. A., The whistler-mode bow wave of an asteroid, 98, 13,761-13,788, 1993. J. Geophys. Res., 101, 21,623-21,629, 1995. Drake, J. F., R. G. Kleva, and M. E. Mandt, Structure of Gurnett, D. A., and L. A. Frank, VLF hiss and related plas- thin current layers: Implication for magnetic reconnec- ma observationsin the polar magnetosphere,J. Geophys. tion, Phys. Rev. Lett., 73, 1251-1254, 1994. Res., 77, 172-190, 1972. Eckersley,T. L., Musical atmospherics,Nature, 135, 104, Gurnett, D.A., and W. S. Kurth, Plasma waves and related 1935. phenomenain the magnetosphereof Neptune, in Neptune Ellingboe, A. R., and R. W. Boswell, Capacitive, inductive and Triton, edited by D. P. Cruikshank, pp. 389-423, and helicon-wavemodes of operationof a heliconplasma Univ. of Ariz. Press, Tucson, 1995. source, Phys. Plasmas, 3, 2797-2804, 1996. Gurnett, D. A., W. S. Kurth, I. H. Cairns, and L. J. Farrell, W. M., D. A. Gurnett, P.M. Banks, R. I. Bush, Granroth, Whistlers in Neptune's magnetosphere: Ev- and W. J. Raitt, An analysis of whistler mode radiation idence of atmospheric lightning, J. Geophys. Res., 95, from the Spacelab2 electronbeam, J. Geophys.Res., 93, 20,967-20,976, 1990. 153-161, 1988. Hansen, H. J., and M. W. J. Scourfield, Whistler duct di- Fisher, R. K., and R. W. Gould, Resonancecones in the field mensionsfrom TV auroral images, Planet. Space$ci., 37, pattern of a radio frequencyprobe in a warm anisotropic 979-985, 1989. plasma, Phys. Fluids, 1J, 857-867, 1971. Harker, K. J., and P.M. Banks, Radiation from pulsed elec- Fomichev, V. V., and S. M. Fainshtein, Theory of the fine tron beams in space plasmas, Radio $ci., 19, 454-470, structure of solar type IV radio bursts, Soy. Astron., 32, 1984. 552-556, 1988. Hayakawa, M., Mid-latitude and plasmaspheric hiss: A re- Fruchtman,A., Penetrationand expulsionof magneticfields view, Planet. Space $ci., J0, 1325-1338, 1992. in plasmasdue to the Hall field, Phys. Fluids B, 3, 1908- Hayakawa, M., Whistlers, in Handbookof Atmospheric Elec- 1912, 1991. trodynamics, edited by D. P. Cruikshank, pp. 155-193, Furdyna, J. K., Interferometric measurement of microwave CRC, Boca Raton, Fla., 1995. helicondispersion and the hole damping effect in intrinsic Hayakawa, M., F. Lefeuvre, and J. L. Rauch, On the system InSb, Phys. Rev. Lett., 1J, 635-638, 1965. of Aureol-3 satellite direction finding for ionosphericand Gallet, R. M., J. M. Richardsen,B. Wieder, G. D. Ward, and magnetospheric ELF waves, Trans. Inst. Electr. Inform. G. N. Harding, Microwavewhistler mode propagationin Comm. Eng. E, 73, 942-951, 1990. a denselaboratory plasma, Phys. Rev. Lett., J, 347-349, 1960. Hayakawa, M., T. Yoshino, and M. V. Morgounov, On the possible influence of seismic activity on the propagation Garner, R. C., M. E. Mauel, S. A. Hokin, R. S. Post, and D. of magnetosphericwhistlers at low latitudes, Phys. Earth L. Smatlak, Warm electron-drivenwhistler instability in Planet. Int., 77, 97-108, 1993. an electron-cyclotron-resonanceheated, mirror-confined plasma, Phys. Rev. Lett., 59, 1821-1824, 1987. Hayashi, K., H. Matsui, H. Kawano, T. Yamamoto, and S. Gary, S. P., E. E. Scime,J. L. Phillips, and W. C. Feldman, Kokubun, Whistler mode waves observedby MGF search The whistler heat flux instability: threshold conditionsin coil magnetometer: Polarization and wave normal fea- the solar wind, J. Geophys.Res., 99, 23,391-23,399, 1994. tures of upstream waves near the bowshock, Geophys. Gendrin, R., Le guidagedes whistlerspar le champsmag- Res. Lett., 21, 2907-2910, 1994. netique, Planet. Space Sci., 5, 274-282, 1961. Helliwell, R. A., Whistlers and Related IonosphericPhenom- GiaRusso,D. P., and J. E. Bergeson,Studies of VLF radia- ena, Stanford Univ. Press, Stanford, Calif., 1965. tion patterns of a dipole in a slightly lossymagnetoplas- Helliwell, R. A., VLF wave stimulation experiments in the ma, Radio $ci., 5, 745-756, 1970. magnetosphere from Siple station, Antarctica, Rev. Geo- Goldman, M. V., and D. Newman, Electromagneticbeam phys., 26, 551-578, 1988. modesdriven by anisotropicelectron streams, Phys. Rev. Helliwell, R. A., and J. Katsufrakis, VLF wave injection Lett., 58, 1849-1852, 1987. into the magnetospherefrom Siple station, Antarctica, J. Golubyatnikov, G., and R. L. Stenzel, Thermal fluctuations Geophys. Res., 79, 2511-2518, 1974. of whistlers in a Maxwellian plasma, Phys. Fluids B, 5, Helliwell, R. A., J.P. Katsufrakis, and M. L. Trimpi, Whis- 3122-3126, 1993. tler-induced amplitude perturbation in VLF propagation, Golubyatnikov,G. Y., S. V. Egorov, A.V. Kostrov, E. A. J. Geophys. Res., 78, 4679-4688, 1973. Mareev, and Y. V. Chugunov, Quasielectrostatic wave Helliwell, R. A., J.P. Katsufrakis, T. F. Bell, and R. Raghu- trapping in the thermal channel formed by the near field ram, VLF line radiation in the Earth's magnetosphereand of an electromagneticantenna in a magnetizedplasma, its association with power system radiation, J. Geophys. Soy. Phys. JETP, 69, 1134-1138, 1989. Res., 80, 4249-4258, 1975. Gonfalone,A., Oblique resonancesin the ionosphere,Radio Hobara, Y., O. A. Molchanov, M. Hayakawa, and K. Ohta, $ci., 9, 1159-1163, 1974. Propagation characteristics of whistler waves in the Jo- Gough,M.P., W. J. Burke, D. A. Hardy, C. Y. Huang, L. vian ionosphere and magnetosphere, J. Geophys. Res., C. Gentile, A. G. Rubin, M. R. Oberhardt, A. T. Drobot, 100, 23,523-23,531, 1995. 14,392 STENZEL: WHISTLER-MODE WAVES IN SPACEAND THE LABORATORY

Huba, J. D., Hall magnetohydrodynamicss in space and lab- Analysis of electromagnetic wave direction finding per- oratory plasmas, Phys. Plasmas, 2, 2504-2513, 1995. formed by spaceborne antennas using singular-value de- Huba, J. D., P. A. Bernhardt, and J. G. Lyon, Preliminary composition techniques, Radio Sci., 30, 1699-1712, 1995. study of the CRRES magnetospheric barium releases, J. Lee, J. C.• Whistler wave propagation in a bounded magne- Geophys. Res., 97, 11-24, 1992. toplasma, Int. J. Electr., 26, 537-551, 1969. Inan, U.S., D. L. Carpenter, R. A. Helliwell, and J.P. Lee, J. C., and F. W. Crawford, Stability analysis of whistler Katsufrakis,Subionosphere VLF/LF phaseperturbations amplification, J. Geophys. Res., 75, 85-96, 1970. produced by lightning-whistler induced particle precipita- Lee, M. C., and S. P. Kuo, Production of lower-hybrid waves tion, J. Geophys. Res., 90, 7457-7469, 1985. and field-aligned plasma density striations by whistlers, J. Isichenko, M. B., and A.M. Marnachev, Nonlinear wave so- Geophys. Res., 89, 10,873-10,880, 1984. lutions of electron MHD in a uniform plasma, Soy. Phys. Litvak, A. G., Observation of self-focusingof electromag- JETP, 66, 702-708, 1987. netic waves in a plasma, Soy. Phys. JETP, 32, 430-432, Johnstone, A.D., Pitch angle diffusion of low energy elec- 1974. trons and positive ions in the inner magnetosphere: a re- Litwin, C., and R. N. Sudan, Steady state whistler turbu- view of observationsand theory. Adv. SpaceRes., 17(10), lence and stability of thermal barriers in tandem mirrors, 89-98, 1996. Phys. Fluids, 29, 3760-3768, 1986. Karpman, V. I., Near zone of an antenna in a magnetoplas- Maggs, J. E., Coherent generation of VLF hiss, J. Geophys. ma, Soy. Phys. JETP, 62, 40-47, 1985. Res., 81, 1707-1724, 1976. Karpman, V. I., Whistler wave leakage from plasma ducts Mahaffey, D. W., Microwave propagation through a plasma and solitons, Phys. Plasmas, 5, 156-166, 1997. in magnetic field, Phys. Rev. A, 129, 1481-1488, 1963. Karpman, V. I., R. N. Kaufman, and A. G. Shagalov, Self- Mann, G., and K. Baumg/Srtel, Coronal magnetic field focusing of whistler waves, Phys. Fluids B, J, 3087-3100, strengths determined from fiber bursts, in Proceedings 1992. of an International Workshop on Reconnection in Space Kaufman, R. N., Angular estimate of the capture of whis- Plasma, Spec. Pub. 285, vol. II, pp. 153-156, edited by tlers in ducts, Geomagn. Aeronomy, 26, 350-353, 1986. T. D. Guyenne and J. J. Hunt, Eur. Space Agency, No- Kelley. M. C., J. G. Ding, and R. H. Holzworth, Intense ordwijk, Neth., 1989. ionospheric electric and magnetic field pulses generated McVey, B. D., and J. E. Scharer, Experimental verification by lightning, Geophys. Res. Lett., 17, 2221-2224, 1990. of collisionlesselectron cyclotron damping, Phys. Fluids, Kellogg, P. J., S. J. Mortson, W. Bernstein, and B. A. 17, 142-147, 1974. Whalen, Observations of waves generated by electron Melrose, D. B., Instabilities in Space and Laboratory Plas- beams in the ionosphere, J. Geophys. Res., 91, 12,065- mas, Cambridge Univ. Press, New York, 1986. 12,077, 1986. Mielke, T. A., C. J. Elkins, R. A. Helliwell, and U.S. Inan, Kennel, C. F., and H. E. Petschek, Limit on stably trapped Excitation of whistler mode signals via injection of polar- particle fluxes, J. Geophys. Res., 71, 1-28, 1966. ized VLF waves with the Siple transmitter, Radio Sci., Kingsep, A. S., K. V. Chukbar, and V. V. Yankov, Electron 27, 31-46, 1992. magnetohydrodynamicss, in Reviews of Plasma Physics, Mieno, T., T. Shoji, and K. Kadota, Control of hydrocarbon vol. 16, edited by B. B. Kadomtsev, pp. 243-291, Consult. radicals and amorphous carbon film deposition by means Bur., New York, 1990. of RF whistler wave discharge,Jpn. J. Appl. Phys. Part Kivelson, M. G., L. F. Bargatze, K. K. Khurana, D. J. 1, 31, 1879-1884, 1992. Southwood, R. J. Walker, and P. J. Coleman Jr., Mag- Moffat, H. K., Magnetic Field Generation in Electrically netic signaturesnear Galileo's closestapproach to Gaspra, Conducting Fluids, Cambridge Univ. Press, New York, Science, 261, 331-334, 1993. 1978. Kolobov, V. I., and D. J. Economou, The anomalous skin Molchanov, O. A., O. A. Mazhaeva, A. N. Goliavin, and M. effect in gas dischargeplasmas, Plasma SourcesSci. Tech- Hayakawa, Observations by the Intercosmos-24 satellite nol., 6, 1-17, 1997. of ELF-VLF electromagnetic emissions associated with Koons, H. C., Whistlers and whistler-stimulated emissions earthquakes, Ann. Geophys., 11, 431-440, 1993. in the outer magnetosphere, J. Geophys. Res., 90, 8547- Molvig, K., G. Hilfer, R. H. Miller, and J. Myczkowski, Self- 8551, 1985. consistenttheory of triggered whistler emissions,J. Geo- Koons, H. C., and D. A. McPherson, Measurement of the phys. Res., 93, 5665-5683, 1988. nonlinear impedance of a satellite-borne, electric dipole Mourenas, D., Near-forward scattering in magnetized plas- antenna, Radio Sci., 9, 547-57, 1974. ma: Are laser spots whistling? Phys. Plasmas, 5, 243- Kostrov, A. V., M. V. Starodubtsev, C. Krafft, G. Mat- 246, 1997. thieussent, and A. S. Volokitin, Interaction of a modulated Muldrew, D. B., and A. Gonfalone, Resonance cone and electron beam with a magnetoactive plasma, Soy. Phys. Bernstein wave interference patterns in a magnetoplasma, JETP, 67, 400-404, 1998a. Radio Sci., 9, 873-880, 1974. Kostrov, A. V., A. I. Smirnov, M. V. Starodubtsev, and Nagano, I., X.-Y. Wu, S. Yagitani, and K. Miyamura, Un- A. A. Shaikin, Influence of nonlinear effects on whistler usual whistler with very large dispersion near the mag- emissionin magnetoactive plasma, Soy. Phys. JETP, 67, netopause: Geotail observation and ray-tracing modeling, 579-583, 1998b. J. Geophys. Res., 103, 11,827-11,840, 1998. Kotsarenko, N.Y., G. V. Lizunov, and A. A. Silivra, Radia- Nakamura, T., J. R. Kan, and T. Tamao, Closure of field- tion of electromagnetic wavesby modulated electron beam aligned currents carried by super-Alfvenicauroral elec- injected into the ionospherealong the magnetic field, Cos- trons, J. Geophys. Res., 9•, 5485-5489, 1989. mic Res., 26, 758-763, 1988. Nakamura, Y., and T. Ohdoh, Whistler-triggered emissions Krafft, C., G. Matthieussent, P. Thevenet, and S. Bresson, observedby ISIS satellites, J. Geophys. Res., 9•, 89-92, Interaction of a density modulated electron beam with 1989. a magnetized plasma: Emission of whistler waves, Phys. Neubert, T., and P.M. Banks, Recent results from studies Plasmas, 1, 2163-2171, 1994. of electron beam phenomena in space plasmas, Planet. Ladreiter, H. P., P. Zarka, A. Lecacheux, W. Macher, H. O. Space Sci., •0, 153-183, 1992. Rucker, R. Manning, R., D. A. Gurnett, and W. S. Kurth, Nishikawa, K.-I., L. A. Frank, and C. Y. Huang, Three- STENZEL:WHISTLER-MODE WAVES IN SPACEAND THE LABORATORY 14,393

dimensional simulation of whistler mode excited by the Russell, C. T., R. L. McPherron, and P. J. Coleman Jr., Spacelab 2 electron beam, J. Geophys. Res., 9J, 6855- Fluctuating magnetic fields in the magnetosphere, Space 6865, 1989. Sci. Rev., 12, 810-856, 1971. Ohkubo, K., and S. Tanaka, Spatial cyclotron damping of Sakamoto, K., Y. Kasahara, I. Kimura, K-vector determi- whistler waves in plasmas II, J. Phys. Soc. Jpn., nation of whistler mode signals by using amplitude data 254-256, 1976. obtained by a spacecraft borne instrument, IEEE Trans. Ohkubo, K., Y. Yamamoto, and S. Tanaka, Electron cy- Geosci. Remote Sens., $$, 528-534, 1995. clotron wave and electrostatic wave in bounded plasmas, Sazhin, S.S., and M. Hayakawa, Magnetospheric chorus Phys. Lett. A, 35, 189-190, 1971. emissions: A review, Planet. Space Sci., J0, 681-697, Ohta, K., T. Kitagawa, M. Hayakawa, and R. L. Dowden, 1992. A new type of mid-latitude multi-path whistler trains in- Sazhin, S.S., and M. Hayakawa, Periodic and quasiperiodic cluding a non-ducted whistler, Geophys. Res. Lett., 2•, VLF emissions,J. Atmos. Terr. Phys., 56, 735-753, 1994. 2937-2940, 1997. Sazhin, S.S., M. Hayakawa and K. Bullough, Whistler di- Orlowski, D. S., and C. T. Russell,Comparison of properties agnostics of magnetospheric parameters: A review, Ann. of upstream whistlers at different planets, Adv. Space Geophys., 10, 293-308, 1992. Res., 16, 137-141, 1995. Sazhin, S.S., K. Bullough, and M. Hayakawa, Auroral hiss: Osherovich,V. A., and E. B. Gliner, Force-freeelectromag- A review, Planet. Space Sci., •1, 153-166, 1993. netic waves, Sol. Phys., 117, 391-397, 1988. Scarf, F. L., Lightning on Venus, Adv. Space Res., 5(8), Papadopoulos, K., H.-B. Zhou, and C.-L. Chang, Cerenkov 31-36, 1985. excitation of whistler/heliconwaves by ionosphericHF Seyler, C. E., Lower hybrid wave phenomena associatedwith heating, Geophys.Res. Lett., 21, 1767-1770, 1994. density depletions, J. Geophys. Res., 99, 19513-19525, Parrot, M., Use of satellitesto detect seismo-electromagnetic 1994. effects,Adv. SpaceRes., 15(11), 27-35, 1995. O111•11,o:• •IL. p. , •r:•,•¾¾111;DtJIUI studies at low •+;+"•'•1oot•it•tlugS. ß a• r•vlCw,' Parrot, M., and Y. Zaslavski, Physical mechanismsof man- Indian J. Radio Space Phys., •, 139-155, 1993. made influenceson the magnetosphere,Surv. Geophys., Singh, R. P., A. K. Singh, and D. K. Singh, Plasmaspheric 17, 67-100, 1996. parameters as determined from whistler spectrograms: a Penzo, P. A., and P. W. Ammann (Eds.), Tethers in Space review, J. Atmos. Solar Terr. Phys., 60, 495-508, 1998. Handbook,2nd ed., NASA, Washington, D.C., 1989. Smith, R. L., Propagation characteristics of whistlers trap- Potter, R. K., Analysis of audio-frequency atmospherics, ped in field-aligned columns of enhanced ionization, J. Proc. Inst. Radio Eng., 39, 1067, 1951. Geophys. Res., 66, 3699-3707, 1961. Preece, W. H., Earth currents, Nature London, J9, 554, Sodha, M. S., and V. K. Tripathi, Steady state selffocussing 1894. and filamentation of whistlersin a plasma, J. Appl. Phys., Ratcliffe, J. A., The Magneto-Ionic Theory and its Appli- dS, 1078-1084, 1977. cations to the Ionosphere, Cambridge Univ. Press, New Sonwalkar, V. S., Magnetospheric LF-, VLF-, and ELF- York, 1959. waves, in Handbookof Atmospheric Electrodynamics,pp. Reeves, G. D., P.M. Banks, T. Neubert, K. J. Harker, D. A. 407-462, CRC, Boca Raton, Fla., 1995. Gurnett, and W. J. Raitt, Spacelab 2 electron beam wave Sonwalkar, V. S., and U.S. Inan, Measurements of Siple stimulation: studiesof important parameters, J. Geophys. transmitter on the DE 1 satellite: Wave normal direction Res., 95, 10655-10670, 1990. and antenna effective length, J. Geophys. Res., 91, 154- Robinson, P. A., A. Melatos, and W. Rozmus, Is there lower 164, 1986. hybrid wave collapseat auroral latitudes?: Theory versus Sonwalkar,V. S., and U.S. Inan, Lightning as an embryonic observations,J. Geophys.Res., 101, 21,545-21,552, 1996. sourceof VLF hiss, J. Geophys. Res., 9•, 6986-6994, 1989. Rodger, C. J., N. R. Thomson, and R. L. Dowden, A search Sonwalkar, V. S., U.S. Inan, T. F. Bell, R. A. Helliwell, O. for ELF/VLF activity associatedwith earthquakesusing A. Molchanov, and J. L. Green, DE I VLF observations ISIS satellite data, J. Geophys.Res., 101, 13,369-13,378, during Activny wave injection experiments, J. Geophys. 1996. Res., 99, 6173-6186, 1994a. Rodger, C. J., N. R. Thomson, and R. L. Dowden, Are whis- Sonwalkar, V. S., U.S. Inan, T. F. Bell, R. A. Helliwell, O. tler ducts created by thunderstorm electrostatic fields? J. A. Molchanov, and J. L. Green, DE 1 VLF observations Geophys.Res., 103, 2163-2169, 1998. during Activny wave injection experiments, J. Geophys. Rohde, V., A. Piel, H. Thiemann, and K. I. Oyama, In situ Res., 99, 6173-6186, 1994b. diagnosticsof ionosphericplasma with the resonancecone Sonwalkar, V. S., U.S. Inan, T. F. Bell, R. A. Helliwell, V. technique, J. Geophys. Res. 98, 19,163-19,172, 1993. M. Chmyrev, Y. P. Sobolev, O. Y. Ovcharenko, and V. Rosenberg, S., and W. Gekelman, Electric field measure- Selegej, Simultaneousobservations of VLF ground trans- ments of directly converted lower hybrid waves at a den- mitter signals on the DE 1 and COSMOS 1809 satellites: sity striation, Geophys. Res. Lett., 25, 865-868, 1998. Detection of a magnetosphericcaustic and a duct, J. Geo- Rousculp, C. L., and R. L. Stenzel, Helicity injection by phys. Res., 99, 17,511-17,522, 1994c. knotted antennas into EMHD plasmas,Phys. Rev. Lett., Stenzel, R. L., Whistler wave propagation in a large magne- 79, 837-840, 1997. toplasma, Phys. Fluids, 19, 857-864, 1976a. Rousculp, C. L., R. L. Stenzel, and J. M. Urrutia, Pulsed Stenzel, R. L., Filamentation instability of a large amplitude currents carried by whistlers. V. Detailed new results of whistler wave, Phys. Fluids, 19, 865-871, 1976b. magnetic antenna excitation, Phys. Plasmas, 2, 4083- Stenzel, R. L., Antenna radiation patterns in the whistler 4093, 1995. wave regime measured in a large laboratory plasma, Radio Rousculp,C. L., R. L. Stenzel, and J. M. Urrutia, A periodic Sci., 11, 1045-1056, 1976c. antenna for exciting Gendrin-mode whistlers (abstract), Stenzel, R. L., Observation of beam-generatedVLF hiss in a Bull. Am. Phys. Soc., J2, 1819, 1997. large laboratory plasma, J. Geophys. Res., 82, 4805-4814, Rowland, H. L., M. J. Keskinen, J. S. Villasenor, and A. 1977. Y. Wong, Observationsand simulations of VLF harmonic Stenzel, R. L., High-frequency instability of the sheath-plas- generation with the high-powerauroral simulation facility, ma resonance, Phys. Fluids B, 1, 2273-2282, 1989. J. Geophys. Res., 101, 27,027-27,033, 1996. Stenzel, R. L., and W. F. Daley, Large, indirectly heated, 14,394 STENZEL: WHISTLER-MODE WAVES IN SPACEAND THE LABORATORY

oxide-coated cathode for producing uniform plasmas, U. of reverse magnetic fields, Phys. Rev. Lett., 33, 1139- S. patent 4,216,405, U.S. Patent Of[., Alexandria, VA., 1141, 1974. August 5, 1980. Thiel, D. V., S. J. Garner, and S. G. O'Keefe, ELF sur- Stenzel, R. L., and W. Gekelman, Nonlinear interactions of face impedancemeasurements for subsurfaceEarth map- focused resonancecone fields with plasmas, Phys. Fluids, ping using discretespherics from distant lightning as a 20, 108-115, 1977. radiation source(abstract), paper presentedat National Stenzel, R. L., and G. Golubyatnikov, Cyclotron harmonic ScienceMeeting, Union Radio Sci. Int., Boulder, Colo., lines in the thermal magnetic fluctuation spectrum of spi- 1996. raling electrons in plasmas, Phys. Fluids B, 5, 3122-3126, Thomson, P., D. J. Southwood, and S. Goodman, Plasma 1993. waves radiated by a moving conducting body between Stenzel, R. L., and J. M. Urrutia, Whistler wings from mov- successivegyrofrequencies, J. Geophys. Res., 101,19849- ing electrodes in a magnetized laboratory plasma, Geo- 19858, 1996. phys. Res. Left., 16, 361-364, 1989. Thomson, R. J., and R. L. Dowden, Simultaneousground Stenzel, R. L., and J. M. Urrutia, Force-free electromagnetic and satellite reception of whistlers. II. P L whistlers, J. pulsesin a laboratory plasma, Phys. Rev. Left., 65, 2011- Atmos. Terr. Phys., 39, 879-890, 1977. 2014, 1990a. Trakhtengerts,V. Y., Nonlinear hydrodynamicVLF wave Stenzel, R. L., and J. M. Urrutia, Currents between tethered scatteringin the Earth's magnetosphere,Planet. Space electrodesin a magnetized laboratory plasma, J. Geophys. Sci., 21, 359-366, 1973. Res., 95, 6209-6226, 1990b. Tsurutani, B. T., G. S. Lakhina, F. M. Neubauer, and K.-H. Stenzel, R. L. and J. M. Urrutia, Pulsed currents carried Glassmeier, A new look at the nature of comet Halley's by whistlers. VII. Helicity and transport, in EMHD heat LF electromagneticwaves: Giotto observations, Geophys. pulses, Phys. Plasmas, 3, 2599-2609, 1996. Res. Left., 2•, 3129-3132, 1997. Stenzel, R. L., and J. M. Urrutia, Generation of dc magnetic Uhm, H. S., K. T. Nguyen, R. F. Schneider, and J. R. Smith, fields by rectifying nonlinear whistlers, Phys. Rev. Left., Wave dispersion theory in a plasma column bounded by 81, 2064-2067, 1998a. a cylindrical waveguide, J. Appl. Phys., 6•, 1108-1115, Stenzel, R. L., and J. M. Urrutia, Transient current collec- 1988. tion and closure for a laboratory tether, Geophys. Res. Urrutia, J. M., and R. L. Stenzel, A new electromagnetic Left., 25, 733-736, 1998b. mode in a non-Maxwellian high-beta plasma, Phys. Rev. Stenzel, R. L., H. C. Kim, and A. Y. Wong, Parametric Left., 53, 1909-1912, 1984. instability of the sheath-plasma resonance,Radio Sci., 10, Urrutia, J. M., and R. L. Stenzel, Transport of current by 485-488, 1975. whistler waves, Phys. Rev. Left., 62, 272-275, 1988. Stevens, J. E., and J. L. Cecchi, Wave propagation and plas- Urrutia, J. M., and R. L. Stenzel, Nonlinear penetration of ma uniformity in an electron cyclotron resonance plasma whistler pulses into collisional plasmas via conductivity etch reactor, Jpn. J. Appl. Phys., Part 1, 32, 3007-3012, modifications, Phys. Rev. Left., 67, 1867-1870, 1991. 1993. Urrutia, J. M., and R. L. Stenzel, Pulsed currents carried Stone, N.H., and C. Bonifazi, The TSS-1R mission: Over- by whistlers. VI. Nonlinear effects, Phys. Plasmas, 3, view and scientific context, Geophys. Res. Left., 25, 409- 2589-2598, 1996. 412, 1998. Urrutia, J. M., and R. L. Stenzel, Pulsed currents carried by Storey, L. R. O., An investigation of whistling atmospherics, whistlers. IX. In-situ measurements of currents disrupted Philos. Trans. R. Soc. London, Set. A 2•6, 113-141, by plasma erosion, Phys. Plasmas, •, 36-52, 1997. 1953. Urrutia, J. M., R. L. Stenzel, and C. L. Rousculp, Three- Strangeways, H. J., Whistler leakage from narrow ducts, J. dimensional currents of electrodynamic tethers obtained Atmos. Terr. Phys., JS, 455-462, 1986. from laboratory models, Geophys. Res. Left., 21, 413- Strangeways, H. J., Lightning, trimpis, and sprites, in Re- 416, 1994a. view of Radio Science 1993-1996, edited by W.R.Stone, Urrutia, J. M., C. L. Rousculp, and R. L. Stenzel, Magnetic pp. 741-780, Oxford Univ. Press, New York, 1996. dipole antennas in moving plasmas: A laboratory simu- Strangeway, R. J., Joule heating by ac electric fields in the lation, in Solar System Plasmas in Space and Time, it ionosphere of Venus- Comment, J. Geophys. Res., 102, Geopys. Monogr. Set., vol 84, edited by J. L. Burch and 11,665-11,667, 1997. J. H. Waite Jr., pp. 129-133, AGU, Washington, D.C., Sugai, H., and S. Takeda, Linear amplitude oscillation of a 1994b. whistler wave excited by high power microwaves, Phys. Vdovichenko, I. A., G. A. Markov, V. A. Mironov, and A.M. Fluids, 23, 194-199, 1980. Sergeev,Ionizational self-ductingof whistlers in a plasma, Sugai, H., M. Maruyama, M. Sato, and S. Takeda, Whistler Soy. Phys. JETP, •, 275-279, 1986. ducting caused by antenna action, Phys. Fluids, 21, 690- Vego, M., Soviet submarine communications, Signal, •2, 65- 694, 1978. 73, 1987. Sugai, H., K. Ido, H. Niki, S. Takeda, and K. Mima, Whistler Voss, H. D., M. Walt, W. L. Imhof, J. Mobilia, and U.S. wave trapping in a narrow density trough, J. Phys. Soc. Inan, Satellite observationsof lightning-induced electron Jpn., 46, 1647-1652, 1979. precipitation, J. Geophys. Res., 103, 11,725-11,744, 1998. Sudan, R. N., and E. Ott, Theory of triggered VLF emis- Walker, A.D. M., The theory of whistler propagation, Rev. sions, J. Geophys. Res., 76, 4463-4476, 1971. Geophys., 1•, 629-638, 1976. Takayama, K., H. Ikegami, and S. Miyazaki, Plasma reso- Wang, T. N. C., and T. F. Bell, VLF/ELF input impedance nance in a radio-frequency probe, Phys. Rev. Left., 5, of an arbitrarily oriented loop antenna in a cold collision- 238-240, 1960. lessplasma, IEEE Trans. Antennas Propag., 20, 394-398, Tanaka, Y., D. Lagoutte, M. Hayakawa, F. Lefeuvre, and S. 1972. Tajima, Spectral broadening of VLF transmitter signals Wang, Z., and M. G. Kivelson, Asteroid interaction with the and sideband structure observed on Aureol-3 satellite at solar wind, J. Geophys. Res., 101, 24,479-24,493, 1996. middle latitude, J. Geophys. Res., 92, 7551-7559, 1987. Washimi, H., Self-focusingof transversewaves in a magne- Taylor, J. B., Relaxation of toroidal plasma and generation toplasma, J. Phys. Soc. Jpn., 3•, 1373-1383, 1973. STENZEL:WHISTLER-MODE WAVES IN SPACEAND THE LABORATORY 14,395

Weber, B. V., R. J. Commisso, P. J.Goodrich , J. M.Gross- diffusion regions during magnetic reconnection in a labo- mann, D. D. Hinshelwood, P. F. Ottinger, and S. B. ratory plasma, Phys. Rev. Lett., 78, 3117-3120, 1997. Swanekamp, Plasma opening switch conduction scaling, Y'ankov, V. V., The "frozen-in" concept in a collision- Phys. Plasmas, 2, 3893-3901, 1995. less plasma and in turbulent processesin tokamaks, Soy. Wilson, T. L., D. Chlouber, and R. J. Jost, Electrodynamic Phys. JETP, 80, 219-227, 1995. tether currentsin the day/night ionosphere:Correlations Yukhimuk, V., and R. Roussel-Depre, Magnetic field pulses with the Plasma Motor Generator mission, J. Geophys. produced via whistler mode wave decay in the ionosphere, Res., 101, 21,657-21,688, 1996. Phys. Plasmas, d, 4388-4393, 1997. Winckler, J. R., J. E. Steffen, P. R. Malcolm, K. N. Er- Zaboronkova, T. M., I. G. Kondrat'ev, and A. V. Kudrin, ickson, Y. Abe, and R. L. Swanson, Ion resonancesand Wave emission from a VLF plasma-waveguide antenna ELF wave production by an electron beam injected into system under ionosphericconditions, Radiophys. Quant. the ionosphere: Echo 6, J. Geophys. Res., 89, 7565-7571, Electr., 39, 145-154, 1996. 1984. Zhou, H. B., K. Papadopoulos, A. S. Sharma, and C. L. Winglee, R. M., Enhanced growth of whistlers due to bunch- Chang, Electromagnetohydrodynamicsresponse of a plas- ing of untrapped electrons, J. Geophys. Res., 90, 5141- ma to an external current pulse, Phys. Plasmas, $, 1484- 5152, 1985. 1494, 1996. Wong, H. K., and M. L. Goldstein, Proton beam generation of whistler waves in the Earth's foreshock, J. Geophys. Res., 92, 12,419-12,424, 1987. R.L. Stenzel, Department of Physicsand Astronomy, Box Wong, H. K., and C. S. Lin, Plasma instabilities of a finite- 951547, University of California, Los Angeles, CA 90095- radius electron beam in a uniform plasma, Radio $ci., 25, 1547. ([email protected]) 277-285, 1990. Yamada, M., H. Ji, S. Hsu, T. Carter, R. Kulsrud, Y. Oho, (Received April 7, 1998; revised November 9, 1998; and F. Perkins, Identification of Y-shaped and O-shaped acceptedNovember 9, 1998.)