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Hiss-triggered chorus emissions at Indian stations
Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 1027 – 1033
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Hiss-triggered chorus emissions at Indian stations R.P. Singh∗ , R.P. Patel Atmospheric Research Laboratory, Physics Department, Banaras Hindu University, Varanasi 221005, India Received 29 April 2003; received in revised form 23 October 2003; accepted 30 March 2004
Abstract Some examples of chorus emissions emanating from the upper edge of the underlying hiss events recorded at the Indian Antarctic Station Maitri (geomag. lat:=62◦ S, long. 57:2◦ E, L=4:5) and low-latitude station Gulmarg (geomag. lat:=24◦ 26 N, long. 147◦ 09 E) are reported, in which intensity seems to decrease with increase in frequency and also it varies from event to event. It is proposed that resonance interaction of energetic electrons with wavelets present in the upper edge of hiss elements propagating in whistler mode under suitable condition behaves as a backward wave oscillator and generates chorus emissions. The minimum and the maximum value of interaction length, beam modulation period and temporal evolution of emitted wave frequency have been evaluated. Modulation period has been used to explain the periodicity in the recorded events and the temporal evolution of wave frequency has been used to explain the shape of dynamic spectrum of hiss-triggered emissions. c 2004 Published by Elsevier Ltd. Keywords: Hiss; Triggered chorus emissions; Whistler mode; Backward wave oscillator
1. Introduction VLF emissions depending upon their dynamic spectrum are classi>ed as hiss or unstructured and chorus or structured emissions. Chorus emissions usually consist of a succession of discrete elements with rising frequency having repetition period of ∼ 0:1–1 s and typical duration of 0.5–1 h. It is accompanied by hiss emission, which serves as a lower frequency background for the discrete elements (Helliwell, 1965, 1969; Reeve and Rycroft, 1976; Koons, 1981; Sazhin and Hayakawa, 1992; Trakhtengerts, 1999). Early observations of chorus came from mid and high latitudes (Sazhin and Hayakawa, 1992 and references there in). Later on chorus emissions were also reported from low latitudes (Sazhin and Hayakawa, 1992; Singh et al., 2000 and references there in). Satellite observations showed a good correlation between chorus emissions, hiss emissions and energetic electron Cuxes (Oliver and Gurnett, 1968; Park et al., 1981; Cornilleau-Wehrlin et al., 1978; Summers et al., 2004) suggesting signi>cant role of energetic electrons in the ∗
Corresponding author. Fax: +91-542-2368174. E-mail address: [email protected] (R.P. Singh).
c 2004 Published by Elsevier Ltd. 1364-6826/$ - see front matter doi:10.1016/j.jastp.2004.03.013
generation of hiss and chorus. Fine resolution spectral analysis showed that some part of hiss are very turbulent and incoherent; the other part contains wavelets or monochromatic wave components specially near the upper edge of hiss band (Tsuji et al., 1989; Hattori et al., 1991a, b). In fact, structures or large-amplitude spectral components present in the hiss band are able to phase bunch the electrons leading to the excitation of chorus emissions. Recently, backward wave oscillator (BWO) regime of magnetospheric cyclotron maser has been used to explain the generation of chorus emissions (Trakhtengerts, 1995, 1999; Trakhtengerts et al., 1996; Titova et al., 2002, 2003). Bell et al. (2000) have reported hiss emissions between 4.0 and 5:6 kHz, highly anisotropic energetic electrons, and unusual VLF triggering eGects at 10:2 kHz from a region near the equatorial plane of the plasmasphere on the L = 3:4 Cux tube. Trakhtengerts et al. (2001) considered this observation as the >rst convincing indirect evidence of the existence of step-like distributions which plays key role in the BWO mechanism. They have also discussed how the simultaneously observed VLF hiss can maintain this deformation in the distribution function. In this paper, we present hiss-triggered chorus emissions recorded at high-latitude Indian Antarctic Station Maitri
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and low-latitude station Gulmarg. The intensity of triggered emission is almost equal to or more than the intensity of triggering source hiss, which has been so far considered to be random and incoherent. The BWO has been considered as the generator of chorus emissions in the magnetosphere. 2. Experimental data and analysis VLF recording setup consisting of T-type antenna of 10 m height and 40 m horizontal length supported by two poles, ampli>er and digital audio tape recorder was used to record VLF data at the Indian Antarctic Station, Maitri. The observations were carried out during January 10–March 10, 2001. The data are stored on digital audiotapes, which were replayed and some of the events were analyzed. Fig. 1 shows discrete chorus emissions (risers) in the frequency range 3.5–5 kHz, which originated from a narrow hiss band (3:5 kHz ¡ f ¡ 3:75 kHz). These events were recorded on February 3, 2001 at 1246 : 50 h GMT. Chorus events in
suIcient numbers were observed for about 1 h. df=dt increases as frequency increases. Further, the events are not present at equal intervals. Hiss emissions in the frequency band 12–14:3 kHz are also present. From the spectrograph we also note that there is strong noise at lower frequencies. In Fig. 2 we have presented hiss-triggered chorus emissions recorded at Gulmarg on March 8, 1986 in the recovery phase of substorm activity of March 7, 1986 (Singh et al., 2000). From the >gure we note that rising-type chorus emissions originated from the upper edge of the underlying hiss band. Hiss-triggered chorus events started at 0256 IST (Indian Standard Time) as shown in Fig. 2. The short discrete chorus elements appeared in the frequency range of about 2.0–5:5 kHz having a small df=dt value. In the course of time, the upper frequency began increasing and it reached 7:5 kHz by 0350 h IST. For the next 2 h, the upper frequency remained approximately constant. From 0550 h IST it started decreasing slowly and by 0653 h IST it reached to 4:6 kHz. The observed mean chorus element has the following parameters: fmin = 2:4 kHz, fmax = 6:5 kHz and
Fig. 1. Examples of hiss-triggered chorus emissions recorded at the Indian Antarctic Station Maitri on February 3, 2001 at 12:46 : 50 h GMT.
R.P. Singh, R.P. Patel / Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 1027 – 1033
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Fig. 2. Examples of hiss-triggered chorus emissions recorded at the low-latitude station Gulmarg.
df=dt=0:16 kHz s−1 . Singh et al. (2000) have reported that chorus generation is enhanced when hiss intensity becomes high.
3. Generation mechanism of chorus emissions: While considering generation mechanisms one needs to explain: (i) the dynamic spectra along with frequency band (ii) origin of monochromatic elements constituting >ne structure elements, (iii) repetition frequency of chorus elements. Recently, Lauben et al. (1998) combined six-channel POLAR PWI (Plasma Wave Instrument) data with two-dimensional ray tracing and showed that chorus sources were located within a few degrees of the magnetic equator with wave-normal angles signi>cantly diGerent from zero. They also deduced that the energies of the responsible electrons were likely to be in the range of 14–30 keV. Bell et al. (2000) have reported energetic electrons (energy in the range 1–20 keV) with an average equatorial pitch angle ¿ 75◦ within 7◦ latitude of magnetic equator associated with hiss emissions (4–5:6 kHz) and
unusual VLF triggering eGect at 10:2 kHz. Santolik and Gurnett (2003) using data from the four Cluster space craft at close separation have shown that the dimensions of source region of chorus situated close to the magnetic equatorial plane are 60–260 km parallel to the >eld line and 7–100 km perpendicular to the >eld line at L=4:4. LeDocq et al. (1998) using Poynting vector measurements from PWI showed that the direction of chorus wave power Cow is universally away from the magnetic equator. Most recently, Lauben et al. (2002) presented source characteristics of ELF/VLF chorus, which support a theory of non-ducted chorus generation akin to that for ducted chorus where by each emission is seeded by embryonic noise at a resonance point located near the magnetic equator, there after rapid coherent wave growth at some starting frequency favoured by the natural wave focusing eGects set by prevailing magnetospheric conditions follows from interaction with subsequently phase-bunched counter streaming electrons. The VLF chorus emissions recorded at the Indian stations may have propagated in the ducted/non-ducted whistler mode along the geomagnetic >eld line from the source region. It is known that the wave energy propagates along the
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magnetic >eld lines when the wave-normal angle is close to the Gendrin angle. Thus, the waves with >nite wave-normal angles in the source region will also reach the Earth-surface propagating in pro-longitudinal non-ducted mode. Accordingly, we may consider the source region to be located in the equatorial zone corresponding to the observation site. Jiricek et al. (1981a, b) had analyzed chorus emissions recorded simultaneously onboard a satellite and at two ground stations Panka Ves (L = 2:1) and Lovozero (L = 5) and found statistically similar spectra. This gave an indication of the common source of emissions in the equatorial region, although there is a relatively large spatial size of the emission occurrence region in the ionosphere (2000–3000 km). The observation of VLF emissions on ground stations separated by large distances may be caused both by a direct illumination from the magnetospheric source (Holzer et al., 1974) or by a wave-guide propagation in the ionosphere (Gross, 1970). Thus, VLF emissions generated in the equatorial zone of higher L-values may propagate in ducted mode though the plasmasphere and illuminate wide region of the upper ionosphere. There may exist an ionospheric zone where most favourable conditions occur for the passing of VLF emissions to the Earth’s surface with subsequent propagation in the Earth–ionosphere waveguide (Jiricek et al., 1986; Singh et al., 1992). In this propagation mechanism wave intensity in the outer zone of illumination would be lesser than that in the inner zone. Thus the waves generated with the same intensity may be recorded at diGerent stations with diGerent intensity. The most probable generation mechanism is the whistler mode Doppler-shifted cyclotron resonance instability (Brice, 1964; Kennel and Petschek, 1966; Hayakawa et al., 1990) operative in the equatorial region. In the oG-equatorial zone inhomogeneity destroys the resonance condition and one has to consider non-linear theory (Helliwell, 1967). Trakhtengerts (1999) has presented a fresh treatment of chorus in terms of the BWO mechanism. He showed that during the development of cyclotron instability, a singularity in the form of the step on the distribution function is formed which serves as a boundary in velocity space between resonant and non-resonant electrons. When the non-resonant region is small the singularity can be neglected and one deals with hiss generation. This is valid in the case of suIciently dense cold plasma. In the case of small resonant region phase eGects become important and backward wave oscillator regime is realized leading to the generation of a discrete emission (Trakhtengerts, 1995, 1999). Titova et al. (2002, 2003) analyzed more than 8500 VLF chorus elements detected onboard Magion-5 satellite, compared spectral and amplitude characteristics of observed chorus with those predicted by the BWO model of chorus generation and found qualitative and quantitative agreement between them. The requirement for a generator to operate in backward wave regime is: (a) the interacting wave phase velocity and particle velocity parallel to the magnetic >eld should be in
opposite direction; (b) well-organized electron beam with small velocity dispersion should be present; (c) interaction region should be well-de>ned and bounded. Requirement (a) is readily satis>ed in the case of Doppler-shifted cyclotron resonance interaction for wave frequency smaller than the electron gyrofrequency. The existence of well-organized beam has not been observed. However, interaction between ELF/VLF emissions with energetic electrons results in the formation of a step-like feature of the distribution function (Bespalov and Trakhtengerts, 1986; Nunn and Sazhin, 1991) which ensures large growth rate of whistler wave and transition to the BWO regime (Trakhtengerts, 1995). Thus, the deformation in the distribution function of energetic electrons in the magnetosphere may satisfy condition (b). There are no >xed boundaries for the BWO operating in the magnetosphere. Inhomogeneity of the geomagnetic >eld controls the interaction length. The BWO regime changes from a continuous regime (when wave amplitude is constant) to a periodic regime, which is accompanied by a periodic modulation of wave intensity and then to a stochastic modulation regime (Trakhtengerts, 1995). The periodic regime is characterized by the modulation period TM = 1:5l
1 1 + vg vm
;
(1)
where l is the length of the generator, vg is group velocity of whistler mode wave and vm is the velocity of step in the distribution function. TM can be connected with the repetition period of chorus element. The length of the interaction region is determined using the phase mismatching condition (Helliwell, 1967)
l=2
−l=2
! − !H − kvm dz = ; vm 2
(2)
where z=0 corresponds to the equator. For a dipolar >eld interaction length is given by (Helliwell, 1967; Trakhtengerts, 1999) 2 2 1=3 l0 ∼ = (RE L =k) ;
(3)
where RE is the Earth’s radius, L is the McIlwain parameter and k is wave number. In deriving the above equation the second-order resonance eGects have been neglected. That is, >xed wave frequency has been considered and phase mismatching up to =2 radian has been allowed. In the real condition for a dipolar magnetic >eld the second-order resonance becomes important, which involves changes in wave frequency !(z) and non-linear change in electron velocity. This leads to the changes in the interaction length. The maximum value of the interaction length for the case of inhomogeneous magnetic >eld of the magnetosphere is obtained
R.P. Singh, R.P. Patel / Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 1027 – 1033
Fig. 3. Variation of minimum interaction length as a function of wave-frequency corresponding to the observations of Maitri and Gulmarg stations.
as (Trakhtengerts, 1999) 1=2 1=2 8!HL z L! ∼ 1 + 4A −1 ; lm ( l0 ) = @!H !HL @z
(4)
where A ≈ 1 and L! = !2 − !1 ; !2 (!1 ) is the maximum (minimum) frequency of the chorus event. !HL is the equatorial electron gyro-frequency for a given L. The actual interaction length l satis>es the condition l0 ¡ l ¡ lm . A succession of quasi-monochromatic wavelets starting from the equatorial region and interacting with the well-de>ned energetic electron beam in the BWO regime may trigger signals with a rising frequency (Trakhtengerts, 1999) whose dynamic spectrum for the maximum value of the non-linear growth rate is described by (Omura et al., 1991; Trakhtengerts, 1999) df ! 3|vm | d!H 1 tr2 2S + = ; (5) 2 dt 2 2! + !H tr d z where the value of inhomogeneity factor S lies between 0.2 and 0.8 (Helliwell, 1967). Eq. (5) reduces to the expression of Trakhtengerts and Rycroft (2000) for |S| = 0:5. The minimum value of interaction length for diGerent frequency corresponding to the Maitri (Antarctica) and the Gulmarg station has been computed and shown in Fig. 3. Interaction length for Maitri station is almost double than that for Gulmarg station for the frequency range 1–8 kHz. For higher frequencies interaction length suddenly drops. The minimum value varies from 600 to 1200 km for the Maitri
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Fig. 4. Variation of modulation time as a function of wave-frequency corresponding to the observations of Maitri and Gulmarg stations.
station when frequency is decreased from 8 to 1 kHz. For the Gulmarg station the value of l0 varies between 120 and 400 km as the frequency is decreased from 400 to 1 kHz. The chorus events recorded at Gulmarg and Maitri stations lies in the frequency range 2.0–7:0 kHz and 3.5–5:0 kHz, respectively. The maximum value of interaction length for the observed frequency range is found to be 1000 and 14000 km for the Gulmarg and Maitri station, respectively. The actual value of the interaction length lies between the minimum and the maximum value. Lauben et al. (2002) have estimated interaction length ∼ 1200 km for 3:5 ¡ L ¡ 6:5 from the chorus measurements. In Fig. 4 we have shown modulation time as a function of frequency for the observations corresponding to Gulmarg and Maitri stations. In the computation of group velocity !P = 5652 kHz, !H = 3198 kHz has been used for the Gulmarg station and corresponding values for the Maitri station are 455 and 60:6 kHz, respectively. The length of the BWO generator region is taken as 500 and 5000 km for the Gulmarg and Maitri station, respectively. Vm is taken to be equal to the average parallel resonance velocity. It is assumed that the step velocity in the distribution function is very close to the resonance velocity (Trakhtengerts, 1999). Modulation time for 1–5 kHz varies between 0.4 and 0:8 s (Maitri station). For lower L-values (Gulmarg station) modulation time decreases with frequency in the frequency range 1–80 kHz and lies between 0.05 and 0:01 s. At higher frequencies, modulation time increases with frequency. This
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puted value. For L = 4:5 in the frequency range 1–4 kHz, df=dt is about 0:4 kHz s−1 which is of the same order as that observed at the Maitri station. For the observed chorus at L = 6, df=dt ∼ 1 kHz s−1 has been reported (Burtis and Helliwell, 1975; Hattori et al., 1991b). Titova et al. (2002, 2003) have computed reduced frequency sweep rate [G 2 = (@f=@t)(2! + !H )=(1:5!)] which increases with chorus amplitude, in accordance with expectations from BWO model. In fact df=dt is proportional to d!H =d z (geomagnetic >eld inhomogeneity) which is quite strong at the lower L-values as compared to the higher L-values. Other parameters which aGect it are trapping frequency and step velocity of the distribution function. An increase in both these parameters increases the value of df=dt. Apparently, more precise and accurate computations of the non-linear stage of the BWO regime is required to explain various parameters of hiss-triggered chorus emissions using computer simulations. 4. Conclusions
Fig. 5. df=dt as a function of wave-frequency for L = 1:2 and 4.5. For L = 1:2 the curves for S = 0:2 and S = 0:8 merge in to a single curve.
increase with frequency is due to abrupt changes in group velocity when the wave frequency approaches close to electron gyrofrequency. The computed modulation time is less than the bounce period of the energetic electrons. The observed repetition period of chorus elements measured at Gulmarg is 0:29 s where as the computed value is 0:04 s. The computed value is smaller than the measured value. The discrepancies could be due to thermal eGect, inhomogeneity in plasma density, time-dependent values of magnetospheric parameters, etc. All these parameters may aGect interaction length and hence modulation time. Satellite and ground-based data exhibit modulation time of the same order as predicted for the Maitri station L = 4:5, (Trakhtengerts, 1999). The computed modulation time at lower L-values are very small as compared to the available data. This shows that apart from inhomogeneity at lower L-values, the curvature of the magnetic >eld may also aGect the generation mechanism of chorus, which should be taken into account in to the model computation. The temporal evolution of wave frequency using Eq. (5) has been computed and shown in Fig. 5 for L=1:2 (Gulmarg) and L = 4:5 (Maitri). In the computation we have considered parabolic approximation for the
geomagnetic >eld so that @!H =@z =2!Heq za−2 , where a=( 2=3)RE L. The >gure shows that for L = 1:2, df=dt increases with frequency. For f=4 kHz, df=dt =60 kHz s−1 , whereas the recorded value is 0:16 kHz s−1 which is smaller than the theoretically com-
In this paper, we have reported hiss-triggered chorus emissions recorded at the Indian Antarctic Station Maitri (Antarctica) and Gulmarg. The generation mechanism is considered to be the BWO generator operating in the magnetosphere. An attempt has been made to explain the periodicity of the events and its frequency–time development. The computed results are in agreement with those reported by others. Acknowledgements The work is supported by the Department of Science and Technology, Government of India, New Delhi under SERC project. We are grateful to the referees for their constructive suggestions which improved the quality of the paper. References Bell, T.F., Inan, U.S., Helliwell, R.A., 2000. Simultaneous triggered VLF emissions and energetic electron distributions observed on POLAR with PWI and HYDRA. Geophysical Research Letters 27, 165. Bespalov, P.A., Trakhtengerts, V.Yu., 1986. The cyclotron instability in the Earth’s radiation belts. In: Leontovich, M.A. (Ed.), Reviews of Plasma Physics, Vol. 10. Plenum, New York, 1986, pp. 155–192. Brice, N.M., 1964. A qualitative explanation of the diurnal variation of chorus. Journal of Geophysical Research 69, 4701. Burtis, W.J., Helliwell, R.A., 1975. Magnetospheric chorus: amplitude and growth rate. Journal of Geophysical Research 80, 3265–3270. Cornilleau-Wehrlin, N., Gendrin, R., Lefeuvre, F., Parrot, M., Grard, R., Jones, D., Bahnsen, A., Ungstrup, E., Gibbons, W., 1978. VLF electromagnetic waves observed onboard GEOS-1. Space Science Review 22, 371.
R.P. Singh, R.P. Patel / Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 1027 – 1033 Gross, S.H., 1970. VLF duct associated with the lowerhybrid-resonance frequency in a multi-ion upper ionosphere. Journal of Geophysical Research 75, 4235. Hattori, K., Ishikawa, K., Hayakawa, M., 1991a. Ray tracing study of the plasmapause eGect on non-ducted whistler-mode wave propagation. Planetary and Space Science 39, 425–434. Hattori, K., Hayakawa, M., Lagoutte, D., Parrot, M., Lefeuvre, F., 1991b. An experimental evidence of the role of hiss in the generation of chorus in the outer magnetosphere, as based on spectral analysis and direction >nding. Proceedings of the NIPR Symposium Upper Atmospheric Physics 4, 20–41. Hayakawa, M., Hattori, K., Shimakura, S., Parrot, M., Lefeuvre, F., 1990. Direction >nding of chorus emissions in the outer magnetosphere and their generation and propagation. Planetary and Space Science 38, 135–143. Helliwell, R.A., 1965. Whistlers and Related Ionospheric Phenomena. Stanford University Press, Stanford. Helliwell, R.A., 1967. A theory of discrete VLF emissions from the magnetosphere. Journal of Geophysical Research 72, 4773–4789. Helliwell, R.A., 1969. Low frequency waves in the magnetosphere. Review of Geophysics 7, 281. Holzer, R.E., Farley, T.A., Burton, R.E., Chapman, M.C., 1974. A correlated study of ELF waves and electron precipitation on OGO 6. Journal of Geophysical Research 79, 1007–1013. Jiricek, F., Triska, P., Yurov, V.E., Titova, E.E., 1981a. On the characteristics of VLF emissions in the upper ionosphere and on the ground. Studia Geophica ET Geodaetica 25 (1), 81. Jiricek, F., Yurov, V.E., Titova, E.E., Triska, P., 1981b. Localization of VLF emissions observed in the plasma-trough region. Advanced Space Research 1, 369–372. Jiricek, F., Maltseva, O.A., Titova, E.E., Triska, P., Yakhnina, T.A., 1986. The propagation features of VLF choruses in the magnetosphere. Geomagnetism and Aeronomy 26 (6), 996. Kennel, C.F., Petschek, H.E., 1966. Limit on stably trapped particle Cuxes. Journal of Geophysical Research 71, 1–28. Koons, H.C., 1981. The role of hiss in magnetospheric chorus emissions. Journal of Geophysical Research 86, 6745–6754. Lauben, D.S., Inan, U.S., Bell, T.F., Kirchner, D.L., Hospodarsky, G.B., Pickett, J.S., 1998. VLF chorus emissions observed by polar during the January 10, 1997, magnetic cloud. Geophysical Research Letters 25, 2995–2998. Lauben, D.S., Inan, U.S., Bell, T.F., Gurnett, D.A., 2002. Source characteristics of ELF/VLF chorus. Journal of Geophysical Research 107 (A12), 1429–1446. LeDocq, M.J., Gurnett, D.A., Hospodarsky, G.B., 1998. Chorus source locations from VLF Poynting Cux measurements with the polar spacecraft. Geophysical Research Letters 25, 4063–4066. Nunn, D., Sazhin, S.S., 1991. On the generation mechanism of hiss-triggered chorus. Annales Geophysique 9, 603–613. Oliver, M.N., Gurnett, D.A., 1968. Microburst phenomena 3, An association between microbursts and VLF chorus. Journal of Geophysical Research 73, 2355–2362.
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Omura, M., Nunn, D., Matsumoto, H., Rycroft, M.J., 1991. A review of observational, theoretical and numerical studies of VLF triggered emissions. Journal of Atmospheric and Terrestrial Physics 53, 351–368. Park, C.G., Lim, C.S., Parks, G.K., 1981. A ground satellite study of wave-particle correlations. Journal of Geophysical Research 86, 37. Reeve, C.D., Rycroft, M.J., 1976. A mechanism for precursors to whistler. Journal of Geophysical Research 81, 5900–5910. Santolik, O., Gurnett, D.A., 2003. Transverse dimensions of chorus in the source region. Geophysical Research Letters 30, 1031. Sazhin, S.S., Hayakawa, M., 1992. Magnetospheric chorus emissions. A review, Planetary and Space Science 40, 681–697. Singh, U.P., Singh, A.K., Lalmani, Singh, R.P., Singh, R.N., 1992. Hybrid mode propagation of whistlers at low latitudes. Indian Journal of Radio & Space Physics 21, 246–249. Singh, R., Patel, R.P., Singh, R.P., Lalmani, 2000. An experimental study of hiss triggered chorus emissions at low latitude. Earth Planet Space 52(1), 37–40. Summers, D., Ma, C., Meredith, N.P., Horne, R.B., Thorne, R.M., Anderson, R.R., 2004. Modeling outer-zone relativistic electron response to whistler-mode chorus activity during substorms. Journal of Atmospheric and Solar Terrestrial Physics 66, 133. Titova, E.E., Kozelov, B.V., Jiricek, F., Smilauer, J., Demekhov, A.G., Trakhtengerts, V.Yu., 2002. VLF chorus characteristics and Predictions from Backward wave oscillator model: a comparison, Physics of the Auroral Phenomenon. Proceedings of the 25th Annual Seminar, Apatity, pp. 81–84. Titova, E.E., Kozelov, B.V., Jiricek, F., Smilauer, J., Demekhov, A.G., Trakhtengerts, V.Yu., 2003. Veri>cation of the backward wave oscillator model of VLF chorus generation using data from MAGION-5 satellite. Annales Geophysicae 21, 1073–1081. Trakhtengerts, V.Y., 1995. Magnetospheric cyclotron maser: backward wave oscillator generation regime. Journal of Geophysical Research 100, 17205–17210. Trakhtengerts, V.Y., 1999. A generation mechanism for chorus emission. Annales Geophysicae 17, 95–100. Trakhtengerts, V.Y., Rycroft, M.J., 2000. Whistler-electron interactions in the magnetosphere: new results and novel approaches. Journal of Atmospheric and Terrestrial Physics 62, 1719–1733. Trakhtengerts, V.Y., Rycroft, M.J., Demekhov, A.G., 1996. Interaction of noise like and discrete ELF/VLF emissions generated by cyclotron interactions. Journal of Geophysical Research 101, 13293–13301. Trakhtengerts, V.Y., Demekov, A.G., Pasmanic, D.L., Titova, E.E., Kozelov, B.V., Nunn, D., Rycroft, M.J., 2001. Highly anisotropic distributions of energetic electrons and triggered VLF emissions. Geophysical Research Letters 28, 2577. Tsuji, S., Hayakawa, M., Shimakura, S., Hattori, K., 1989. On the statistical properties of magnetospheric ELF/VLF hiss. Proceedings of the NIPR Symposium Upper Atmospheric Physics 2, 74.
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Hiss-triggered chorus emissions at Indian stations R.P. Singh∗ , R.P. Patel Atmospheric Research Laboratory, Physics Department, Banaras Hindu University, Varanasi 221005, India Received 29 April 2003; received in revised form 23 October 2003; accepted 30 March 2004
Abstract Some examples of chorus emissions emanating from the upper edge of the underlying hiss events recorded at the Indian Antarctic Station Maitri (geomag. lat:=62◦ S, long. 57:2◦ E, L=4:5) and low-latitude station Gulmarg (geomag. lat:=24◦ 26 N, long. 147◦ 09 E) are reported, in which intensity seems to decrease with increase in frequency and also it varies from event to event. It is proposed that resonance interaction of energetic electrons with wavelets present in the upper edge of hiss elements propagating in whistler mode under suitable condition behaves as a backward wave oscillator and generates chorus emissions. The minimum and the maximum value of interaction length, beam modulation period and temporal evolution of emitted wave frequency have been evaluated. Modulation period has been used to explain the periodicity in the recorded events and the temporal evolution of wave frequency has been used to explain the shape of dynamic spectrum of hiss-triggered emissions. c 2004 Published by Elsevier Ltd. Keywords: Hiss; Triggered chorus emissions; Whistler mode; Backward wave oscillator
1. Introduction VLF emissions depending upon their dynamic spectrum are classi>ed as hiss or unstructured and chorus or structured emissions. Chorus emissions usually consist of a succession of discrete elements with rising frequency having repetition period of ∼ 0:1–1 s and typical duration of 0.5–1 h. It is accompanied by hiss emission, which serves as a lower frequency background for the discrete elements (Helliwell, 1965, 1969; Reeve and Rycroft, 1976; Koons, 1981; Sazhin and Hayakawa, 1992; Trakhtengerts, 1999). Early observations of chorus came from mid and high latitudes (Sazhin and Hayakawa, 1992 and references there in). Later on chorus emissions were also reported from low latitudes (Sazhin and Hayakawa, 1992; Singh et al., 2000 and references there in). Satellite observations showed a good correlation between chorus emissions, hiss emissions and energetic electron Cuxes (Oliver and Gurnett, 1968; Park et al., 1981; Cornilleau-Wehrlin et al., 1978; Summers et al., 2004) suggesting signi>cant role of energetic electrons in the ∗
Corresponding author. Fax: +91-542-2368174. E-mail address: [email protected] (R.P. Singh).
c 2004 Published by Elsevier Ltd. 1364-6826/$ - see front matter doi:10.1016/j.jastp.2004.03.013
generation of hiss and chorus. Fine resolution spectral analysis showed that some part of hiss are very turbulent and incoherent; the other part contains wavelets or monochromatic wave components specially near the upper edge of hiss band (Tsuji et al., 1989; Hattori et al., 1991a, b). In fact, structures or large-amplitude spectral components present in the hiss band are able to phase bunch the electrons leading to the excitation of chorus emissions. Recently, backward wave oscillator (BWO) regime of magnetospheric cyclotron maser has been used to explain the generation of chorus emissions (Trakhtengerts, 1995, 1999; Trakhtengerts et al., 1996; Titova et al., 2002, 2003). Bell et al. (2000) have reported hiss emissions between 4.0 and 5:6 kHz, highly anisotropic energetic electrons, and unusual VLF triggering eGects at 10:2 kHz from a region near the equatorial plane of the plasmasphere on the L = 3:4 Cux tube. Trakhtengerts et al. (2001) considered this observation as the >rst convincing indirect evidence of the existence of step-like distributions which plays key role in the BWO mechanism. They have also discussed how the simultaneously observed VLF hiss can maintain this deformation in the distribution function. In this paper, we present hiss-triggered chorus emissions recorded at high-latitude Indian Antarctic Station Maitri
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and low-latitude station Gulmarg. The intensity of triggered emission is almost equal to or more than the intensity of triggering source hiss, which has been so far considered to be random and incoherent. The BWO has been considered as the generator of chorus emissions in the magnetosphere. 2. Experimental data and analysis VLF recording setup consisting of T-type antenna of 10 m height and 40 m horizontal length supported by two poles, ampli>er and digital audio tape recorder was used to record VLF data at the Indian Antarctic Station, Maitri. The observations were carried out during January 10–March 10, 2001. The data are stored on digital audiotapes, which were replayed and some of the events were analyzed. Fig. 1 shows discrete chorus emissions (risers) in the frequency range 3.5–5 kHz, which originated from a narrow hiss band (3:5 kHz ¡ f ¡ 3:75 kHz). These events were recorded on February 3, 2001 at 1246 : 50 h GMT. Chorus events in
suIcient numbers were observed for about 1 h. df=dt increases as frequency increases. Further, the events are not present at equal intervals. Hiss emissions in the frequency band 12–14:3 kHz are also present. From the spectrograph we also note that there is strong noise at lower frequencies. In Fig. 2 we have presented hiss-triggered chorus emissions recorded at Gulmarg on March 8, 1986 in the recovery phase of substorm activity of March 7, 1986 (Singh et al., 2000). From the >gure we note that rising-type chorus emissions originated from the upper edge of the underlying hiss band. Hiss-triggered chorus events started at 0256 IST (Indian Standard Time) as shown in Fig. 2. The short discrete chorus elements appeared in the frequency range of about 2.0–5:5 kHz having a small df=dt value. In the course of time, the upper frequency began increasing and it reached 7:5 kHz by 0350 h IST. For the next 2 h, the upper frequency remained approximately constant. From 0550 h IST it started decreasing slowly and by 0653 h IST it reached to 4:6 kHz. The observed mean chorus element has the following parameters: fmin = 2:4 kHz, fmax = 6:5 kHz and
Fig. 1. Examples of hiss-triggered chorus emissions recorded at the Indian Antarctic Station Maitri on February 3, 2001 at 12:46 : 50 h GMT.
R.P. Singh, R.P. Patel / Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 1027 – 1033
1029
Fig. 2. Examples of hiss-triggered chorus emissions recorded at the low-latitude station Gulmarg.
df=dt=0:16 kHz s−1 . Singh et al. (2000) have reported that chorus generation is enhanced when hiss intensity becomes high.
3. Generation mechanism of chorus emissions: While considering generation mechanisms one needs to explain: (i) the dynamic spectra along with frequency band (ii) origin of monochromatic elements constituting >ne structure elements, (iii) repetition frequency of chorus elements. Recently, Lauben et al. (1998) combined six-channel POLAR PWI (Plasma Wave Instrument) data with two-dimensional ray tracing and showed that chorus sources were located within a few degrees of the magnetic equator with wave-normal angles signi>cantly diGerent from zero. They also deduced that the energies of the responsible electrons were likely to be in the range of 14–30 keV. Bell et al. (2000) have reported energetic electrons (energy in the range 1–20 keV) with an average equatorial pitch angle ¿ 75◦ within 7◦ latitude of magnetic equator associated with hiss emissions (4–5:6 kHz) and
unusual VLF triggering eGect at 10:2 kHz. Santolik and Gurnett (2003) using data from the four Cluster space craft at close separation have shown that the dimensions of source region of chorus situated close to the magnetic equatorial plane are 60–260 km parallel to the >eld line and 7–100 km perpendicular to the >eld line at L=4:4. LeDocq et al. (1998) using Poynting vector measurements from PWI showed that the direction of chorus wave power Cow is universally away from the magnetic equator. Most recently, Lauben et al. (2002) presented source characteristics of ELF/VLF chorus, which support a theory of non-ducted chorus generation akin to that for ducted chorus where by each emission is seeded by embryonic noise at a resonance point located near the magnetic equator, there after rapid coherent wave growth at some starting frequency favoured by the natural wave focusing eGects set by prevailing magnetospheric conditions follows from interaction with subsequently phase-bunched counter streaming electrons. The VLF chorus emissions recorded at the Indian stations may have propagated in the ducted/non-ducted whistler mode along the geomagnetic >eld line from the source region. It is known that the wave energy propagates along the
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magnetic >eld lines when the wave-normal angle is close to the Gendrin angle. Thus, the waves with >nite wave-normal angles in the source region will also reach the Earth-surface propagating in pro-longitudinal non-ducted mode. Accordingly, we may consider the source region to be located in the equatorial zone corresponding to the observation site. Jiricek et al. (1981a, b) had analyzed chorus emissions recorded simultaneously onboard a satellite and at two ground stations Panka Ves (L = 2:1) and Lovozero (L = 5) and found statistically similar spectra. This gave an indication of the common source of emissions in the equatorial region, although there is a relatively large spatial size of the emission occurrence region in the ionosphere (2000–3000 km). The observation of VLF emissions on ground stations separated by large distances may be caused both by a direct illumination from the magnetospheric source (Holzer et al., 1974) or by a wave-guide propagation in the ionosphere (Gross, 1970). Thus, VLF emissions generated in the equatorial zone of higher L-values may propagate in ducted mode though the plasmasphere and illuminate wide region of the upper ionosphere. There may exist an ionospheric zone where most favourable conditions occur for the passing of VLF emissions to the Earth’s surface with subsequent propagation in the Earth–ionosphere waveguide (Jiricek et al., 1986; Singh et al., 1992). In this propagation mechanism wave intensity in the outer zone of illumination would be lesser than that in the inner zone. Thus the waves generated with the same intensity may be recorded at diGerent stations with diGerent intensity. The most probable generation mechanism is the whistler mode Doppler-shifted cyclotron resonance instability (Brice, 1964; Kennel and Petschek, 1966; Hayakawa et al., 1990) operative in the equatorial region. In the oG-equatorial zone inhomogeneity destroys the resonance condition and one has to consider non-linear theory (Helliwell, 1967). Trakhtengerts (1999) has presented a fresh treatment of chorus in terms of the BWO mechanism. He showed that during the development of cyclotron instability, a singularity in the form of the step on the distribution function is formed which serves as a boundary in velocity space between resonant and non-resonant electrons. When the non-resonant region is small the singularity can be neglected and one deals with hiss generation. This is valid in the case of suIciently dense cold plasma. In the case of small resonant region phase eGects become important and backward wave oscillator regime is realized leading to the generation of a discrete emission (Trakhtengerts, 1995, 1999). Titova et al. (2002, 2003) analyzed more than 8500 VLF chorus elements detected onboard Magion-5 satellite, compared spectral and amplitude characteristics of observed chorus with those predicted by the BWO model of chorus generation and found qualitative and quantitative agreement between them. The requirement for a generator to operate in backward wave regime is: (a) the interacting wave phase velocity and particle velocity parallel to the magnetic >eld should be in
opposite direction; (b) well-organized electron beam with small velocity dispersion should be present; (c) interaction region should be well-de>ned and bounded. Requirement (a) is readily satis>ed in the case of Doppler-shifted cyclotron resonance interaction for wave frequency smaller than the electron gyrofrequency. The existence of well-organized beam has not been observed. However, interaction between ELF/VLF emissions with energetic electrons results in the formation of a step-like feature of the distribution function (Bespalov and Trakhtengerts, 1986; Nunn and Sazhin, 1991) which ensures large growth rate of whistler wave and transition to the BWO regime (Trakhtengerts, 1995). Thus, the deformation in the distribution function of energetic electrons in the magnetosphere may satisfy condition (b). There are no >xed boundaries for the BWO operating in the magnetosphere. Inhomogeneity of the geomagnetic >eld controls the interaction length. The BWO regime changes from a continuous regime (when wave amplitude is constant) to a periodic regime, which is accompanied by a periodic modulation of wave intensity and then to a stochastic modulation regime (Trakhtengerts, 1995). The periodic regime is characterized by the modulation period TM = 1:5l
1 1 + vg vm
;
(1)
where l is the length of the generator, vg is group velocity of whistler mode wave and vm is the velocity of step in the distribution function. TM can be connected with the repetition period of chorus element. The length of the interaction region is determined using the phase mismatching condition (Helliwell, 1967)
l=2
−l=2
! − !H − kvm dz = ; vm 2
(2)
where z=0 corresponds to the equator. For a dipolar >eld interaction length is given by (Helliwell, 1967; Trakhtengerts, 1999) 2 2 1=3 l0 ∼ = (RE L =k) ;
(3)
where RE is the Earth’s radius, L is the McIlwain parameter and k is wave number. In deriving the above equation the second-order resonance eGects have been neglected. That is, >xed wave frequency has been considered and phase mismatching up to =2 radian has been allowed. In the real condition for a dipolar magnetic >eld the second-order resonance becomes important, which involves changes in wave frequency !(z) and non-linear change in electron velocity. This leads to the changes in the interaction length. The maximum value of the interaction length for the case of inhomogeneous magnetic >eld of the magnetosphere is obtained
R.P. Singh, R.P. Patel / Journal of Atmospheric and Solar-Terrestrial Physics 66 (2004) 1027 – 1033
Fig. 3. Variation of minimum interaction length as a function of wave-frequency corresponding to the observations of Maitri and Gulmarg stations.
as (Trakhtengerts, 1999) 1=2 1=2 8!HL z L! ∼ 1 + 4A −1 ; lm ( l0 ) = @!H !HL @z
(4)
where A ≈ 1 and L! = !2 − !1 ; !2 (!1 ) is the maximum (minimum) frequency of the chorus event. !HL is the equatorial electron gyro-frequency for a given L. The actual interaction length l satis>es the condition l0 ¡ l ¡ lm . A succession of quasi-monochromatic wavelets starting from the equatorial region and interacting with the well-de>ned energetic electron beam in the BWO regime may trigger signals with a rising frequency (Trakhtengerts, 1999) whose dynamic spectrum for the maximum value of the non-linear growth rate is described by (Omura et al., 1991; Trakhtengerts, 1999) df ! 3|vm | d!H 1 tr2 2S + = ; (5) 2 dt 2 2! + !H tr d z where the value of inhomogeneity factor S lies between 0.2 and 0.8 (Helliwell, 1967). Eq. (5) reduces to the expression of Trakhtengerts and Rycroft (2000) for |S| = 0:5. The minimum value of interaction length for diGerent frequency corresponding to the Maitri (Antarctica) and the Gulmarg station has been computed and shown in Fig. 3. Interaction length for Maitri station is almost double than that for Gulmarg station for the frequency range 1–8 kHz. For higher frequencies interaction length suddenly drops. The minimum value varies from 600 to 1200 km for the Maitri
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Fig. 4. Variation of modulation time as a function of wave-frequency corresponding to the observations of Maitri and Gulmarg stations.
station when frequency is decreased from 8 to 1 kHz. For the Gulmarg station the value of l0 varies between 120 and 400 km as the frequency is decreased from 400 to 1 kHz. The chorus events recorded at Gulmarg and Maitri stations lies in the frequency range 2.0–7:0 kHz and 3.5–5:0 kHz, respectively. The maximum value of interaction length for the observed frequency range is found to be 1000 and 14000 km for the Gulmarg and Maitri station, respectively. The actual value of the interaction length lies between the minimum and the maximum value. Lauben et al. (2002) have estimated interaction length ∼ 1200 km for 3:5 ¡ L ¡ 6:5 from the chorus measurements. In Fig. 4 we have shown modulation time as a function of frequency for the observations corresponding to Gulmarg and Maitri stations. In the computation of group velocity !P = 5652 kHz, !H = 3198 kHz has been used for the Gulmarg station and corresponding values for the Maitri station are 455 and 60:6 kHz, respectively. The length of the BWO generator region is taken as 500 and 5000 km for the Gulmarg and Maitri station, respectively. Vm is taken to be equal to the average parallel resonance velocity. It is assumed that the step velocity in the distribution function is very close to the resonance velocity (Trakhtengerts, 1999). Modulation time for 1–5 kHz varies between 0.4 and 0:8 s (Maitri station). For lower L-values (Gulmarg station) modulation time decreases with frequency in the frequency range 1–80 kHz and lies between 0.05 and 0:01 s. At higher frequencies, modulation time increases with frequency. This
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puted value. For L = 4:5 in the frequency range 1–4 kHz, df=dt is about 0:4 kHz s−1 which is of the same order as that observed at the Maitri station. For the observed chorus at L = 6, df=dt ∼ 1 kHz s−1 has been reported (Burtis and Helliwell, 1975; Hattori et al., 1991b). Titova et al. (2002, 2003) have computed reduced frequency sweep rate [G 2 = (@f=@t)(2! + !H )=(1:5!)] which increases with chorus amplitude, in accordance with expectations from BWO model. In fact df=dt is proportional to d!H =d z (geomagnetic >eld inhomogeneity) which is quite strong at the lower L-values as compared to the higher L-values. Other parameters which aGect it are trapping frequency and step velocity of the distribution function. An increase in both these parameters increases the value of df=dt. Apparently, more precise and accurate computations of the non-linear stage of the BWO regime is required to explain various parameters of hiss-triggered chorus emissions using computer simulations. 4. Conclusions
Fig. 5. df=dt as a function of wave-frequency for L = 1:2 and 4.5. For L = 1:2 the curves for S = 0:2 and S = 0:8 merge in to a single curve.
increase with frequency is due to abrupt changes in group velocity when the wave frequency approaches close to electron gyrofrequency. The computed modulation time is less than the bounce period of the energetic electrons. The observed repetition period of chorus elements measured at Gulmarg is 0:29 s where as the computed value is 0:04 s. The computed value is smaller than the measured value. The discrepancies could be due to thermal eGect, inhomogeneity in plasma density, time-dependent values of magnetospheric parameters, etc. All these parameters may aGect interaction length and hence modulation time. Satellite and ground-based data exhibit modulation time of the same order as predicted for the Maitri station L = 4:5, (Trakhtengerts, 1999). The computed modulation time at lower L-values are very small as compared to the available data. This shows that apart from inhomogeneity at lower L-values, the curvature of the magnetic >eld may also aGect the generation mechanism of chorus, which should be taken into account in to the model computation. The temporal evolution of wave frequency using Eq. (5) has been computed and shown in Fig. 5 for L=1:2 (Gulmarg) and L = 4:5 (Maitri). In the computation we have considered parabolic approximation for the
geomagnetic >eld so that @!H =@z =2!Heq za−2 , where a=( 2=3)RE L. The >gure shows that for L = 1:2, df=dt increases with frequency. For f=4 kHz, df=dt =60 kHz s−1 , whereas the recorded value is 0:16 kHz s−1 which is smaller than the theoretically com-
In this paper, we have reported hiss-triggered chorus emissions recorded at the Indian Antarctic Station Maitri (Antarctica) and Gulmarg. The generation mechanism is considered to be the BWO generator operating in the magnetosphere. An attempt has been made to explain the periodicity of the events and its frequency–time development. The computed results are in agreement with those reported by others. Acknowledgements The work is supported by the Department of Science and Technology, Government of India, New Delhi under SERC project. We are grateful to the referees for their constructive suggestions which improved the quality of the paper. References Bell, T.F., Inan, U.S., Helliwell, R.A., 2000. Simultaneous triggered VLF emissions and energetic electron distributions observed on POLAR with PWI and HYDRA. Geophysical Research Letters 27, 165. Bespalov, P.A., Trakhtengerts, V.Yu., 1986. The cyclotron instability in the Earth’s radiation belts. In: Leontovich, M.A. (Ed.), Reviews of Plasma Physics, Vol. 10. Plenum, New York, 1986, pp. 155–192. Brice, N.M., 1964. A qualitative explanation of the diurnal variation of chorus. Journal of Geophysical Research 69, 4701. Burtis, W.J., Helliwell, R.A., 1975. Magnetospheric chorus: amplitude and growth rate. Journal of Geophysical Research 80, 3265–3270. Cornilleau-Wehrlin, N., Gendrin, R., Lefeuvre, F., Parrot, M., Grard, R., Jones, D., Bahnsen, A., Ungstrup, E., Gibbons, W., 1978. VLF electromagnetic waves observed onboard GEOS-1. Space Science Review 22, 371.
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