- Email: [email protected]
Generation of the Auroral Kilometric Radiation in plasma cavities—I. Experimental study
Pluwt. Spuw SG., Vol. 44. No. 3. pp. 199~~ZlO.1996
Pergamon
Coovrieht sYj 1996 Elsevier Science Ltd Printed’& &eat Britain. All rights reserved 0032m-0633,‘96 $15.00+0.00
0032-0633(95)00121-2
Generation of the Aurora1 Kilometric Radiation in plasma cavities-I. Experimental study Philippe Louarn’
and Dominique
Le Q&au’
‘Laboratoire d’Astrophysique de Toulouse. Observatoire Midi-PyrCnCes. 14, Avenue Edouard Belin, 31400 Toulouse. 3 ‘entre d’Etude des Environnements Terrestres et Planetaires, Velizy, France Received 27 January
1995; revised
I4 September
1995 ; accepted
15 September
France
1995
I. Introduction
the sounx.
studies.
The Amoral Kilometric Radiation (AKR hereafter) is the most powerful natural radio emission emanating from the Earth magnetosphere. This strongly polarized emission is generated in the night sector. at altitudes ranging from less than 5000 km to more than 15,000 km and in close association with the development of aurora] discrete arcs (Gurnett, 1974; Green et al., 1977: Benson and Akasofu. 1984). Its frequency bandwidth is roughly 50-500 kHz with a maximum spectral density around 250 kHz. This radiation mainly propagates on the X mode with electric field amplitudes that reach IO-” V mm-’ Hz- I’. Such high values cannot be explained by classical thermal or incoherent generation mechanisms and non-thermal emission processes such as plasma instabilities must be invoked. In many aspects-its non-thermal origin. its high polarization, its temporal variability and its organization in many fine spectral structures---the AKR presents strong analogies with the powerful radio emissions that emanate from the aurora1 regions of the other magnetized planets : Jupiter, Saturn. Uranus and Neptune (Zarka. 1992). It can also be compared to certain solar radio bursts (the socalled microwave spike bursts) (Dulk. 1985 ; Aschwanden and Benz, 1988) and some stellar radio emissions (Melrose and Dulk. 1982 : Louarn et trl.. 1986). Then. the radio emission generation mechanism operating in the terrestrial magnetosphere could well be a universal process associated with the acceleration of particles in strongly magnetized plasma. The &king experiment has allowed some significant progress in the understanding of the generation mechanism of the AKR. This Swedish spacecraft was the first to explore, with a complete set of experiments, the heart of AKR sources. Most of the Viking experimental works accomplished so far on this particular problem of AKR generation are summarized in a review article by Roux rt ul. (1993). The most important conclusions of these studies are given below.
200
P. Louarn and D. Le QuCau : Generation
The AKR propagates mainly on the X mode with. nevertheless, possible faint components on the Z and 0 mode. It is generated within strongly magnetized regions (f& < 0. I where ,fpis the plasma frequency and .f: the electron gyrofrequency), at frequencies close to the local cut-off of the X mode: Jx = (.f,+(.f’f+4f’z)’ ‘)/2 and propagates outside the sources in a direction rather perpendicular to the geomagnetic field. An important result of the Vi/&g observations is that the sources have a small extension (a few km) perpendicular to the geomagnetic field. The plasma of these regions is tenuous 01, = 1 cm-‘) with an electron population essentially constituted by energetic particles ((E) = 3-10 keV) (Bahnsen ~1 nl., 1987; Pottelette rt cd.. 1988; Bahnsen et ul., 1989; Ungstrup et al., 1990; Louarn et al.. 1990). It is separated from the denser and colder external plasma (n, = 5-10 cm’.“, (E) = a few 10 eV) by a sharp density and energy gradient with typical scale length smaller than 1 km. An important feature of the electron distribution function observed inside the sources is an accumulation of particles with low parallel velocities and keV energies. This distribution presents positive cf/?z:, slopes that could well be the source of free energy of the plasma instability responsible for the wave generation (the cyclotron maser instability (Wu and Lee, 1979)). Inside the sources, the simultaneous observation of downward directed electron beams and upward ion ones indicates that these regions are also the acceleration regions linked to the discrete amoral arcs (Louarn et ul., 1990). A statistical study made over more than 30 source crossings (Hilgers et a/., 1991) has generalized these observations. In the plasma depleted regions that constitute the sources, simple physical considerations (Pritchett, 1984) show that, even in a moderately energetic plasma ((E) = 1 keV), relativistic effects must be taken into account in the study of wave propagation. whatever the mechanism of generation is. The cyclotron maser instability is nothing but the relativistic negative absorption effect occurring when positive 3f;ii?rl, slopes are present in the electron distribution function. In that sense. the relativistic dispersion has to be considered as a “zero order” theory for any realistic theory of the generation of the AKR. This does not preclude other processes from having a role in the wave generation. In these two articles, an analysis of the role of the finite geometry of the source regions on the mechanism of generation of the AKR is proposed. In this paper (paper I), we re-analyze some Viki~zg observations with special attention to the effects of the source frontiers on the wave propagation. This study is organized as follows. In Section 2, the dynamic spectra recorded during four AKR source crossings (orbits 165, 176, 237 and 1260) are presented and the role of the plasma gradients is qualitatively discussed. In Section 3, the polarization and the radiating diagram of the waves observed inside the source are determined. In Section 4, the properties of the waves at the exit of the source are studied. The angle of propagation is evaluated and the efficiency of the transmission coefficients across the source frontiers is estimated for the different modes. These results. summarized in a discussion (Section 5). have to be considered as experimental and observational inputs for the theoretical analysis of the
of the AKR in plasma cavities--I
cyclotron maser mechanism in a finite geometry that will be presented in paper II. It is important to note that this work presents important differences with the study made by Calvert ( 198 1). The plasma cavities discussed here have a much smaller scale than the ones discussed by Calvert. that. in fact would correspond to the whole aurora1 region. In addition, as it will be shown in the observational study, the cavities described here have very well-defined boundaries. The problem under interest then presents strong analogies with the study of the propagation in wave-guides.
2. Viking wave experiment observations near and inside sources of AKR 2.1. Insttunwntation The high-frequency wave experiment onboard C.iliing (V4H) measures the amplitude of one electric and one magnetic component of the electromagnetic field in the frequency range lo-510 kHz. Two types of analyzers are used : a filter bank (8 channels with a bandwidth of 30% of central frequency and a time resolution of 37 ms) and a swept frequency analyzer (SFA). For the observations presented here, a full spectrum constituted by 256 joint frequency channels is obtained every 2.4 s, simultaneously for the E and B components. The frequency gap between two channels is 1 kHz in the range 9-128 kHz. 2 kHz in the range 128-256 kHz and 4 kHz at higher frequencies. The total dynamic is 120 dB, allowing measurements between lo-” and lo-” V m-’ Hz-“‘. The spacecraft spin period is 20 s, the spin axis being perpendicular to the plane of the orbit (cartwheel mode) which also means in the present case, roughly perpendicular to the geomagnetic field (B,,). The electric antenna is thus alternatively (every 5 s; more or less every two spectra) parallel and perpendicular to the geomagnetic field. Supposing that the waves are polarized and that they have not a too variable amplitude, the rotation of the antenna then results into a spin modulation of the received signal. This modulation can be used to determine the direction of the electric plane of the wave and to identify the modes of propagation (de Feraudy et al.. 1987). The magnetic antenna is aligned with the spin axis and then, more or less perpendicular to the geomagnetic field. The B component does not present a spin modulation and. except for checking the electromagnetic nature of waves, it is of less interest for the study of the polarization. This B component will not be discussed.
2.2. Examples and 1260
ofsource
crossing : orhits 165. 176. 237
In Fig. 1, the dynamic spectra of the electric component are shown for four source crossings. The electron gyrofrequency is indicated by a dotted line. For twro of these orbitsI65 and 176-the general wave characteristics have been studied by de Feraudy c>t rrl. ( 1987) and a discussion about the results of the other I’ikiry exper-
P. Louarn and II. Lr Qu&u : Generation
of the AKR in plasma cavitiz> -I
;&:.”
. O-5
O-7
23 10
23 15
time Fig. 1. Four examples of dynamic spectra measured in the AKR and the hiss range during xxuce crossings (from up to down. orbits 165, 176. 137 and 1360). The dotted line is the electron gyrofrequency. For each orbit. black lines between the hiss and the AKR panels mark the position of the sources
P. Louarn and D. Le @I&U : Generation
90.
-
-
_
_
---
-
07
-
-
----_
--_--
-_
-
-
3230
-
-
-
-
-
--
--
of the AKR in plasma cavities
-
3330
1
g
J -_ _- -- - _-
-- - -- - - --
O-39
40
14
time Fig. 2. Zooms on the source crossing themselves (from up to down. orbits 165, 176, -337 and 1360). The dynamic spectra in the AKR range. the compressed dynamic spectra in the hiss range and the angle between the electric antenna and the static magnetic field are given. The position of the interfaces t, and f; (,,,, are also indicated
P. Lou;ml and D. Le QuCau : Generation
of the AKR in plasma cavities- -1
103
Table 1. Main characteristics of the source crossings 165A f (1\Hz) 1,.(hk) t, 1, iI/, (kHz) /:,,, (kV) /.., (keV) /-,,,, , (km)
211 212 >?I* > 30* 0.099 0.141 2.1 1.2 .~ 10 20
165B
16X‘ _____~~~.__.. ‘II 305 307 705 33 30 91 30 0.156 0. 146 0.130 0.146 5.13 4.1 3.5 4.4 2-4 3-5 180 20 30
iments, in particular. the particles experiment. can be found in Ungstrup rt al. (1990). For each orbit. two frequency ranges have been selected. The IO-60 kHz band contains the so-called “aurora1 hiss”. This radiation is formed by waves that propagate on the whistler mode. Its high frequency cut-off (typically between 20 and 40 kHz) is the local plasma frequency. The radiation seen on the upper band and that propagates above the electron gyrofrequency is the AKR. During small periods of time (a few 10 s at most), the AKR intensifies and. simultaneously. its low-frequency cut-ofY shifts down to the frequency channel that c0ntains.f;. These periods of maximum activity are indicated by an enlarged black line below the AKR panels. For the orbits 165 and 247. respectively three and two such regions are successively crossed. These periods of maximum AKR activity always correspond to a decrease of the level of the aurora1 hiss and to the disappearance of its upper cut-off frequency, indicating that the cut-off‘ of the hiss and then, the plasma frequency, is locally belon the band of analysis (9 kHz) (Perraut et 01.. 1990: Lo~~arn CI t/l., 1990). Thus. the maximum AKR level is detected inside plasma cavities. a result widely confirmed b> direct particle measurements (Hilgers et L/I.. 1991). The examples shown in Fig. I are representative of the typical sources of AKR crossed by rikillg. They have been chosen because the spacecraft has crossed them for ;I sufficiently long time so that the spin modulation can be observed inside them, thus allowing the study of the polarization of the waves. For each source. one can consider two interfaces corresponding to the first and to the second crossings of the source frontiers. In Table I, the value of/, at each interface is deduced from the position of the cut-otf of the hiss. In some cases (orbit 1260. for example). the Interface is also ;I region of broad-band electrostatic noises (BEN) and the upper cut-off frequency is then diecult In measure. We have noted these uncertain evaluations of f,, by an asterisk. For these cases. ,/A is evaluated from the hiss cut-ofi aside the BEN region. Since particle measurements suggest that the regions of BEN have a higher density than both the source and the external plasm;l adjacent to the BEN. our estimates are below the actual value of,f, at the interface. These minimum values arc noted by the sign “>“. As seen in Table I. these four \ources present quite different characteristics which is another justification of our choice. In particular.
176
237A
237B
I?60
16X 166 35 33 0.208 0. I99 7.3 6.6 8-10 S-10 I IO
183 1x3 36 33 0. I Y7 0.1 x0 7.1 5.Y
179 I76 33 30 0. I s4 0. I70 6.1 5.1 7 6-7 130
32-I ii? ‘(I 20 0.00 O.Oh 1.2 I: J 5 1%
30
the ratio ,/,‘$i of the external plasma varies significantly. The lower value (0.06) is obtained for the orbit 1260 and the higher (0.208) for the orbit I76 (at the first crossing of the source frontier). Although modest. these variations correspond to values of the frequency gap between,/, and the cut-off frequency of the X mode in the external plasma (f\,>,,,) that vary from 1.2 kHz to more than 7 kHz. Since the waves are generated very close to /;. this is also the frequency gap existing between the frequency of generation and the frequency above which an eventual connection with the external X mode becomes possible. When measurements are available, the values of the electron and proton energy are also given. The proton energy corresponds to the energy of the upward beam observed in the source. It gives an estimate of the difference of potential occurring on tield lines below the spacecraft. The electron energy is the typical energy of the trapped population. This could well be the energy of the electrons responsible for the maser process (Louarn VI t/l.. 1990). The density inside the source is not known with precision. However. the different methods of measurement (Langmuir probe. direct particle measurements. cutoff of the hiss or of the AKR) show that the internal density is at least a factor 2 or 3 below the density of the external plasma. In the following, we will consider that :I density of 1 or ? cm ’ is reasonable for the AKR sources presented here. As seen later. an important source of uncertainty for the interpretation of the observations is that the geometr!, of the crossing is not kno\vn with precision. II can be checked that the spacecraft ebsentially moves in the north south direction in a meridian plane hut. even if statistically aurora1 discrete arcs are elongated in the east -west direction. nothing guarantees that the sources or the acceleration regions are crossed perpendicularly (along their smallest widths). Note howe\,er that. if a typical pcrpendicular scale exists for the acceleration structures. the fact that we have selected long source crossings would mean that the plane of the orbit is more or less tangential to the laminar structures constituted by the sources.
Two components in the AKR can be distinguished in Fig. I. The most intense has a howl shaped lower cut-oft‘ that
204
P. Louarn and D. Le QuCau : Generation
occurs a few frequency channels above,f,. As shown later, its spin modulation is consistent with the polarization of X mode waves (maximum E perpendicular to B,,). Between this component and ,fi, a fainter radiation can also be detected. This could either be 0 or Z mode waves. The analysis of the spin modulation will nevertheless show that it is dominated by the 0 mode (maximum E parallel to B,,). In Fig. 2, zooms on the source crossings are presented. For the different orbits, we have plotted (1) the dynamic spectra at frequencies close t0.f: (upper panel). (2) a compressed dynamic spectra for the hiss (intermediate panel) and (3) the angle between the antenna and the geomagnetic field (lower panel). On the upper panels, each pixel corresponds to 2.4 s along the temporal axis and 2 kHz along the frequency axis (4 kHz for the orbit 1260). In the following, the interfaces between the sources and the external plasma will be referenced by the number of the orbit, the order of occurrence of the source when different sources exist (A, B, C.. . .) and the position of the interface: (a) or (b). Ticks mark the position of the interfaces. A shift of one spectrum can exist between the apparent position of the interface on the “AKR” panel and the one on the “hiss” panel. This corresponds to the time delay between the measurements at high and low frequencies. The spectra are indeed obtained by a sweep frequency analyzer that begins its analysis at the highest frequency. More than 1 s can then exist between measurements in the AKR frequency range and measurements in the hiss one. Thus, more than 5 km along the spacecraft orbit can separate the two measurements, a distance largely sufficient to enter or exit out of the source. When entering into the source, on the same spectrum, the AKR can then be measured out of the source and the hiss inside the source (e.g. interfaces 176a and 237Aa). The opposite is observed at the exit (on the same spectrum, the AKR can be measured inside and the hiss outside-examples : 165Bb, 237Bb). For the different interfaces. ticks indicate the gyrofrequency and the X mode cut-off deduced from the values of.f, given in Table 1. For the first few channels just above the gyrofrequency, in particular between,f; and ,& (,“I’ the level of the AK R is more than 20 dB greater inside the sources than outside. This is particularly clear when the antenna is perpendicular to the geomagnetic field during the acquisition of the first or the last spectrum measured inside the source-interfaces 165Bb, 165Ca.b. 237Bb. At higher frequencies. the decrease of the wave level linked to the crossing of the frontiers is smaller or even absent-interfaces 165Ba, 176b. This suggests that the electromagnetic energy created just above,f, is somewhat confined inside the sources. Conversely, at frequencies a few percent abovc.L oUI,it can propagate outward more easily or even freely. The most intense waves are then observed above in the external plasma, as it must be the case for a fYout radiation dominated by X mode waves. From an analysis of the spin modulation, a determination of the polarization and then. of the mode of propagation, can be precisely performed. In the case of a quasi-perpendicular propagation, the electric held of extraordinary mode waves (X or Z) is perpendicular to the static B,, field. For the ordinary mode (0). it is rather
of the AKR in plasma cavities-
-I
parallel. An anticorrelation of the spin modulation must then exist for the two types of waves. Inside the sources. it can be checked in Fig. 2 that the minimum levels of the radiation are observed for a parallel orientation of the antenna. This is consistent with the result of Hilgers CT al. (1992) and corresponds to the extraordinary mode polarization (essentially X mode, since the level of the radiation is strong at frequencies above the upper hybrid). Outside the sources and above,fi c,L,,.the minima of E-field are also observed when the antenna is roughly parallel to the static Bfield. For,f’>,fl I,“,, the internal and the external electromagnetic fields have thus a similar polarization. This could explain the observed easy access of the electromagnetic energy to the external in this frequency range. Still outside the sources. when a radiation is detected between ,f; and the bowl-shaped main component (orbit 176 and before the interface 237Ba). the minima are now obtained for a perpendicular orientation of the antenna. This polarization corresponds to 0 mode waves. The phase shift in the spin modulation between the 0 and the X components can be clearly apparent (for example. after the interface 176b). Forj:. < ,f’< .f; o,l,. the strong difference in the polarization between the internal and the external waves could explain the important attenuation at the crossing of the frontier. It is noticeable that the relative importance of the X and 0 component varies with the ratio,fJfi. at the interfaces. For high values (orbit 176), the 0 component is relatively intense. It is even higher than the X mode level (interface 176a) for the most dense case. For low values of this ratio (interfaces 165a and b). the 0 component has a lower density and can be undetectable (interfaces 1260a and b). An important point to note is that there is no significant Z mode emitted from the sources studied here. Indeed. a significant level of Z mode would imply the detection of noise at frequencies below the upper hybrid frequency when the antenna is perpendicular to the geomagnetic B field. As it is not the case, one can conclude that the level of the Z mode is largely below the 0 mode one. As discussed in paper Il. this very weak level of the Z mode is unexpected and puts strong constraints on the theory of the cyclotron maser instability in a limited geometry.
3. Structure of the electromagnetic field inside the source regions
In Fig. 3, the amplitude of the spin modulation (ratio E,,/E, between the electric field measured when the antenna is parallel and perpendicular to the geomagnetic field) for the sources 165B, 176. 237B and 1260 is plotted as a function of the frequency. A quarter of spin period (5 s) systematically separates the measurements of E,i and EL. Despite some fluctuations due to temporal variations of the AKR amplitude. the ratio E,,/E_ clearly increases as the frequency increases : E, /E, ‘z 0. I for (f’-,f,)jf, = 0.01 ; for (f‘-.fi)/f; = 0.05 and E,iE, z 0.8 for E,.!E, = 0.5f0.1 (.f’-fi)jf, = 0.1. Since the X mode is largely dominant
I’. Louarn xnd D. Le Qukau : Generation
of the AKR in plasma cavities-- I
0.00
0.10
0.00
0.10
- 0.8d w'
0.10
0.00
0.00
(f-fc)/fc
0.10
(f-fc)/fc
Fig. 3. Amplitude of the spin modulation measured inside the sources (from left to right and up to down. orbits 165. 176. 237 and 1360). In each case. two cur\cs are prrsented corresponding trj measurements made at two different times
inside the ~urcc. the evolution of the ratio E,,iE, with the frequency cannot be explained by a variation of the relative amount of the X and 0 mode with the frequency. This evolution has: rather to be interpreted as a variation of the polari/;~Gon of X mode waves due to their refraction when propagating upward throughout the source. As the waves are generated \ery close to ,fi. studying waves at increasing frequencies is equivalent to studying waves generated further bdow the altitude of observation. In principle, it is Lhcn possible to describe the evolution of the wave vector due to the upward propagation from the evolution of the spin modulation with the frequency. Hefore this study of the refraction. let us compare these measurement\ with theoretical results.
l‘he derivation of a simplified dispersion equation for the S mode in an idealized relativistic plasma is made in Le Qdau and Louarn ( 1989) (see also paper 11). It is written >I‘; ,~’ = I-2x-N’ 1 i--x
--
with
a Atv + (iN2 x = - -~ 2 (Atu + 6)’
(1)
where N :~nd h’! arc respectively the parallel and perpendicul;lr inties of the wave. Here ACU= ((u-oJ~):~(u~. (1 = (~u,,;w, )‘and 6 is the normalized energy of the plasma : 0 = (r,,,3c)’ for an idealized plasma distribution : ). Taking the E, com/(Z.,J,) = (ZJW,,) !Ci(J._-r,,)ij(r ponent as reference. E, and E_ can be written as
and
NIN (l-xE, = id_-__----; (1 -NI)x
.V’)/I, ‘1
(2)
: is the direction of the geomagnetic field and the k \vave vector is in the .\- : plane. In Fig. 4. wc have respectively \VklVtZ the perpendicular index 01‘ the plotted (,Yi = klc, (I)~). the ratio E,, E, and the ratio E, E, x functions of the parallel index and the normali/.ed frequency (,/‘-,f,) ,/i. The parameters are:
P. Louarn and D. Le Queau : Generation
206
of the AKR in plasma cavities-1
0.6-----4/ 0.82
.6 Yl Fig. 5. Expected spin modulation (ratio E,:E,) for an isotropic radiating diagram as a function of N, and the normalized frequency (here multiplied by 100)
o.Th.J/
.
0.82
Fig. 4. Perpendicular index and orientation of the electric field of an X mode wave that propagates in a relativistic plasma. as
ram, the observed high values of E,;'E,(0.8)can then be easily explained if one supposes that the plane of the antenna is close to the main direction of the radiating diagram (see Fig. 7). Given the geometry of the C’ih-iwy orbit and its cartwheel mode. this would mean that the radiation is mainly emitted in the meridian plane It could
functions of the frequency and the parallel index
the measured values of the E, /El ratio. Conversely, if the radiating diagram is anisotropic, depending on the angle between the plane of the antenna and the direction of maximum radiation, the E,,'E_l ratio can be higher. Assuming that the radiating diagram is completely anisotropic (k wave vector in the s-z plane only), we have plotted in Fig. 6 the ratio E,,/ELfor various values of the parallel index N8 and various orientations of the antenna in the .v-.I. plane (angle fI made between the plane of the antenna and the direction of the k vector). The ratio E,/E, can reach much higher values than in the isotropic case, even if the waves propagate close to the perpendicular direction. For example, if N i z 0.1, E'!can even be higher than El if the antenna is more or less parallel to the .Y direction and then, if it is also in the main direction of the radiating diagram. Making the hypothesis of an anisotropic radiating diag-
.2
.6 N/l
Fig. 6. Expected spin modulation (ratio E /L’, ) for an anisotropic radiating diagram (k wave vectors in the .I- direction) as a function of N, and the angle between the antenna and the k vector (0). The normalized frequency is 0.05
P. Louarn and I>. Le QU&LI : Generation
of the AKR in plasma cavities-
planeof the antenna
Ifi
Fig. 7. Geometry
of the source :md of the radiating
diagram
appear surprising that for the four orbits studied here. the plane of the antenna has been always roughly in the main direction of the radiating diagram. A possible explanation is that. by the choice of particularly wide source crossings. tangential-to-the-source crossings have been selected (Fig. 7) and then. for the four examples studied here, the geometry of the crossing is likely similar. The anisotropy of the radiating diagram can be considered as a consequence of the limited source geometry. Unfortunately. we have not found a method for directly deducing the main orientation of the radiating diagram with respect to the emitting structure. However, as shown in paper II. the fact that Z mode waves are not emitted implies that the radiating diagram is more or less oriented tangential to the emitting structure. Note that such an orientation of the radiating diagram is consistent with the fact that long lasting source crossings (tangential crohsings) correspond to a minimum of E, measurements and then to a maximum of E,,:‘E, measurements. In order to study the wave refraction. we have chosen the source 176. Assuming a completely anisotropic radiating diagram. values of E, ;E, of the order of 0.7-0.8 are only obtained if the angle fl between the antenna and the dominant direction of the E field is smaller than roughly 71) In Fig. 8. we have made a zoom of Fig. 6 for
Fig. 8. Salr te plot ;LSFig. 6 but fhr contour levels of E ;E _ that correspond to experimental points. This illustrates the wave refraction Iinked to the upward propagation
I
‘07
0.01 < IV < 0.3 and 5 < (I < 25 Wc have plotted the contours of E !E, corresponding to the observed values of E :E at six successive frequency channels ( 16X. 170. 172. 174. 176 and I78 kHz, the gyrofrequency being around 167 kHz). The last frequency. 178 kHz, is close to the X mode cut-off in the external plasma. For a given angle between the main direction of the radiating diagram and the plane of the antenna. the plot shows the evolution of ‘2’ as a function of (,f-,f,) ,/,. which is proportional to the \.ertical distance between the region of generation and the spacecraft. The frequency gap (2 kH7) berbcen tL\ o successive measurements (two successive contours on the plot) corresponds to an altitude difference of tho order c)l‘ 25 km. The figure shows the regular rotation of the I, \.ector as the waves are progressively refracted upward. For this particular source. 13 kH/ scparatc the frequency of generation from the frequency cjfcxit OLI[ of the source. This corresponds to an upward propagation of the waves of roughly 150 km before their exit. The determination 01 the final angle of propagation. just hefi>re the connection with the external X mode. depend< on the value c~f 0. Typically. for :t 0 of the order of 10 , the measured ~aluc of E E_ at 178 kHz (just beforc the evit out ofthc source) would correspond to‘iV of the order ol‘0. I5 (angle (k.B,,) inside the source of the order of X0 I.
4. Connection of the internal waves to the external plasma
In Fig. 9. we have plotted for each of the interfaces of‘ sources 165B. 176 and 1260 the measurements of El (dotted line) and E_ (continuous line) just outside (thin lineb) and just inside (thick lines) the sources. On these plots. we have also marked the gyrofrequency and the X mode external cut-off deduced from Table 1. The orbit 237 i\ not presented because for its tirst interface (see Fig. 2) two spectra have been cancelled due to problems of teletnetry. From this plot. one can again identify the different modes of propagation. Inside the sources. E, is always much larger than E, asexpected for a dominant X. Outside the source. the polarization strongly varies around f; ,,(!,. ~eh,t\ ol,l> Ei exceeds E,, as it must be the case for waves mainly propagating on the 0 mode. Above /,,?,,,. E, rise5 and becomes higher than E. indicating that. at these frequencies. X mode wave> escape from the sources. Finally. at frequencies a few percent abo\,c /,,,,,,. E, outside and inside the sources is comparable. Some typical values for the transmission coelficients acre<\ the source\ frontiers can then be deduced. ( I ) Itttnx~I .Y ttto(i~~~c~.~tc,r.ttctl 0 tttocic cottttclc.tiott. This coefficient is obtained by comparing E, inside the source and E outside. Bel0w.f; ,,il,. Emmeasured outside the source is 20P30 dB below E, measured inside the source. In this frequency range, the connection between the internal and the external waves then corresponds to an attenuation of the order of 25 dB. In this frequency domain, the waves
208
P. Louarn
and D. Le QuCau : Generation
of the AKR in plasma cavities--l
b-
220 120 ““”
L.I...!.
2lO
230
“1.“.
...,,...,*
.-...h...
220
.--..a...J
230
a:
a:
330
350
330
370 FREQUENCY
350
370
@Hz)
Fig. 9. Spectra obtained for a parallel (dotted lines) and perpendicular (continuous lines) orientation of the antenna iust inside the sources (thick lines) and just outside the sources (thin lines). From up to down, source 165B. 176 and 1260
can then be considered as actually confined inside the source. (2) Internal Xnlodejesternal Xmode connection. Below coefficient corresponding to this f xout, the transmission connection is null. It slowly increases abovef; Outsuch that a frequency gap of 2% (orbit 176) to 10% (orbit 1260) exists between ,f; OUtand the frequency where a free connection is observed. At a frequency a few percent above ,fi. there is then no attenuation at the crossing of the interfaces. Almost all the energy created inside the sources that, after a more or less long upward propagation, reaches the altitude of a possible connection with the X mode, finally escapes outside. Nevertheless, during the upward propagation a part of the energy could have been converted into 0 mode waves. Let us note that the efficiency of this conversion could increase with the ratio ,fJf:. Thus, fo r th e interface I76a, that presents the highest ,f,/fi ratio, the level of the X mode is below the level of the 0 mode.
4.2. Angle qf‘propagatioll
at the e.vit
qf the
sources
The dynamic spectra can also be used to estimate the angle of propagation (angle between the k vector and the geomagnetic field) of the different components of the AKR. Indeed, knowing the spacecraft trajectory, the angle of propagation can be deduced from the shape of the low frequency cut-off of the radiation. For a given position of the spacecraft, the lower cut-off of the radi-
ation gives the maximum altitude at which the observed waves have been emitted. Since the distance to the point of crossing of the source frontier can be known. an angle of propagation can be calculated if it is supposed that the ray path is a straight line. This angle is the projection in the plane of the orbit (not far from the meridian plane) of the angle made by the wave vectors and the geomagnetic field (see Fig. 10). When studying the dynamic spectra, one notes that the 0 and X components do not propagate at the same angle. When it exists. the 0 component is observed close to,f, even if the spacecraft is relatively far from the source. Conversely, the X component rapidly diverges from ,f:. A simple interpretation is that the 0 component is essentially constituted by waves propagating perpendicularly to the geomagnetic field and that the X component is constituted by waves propagating upward at oblique angles. X mode waves detected far from the source then come from regions far below the spacecraft, where they are generated at frequencies largely above the gyrofrequency measured at the spacecraft position. This angle of propagation has been evaluated for the interfaces of the sources 165B, 176, 237B and 1260. It is plotted as a function of./$; in Fig. 11. Clearly. this parameter organizes the data well : as it increases. the angle of propagation decreases indicating that the waves propagate in a more parallel direction. For high,f$fl (case of the orbit 176). very oblique angles of propagation (20’ ) are observed. This angle is small compared to the angles of propagation inside the source which shows the strong
: Generation
P. Louarn and I). Le Q&u Geometry
of the AKR in plasma cavities--l
of the crossing
‘09
N, is small. Since N, is conserved across the surface. .t; 0111. the crossing of the frontiers obviously corresponds to a strong upward refraction. An important consequence of this refraction is that the angle of propagation outside the source is not determined by the generation mechanism itself but by the macroscopic properties of the source. in particular the density gap at its frontiers.
5. Conclusion For this experimental study of the generation of the AKR and more specifically of the role of the finite geometry 01 the sources on the characteristics of the radiation. we have chosen four typical sources of AKR crossed by I’iking and we have analyzed how the existence of well-defined source frontiers modifies the structure of the clectromagnetic tield. Our main conclusions are the following:
Dvnamic stxctra
I Fig.
10.
Cieometrical
I tc
, tA
tB construction
c used for estimating
the angle of propagation of the AKR. \I,, and k, are deduced from ,j,, and,IB; CA and CB are calculated from the spacecraft velocity. knowing r \. I,, and t( The apparent angle of propagation is then easily deduced
wave refraction that occurs at the source frontiers. The characteristics of the X mode dispersion easily explain this strong refraction. Inside the source, the waves have a rather high N, (N i z I ). Outside the sources, just above
( I ) l%cry~~ cmfinirzg imirke t/w .YOU~W.As seen in Figs 1 and 2. the electromagnetic energy created InsIde the plasma cavity that constitutes the source is confined to a frequency range extending a few percent above the gyrofrequency. In this frequency domain [,/,.,/i ,J. the external waves mainly propagate on the 0 mode. the level of the Z mode being very low and practically unmeasurable. A typical attenuation between the internal X mode and the external 0 mode is 35 dB.
l Orbit 1260 l No Mode 0 Orbit 165 l
+
Orbit 237 l
+ +
Orbit 176 l
Mode 0 don&an
0
0,05
O,l
0,15
0,2
fp/fc Fig. 11. Apparent
angles
of propagation
for the different
sources
0.25
210
P. Louarn and D. Le Q&au : Generation
X mode, the internal waves have to propagate upward inside the source. This upward propagation corresponds to the altitude range that must be covered by a wave generated at./; before it can connect with the external X mode above I;..,. The frequency gap that must be overcome is of a few kHz which means an altitude range of about 100 km. (3) TIP aryk of’ pmopugution in the e.x-ternul plustm could be quite oblique ad nluinlj~ clepemh on the ciensit>~ gup at the sowce .fj.ontiers. The upward propagation is
followed by a progressive rotation of the wave vector. Values of N,, of the order of 0.15 are plausible just before the wave exits out of the source. The index of the wave being close to 1, this means that the internal angle of propagation is of the order of 80’ A study of the propagation outside the sources shows that the waves propagate there in a much more parallel direction (from 70 to less than 20’ , depending on.fJfc). (4) The radiutirzg diagram bus no qkh+cul s~mrnetr~~. The analysis of the evolution of the wave polarization as the waves propagates upward has revealed that the radiating diagram of a source is likely anisotropic in a plane perpendicular to the geomagnetic field, the preferential direction of emission being likely the direction of invariance of the source (tangential direction for a laminar structure). These unexpected consequences of the existence of well defined frontiers for the sources will be discussed in detail in paper II. There we will study the properties of the cyclotron maser instability in a limited source region and will in particular provide an interpretation to our conclusions 1, 2 and 4.
References Aschwanden, M. J. and Benz, A. O., On the electron cyclotron instability : 11. Pulsation in the quasi-stationary state. Astrophjx /. 332, 466. 1988. Bahnsen, A. B., Jespersen, M., Ungstrup, E. and Iversen, I. B., Aurora1 hiss and kilometric radiation measured from the Viking satellite. Groph~ss. Rrs. Lett. 14, 471, 1987. Bahnsen, A., Pedersen, B. M., Jespersen, M., Ungstrup, E., Eliasson, L., Murphree, J. S., Elphinstone, D., Blomberg, L., Holmgren. G. and Zanetti, L. J., Viking observations at the source of the AKR. J. gPr)plz~s. Rr.r. 94, 6643. 1989. Benson, R. F. and Akasofu, S. I., Aurora1 kilometric radiationl’aurora correlation. Radio Sci. 19, 527. 1984.
of the AKR in plasma cavities---~1
Calvert, W., The aurora1 plasma cavity. Guoph~~s. Res. Lctt. X, 919, 1981. de Feraudy, H., Pedersen, B. M., Bahnsen, A. and Jespersen, M., Viking observations of AKR from plasmasphere to night aurora1 oval source region. Gco$z~t.r. Res. Lptt. 14, 51 1. 1957. Dulk, G. A., Radio emission from the sun and the stars. Aw. Ru. A.stron. Awophys. 23, 169, 1985. Green, J. L., Gurnett, D. A. and Shawhan, S. D., The angular distribution of the aurora1 kilometric radiation. J. grwpl7~~. Res. 82, 1825, 1977. Gurnett, D. A., The Earth as a radio source : terrestrial kilometric radiation. J. yeoph~~.s. Res. 79, 4227. 1974. Hilgers, A., Roux, A. and Lundin, R.. Characteristics of AKR sources : a statistical description. Gmpl7~1~.s.Re.r. Lc,tt. 18. 1493, 1991. Hilgers, A., de Feraudy, H. and Le Queau, D., Measurement of the direction of the aurora1 kilometric radiation electric field inside the source with the Viking satellite. J. geoph)x. RCS. 79,8381, 1992. Le Queau, D. and Louarn, P., Analytical study of the relativistic dispersion: application to the generation of the AKR. J. grr)pl+. Rev. 94, 2605, 1989. Louarn, P., Le Q&au, D. and Roux, A., A new mechanism for stellar radio bursts : the fully relativistic electron maser. Asmu. A.stroplgx. 165, 211, 1986. Louarn, P., Roux, A., de Feraudy, H., Le Q&au, D., And+ M. and Matson, L., Trapped electrons as a free energy source for the aurora1 kilometric radiation. J. gr@~~.s. RKS. 95, 5983, 1990. Melrose, D. B. and Dulk, G. A., Electron cyclotron maser as the source of certain solar and stellar radio bursts. A.stmph~~.s. .I. 259,844, 1982. Perraut, S., de Feraudy, H., Roux, A., Decreau, P. M. E., Paris, J. and Matson, L., Density measurements in key regions of the Earth’s magnetosphere: cusp and aurora1 region. J. geopi7y~. Res. 95, 5997. 1990. Pottelette, R., Malingre, M., Bahnsen, A., Eliasson, L. and Stasiewicz, K., Viking observations of bursts of intense broadband noise in the source region of aurora1 kilometric radiation. .4r777.Gropl7~~.r.6, 573. 1988. Pritchett, P. L., Relativistic dispersion, the cyclotron maser instability and aurora1 kilometric radiation. J. ,q~wp/7~~.~. RCY. 89, 8957. 1984. Roux, A., Hilgers, A., de Feraudy, H., Le Qubau, D., Louarn, P., Perraut, S., Bahnsen, A., Jespersen, M., Ungstrup, E. and Andre, M., Aurora1 kilometric radiation sources : in situ and remote sensing observations from Viking. J. y~plr~~.s. Re.\. 98, 11657, 1993. Ungstrup, E., Bahnsen, A., Wong, H. K., And& M. and Matson, L., Energy source and generation mechanism for AKR. ./. geo/lh~x Res. 95, 5973. 1990. Wu, C. S. and Lee, L. C., A theory of the terrestrial kilometric radiation. ,4.stroph~~s.J. 230, 621, 1979. Zarka, P., The aurora1 radio emissions from planetary magnetospheres : what do we know, what don’t we know. what do we learn from them’? A&. SJJUW Res. 12, (8)99%(X) 1 IS. 1992.
Pergamon
Coovrieht sYj 1996 Elsevier Science Ltd Printed’& &eat Britain. All rights reserved 0032m-0633,‘96 $15.00+0.00
0032-0633(95)00121-2
Generation of the Aurora1 Kilometric Radiation in plasma cavities-I. Experimental study Philippe Louarn’
and Dominique
Le Q&au’
‘Laboratoire d’Astrophysique de Toulouse. Observatoire Midi-PyrCnCes. 14, Avenue Edouard Belin, 31400 Toulouse. 3 ‘entre d’Etude des Environnements Terrestres et Planetaires, Velizy, France Received 27 January
1995; revised
I4 September
1995 ; accepted
15 September
France
1995
I. Introduction
the sounx.
studies.
The Amoral Kilometric Radiation (AKR hereafter) is the most powerful natural radio emission emanating from the Earth magnetosphere. This strongly polarized emission is generated in the night sector. at altitudes ranging from less than 5000 km to more than 15,000 km and in close association with the development of aurora] discrete arcs (Gurnett, 1974; Green et al., 1977: Benson and Akasofu. 1984). Its frequency bandwidth is roughly 50-500 kHz with a maximum spectral density around 250 kHz. This radiation mainly propagates on the X mode with electric field amplitudes that reach IO-” V mm-’ Hz- I’. Such high values cannot be explained by classical thermal or incoherent generation mechanisms and non-thermal emission processes such as plasma instabilities must be invoked. In many aspects-its non-thermal origin. its high polarization, its temporal variability and its organization in many fine spectral structures---the AKR presents strong analogies with the powerful radio emissions that emanate from the aurora1 regions of the other magnetized planets : Jupiter, Saturn. Uranus and Neptune (Zarka. 1992). It can also be compared to certain solar radio bursts (the socalled microwave spike bursts) (Dulk. 1985 ; Aschwanden and Benz, 1988) and some stellar radio emissions (Melrose and Dulk. 1982 : Louarn et trl.. 1986). Then. the radio emission generation mechanism operating in the terrestrial magnetosphere could well be a universal process associated with the acceleration of particles in strongly magnetized plasma. The &king experiment has allowed some significant progress in the understanding of the generation mechanism of the AKR. This Swedish spacecraft was the first to explore, with a complete set of experiments, the heart of AKR sources. Most of the Viking experimental works accomplished so far on this particular problem of AKR generation are summarized in a review article by Roux rt ul. (1993). The most important conclusions of these studies are given below.
200
P. Louarn and D. Le QuCau : Generation
The AKR propagates mainly on the X mode with. nevertheless, possible faint components on the Z and 0 mode. It is generated within strongly magnetized regions (f& < 0. I where ,fpis the plasma frequency and .f: the electron gyrofrequency), at frequencies close to the local cut-off of the X mode: Jx = (.f,+(.f’f+4f’z)’ ‘)/2 and propagates outside the sources in a direction rather perpendicular to the geomagnetic field. An important result of the Vi/&g observations is that the sources have a small extension (a few km) perpendicular to the geomagnetic field. The plasma of these regions is tenuous 01, = 1 cm-‘) with an electron population essentially constituted by energetic particles ((E) = 3-10 keV) (Bahnsen ~1 nl., 1987; Pottelette rt cd.. 1988; Bahnsen et ul., 1989; Ungstrup et al., 1990; Louarn et al.. 1990). It is separated from the denser and colder external plasma (n, = 5-10 cm’.“, (E) = a few 10 eV) by a sharp density and energy gradient with typical scale length smaller than 1 km. An important feature of the electron distribution function observed inside the sources is an accumulation of particles with low parallel velocities and keV energies. This distribution presents positive cf/?z:, slopes that could well be the source of free energy of the plasma instability responsible for the wave generation (the cyclotron maser instability (Wu and Lee, 1979)). Inside the sources, the simultaneous observation of downward directed electron beams and upward ion ones indicates that these regions are also the acceleration regions linked to the discrete amoral arcs (Louarn et ul., 1990). A statistical study made over more than 30 source crossings (Hilgers et a/., 1991) has generalized these observations. In the plasma depleted regions that constitute the sources, simple physical considerations (Pritchett, 1984) show that, even in a moderately energetic plasma ((E) = 1 keV), relativistic effects must be taken into account in the study of wave propagation. whatever the mechanism of generation is. The cyclotron maser instability is nothing but the relativistic negative absorption effect occurring when positive 3f;ii?rl, slopes are present in the electron distribution function. In that sense. the relativistic dispersion has to be considered as a “zero order” theory for any realistic theory of the generation of the AKR. This does not preclude other processes from having a role in the wave generation. In these two articles, an analysis of the role of the finite geometry of the source regions on the mechanism of generation of the AKR is proposed. In this paper (paper I), we re-analyze some Viki~zg observations with special attention to the effects of the source frontiers on the wave propagation. This study is organized as follows. In Section 2, the dynamic spectra recorded during four AKR source crossings (orbits 165, 176, 237 and 1260) are presented and the role of the plasma gradients is qualitatively discussed. In Section 3, the polarization and the radiating diagram of the waves observed inside the source are determined. In Section 4, the properties of the waves at the exit of the source are studied. The angle of propagation is evaluated and the efficiency of the transmission coefficients across the source frontiers is estimated for the different modes. These results. summarized in a discussion (Section 5). have to be considered as experimental and observational inputs for the theoretical analysis of the
of the AKR in plasma cavities--I
cyclotron maser mechanism in a finite geometry that will be presented in paper II. It is important to note that this work presents important differences with the study made by Calvert ( 198 1). The plasma cavities discussed here have a much smaller scale than the ones discussed by Calvert. that. in fact would correspond to the whole aurora1 region. In addition, as it will be shown in the observational study, the cavities described here have very well-defined boundaries. The problem under interest then presents strong analogies with the study of the propagation in wave-guides.
2. Viking wave experiment observations near and inside sources of AKR 2.1. Insttunwntation The high-frequency wave experiment onboard C.iliing (V4H) measures the amplitude of one electric and one magnetic component of the electromagnetic field in the frequency range lo-510 kHz. Two types of analyzers are used : a filter bank (8 channels with a bandwidth of 30% of central frequency and a time resolution of 37 ms) and a swept frequency analyzer (SFA). For the observations presented here, a full spectrum constituted by 256 joint frequency channels is obtained every 2.4 s, simultaneously for the E and B components. The frequency gap between two channels is 1 kHz in the range 9-128 kHz. 2 kHz in the range 128-256 kHz and 4 kHz at higher frequencies. The total dynamic is 120 dB, allowing measurements between lo-” and lo-” V m-’ Hz-“‘. The spacecraft spin period is 20 s, the spin axis being perpendicular to the plane of the orbit (cartwheel mode) which also means in the present case, roughly perpendicular to the geomagnetic field (B,,). The electric antenna is thus alternatively (every 5 s; more or less every two spectra) parallel and perpendicular to the geomagnetic field. Supposing that the waves are polarized and that they have not a too variable amplitude, the rotation of the antenna then results into a spin modulation of the received signal. This modulation can be used to determine the direction of the electric plane of the wave and to identify the modes of propagation (de Feraudy et al.. 1987). The magnetic antenna is aligned with the spin axis and then, more or less perpendicular to the geomagnetic field. The B component does not present a spin modulation and. except for checking the electromagnetic nature of waves, it is of less interest for the study of the polarization. This B component will not be discussed.
2.2. Examples and 1260
ofsource
crossing : orhits 165. 176. 237
In Fig. 1, the dynamic spectra of the electric component are shown for four source crossings. The electron gyrofrequency is indicated by a dotted line. For twro of these orbitsI65 and 176-the general wave characteristics have been studied by de Feraudy c>t rrl. ( 1987) and a discussion about the results of the other I’ikiry exper-
P. Louarn and II. Lr Qu&u : Generation
of the AKR in plasma cavitiz> -I
;&:.”
. O-5
O-7
23 10
23 15
time Fig. 1. Four examples of dynamic spectra measured in the AKR and the hiss range during xxuce crossings (from up to down. orbits 165, 176. 137 and 1360). The dotted line is the electron gyrofrequency. For each orbit. black lines between the hiss and the AKR panels mark the position of the sources
P. Louarn and D. Le @I&U : Generation
90.
-
-
_
_
---
-
07
-
-
----_
--_--
-_
-
-
3230
-
-
-
-
-
--
--
of the AKR in plasma cavities
-
3330
1
g
J -_ _- -- - _-
-- - -- - - --
O-39
40
14
time Fig. 2. Zooms on the source crossing themselves (from up to down. orbits 165, 176, -337 and 1360). The dynamic spectra in the AKR range. the compressed dynamic spectra in the hiss range and the angle between the electric antenna and the static magnetic field are given. The position of the interfaces t, and f; (,,,, are also indicated
P. Lou;ml and D. Le QuCau : Generation
of the AKR in plasma cavities- -1
103
Table 1. Main characteristics of the source crossings 165A f (1\Hz) 1,.(hk) t, 1, iI/, (kHz) /:,,, (kV) /.., (keV) /-,,,, , (km)
211 212 >?I* > 30* 0.099 0.141 2.1 1.2 .~ 10 20
165B
16X‘ _____~~~.__.. ‘II 305 307 705 33 30 91 30 0.156 0. 146 0.130 0.146 5.13 4.1 3.5 4.4 2-4 3-5 180 20 30
iments, in particular. the particles experiment. can be found in Ungstrup rt al. (1990). For each orbit. two frequency ranges have been selected. The IO-60 kHz band contains the so-called “aurora1 hiss”. This radiation is formed by waves that propagate on the whistler mode. Its high frequency cut-off (typically between 20 and 40 kHz) is the local plasma frequency. The radiation seen on the upper band and that propagates above the electron gyrofrequency is the AKR. During small periods of time (a few 10 s at most), the AKR intensifies and. simultaneously. its low-frequency cut-ofY shifts down to the frequency channel that c0ntains.f;. These periods of maximum activity are indicated by an enlarged black line below the AKR panels. For the orbits 165 and 247. respectively three and two such regions are successively crossed. These periods of maximum AKR activity always correspond to a decrease of the level of the aurora1 hiss and to the disappearance of its upper cut-off frequency, indicating that the cut-off‘ of the hiss and then, the plasma frequency, is locally belon the band of analysis (9 kHz) (Perraut et 01.. 1990: Lo~~arn CI t/l., 1990). Thus. the maximum AKR level is detected inside plasma cavities. a result widely confirmed b> direct particle measurements (Hilgers et L/I.. 1991). The examples shown in Fig. I are representative of the typical sources of AKR crossed by rikillg. They have been chosen because the spacecraft has crossed them for ;I sufficiently long time so that the spin modulation can be observed inside them, thus allowing the study of the polarization of the waves. For each source. one can consider two interfaces corresponding to the first and to the second crossings of the source frontiers. In Table I, the value of/, at each interface is deduced from the position of the cut-otf of the hiss. In some cases (orbit 1260. for example). the Interface is also ;I region of broad-band electrostatic noises (BEN) and the upper cut-off frequency is then diecult In measure. We have noted these uncertain evaluations of f,, by an asterisk. For these cases. ,/A is evaluated from the hiss cut-ofi aside the BEN region. Since particle measurements suggest that the regions of BEN have a higher density than both the source and the external plasm;l adjacent to the BEN. our estimates are below the actual value of,f, at the interface. These minimum values arc noted by the sign “>“. As seen in Table I. these four \ources present quite different characteristics which is another justification of our choice. In particular.
176
237A
237B
I?60
16X 166 35 33 0.208 0. I99 7.3 6.6 8-10 S-10 I IO
183 1x3 36 33 0. I Y7 0.1 x0 7.1 5.Y
179 I76 33 30 0. I s4 0. I70 6.1 5.1 7 6-7 130
32-I ii? ‘(I 20 0.00 O.Oh 1.2 I: J 5 1%
30
the ratio ,/,‘$i of the external plasma varies significantly. The lower value (0.06) is obtained for the orbit 1260 and the higher (0.208) for the orbit I76 (at the first crossing of the source frontier). Although modest. these variations correspond to values of the frequency gap between,/, and the cut-off frequency of the X mode in the external plasma (f\,>,,,) that vary from 1.2 kHz to more than 7 kHz. Since the waves are generated very close to /;. this is also the frequency gap existing between the frequency of generation and the frequency above which an eventual connection with the external X mode becomes possible. When measurements are available, the values of the electron and proton energy are also given. The proton energy corresponds to the energy of the upward beam observed in the source. It gives an estimate of the difference of potential occurring on tield lines below the spacecraft. The electron energy is the typical energy of the trapped population. This could well be the energy of the electrons responsible for the maser process (Louarn VI t/l.. 1990). The density inside the source is not known with precision. However. the different methods of measurement (Langmuir probe. direct particle measurements. cutoff of the hiss or of the AKR) show that the internal density is at least a factor 2 or 3 below the density of the external plasma. In the following, we will consider that :I density of 1 or ? cm ’ is reasonable for the AKR sources presented here. As seen later. an important source of uncertainty for the interpretation of the observations is that the geometr!, of the crossing is not kno\vn with precision. II can be checked that the spacecraft ebsentially moves in the north south direction in a meridian plane hut. even if statistically aurora1 discrete arcs are elongated in the east -west direction. nothing guarantees that the sources or the acceleration regions are crossed perpendicularly (along their smallest widths). Note howe\,er that. if a typical pcrpendicular scale exists for the acceleration structures. the fact that we have selected long source crossings would mean that the plane of the orbit is more or less tangential to the laminar structures constituted by the sources.
Two components in the AKR can be distinguished in Fig. I. The most intense has a howl shaped lower cut-oft‘ that
204
P. Louarn and D. Le QuCau : Generation
occurs a few frequency channels above,f,. As shown later, its spin modulation is consistent with the polarization of X mode waves (maximum E perpendicular to B,,). Between this component and ,fi, a fainter radiation can also be detected. This could either be 0 or Z mode waves. The analysis of the spin modulation will nevertheless show that it is dominated by the 0 mode (maximum E parallel to B,,). In Fig. 2, zooms on the source crossings are presented. For the different orbits, we have plotted (1) the dynamic spectra at frequencies close t0.f: (upper panel). (2) a compressed dynamic spectra for the hiss (intermediate panel) and (3) the angle between the antenna and the geomagnetic field (lower panel). On the upper panels, each pixel corresponds to 2.4 s along the temporal axis and 2 kHz along the frequency axis (4 kHz for the orbit 1260). In the following, the interfaces between the sources and the external plasma will be referenced by the number of the orbit, the order of occurrence of the source when different sources exist (A, B, C.. . .) and the position of the interface: (a) or (b). Ticks mark the position of the interfaces. A shift of one spectrum can exist between the apparent position of the interface on the “AKR” panel and the one on the “hiss” panel. This corresponds to the time delay between the measurements at high and low frequencies. The spectra are indeed obtained by a sweep frequency analyzer that begins its analysis at the highest frequency. More than 1 s can then exist between measurements in the AKR frequency range and measurements in the hiss one. Thus, more than 5 km along the spacecraft orbit can separate the two measurements, a distance largely sufficient to enter or exit out of the source. When entering into the source, on the same spectrum, the AKR can then be measured out of the source and the hiss inside the source (e.g. interfaces 176a and 237Aa). The opposite is observed at the exit (on the same spectrum, the AKR can be measured inside and the hiss outside-examples : 165Bb, 237Bb). For the different interfaces. ticks indicate the gyrofrequency and the X mode cut-off deduced from the values of.f, given in Table 1. For the first few channels just above the gyrofrequency, in particular between,f; and ,& (,“I’ the level of the AK R is more than 20 dB greater inside the sources than outside. This is particularly clear when the antenna is perpendicular to the geomagnetic field during the acquisition of the first or the last spectrum measured inside the source-interfaces 165Bb, 165Ca.b. 237Bb. At higher frequencies. the decrease of the wave level linked to the crossing of the frontiers is smaller or even absent-interfaces 165Ba, 176b. This suggests that the electromagnetic energy created just above,f, is somewhat confined inside the sources. Conversely, at frequencies a few percent abovc.L oUI,it can propagate outward more easily or even freely. The most intense waves are then observed above in the external plasma, as it must be the case for a fYout radiation dominated by X mode waves. From an analysis of the spin modulation, a determination of the polarization and then. of the mode of propagation, can be precisely performed. In the case of a quasi-perpendicular propagation, the electric held of extraordinary mode waves (X or Z) is perpendicular to the static B,, field. For the ordinary mode (0). it is rather
of the AKR in plasma cavities-
-I
parallel. An anticorrelation of the spin modulation must then exist for the two types of waves. Inside the sources. it can be checked in Fig. 2 that the minimum levels of the radiation are observed for a parallel orientation of the antenna. This is consistent with the result of Hilgers CT al. (1992) and corresponds to the extraordinary mode polarization (essentially X mode, since the level of the radiation is strong at frequencies above the upper hybrid). Outside the sources and above,fi c,L,,.the minima of E-field are also observed when the antenna is roughly parallel to the static Bfield. For,f’>,fl I,“,, the internal and the external electromagnetic fields have thus a similar polarization. This could explain the observed easy access of the electromagnetic energy to the external in this frequency range. Still outside the sources. when a radiation is detected between ,f; and the bowl-shaped main component (orbit 176 and before the interface 237Ba). the minima are now obtained for a perpendicular orientation of the antenna. This polarization corresponds to 0 mode waves. The phase shift in the spin modulation between the 0 and the X components can be clearly apparent (for example. after the interface 176b). Forj:. < ,f’< .f; o,l,. the strong difference in the polarization between the internal and the external waves could explain the important attenuation at the crossing of the frontier. It is noticeable that the relative importance of the X and 0 component varies with the ratio,fJfi. at the interfaces. For high values (orbit 176), the 0 component is relatively intense. It is even higher than the X mode level (interface 176a) for the most dense case. For low values of this ratio (interfaces 165a and b). the 0 component has a lower density and can be undetectable (interfaces 1260a and b). An important point to note is that there is no significant Z mode emitted from the sources studied here. Indeed. a significant level of Z mode would imply the detection of noise at frequencies below the upper hybrid frequency when the antenna is perpendicular to the geomagnetic B field. As it is not the case, one can conclude that the level of the Z mode is largely below the 0 mode one. As discussed in paper Il. this very weak level of the Z mode is unexpected and puts strong constraints on the theory of the cyclotron maser instability in a limited geometry.
3. Structure of the electromagnetic field inside the source regions
In Fig. 3, the amplitude of the spin modulation (ratio E,,/E, between the electric field measured when the antenna is parallel and perpendicular to the geomagnetic field) for the sources 165B, 176. 237B and 1260 is plotted as a function of the frequency. A quarter of spin period (5 s) systematically separates the measurements of E,i and EL. Despite some fluctuations due to temporal variations of the AKR amplitude. the ratio E,,/E_ clearly increases as the frequency increases : E, /E, ‘z 0. I for (f’-,f,)jf, = 0.01 ; for (f‘-.fi)/f; = 0.05 and E,iE, z 0.8 for E,.!E, = 0.5f0.1 (.f’-fi)jf, = 0.1. Since the X mode is largely dominant
I’. Louarn xnd D. Le Qukau : Generation
of the AKR in plasma cavities-- I
0.00
0.10
0.00
0.10
- 0.8d w'
0.10
0.00
0.00
(f-fc)/fc
0.10
(f-fc)/fc
Fig. 3. Amplitude of the spin modulation measured inside the sources (from left to right and up to down. orbits 165. 176. 237 and 1360). In each case. two cur\cs are prrsented corresponding trj measurements made at two different times
inside the ~urcc. the evolution of the ratio E,,iE, with the frequency cannot be explained by a variation of the relative amount of the X and 0 mode with the frequency. This evolution has: rather to be interpreted as a variation of the polari/;~Gon of X mode waves due to their refraction when propagating upward throughout the source. As the waves are generated \ery close to ,fi. studying waves at increasing frequencies is equivalent to studying waves generated further bdow the altitude of observation. In principle, it is Lhcn possible to describe the evolution of the wave vector due to the upward propagation from the evolution of the spin modulation with the frequency. Hefore this study of the refraction. let us compare these measurement\ with theoretical results.
l‘he derivation of a simplified dispersion equation for the S mode in an idealized relativistic plasma is made in Le Qdau and Louarn ( 1989) (see also paper 11). It is written >I‘; ,~’ = I-2x-N’ 1 i--x
--
with
a Atv + (iN2 x = - -~ 2 (Atu + 6)’
(1)
where N :~nd h’! arc respectively the parallel and perpendicul;lr inties of the wave. Here ACU= ((u-oJ~):~(u~. (1 = (~u,,;w, )‘and 6 is the normalized energy of the plasma : 0 = (r,,,3c)’ for an idealized plasma distribution : ). Taking the E, com/(Z.,J,) = (ZJW,,) !Ci(J._-r,,)ij(r ponent as reference. E, and E_ can be written as
and
NIN (l-xE, = id_-__----; (1 -NI)x
.V’)/I, ‘1
(2)
: is the direction of the geomagnetic field and the k \vave vector is in the .\- : plane. In Fig. 4. wc have respectively \VklVtZ the perpendicular index 01‘ the plotted (,Yi = klc, (I)~). the ratio E,, E, and the ratio E, E, x functions of the parallel index and the normali/.ed frequency (,/‘-,f,) ,/i. The parameters are:
P. Louarn and D. Le Queau : Generation
206
of the AKR in plasma cavities-1
0.6-----4/ 0.82
.6 Yl Fig. 5. Expected spin modulation (ratio E,:E,) for an isotropic radiating diagram as a function of N, and the normalized frequency (here multiplied by 100)
o.Th.J/
.
0.82
Fig. 4. Perpendicular index and orientation of the electric field of an X mode wave that propagates in a relativistic plasma. as
ram, the observed high values of E,;'E,(0.8)can then be easily explained if one supposes that the plane of the antenna is close to the main direction of the radiating diagram (see Fig. 7). Given the geometry of the C’ih-iwy orbit and its cartwheel mode. this would mean that the radiation is mainly emitted in the meridian plane It could
functions of the frequency and the parallel index
the measured values of the E, /El ratio. Conversely, if the radiating diagram is anisotropic, depending on the angle between the plane of the antenna and the direction of maximum radiation, the E,,'E_l ratio can be higher. Assuming that the radiating diagram is completely anisotropic (k wave vector in the s-z plane only), we have plotted in Fig. 6 the ratio E,,/ELfor various values of the parallel index N8 and various orientations of the antenna in the .v-.I. plane (angle fI made between the plane of the antenna and the direction of the k vector). The ratio E,/E, can reach much higher values than in the isotropic case, even if the waves propagate close to the perpendicular direction. For example, if N i z 0.1, E'!can even be higher than El if the antenna is more or less parallel to the .Y direction and then, if it is also in the main direction of the radiating diagram. Making the hypothesis of an anisotropic radiating diag-
.2
.6 N/l
Fig. 6. Expected spin modulation (ratio E /L’, ) for an anisotropic radiating diagram (k wave vectors in the .I- direction) as a function of N, and the angle between the antenna and the k vector (0). The normalized frequency is 0.05
P. Louarn and I>. Le QU&LI : Generation
of the AKR in plasma cavities-
planeof the antenna
Ifi
Fig. 7. Geometry
of the source :md of the radiating
diagram
appear surprising that for the four orbits studied here. the plane of the antenna has been always roughly in the main direction of the radiating diagram. A possible explanation is that. by the choice of particularly wide source crossings. tangential-to-the-source crossings have been selected (Fig. 7) and then. for the four examples studied here, the geometry of the crossing is likely similar. The anisotropy of the radiating diagram can be considered as a consequence of the limited source geometry. Unfortunately. we have not found a method for directly deducing the main orientation of the radiating diagram with respect to the emitting structure. However, as shown in paper II. the fact that Z mode waves are not emitted implies that the radiating diagram is more or less oriented tangential to the emitting structure. Note that such an orientation of the radiating diagram is consistent with the fact that long lasting source crossings (tangential crohsings) correspond to a minimum of E, measurements and then to a maximum of E,,:‘E, measurements. In order to study the wave refraction. we have chosen the source 176. Assuming a completely anisotropic radiating diagram. values of E, ;E, of the order of 0.7-0.8 are only obtained if the angle fl between the antenna and the dominant direction of the E field is smaller than roughly 71) In Fig. 8. we have made a zoom of Fig. 6 for
Fig. 8. Salr te plot ;LSFig. 6 but fhr contour levels of E ;E _ that correspond to experimental points. This illustrates the wave refraction Iinked to the upward propagation
I
‘07
0.01 < IV < 0.3 and 5 < (I < 25 Wc have plotted the contours of E !E, corresponding to the observed values of E :E at six successive frequency channels ( 16X. 170. 172. 174. 176 and I78 kHz, the gyrofrequency being around 167 kHz). The last frequency. 178 kHz, is close to the X mode cut-off in the external plasma. For a given angle between the main direction of the radiating diagram and the plane of the antenna. the plot shows the evolution of ‘2’ as a function of (,f-,f,) ,/,. which is proportional to the \.ertical distance between the region of generation and the spacecraft. The frequency gap (2 kH7) berbcen tL\ o successive measurements (two successive contours on the plot) corresponds to an altitude difference of tho order c)l‘ 25 km. The figure shows the regular rotation of the I, \.ector as the waves are progressively refracted upward. For this particular source. 13 kH/ scparatc the frequency of generation from the frequency cjfcxit OLI[ of the source. This corresponds to an upward propagation of the waves of roughly 150 km before their exit. The determination 01 the final angle of propagation. just hefi>re the connection with the external X mode. depend< on the value c~f 0. Typically. for :t 0 of the order of 10 , the measured ~aluc of E E_ at 178 kHz (just beforc the evit out ofthc source) would correspond to‘iV of the order ol‘0. I5 (angle (k.B,,) inside the source of the order of X0 I.
4. Connection of the internal waves to the external plasma
In Fig. 9. we have plotted for each of the interfaces of‘ sources 165B. 176 and 1260 the measurements of El (dotted line) and E_ (continuous line) just outside (thin lineb) and just inside (thick lines) the sources. On these plots. we have also marked the gyrofrequency and the X mode external cut-off deduced from Table 1. The orbit 237 i\ not presented because for its tirst interface (see Fig. 2) two spectra have been cancelled due to problems of teletnetry. From this plot. one can again identify the different modes of propagation. Inside the sources. E, is always much larger than E, asexpected for a dominant X. Outside the source. the polarization strongly varies around f; ,,(!,. ~eh,t\ ol,l> Ei exceeds E,, as it must be the case for waves mainly propagating on the 0 mode. Above /,,?,,,. E, rise5 and becomes higher than E. indicating that. at these frequencies. X mode wave> escape from the sources. Finally. at frequencies a few percent abo\,c /,,,,,,. E, outside and inside the sources is comparable. Some typical values for the transmission coelficients acre<\ the source\ frontiers can then be deduced. ( I ) Itttnx~I .Y ttto(i~~~c~.~tc,r.ttctl 0 tttocic cottttclc.tiott. This coefficient is obtained by comparing E, inside the source and E outside. Bel0w.f; ,,il,. Emmeasured outside the source is 20P30 dB below E, measured inside the source. In this frequency range, the connection between the internal and the external waves then corresponds to an attenuation of the order of 25 dB. In this frequency domain, the waves
208
P. Louarn
and D. Le QuCau : Generation
of the AKR in plasma cavities--l
b-
220 120 ““”
L.I...!.
2lO
230
“1.“.
...,,...,*
.-...h...
220
.--..a...J
230
a:
a:
330
350
330
370 FREQUENCY
350
370
@Hz)
Fig. 9. Spectra obtained for a parallel (dotted lines) and perpendicular (continuous lines) orientation of the antenna iust inside the sources (thick lines) and just outside the sources (thin lines). From up to down, source 165B. 176 and 1260
can then be considered as actually confined inside the source. (2) Internal Xnlodejesternal Xmode connection. Below coefficient corresponding to this f xout, the transmission connection is null. It slowly increases abovef; Outsuch that a frequency gap of 2% (orbit 176) to 10% (orbit 1260) exists between ,f; OUtand the frequency where a free connection is observed. At a frequency a few percent above ,fi. there is then no attenuation at the crossing of the interfaces. Almost all the energy created inside the sources that, after a more or less long upward propagation, reaches the altitude of a possible connection with the X mode, finally escapes outside. Nevertheless, during the upward propagation a part of the energy could have been converted into 0 mode waves. Let us note that the efficiency of this conversion could increase with the ratio ,fJf:. Thus, fo r th e interface I76a, that presents the highest ,f,/fi ratio, the level of the X mode is below the level of the 0 mode.
4.2. Angle qf‘propagatioll
at the e.vit
qf the
sources
The dynamic spectra can also be used to estimate the angle of propagation (angle between the k vector and the geomagnetic field) of the different components of the AKR. Indeed, knowing the spacecraft trajectory, the angle of propagation can be deduced from the shape of the low frequency cut-off of the radiation. For a given position of the spacecraft, the lower cut-off of the radi-
ation gives the maximum altitude at which the observed waves have been emitted. Since the distance to the point of crossing of the source frontier can be known. an angle of propagation can be calculated if it is supposed that the ray path is a straight line. This angle is the projection in the plane of the orbit (not far from the meridian plane) of the angle made by the wave vectors and the geomagnetic field (see Fig. 10). When studying the dynamic spectra, one notes that the 0 and X components do not propagate at the same angle. When it exists. the 0 component is observed close to,f, even if the spacecraft is relatively far from the source. Conversely, the X component rapidly diverges from ,f:. A simple interpretation is that the 0 component is essentially constituted by waves propagating perpendicularly to the geomagnetic field and that the X component is constituted by waves propagating upward at oblique angles. X mode waves detected far from the source then come from regions far below the spacecraft, where they are generated at frequencies largely above the gyrofrequency measured at the spacecraft position. This angle of propagation has been evaluated for the interfaces of the sources 165B, 176, 237B and 1260. It is plotted as a function of./$; in Fig. 11. Clearly. this parameter organizes the data well : as it increases. the angle of propagation decreases indicating that the waves propagate in a more parallel direction. For high,f$fl (case of the orbit 176). very oblique angles of propagation (20’ ) are observed. This angle is small compared to the angles of propagation inside the source which shows the strong
: Generation
P. Louarn and I). Le Q&u Geometry
of the AKR in plasma cavities--l
of the crossing
‘09
N, is small. Since N, is conserved across the surface. .t; 0111. the crossing of the frontiers obviously corresponds to a strong upward refraction. An important consequence of this refraction is that the angle of propagation outside the source is not determined by the generation mechanism itself but by the macroscopic properties of the source. in particular the density gap at its frontiers.
5. Conclusion For this experimental study of the generation of the AKR and more specifically of the role of the finite geometry 01 the sources on the characteristics of the radiation. we have chosen four typical sources of AKR crossed by I’iking and we have analyzed how the existence of well-defined source frontiers modifies the structure of the clectromagnetic tield. Our main conclusions are the following:
Dvnamic stxctra
I Fig.
10.
Cieometrical
I tc
, tA
tB construction
c used for estimating
the angle of propagation of the AKR. \I,, and k, are deduced from ,j,, and,IB; CA and CB are calculated from the spacecraft velocity. knowing r \. I,, and t( The apparent angle of propagation is then easily deduced
wave refraction that occurs at the source frontiers. The characteristics of the X mode dispersion easily explain this strong refraction. Inside the source, the waves have a rather high N, (N i z I ). Outside the sources, just above
( I ) l%cry~~ cmfinirzg imirke t/w .YOU~W.As seen in Figs 1 and 2. the electromagnetic energy created InsIde the plasma cavity that constitutes the source is confined to a frequency range extending a few percent above the gyrofrequency. In this frequency domain [,/,.,/i ,J. the external waves mainly propagate on the 0 mode. the level of the Z mode being very low and practically unmeasurable. A typical attenuation between the internal X mode and the external 0 mode is 35 dB.
l Orbit 1260 l No Mode 0 Orbit 165 l
+
Orbit 237 l
+ +
Orbit 176 l
Mode 0 don&an
0
0,05
O,l
0,15
0,2
fp/fc Fig. 11. Apparent
angles
of propagation
for the different
sources
0.25
210
P. Louarn and D. Le Q&au : Generation
X mode, the internal waves have to propagate upward inside the source. This upward propagation corresponds to the altitude range that must be covered by a wave generated at./; before it can connect with the external X mode above I;..,. The frequency gap that must be overcome is of a few kHz which means an altitude range of about 100 km. (3) TIP aryk of’ pmopugution in the e.x-ternul plustm could be quite oblique ad nluinlj~ clepemh on the ciensit>~ gup at the sowce .fj.ontiers. The upward propagation is
followed by a progressive rotation of the wave vector. Values of N,, of the order of 0.15 are plausible just before the wave exits out of the source. The index of the wave being close to 1, this means that the internal angle of propagation is of the order of 80’ A study of the propagation outside the sources shows that the waves propagate there in a much more parallel direction (from 70 to less than 20’ , depending on.fJfc). (4) The radiutirzg diagram bus no qkh+cul s~mrnetr~~. The analysis of the evolution of the wave polarization as the waves propagates upward has revealed that the radiating diagram of a source is likely anisotropic in a plane perpendicular to the geomagnetic field, the preferential direction of emission being likely the direction of invariance of the source (tangential direction for a laminar structure). These unexpected consequences of the existence of well defined frontiers for the sources will be discussed in detail in paper II. There we will study the properties of the cyclotron maser instability in a limited source region and will in particular provide an interpretation to our conclusions 1, 2 and 4.
References Aschwanden, M. J. and Benz, A. O., On the electron cyclotron instability : 11. Pulsation in the quasi-stationary state. Astrophjx /. 332, 466. 1988. Bahnsen, A. B., Jespersen, M., Ungstrup, E. and Iversen, I. B., Aurora1 hiss and kilometric radiation measured from the Viking satellite. Groph~ss. Rrs. Lett. 14, 471, 1987. Bahnsen, A., Pedersen, B. M., Jespersen, M., Ungstrup, E., Eliasson, L., Murphree, J. S., Elphinstone, D., Blomberg, L., Holmgren. G. and Zanetti, L. J., Viking observations at the source of the AKR. J. gPr)plz~s. Rr.r. 94, 6643. 1989. Benson, R. F. and Akasofu, S. I., Aurora1 kilometric radiationl’aurora correlation. Radio Sci. 19, 527. 1984.
of the AKR in plasma cavities---~1
Calvert, W., The aurora1 plasma cavity. Guoph~~s. Res. Lctt. X, 919, 1981. de Feraudy, H., Pedersen, B. M., Bahnsen, A. and Jespersen, M., Viking observations of AKR from plasmasphere to night aurora1 oval source region. Gco$z~t.r. Res. Lptt. 14, 51 1. 1957. Dulk, G. A., Radio emission from the sun and the stars. Aw. Ru. A.stron. Awophys. 23, 169, 1985. Green, J. L., Gurnett, D. A. and Shawhan, S. D., The angular distribution of the aurora1 kilometric radiation. J. grwpl7~~. Res. 82, 1825, 1977. Gurnett, D. A., The Earth as a radio source : terrestrial kilometric radiation. J. yeoph~~.s. Res. 79, 4227. 1974. Hilgers, A., Roux, A. and Lundin, R.. Characteristics of AKR sources : a statistical description. Gmpl7~1~.s.Re.r. Lc,tt. 18. 1493, 1991. Hilgers, A., de Feraudy, H. and Le Queau, D., Measurement of the direction of the aurora1 kilometric radiation electric field inside the source with the Viking satellite. J. geoph)x. RCS. 79,8381, 1992. Le Queau, D. and Louarn, P., Analytical study of the relativistic dispersion: application to the generation of the AKR. J. grr)pl+. Rev. 94, 2605, 1989. Louarn, P., Le Q&au, D. and Roux, A., A new mechanism for stellar radio bursts : the fully relativistic electron maser. Asmu. A.stroplgx. 165, 211, 1986. Louarn, P., Roux, A., de Feraudy, H., Le Q&au, D., And+ M. and Matson, L., Trapped electrons as a free energy source for the aurora1 kilometric radiation. J. gr@~~.s. RKS. 95, 5983, 1990. Melrose, D. B. and Dulk, G. A., Electron cyclotron maser as the source of certain solar and stellar radio bursts. A.stmph~~.s. .I. 259,844, 1982. Perraut, S., de Feraudy, H., Roux, A., Decreau, P. M. E., Paris, J. and Matson, L., Density measurements in key regions of the Earth’s magnetosphere: cusp and aurora1 region. J. geopi7y~. Res. 95, 5997. 1990. Pottelette, R., Malingre, M., Bahnsen, A., Eliasson, L. and Stasiewicz, K., Viking observations of bursts of intense broadband noise in the source region of aurora1 kilometric radiation. .4r777.Gropl7~~.r.6, 573. 1988. Pritchett, P. L., Relativistic dispersion, the cyclotron maser instability and aurora1 kilometric radiation. J. ,q~wp/7~~.~. RCY. 89, 8957. 1984. Roux, A., Hilgers, A., de Feraudy, H., Le Qubau, D., Louarn, P., Perraut, S., Bahnsen, A., Jespersen, M., Ungstrup, E. and Andre, M., Aurora1 kilometric radiation sources : in situ and remote sensing observations from Viking. J. y~plr~~.s. Re.\. 98, 11657, 1993. Ungstrup, E., Bahnsen, A., Wong, H. K., And& M. and Matson, L., Energy source and generation mechanism for AKR. ./. geo/lh~x Res. 95, 5973. 1990. Wu, C. S. and Lee, L. C., A theory of the terrestrial kilometric radiation. ,4.stroph~~s.J. 230, 621, 1979. Zarka, P., The aurora1 radio emissions from planetary magnetospheres : what do we know, what don’t we know. what do we learn from them’? A&. SJJUW Res. 12, (8)99%(X) 1 IS. 1992.