ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus PublicationsGöttingen, Germany10.5194/angeo-35-1241-2017Nonlinear radiation generation processes in the auroral acceleration regionPotteletteRaymondraymond.pottelette@lpp.polytechnique.frBerthomierMatthieuLaboratoire de Physique des Plasmas, UPMC, CNRS UMR 7648, 4 place Jussieu, 75252 Paris CEDEX 05, FranceRaymond Pottelette (raymond.pottelette@lpp.polytechnique.fr)22November20173561241124819May201717October201718October2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://angeo.copernicus.org/articles/35/1241/2017/angeo-35-1241-2017.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/35/1241/2017/angeo-35-1241-2017.pdf
It is known from laboratory plasma
experiments that double layers (DLs) radiate in the electromagnetic
spectrum; but this is only known qualitatively. In these experiments, it was shown that the electron beam created
on the high-potential side of a DL generates nonlinear structures which
couple to electromagnetic waves and act as a sender antenna. In the Earth
auroral region, observations performed by auroral spacecraft have shown that
DLs occur naturally in the source region of intense radio emissions called
auroral kilometric radiation (AKR). Very high time-, spatial-, and temporal-resolution measurements are needed in order to characterize waves and
particle distributions in the vicinity of DLs, which are moving transient
structures. We report observations from the FAST satellite of a localized
large-amplitude parallel electric field (∼ 300 mV m-1) recorded
at the edges of the auroral density cavity. In agreement with laboratory
experiments, on the high-potential side of the DL, elementary radiation
events are detected. They occur substantially above the local electron
gyrofrequency and are associated with the presence of electron holes. The
velocity of these nonlinear structures can be derived from the measurement
of the Doppler-shifted AKR frequency spectrum above the electron
gyrofrequency. The generated electron holes appear as the nonlinear
evolution of electrostatic waves generated by the electron–electron two-stream instability because they propagate at about half the beam velocity.
It is pointed out that, in the vicinity of a DL, the shape of the electron
distribution gives rise to a significant power recorded in the left-hand
polarized ordinary (LO) mode.
Space plasma physics (radiation processes)Introduction
Electromagnetic radiation from double layers (DLs) has been extensively
studied in laboratory plasma experiments (Volwerk, 1993; Lindberg, 1993;
Brenning et al., 2004). The spectrum was found to contain characteristic
peaks around the electron gyrofrequency and electron plasma frequency
(Gunell and Löfgren, 1997; Löfgren and Gunell, 1998). It was shown
that the electron beam, created on the high-potential side of the DL,
generates high-frequency nonlinear structures which couple to
electromagnetic waves and act as a sender antenna. These experimental
results demonstrated that there is a possibility of very high efficiency in
converting electric energy to radiation.
In space, spacecraft observations have revealed that the direct consequence
of the electron parallel acceleration processes is that the Earth acts as an
intense radio source in the kilometre wavelength range (Benediktov et al.,
1965; Gurnett, 1974). This offers the possibility of investigating locally the
eventual mechanisms leading to electromagnetic radiation generation in the
vicinity of a DL. The cyclotron maser instability is now widely acknowledged
as being the most likely mechanism leading to auroral kilometric radiation
(AKR) generation (Wu and Lee, 1979; Louarn et al., 1990; Ergun et al., 2000).
In the source region identified as the auroral density cavity, an unstable
horseshoe electron distribution exhibiting large positive velocity gradients
in the direction perpendicular to the local magnetic field provides the free
energy for AKR (Ergun et al., 2000; Treumann, 2006). Such a distribution is
generated when a localized DL accelerates the electrons earthward that
propagate into an increasing magnetic field (Chiu and Schulz, 1978). The
parallel accelerated electrons need to travel a long distance (several
thousand kilometres) before forming a horseshoe distribution; this implies
that in the auroral region the AKR generation takes place far away from a DL.
Therefore, these observational results disagree with those obtained in
laboratory experiments unless another mechanism leading to radiation
generation is identified. Accordingly, there is a need to determine what kind
of electron distribution is present and how the auroral plasma may radiate in
the vicinity of a DL. High time-resolution measurements, both for waves and
particles, are required to identify the presence of DLs which are localized
moving transient structures. The higher resolution of FAST measurements as
compared to previous auroral missions offers the opportunity to investigate
the physical processes taking place in the neighbourhood of DLs. These
localized parallel electric fields appear to be located at the interface of
the auroral density cavity. We present some observations, recorded on the
high-potential side of a large-amplitude DL
(∼ 300 mV m-1),
which highlight the generation of electromagnetic sporadic emissions in
association with nonlinear coherent structures (electron holes). These
emissions take place substantially (∼ 10 %) above the local
electron gyrofrequency and the associated wave electric fields are partially
polarized in a direction parallel to the magnetic field indicating the
probable presence of left-hand polarized ordinary (LO)-mode radiation. The measurement of the Doppler-shifted AKR frequency spectrum allows the determination of the electrons hole
velocity. It turns out that the velocity range is about half the beam
velocity, in fair agreement with the electron–electron two-stream instability.
The generated electron holes appear as the nonlinear evolution of
electrostatic waves generated by this instability.
Observations
Figure 1 displays 12 s of data (horizontal axis) illustrating the crossing
of an anti-earthward-directed large-amplitude DL (320 mV m-1) located
in the AKR source region. The FAST spacecraft was at invariant latitude
∼ 68∘ and altitude ∼ 4150 km (orbit 1761). As evidenced
in the top panels (a) the spacecraft approaches the DL from the low-potential
side at ∼ 06:44:44 UT and enters a region of a steep density gradient.
Figure 1b and c show the electric field spectral power density as a function
of frequency and time. Panel (b) represents the electric field spectral power
density measured by the on-board sweep frequency analyser (SFA) as a function
of frequency and time. The frequency span is from 0 to 500 kHz at 15 kHz
bandwidth. The dark line around 365 kHz is fce, the local
electron cyclotron frequency. The waves recorded near and above
fce are AKR; at low frequency (less than ∼ 20 kHz), intense
VLF waves can be identified as hiss emissions, which present an upper cut-off
near the local plasma frequency fp (Persoon et al., 1988); the
observations imply that fp≪fce. Panel (c) displays
plasma wave tracker data, which has a fine-frequency resolution over a limited
bandwidth. The frequency axis is from 400 to 420 kHz, with a 32 Hz
resolution.
FAST spacecraft observations during the crossing of a localized
double layer. The time duration is 12 s. Panel (a) plots the
parallel component of the anti-earthward-directed DC electric field together with
the density variation. Panel (b) shows the electric power density as
a function of frequency. The on-board sweep frequency analyser spans 0 to
500 kHz, with a 4 kHz bandwidth. The dark horizontal line is the
non-relativistic electron gyrofrequency fce. Panel (c)
reveals the presence of large-amplitude fine spectral AKR features measured
by the plasma tracker. The frequency axis is from 400 to 420 kHz, with a
32 Hz resolution. In (b, c) the shaded blue region is correlated
with the crossing of the parallel electric field.
From 06:44:38.717 UT as illustrated in Fig. 1a, according to the electron
flux measurements, the FAST spacecraft stays in a region of depressed density
(∼ 0.3 cm-3) during ∼ 3 s. In the time interval 3–6 s
the spacecraft enters a region of sharp density gradient. The density is
substantially increased (roughly by a factor 5) and reaches
∼ 1.4 cm-3 in agreement with the cut-off frequency of the hiss
emissions (Fig. 1b); then it decreases to 0.8 cm-3 and stays more or
less constant during the rest of the selected time sequence. In accordance
with the previous observations from the Polar spacecraft (Hull et al., 2003),
the recorded large-amplitude parallel electric field takes place at the
boundary separating high- and low-density plasma; this is probably the result
of an ambipolar response of the plasma.
The power displayed in Fig. 1b was measured thanks to an electric antenna
located in the satellite spin plane which contains the magnetic field. This
antenna rotates at spacecraft spin period (5 s) and alternately measures the parallel and perpendicular components of the generated AKR electric
fields. It can be seen that, in the region of depressed density, the AKR
emissions occurring near fce are modulated at twice the spacecraft
spin period. This modulation is such that the largest amplitudes of the
recorded electric fields take place when the antenna is located in the
direction perpendicular to the local magnetic field; only very weak amplitudes are
registered in the parallel direction. This indicates that, in the density
cavity, the wave electric field is polarized perpendicular to the ambient
magnetic field, which implies that the radiation is generated in the right-hand circularly polarized extraordinary (RX) mode
(Ergun et al., 1998). In contrast, in the enhanced-density region, the
recorded AKR electric field displays a significant parallel component, which
denotes that part of the radiation is generated in the LO mode.
The most striking feature in Fig. 1b occurs from ∼ 06:44:45 UT, in
connection with the AKR LO-mode generation, when powerful AKR emissions are
recorded at frequencies located significantly (∼ 10 %) above the
local electron gyrofrequency (fce∼ 365 kHz). The AKR power
associated with this event reaches
∼ 10-6 (V/m)2/Hz; almost 2 orders of magnitude greater than the one measured in
the cavity.
As illustrated in Fig. 1c, in association with the powerful AKR emissions
which take place on the high-potential side of the DL, the FAST tracker
detects AKR fine spectral features. These small-scale radiators appear as
quasi-vertical structures with several hundred hertz bandwidths; they exhibit
predominantly positive frequency drifts (df/dt>0) implying
that the radiating structures propagate earthward.
Figure 2 reveals a 10 ms time sequence of the parallel electric field
waveform recorded during the AKR elementary radiators generation. One
distinguishes a series of large-amplitude (∼ 120 mV m-1) bipolar
electric field structures which characterize the presence of electron holes
(EHs); each of them lasts for about 150 µs. These nonlinear
structures have a spatial extend of a few Debye lengths and are associated
with a localized positive potential (Schamel, 1979). They have the polarity
of a positive potential pulse. In the reference frame we are using, a positive
value of the associated parallel electric field corresponds to the earthward
direction which coincides with the beam propagation. It can be seen that in
the present case, EHs always have a parallel electric field first directed
earthward then anti-earthward; such a polarity indicates that they are indeed
travelling in the electron beam direction. The present observations are
consistent with the results of numerical simulations which show that EHs are
generated on the high-potential side of a DL; they have a velocity of the
order of the drift velocity of the associated electron beam (Newman et al.,
2001; Goldman et al., 2003). All through the end of the selected time
sequence from ∼ 5 to 12 s, the EHs appear in the spectrogram measured
by the SFA as brief emissions of broadband noise (see Fig. 1b); they are
associated with fine AKR spectral features detected by the tracker.
A 10 ms sequence of the fluctuations observed in the 32 kHz
quasi-parallel electric field waveform. The data were acquired on the high-potential side of the recorded DL at ∼ 06:44:45 UT. They characterize
the presence of EHs which have time spans of about 150 µs with
amplitudes of ∼ 120 mV m-1. All
the EHs have a positive then a negative polarity indicating that they are
travelling earthward.
Figure 3a and b display two electron distributions recorded during the
selected time sequence; they are averaged on 0.8 s. The horizontal axis is
the velocity parallel to the magnetic field; the vertical axis is the
perpendicular velocity. At 06:44:42 UT, inside the density cavity, the
distribution illustrated in Fig. 3a exhibits a well-defined horseshoe shape
and is associated with AKR emissions recorded at (and slightly below)
fce. This distribution exhibits a positive slope, ∂Fe(v//,v⊥)/∂v⊥>0, in a large pitch
angle range and provides the free energy for AKR generation via the
cyclotron maser instability (Ergun et al., 2000; Mutel et al., 2007); the
excited waves propagate in the RX mode.
Panel (a) plots the full-ring horseshoe electron
distribution recorded inside the density cavity at ∼ 06:44:42 UT
before the DL crossing. Panel (b) displays the electron distribution
measured at 06:44:45 UT in the regions of enhanced density located on the
high-potential side of the recorded DL; it exhibits a pronounced beam-like
character. The distributions are plotted in perpendicular, parallel velocity
space. Positive values of the parallel velocities correspond to earthward
propagation. Both distributions are averaged over ∼ 0.8 s. The
background electron fluxes with energy less than ∼ 1 keV have been
disregarded.
Figure 3b reveals the electron distribution recorded at 06:44:45 UT in the
regions of enhanced density located on the high-potential side of the
recorded DL; it exhibits a pronounced beam-like character. The peak parallel
energy of the electron beam reaches ∼ 14 keV; it is ∼ 7 keV
larger than in the cavity. The recorded electron distribution can be
reproduced assuming that the electrons which form the horseshoe distribution,
previously shown in Fig. 3a, have passed through a localized parallel
potential drop of ∼ 7 keV. It can be seen that the highest energetic
electrons form an incomplete ring in the pitch angle range θ∼±45∘. At the same time, an anti-earthward parallel
electric field component is measured to be of ∼ 300 mV m-1, implying the crossing of an accelerating structure with a parallel extension of
∼ 25 km which supports the potential drop. In these regions powerful
recorded AKR emissions occur significantly above fce (see Fig. 1b).
DiscussionFree energy for AKR generation
It is worth remembering that in the theory of the electron maser emission the
gradient relevant to the generation of the radiation is the partial
perpendicular velocity gradient on the electron distribution function. It can
be expressed as the sum of two terms, namely
∂Fe(v//,v⊥)/∂v⊥=sinθ∂Fe(v//,v⊥)∂v+cosθv∂Fe(v//,v⊥)∂θ.
The first one is the derivative with respect to the electron velocity v;
the second is the derivative with respect to the electron pitch angle θ.
The present observations provide interesting information about the
characteristics of electron distributions which provide free energy for AKR
generation. Two main generation regions are identified:
Inside the density, cavity the presence of a horseshoe electron
distribution supplies the free energy for AKR generation. Because of the
symmetry of this distribution function, the derivative ∂/∂θ≈0 with respect to θ can be neglected, resulting in ∂Fe(v//,v⊥)/∂v⊥≈sinθ∂Fe(v//,v⊥)/∂v. The dominant
emission is the RX mode; it
is recorded at frequencies in the neighbourhood of fce. This is in
agreement with previous observations (Louarn et al., 1990; Ergun et al.,
2000).
At the cavity interface, where sharp density gradients are located, large-amplitude AKR emissions are recorded in the presence of a DL; they take place
on the high-potential side of the DL. The free energy is supplied by an
electron distribution exhibiting perpendicular velocity gradients induced by
the presence of an incomplete ring of energetic electrons together with the
existence of a lower-energy tail at localized pitch angles; in these
circumstances both terms in Eq. (1) must be taken into account. The recorded
AKR emissions occur at frequencies located significantly above fce, and the polarization of the waves indicates the presence of a significant
power in the LO-mode radiation.
Radiation from electron holes
The present experimental observations show that band-limited radiation above
fce takes place in the presence of EHs, which may distort the
electron distribution and therefore modulate the electron cyclotron
instability (Pottelette et al., 2001; Treumann et al., 2011).
In the auroral acceleration region the typical spatial extension of the EH
parallel to the magnetic field amounts to L//∼1 km (several Debye
lengths). Observations from the POLAR spacecraft indicate that, when the
plasma frequency is small as compared to the electron gyrofrequency, EHs are
rather spherically symmetric (Franz et al., 2000); a conclusion which has
also been drawn by Berthomier et al. (2003) from simplified
magnetized theory in a strong magnetic field. Having a perpendicular size
L⊥≈L//, an EH is well-suited for acting as an efficient
radiating antenna in the kilometre wavelength range. At FAST altitudes such
a radial size is well suited to the generation of AKR elementary events
characterized by a Δf∼100 Hz bandwidth (Pottelette and Pickett,
2007).
Numerical simulations demonstrate that EHs occupy a substantial part of
velocity space while being very narrow in configuration space (Newman et al.,
2001; Goldman et al., 2003). Due to the finite gyroradius of the trapped
electrons, any EHs generated in magnetized plasmas will necessarily have a
finite extension in perpendicular velocity space. This extension gives rise
to perpendicular velocity space gradients on the electron distribution
function which are confined to the edges of the EHs in parallel and
perpendicular direction (Treumann et al., 2011). The radiation generated from
the outer boundary of the hole can be powerful if the localized phase space
gradients are sharp enough. Unfortunately these gradients cannot be
experimentally quantified because the characteristic transit time of EHs
across the spacecraft antenna lasts for a few hundred microseconds. One would
need to measure the electron distribution, say, from 10 eV to 20 keV on the
same timescale. Clearly, for the time being, an instrumentation capable of
this cannot be based on a spacecraft.
In terms of the electron velocity components, the resonance condition, for
mildly relativistic electrons satisfying the cyclotron instability, is
fulfilled around the following resonant circle (Wu and Lee, 1979):
(v//-va)2+v⊥2=vr2,
where va is the centre of the circle in the direction parallel to
the magnetic field
va=k//c2ωce,
while the radius is
vr=va2+2c2(1-ω/ωce).
In both equations ω is the angular wave frequency, ωce
the angular electron gyrofrequency, k// the wave vector parallel to the
magnetic field, and c the speed of light.
In order to satisfy the general weakly relativistic resonance condition for the
maser instability, the velocity Vh of the hole must be such that
the perpendicular gradients localized at the hole coincide with the resonance
contour given by (2), which implies Vh=Va. This equality
provides a determination of the parallel wave number through the EH velocity
k//=ωceVhc2.
The above parallel wave number does not vanish as long as Vh≠0.
In the observer frame the radiation emitted by an EH is oblique, while in the
electron hole reference frame (where Vh and consequently k//
are 0) the radiation is predominantly generated in a perpendicular direction
and occurs in a frequency range located at or slightly beneath the local
non-relativistic electron-cyclotron frequency fce. As such
nonlinear structures propagate earthward, at a velocity of the order of the
electron beam velocity, a satellite located below the altitude of an
accelerating DL will mainly observe radiation from incoming holes. In these
circumstances, the change in frequency due to the displacement of an EH along
the magnetic field is described by the relativistic Doppler effect which, for the observed frequency of the
radiation, results in
f=fce1-βh21-βh,
where βh=Vh/c. Fig. 1c shows that, in the
presence of EHs, the excited AKR frequency range is
∼ 410 ± 10 kHz. The local electron gyrofrequency is
fce∼ 365 kHz; the use of Eq. (6) leads to
Vh∼ (35 000 ± 5000) km s-1. This is almost
half the value of the beam velocity (see Fig. 3b). Such a velocity range is
in excellent agreement with the electron–electron two-stream instability as
the generation mechanism of these nonlinear structures (Treumann and
Baumjohann, 1997). It can be seen in Fig. 3b that the drift velocity of the
propagating electron beam is much larger than the electron thermal stream;
this induces an appreciable growth rate of this instability.
As previously emphasized, radiation generation via the cyclotron maser
implies the production of a steep positive velocity gradient at the boundary
of the EHs, particularly near the electron beam bounding this nonlinear
structure from the high-speed side. EHs extend in configuration space in the
perpendicular direction, at least over distances of the trapped electron
gyro radius. The presence of these trapped electrons induces the required
velocity space gradients in the perpendicular direction.
An example of an integration surface satisfying the requests ∂Fe(v//,v⊥)/∂v⊥>0 is indicated by a dashed line in Fig. 4. This figure is an enlargement of Fig. 3b, which
displays the two-dimensional electron distribution recorded on the high-potential side of the DL; the radius of the resonant circle is Vr=Vb-Vh.
Enlargement of Fig. 3b illustrating the integration surface in the
EH stationary frame. The centre of the resonant circle (dashed line) is at parallel velocity Vh, equal to half the beam
velocity. Only the part of this circle which passes the positive
perpendicular velocity space gradient contributes to a positive growth rate
for the cyclotron maser instability; it is limited to
-45∘<θ< 45∘.
Electron cyclotron maser growth rate
Using polar coordinates, the growth rates for the RX and LO modes can be
respectively written as (Mutel et al., 2007)
ωiωceRX=μR(πvrc)24neωpeωce2∫0πdθsin2(θ)∂Fe(v)∂v⊥v=vr
and
ωiωceLO=π2vr416neωpeωce2∫0πdθsin2(2θ)∂Fe(v)∂v⊥v=vr,
where ne is the number density of energetic electrons and
ωpe is the angular plasma frequency. The integrals must be
solved accounting for resonance along the resonant circle in velocity space
defined by Eq. (2); only the part of this circle which passes the positive
perpendicular velocity space gradient contributes to a positive growth rate.
The dimensionless factor μR∼0.14 corrects for the effect of the
plasma dispersion. Note that the dependence of the growth rate on the
velocity distribution appears as a linear function of the perpendicular
derivative weighted by a simple geometrical factor centred at 90∘
(RX mode) or 45 and 135∘ (LO mode). Without the influence of
this geometrical factor, the growth rate for the ordinary mode is smaller
than that of the extraordinary mode by O(vr2/μRc2).
Using Eqs. (7) and (8), it can be shown that in the auroral cavity,
characterized by the presence of a horseshoe distribution of the type
illustrated in Fig. 3a, the RX to LO growth rate ratio is ∼ 10-3
(Mutel et al., 2007). In the cavity, the resonant circle which encompasses
the largest velocity gradients is located at the origin of the velocity space
of Fig. 3a (Ergun et al., 2000); its radius is
Vr=c2(1-f/fce). The recorded polarization of the
radiation is consistent with X-mode generation at a frequency located slightly
below fce; it requires k//=0 in order to fulfill Eq. (2).
As emphasized earlier, in order to quantify the emission of radiation
generated by an EH, it is useful to work in the reference frame of the hole
which is not centred at the origin of the velocity space. Given the order of
magnitude of the velocity range of the EHs recorded at the edge of the
cavity, a resonant circle which satisfies the condition for strong maser
emission is plotted with a dashed line in Fig. 4. Only the part of this circle
which passes the positive perpendicular velocity space gradient contributes
to a positive growth rate; it is limited to -45∘<θ< 45∘. As seen in Eqs. (7) and (8), the growth rates of the RX
and LO modes are a sensitive function of sin2(θ) and
sin2(2θ), respectively. Given the integration interval restricted
to -45∘<θ< 45∘, the value of the
geometrical factor is much larger for the LO mode than for the RX mode. This
may explain the significant power recorded in the LO at the edges of the auroral density cavity which is sometimes
observed (Louarn, 2006).
Conclusions
The present paper provides new additional evidence related to the generation
of elementary-scale radiation by the EHs.
There is undeniable cross-fertilization between laboratory and space
experiments regarding radiation generation. The observations performed in the
AKR source region strengthen those previously acquired from laboratory
experiments (Gunell and Löfgren, 1997; Brenning et al., 2004). Actually, part of the AKR radiation appears
to be generated thanks to the existence of nonlinear structures, located on
the high-potential side of a DL, which act as a sender antenna. Such localized
large-amplitude parallel electric fields are recorded inside high-density
gradients located at the interface of the auroral cavity. In agreement with
previous studies (Pottelette et al., 2001, 2014; Treumann et al., 2011), the
nonlinear structures which give rise to the fine structure in the AKR
spectrum can be identified as electron holes. A recent theoretical study
calculating the AKR growth rates in the presence of EHs embedded in the
electron distribution supports this interpretation (Zhao et al., 2016).
In the hole frame, the radiation is excited near the local gyrofrequency, while, in the satellite frame, the excited frequency range appears to be shifted up because of the Doppler effect generated by approaching holes
(Treumann et al., 2011). The use of the measurement of the frequency shift
allows the determination of the EHs velocity; it turns out that these
nonlinear structures move at about half the value of the beam velocity. Such
a velocity range is in excellent agreement with the electron–electron two-stream instability and implies that the EHs are caused by the nonlinear
evolution of the electrostatic waves generated by this instability. This is
a very fundamental result which shows that the generation mechanism of EHs
can be derived from the characteristics of the radiation they transmit.
The radiation emitted by an EH has a finite k// and can consequently
escape from the source region. Regarding the AKR polarization, it has also
been underlined that, on the high-potential side of a DL, the shape of the
electron distribution notably enhances the growth rate of the LO mode as
compared to its value in the density cavity.
As EHs seem to be strong sources of non-thermal radio radiation from the
aurora, all these observations suggest that they should play an important
role in other magnetized planetary objects and more generally in
astrophysical plasmas. The formation of EHs and their associated radiation
mechanism are highly nonlinear and cannot be accessed by a perturbation
approach. The only way of investigating such processes is through numerical
simulations. For the time being, it is generally believed that the short
spatial-scale perpendicular velocity gradient at the hole boundary,
generated by the presence of trapped electrons, is steep and contributes to
the electron cyclotron maser. However, the migration of the EHs in velocity
space, as the electron velocity distribution function evolves from a beam
near the high-potential side of the DL, is crucial to the understanding of
the role of these nonlinear structures as small-scale radiators.
Unfortunately, in the presence of the converging Earth's magnetic field, the
evolution of an EH, including its structure, stability (life time) and
propagation speed, remain essentially unexplored by numerical
simulations.
The data are publicly accessible at the following address: http://sprg.ssl.berkeley.edu/fast/scienceprod/welcome.html.
The authors declare that they have no conflict of
interest.
Acknowledgements
The FAST mission is a project of the Space Sciences Laboratory of the
University of California at Berkeley run under the auspices of NASA. The
authors are indebted to Charles W. Carlson and Robert E. Ergun for providing particle and wave data as well as for some useful
discussions. This research has been initiated within the France–Berkeley
program. The topical editor, Elias
Roussos, thanks two anonymous referees for help in evaluating this paper.
References
Benediktov, E. A., Getmantsev, C. G., Sazonoy, Y. A., and Tarasov, A. F.:
Preliminary results of measurement of the intensity of distributed
extraterrestrial radio-frequency emission at 725 and 1525-kHZ frequencies by
the satellite elektron-2, Kosm. Issled., 3, 614–618, 1965.Berthomier, M., Pottelette, R., Muschietti L., Roth, I., and Carlson, C. W.:
Scaling of three dimensional electron phase space density holes observed by
FAST in the auroral downward current region, Geophys. Res. Lett., 30,
2148–152, 10.1029/2003GL018491, 2003.
Brenning, N., Koepke, M. E., Axnäs, I., and Raadu, M. A.: Electromagnetic
radiation from double layers, 12th International Congress on Plasma Physics,
25–29 October, Nice, France, 2004.Chiu, Y. T. and Schulz, M.: Self-consistent particle and parallel
electrostatic field distributions in the magnetospheric-ionopheric auroral
region, J. Geophys. Res., 83, 629–642, 10.1029/JA083iA02p00629, 1978.Ergun, R. E., Carlson, C. W., McFadden, J. P., Mozer, F. S., Delory, G. T.,
Peria, W., Chaston, C., Temerin, M., Elphic, R., Strangeway, R. J., Pfaff, R.,
Cattel, C. A., Klumpar, D., Shelly, E., Peterson, W., Moebius, E., and Kistler, L.:
FAST satellite wave observations in the AKR source region, Geophys. Res. Lett., 25, 2061–2064, 10.1029/98GL00570, 1998.Ergun, R. E., Carlson, C. W., McFadden, J. P., Delory, G. T., Strangeway, R.
J., and Pritchett, P. L.: Electron-Cyclotron Maser Driven by Charged-Particle
Acceleration from Magnetic Field-aligned Electric Fields, Astrophys J., 538,
456, 10.1086/309094, 2000.Franz, J. R., Kintner, P. M., Seyler, C. E., Pickett, J. S., and Scudder, J.
D.: On the perpendicular scale of electron phase-space holes, Geophys. Res.
Lett., 27, 169–173, 10.1029/1999GL010733, 2000.Goldman, M. V., Newman, D. L., and Ergun, R. E.: Phase-space holes due to
electron and ion beams accelerated by a current-driven potential ramp,
Nonlin. Processes Geophys., 10, 37–44,
10.5194/npg-10-37-2003, 2003.Gunell, H. and Löfgren, T.: Electric field spikes formed by electron
beam-plasma interaction in plasma density gradients, Phys. Plasma, 4, 2805,
10.1063/1.872413, 1997.Gurnett, D. A.: The earth as a radio source – Terrestrial kilometric
radiation, J. Geophys. Res., 79, 4227–4238, 10.1029/JA079i028p04227,
1974.Hull, A. J., Bonnell, J. W., Mozer, F. S., Scudder, J. D., and Chaston, C.
C.: Large parallel electric fields in the upward current region of the
aurora: Evidence for ambipolar effects, J. Geophys. Res., 108, 1265,
10.1029/2002JA009682, 2003.Lindberg, L.: Observations of Electromagnetic Radiation from Plasma in
Presence of a Double Layer, Phys. Scripta, 47, 92–95,
10.1088/0031-8949/47/1/016, 1993.Löfgren, L. and Gunell, H.: Interacting eigenmodes of a plasma diode with
a density gradient, Phys. Plasmas, 5, 590, 10.1063/1.872751, 1998.
Louarn, P.: Generation of auroral kilometric radiation in bounded source
regions, in Geospace Electromagnetic Waves and Radiation, Lecture Notes in
Physics (LNP), Vol. 687, Springer-Verlag, Berlin-Heidelberg-New York, 55–86,
2006.Louarn, P., Roux, A., De Feraudy, H., Le Quéau, D., André, M., and
Matson, L.: Trapped electrons as a free energy source for the auroral
kilometric radiation, J. Geophys. Res., 95, 5983,
10.1029/JA095iA05p05983, 1990.Mutel, R. L., Peterson, W. M., Jaeger, T. R., and Scudder J. D.: Dependence
of cyclotron maser instability on electron velocity distributions and
perturbations by solitary waves, J. Geophys. Res., 112, A07211,
10.1029/2007JA012442, 2007.Newman, D. L., Goldman, M. V., Ergun, R. E., and Mangeney, A.: Formation of
Double Layers and Electron Holes in a Current-Driven Space Plasma, Phys. Rev.
Lett., 87, 255001, 10.1103/PhysRevLett.87.255001, 2001.Persoon, A. M., Gurnett, D. A., Peterson, W. K., Waite, Jr., J. H., Burch, J.
L., and Green, J. L.: Electron density depletion in the nightside auroral
zone, J. Geophys. Res., 93, 1871, 10.1029/JA093iA03p01871, 1988.Pottelette, R. and Pickett, J.: Phase space holes and elementary radiation
events, Nonlin. Processes Geophys., 14, 735–742,
10.5194/npg-14-735-2007, 2007.Pottelette, R., Treumann, R. A., and Berthomier, M.: Auroral Plasma
Turbulence and the cause of AKR fine structure, J. Geophys. Res., 106,
8465–8476, 10.1029/2000JA000098, 2001.Pottelette, R., Berthomier, M., and Pickett, J.: Radiation in the
neighbourhood of a double layer, Ann. Geophys., 32, 677–687,
10.5194/angeo-32-677-2014, 2014.Schamel, H.: Theory of electron holes, Phys. Scripta, 20, 336–342,
10.1088/0031-8949/20/3-4/006, 1979.Treumann, R. A.: The electron-cyclotron maser for astrophysical application,
Astron. Astrophys. Rev., 13, 229–315, 10.1007/s00159-006-0001-y, 2006.
Treumann, R. A. and Baumjohann, W.: Advanced Space Plasma Physics, Imperial
College Press, London, 1997.Treumann, R. A., Baumjohann, W., and Pottelette, R.: Electron-cylotron maser radiation from electron holes:
upward current region, Ann. Geophys., 29, 1885–1904, 10.5194/angeo-29-1885-2011, 2011.Volwerk, M.: Radiation from electrostatic double layers in laboratory
plasmas, J. Phys. D Appl. Phys., 26, 1192–1202,
10.1088/0022-3727/26/8/007, 1993.
Wu, C. S. and Lee, L. C.: A theory of the terrestrial kilometric radiation,
Astrophys. J., 230, 621–626, 10.1086/157120, 1979.Zhao, G. Q., Chu, Y. H., Feng, H. Q., and Wu, D. J.: The effect of electron
holes on cyclotron maser emission driven by horseshoe distributions, Phys.
Plasmas, 23, 114505, 10.1063/1.4968220, 2016.