Introduction
Electromagnetic high-frequency (HF) pumping of ionospheric plasma from
ground-based transmitters yields the strongest plasma response when the HF
beam is directed in magnetic zenith, antiparallel to the geomagnetic field
(B0) in the Northern Hemisphere. This magnetic zenith effect has been
observed in several plasma phenomena. Experiments with the high-latitude
EISCAT (European Incoherent SCATter association) high-power HF facility
(named Heating) in northern Norway and the HAARP (High frequency Active Auroral
Research Program) HF facility in Alaska, USA, show intensified optical
emissions and
self-focusing in magnetic zenith.
Further, electron temperature enhancements are the largest when pumping near
magnetic zenith and pump-excited
geomagnetic field-aligned density striations give the strongest HF-radar
backscatter, as observed in experiments with EISCAT Heating
, and the mid-latitude
Sura HF facility in Russia . The question is,
what causes the strong plasma response in magnetic zenith?
We present experimental results from EISCAT Heating ;
this HF facility was used to pump the plasma with left-hand circularly polarized (LHCP)
HF radio waves. Here “left-hand” is defined from the point of view of
B0: the wave electric field rotates in the opposite sense to the
electron gyromotion. The HF beam was directed in magnetic zenith at
12∘ from vertical to the south and the pump frequency (f0) was
chosen to be a few 100 kHz below the maximum electron plasma frequency of
the F2 region (O-mode critical frequency, foF2) in the overhead daytime
ionosphere. The plasma response to the HF pumping was observed with the
EISCAT UHF (ultra high frequency) incoherent scatter radar at the Ramfjordmoen site.
The polar-orbiting CASSIOPE (CAScade, Smallsat and IOnospheric Polar
Explorer) satellite in the topside ionosphere (perigee 325 × apogee 1500 km altitude,
80∘ inclination) was used to detect pump radiation above the
F-region peak. The electromagnetic radiation was observed with the RRI (Radio
Receiver Instrument) in the e-POP (enhanced Polar Outflow Probe) package on
the fixed platform of CASSIOPE . The RRI
is equipped with four monopole antennas, configured into two 6 m crossed
dipoles, d1 and d2, that provide voltage magnitudes (V1, V2) and
phases (Φ1, Φ2) of the detected signals. In some cases the
detected signals enabled determination of the direction of arrival (DOA) of
the incoming wave .
It is commonly assumed that a LHCP wave transmitted near-vertically from the
ground propagates in the O-mode when entering the ionosphere. An O-mode
wave propagating near-vertically reflects at the plasma resonance height,
where the local plasma frequency fp=f0. However, our
experimental results show that the pump wave passed through the ionospheric
density peak although f0<foF2. This suggests that the pump wave
transmitted near magnetic zenith propagated instead in the L-mode, which is
a LHCP mode that has the wave vector parallel or antiparallel to the ambient
magnetic field. A wave in the L-mode can propagate both on the O-mode
dispersion surface and the Z-mode surface (also referred to as the slow
extraordinary mode), and propagates from one surface to the other without
linear conversion, always with the wave vector parallel to the ambient
magnetic field. The square of the refractive index for the L-mode as
obtained from the dispersion equation for a cold magnetized and homogeneous
plasma is given by n∥2=1-fp2/f(f-fe), where f is the wave frequency and fe is the
electron gyrofrequency . Based on ray tracing
analyses, it has been proposed that the pump wave can be guided in the
L-mode by pump-induced kilometre-scale geomagnetic field-aligned plasma
density ducts .
Experimental results
In November 2015, EISCAT Heating was used to transmit a LHCP pump wave
continuously for several minutes during CASSIOPE passages approximately
through the extension of the Heating beam in the topside ionosphere. A total
of six conjunctions occurred during daytime, out of which two had the desired
conditions of sufficiently low ionospheric absorption and f0<foF2<f0+fe/2, where the latter frequency corresponds
to the L-mode cutoff (fp≈f0+fe/2). The
EISCAT UHF radar beam was scanned in steps of 1∘ every 10 s
between eight elevations around magnetic zenith in the plane containing the
vertical to measure background plasma parameter values.
On 12 November, f0=3.900 MHz and the pump wave was transmitted
continuously between 14:00:05 and 14:15:00 UT with an effective radiated power
(ERP) of 134 MW (UT is local time minus 1 h). Figure shows
the height profile of fp during the satellite pass as obtained
with the UHF radar. It is seen that foF2 ≈4.3 MHz >f0=3.900 MHz. Further, according to the IGRF geomagnetic field model
, fe≈1.363 MHz at ∼215 km
where fp≈f0, implying that f0<3fe≈4.089 MHz.
Height profile of fp with f0=3.900 MHz shown as a
solid line (14:11:15 UT and integrated for 10 s on 12 November 2015). The
data were obtained with the EISCAT UHF radar from the ion line and the width
of the profile shows the approximate standard deviation.
Measurements of stimulated electromagnetic emission (SEE) on the ground were
attempted, but no emissions were observed during this conjunction. This is
consistent with ionograms from the EISCAT Dynasonde at the Ramfjordmoen
site that indicate high D-region absorption of HF waves. The pump wave may
therefore have been too weak to excite SEE or the SEE itself was absorbed
when propagating through the D region on its way to the ground.
CASSIOPE detected the HF wave transmitted from Heating at an altitude of
553 km, above the F-region plasma density peak at ∼250 km
(Fig. ). The RRI swept 13 different frequency bands during the
experiments. Figure shows an overview of the voltage on
the two antenna dipoles in that frequency band which contained the Heating
signal. The signal from the continuously transmitted pump wave at f0=3.900 MHz can be seen from about 14:07:34 UT. The ratio of the detected
voltage magnitudes on dipoles 1 and 2 is approximately constant with RV=V1/V2≈1.6 and the phase difference between the two signals
ΔΦ=Φ1-Φ2≈280∘. The pump wave thus
passed through the ionospheric density peak although f0<foF2.
Overview of the detected voltage on the two antenna dipoles for the
CASSIOPE passage over EISCAT Heating from 14:06:44.630 to 14:08:41.209 UT on
12 November 2015. The RRI was pre-programmed to sweep between 13 different
frequency bands, one of which contained the Heating signal at f0=3.900 MHz. The panels show the signal level in the 60 kHz wide frequency
band around the Heating signal at f0, which can be seen from about
14:07:34 UT.
The I and Q baseband voltages induced on each of the two dipoles of the
RRI were used to calculate the DOA of the detected electromagnetic field. The
theory and numerical technique for inverting the voltages to the DOA is
discussed by . The subject was also treated in
, however, with additional approximations for the included
outline of the DOA calculations. For the computations of the DOA, it is
assumed that the waves obey the cold-plasma theory. In addition,
fp, fe (fe≪fp, f0 for
the discussed experiments) and B0 are assumed independently known and
hence allow the wave polarization to be determined in a spacecraft coordinate
reference system for a given propagation direction. The RRI tubular BeCu
dipoles are assumed to have an effective length equal to half their
tip-to-tip length permitting the induced open-circuit voltage input to the
RRI to be calculated. This direction determination depends on the accuracy of
the polarization measurement and on the relevance of the cold plasma theory.
While this seems defensible for propagation in the upper-branch O- and X-modes
at frequencies above their respective cutoff frequencies, it does require
knowledge of the plasma parameters at the receiver, and can be an imprecise
approach when polarization becomes longitudinal; this is, however, not a
problem for the examples presented below. It has the advantages of not
requiring spatially coherent receivers for wave-front detection, and of
avoiding the need for absolute electric field measurement.
Direction of the pump wave vector (k) detected by the RRI on
CASSIOPE at an altitude of 553 km as viewed from two angles (14:08:02 UT on
12 November 2015, corresponding to the plasma profile in
Fig. ). Also shown is the direction of the straight line
between Heating and CASSIOPE (k0), B0 and the two receiver dipoles
(d1, d2). The vertical dotted lines indicate the projection of the
vectors on the horizontal south–east plane. The dashed ellipse indicates the
polarization of the wave electric field and the right diagram is from
approximately normal to that ellipse. The DOA calculations were done with
fp=2.00 MHz and fe=1.20 MHz at the CASSIOPE
altitude.
Figure shows the directions of the pump wave vector (k),
the straight line between Heating and CASSIOPE (k0), B0 and the two
receiver dipoles (d1, d2) for 12 November. The wave vector is directed
towards the north-east and closer to horizontal than to B0, although the
Heating beam was transmitted near magnetic zenith. The dashed ellipse
outlines the polarization of the wave electric field with the right diagram
viewing approximately normal to the polarization plane. The wave is nearly
linearly polarized which is consistent with the direction of the wave vector
near-orthogonal to B0.
On 26 November, the pump wave was transmitted continuously between
12:07:00 and 12:17:00 UT with f0=5.423 MHz and an ERP of 490 MW.
Figure shows the height profile of fp with
foF2≈5.6 MHz >f0=5.423 MHz.
Height profile of fp with f0=5.423 MHz shown as a
solid line (12:04:50 UT and integrated for 10 s on 26 November 2015). The
data were obtained from the plasma line up to ∼300 km altitude and from
the ion line at higher altitudes. The width of the profile shows the
approximate standard deviation. The time for the profile, a few minutes
before the conjunction between the Heating beam and CASSIOPE, was the last
time with a usable plasma line height profile that enables determination of
fp with high accuracy.
SEE was well developed during this conjunction and exhibited downshifted
maximum features in the lower sideband of the pump . The
frequency spectra indicate that f0<4fe in the region where
the SEE is excited. According to the IGRF model, fe≈1.357 MHz at the plasma resonance height of approximately 225 km, which
implies that f0=5.423 MHz ≲4fe≈5.428 MHz. However, the well-developed SEE suggests that it is excited
where f0 is at least some 10 kHz below 4fe, which would
indicate that the SEE is excited at a lower altitude (larger fe)
than the plasma resonance height, at which 4fe-f0≈5 kHz. The observation of SEE on 26 November is also consistent with
the ionograms from the EISCAT Dynasonde that indicate low D-region absorption of
HF waves, contrary to the situation on 12 November.
The RRI detected the HF wave transmitted from Heating at an altitude of
352 km, above the F2-region peak at ∼235 km (Fig. ).
Figure shows an overview of the voltage on the two
antenna dipoles in the frequency band that contained the Heating signal,
similar to Fig. . The signal from the continuously
transmitted pump wave at f0=5.423 MHz can be seen from about
12:11:45 UT. For this case, the detected signals have RV≈1.2 and
ΔΦ≈190∘.
Overview of the detected voltage on the two antenna dipoles for the
CASSIOPE passage over EISCAT Heating from 12:10:59.636 to 12:13:41.357 UT on
26 November 2015. The RRI was pre-programmed to sweep between 13 different
frequency bands, one of which contained the Heating signal at f0=5.423 MHz. The two panels show the signal level in the 60 kHz wide
frequency band around the Heating signal at f0, which can be seen from
about 12:11:45 UT.
Figure shows that the direction of the wave vector (k) of
the detected pump wave is close to magnetic zenith. Specifically, k
deviates from -B0 by only 0.14∘. As seen from the left part of
Fig. , the electric field polarization is approximately
circular, consistent with the wave vector being near-parallel to -B0.
Discussion
The EISCAT Heating facility was used for transmission of a LHCP
electromagnetic wave beam directed in magnetic zenith into the ionosphere
with f0<foF2<f0+fe/2. These conditions were
fulfilled for two of the six conjunctions in our experiments. In both of these
conjunctions, the pump wave was detected by CASSIOPE in the topside
ionosphere, above the daytime F2-region density peak. For 12 November 2015,
f0=3.900 MHz and foF2≈4.3 MHz
(Fig. ). On 26 November 2015, f0=5.423 MHz and foF2≈5.6 MHz (Fig. ). Thus, the wave propagated through
the F-region peak although f0<foF2.
An O-mode wave propagating upward in a horizontally stratified ionosphere
with increasing plasma density with height will reach a maximum density at
which fp=f0 for angles of incidence θ≤θc, where the critical or Spitze angle θc=arcsin[Y/(1+Y)cosI]≈6∘ ,
Y=fe/f0 and I≈78.4∘ is the inclination of B0 at fp=f0 above Heating.
For increasing θ beyond θc, an O-mode wave reflects
at successively lower fp, as in magnetic zenith at θ=90∘-I≈12∘.
Based on ray-tracing computations, it has been shown that a LHCP wave can be
guided in the L-mode in magnetic zenith by kilometre-scale magnetic
field-aligned density ducts in an otherwise horizontally stratified
ionosphere . A wave in the
L-mode has a wave vector parallel or antiparallel to the ambient magnetic
field. For fp<f0, the L-mode follows the O-mode dispersion
surface. Whereas the O-mode has a cutoff at fp=f0, the
L-mode passes through the radio window in a horizontally stratified
ionosphere for θ=θc or is guided along B0 by
density ducts through radio windows that are opened by the ducts. In a
horizontally stratified ionosphere, the radio window denotes that case for
which waves transmitted from the ground have their wave vector antiparallel
to B0 when reaching fp=f0 and thus propagate in the
L-mode, which occurs for rays launched at θ=θc.
For fp>f0 the L-mode continues on the Z-mode dispersion
surface, until encountering its cutoff at fp≈f0+fe/2. A wave in the L-mode can therefore propagate in higher
plasma densities and at higher ionospheric altitudes than in the O-mode.
Direction of the pump wave vector (k) at an altitude of 352 km
(12:12:10 UT on 26 November 2015, corresponding to the plasma profile in
Fig. ). See Fig. for a description of the
diagram. The DOA calculations were done with fp=5.00 and
fe=1.29 MHz at the CASSIOPE altitude.
Note that the O- and Z-mode dispersion surfaces only touch at fp=f0 for a wave vector parallel to the ambient magnetic field
. A real wave field propagating along ±B0
involves a range of wave vectors around the parallel direction. In order to
pass through a radio window, whether the natural radio window in a
horizontally stratified ionosphere or pump-induced windows by large-scale
density irregularities associated with ducts, non-parallel rays therefore
have to undergo O–Z conversion. This linear conversion must be
considered in order to calculate the energy transmitted through the radio
window. The L-mode, however, switches between the O- and Z-mode
dispersion surfaces without conversion, which is one motivation for the
distinction of L, O and Z-modes.
We conclude that the pump wave observed in the topside ionosphere in our
experiments propagated some distance in the L-mode, particularly where
fp>f0 near the F-region peak. Since in our case foF2<f0+fe/2, the L wave did not reach its cutoff but in the
topside ionosphere where fp=f0 must again have passed through
a radio window and where fp<f0 continued on the O-mode
dispersion surface up to CASSIOPE.
It may be noted that an electromagnetic wave that is ducted by a cylindrical
density irregularity has quasi-helical ray paths wherein propagation does not
pass through the axis of the duct . Ducted waves therefore
do not have wave vectors that are strictly parallel to ±B0.
Nevertheless, ray tracing computations show the ducted waves to propagate in
the L-mode where fp>f0
. Further, strictly speaking
the dispersion properties of the L-mode discussed in the present treatment
concern a homogeneous plasma. The dispersion properties in the inhomogeneous
plasma of a density duct should be studied in more detail.
The transionospherically propagated signals detected on 12 November were
weaker than those on 26 November. There are several reasons that may have
contributed to this. The ERP on 12 November was lower than on 26 November
(134 and 490 MW, respectively), D-region absorption as indicated in
ionograms from the EISCAT Dynasonde was higher on 12 November than on
26 November, and the weaker signals were detected at a higher altitude and
larger distance from Heating than the stronger signals (altitudes 553 and
352 km, respectively).
Further, the wave fields detected by CASSIOPE correspond to different DOA. On
12 November the wave vector was closer to horizontal than parallel to
-B0 (Fig. ), while on 26 November it was parallel to
-B0 (Fig. ).
As the pump wave on 12 November propagated a further distance in the topside
ionosphere than on 26 November, refraction was probably also larger in the
former case, which may have contributed to the larger DOA angle. Furthermore, for
12 November, f0 was ∼0.4 MHz below foF2 which implies
approximately 0.2 MHz below the L-mode cutoff at fp≈f0+fe/2. When an L-mode wave approaches its cutoff, the ray path
bends towards the horizontal in the reflection region. Since at the F-region
peak the L-mode wave is only 0.2 MHz from its cutoff, the ray may have
started to bend, which could have contributed to the obtained DOA. In
addition, a ducted wave propagating upwards in the topside ionosphere towards
decreasing plasma densities will eventually reach an ambient density for
which the wave is no longer trapped in the duct. The question arises whether
there could be diffraction effects when the wave exits the duct that could
contribute to the observed DOA. All these possibilities should be analysed.
Transionospheric propagation of HF pump waves transmitted from the ground
with f0<foF2 in the unperturbed ionosphere has been reported previously.
The electric field of a beam from the Sura facility was detected by the
DEMETER satellite at about 670 km altitude, near magnetic zenith
. This was observed for f0 down to 0.5–0.7 MHz
below foF2, which corresponds to foF2-f0≲fe/2. The observations were attributed to the development of a
large-scale density cavity in the evening and nighttime pump–plasma
interaction region that was suggested to focus the beam and redirect it
towards magnetic zenith. The cavity was proposed to result in locally
underdense plasma for the O-mode wave (fp<f0) so that it
could pass through the F-region peak. Transionospheric propagation was not
observed during daytime, consistent with ionospheric conditions for
development of large-scale cavities by HF pumping that are less favourable during
daytime than during evening and nighttime.
argued that conversion of the wave from O-mode to Z-mode in
the bottomside ionosphere and vice versa on the topside could not explain the
observations because the Z-mode was expected to be strongly absorbed where
fp≈f0 in the topside. The observations were done with
ERP levels of 40–150 MW during evening and nighttime with probably only a
minimum of D-region absorption. In our case the ERPs were 134 and 490 MW
during daytime. Assuming a D-region absorption of 6 dB, the ERP levels are
comparable in the two experiments. Since in our case transionospheric
propagation with f0<foF2 was observed, the absorption cannot have been
too strong. We therefore suggest that L- and associated Z-mode
propagation cannot be ruled out for the cases discussed by
. L-mode propagation would explain why
transionospheric propagation was indeed observed near magnetic zenith and
only for foF2-f0≲fe/2, as the L-mode has
its cutoff at fp≈f0+fe/2 and is evanescent
for higher fp.
presented experimental results concerning large-scale
density irregularities induced by the Sura facility together with
tomography-like reconstruction of the ionospheric plasma density profile
using VHF (very high frequency) signals from PARUS beacon satellites that were received on the
ground. The results from the reconstruction of the ionospheric electron
density distribution indicate that as f0 approaches foF2, density
troughs may form that stretch along the entire F2 layer. Ray tracing
calculations suggest that in these troughs the plasma became locally
underdense for O-mode propagation so that pump energy could be transmitted
through the F-region density peak into the topside ionosphere with the pump
wave propagating along the geomagnetic field, thus arriving at similar
conclusions as those of .
reported transmissions from the Sura facility to
CASSIOPE at an altitude of about 1300 km, for foF2 ∼0.1 MHz above
f0 of the transmitted O-mode wave. VHF/UHF transmissions from the
CASSIOPE/e-POP radio beacon were received on the ground to measure total
electron content. Based on tomography-like reconstruction using the received
wave data, it was concluded that the transionospheric propagation was
maintained by O-mode ducting in locally underdense magnetic field-aligned
density irregularities.
L-mode propagation of a ducted pump wave is expected to cause stronger
plasma perturbations than O-mode propagation alone and therefore to be
instrumental in the magnetic zenith effect. The pump wave can be guided in
the L-mode by a density duct that has been excited by the pump in the
O-mode or is naturally present. Such a duct is heated by collisional
absorption of the L-mode wave as it propagates first on the O-mode
dispersion surface and then continues on the Z-mode dispersion surface
above the O-mode reflection height. The resulting expected deepening of the
duct locally moves the upper hybrid resonance height upward. Since in the
L-mode the wave electric field is perpendicular to B0 at higher plasma
densities than in the O-mode, the L-mode facilitates excitation of upper
hybrid phenomena localized in the density depletions of small-scale
striations
and associated anomalous absorption deeper into the plasma (at higher ambient
plasma densities) and in a wider altitude range than for pure O-mode
propagation. The duct, so to speak, tells the pump wave where to propagate
and the pump wave tells the duct where to deepen, which may lead to
self-focusing in magnetic zenith.
The excitation of upper hybrid phenomena occurs from the L-mode on the
O-mode dispersion surface, at least initially. For small-scale striations
with sufficiently deep density depletions, the L-mode with its
perpendicular electric field and propagation on the Z-mode surface at
altitudes above the O-mode reflection height could excite upper hybrid
phenomena localized in the depletions even above the ambient plasma resonance
height. Because of its possibility to propagate above the O-mode reflection
height, pump wave propagation in the L-mode is in any case expected to
cause additional heating and plasma depletion than for O-mode propagation
alone. L-mode propagation, therefore, could account for the strong plasma
response observed in magnetic zenith. Already, early experiments in the 1970s
showed that HF pumping can facilitate L-mode propagation and associated
O–Z conversion, as evidenced by the appearance of so-called Z traces
in ionograms .
Ducted L-mode propagation of the pump wave can explain previously observed
slow temporal evolution of optical emissions from the O(1S) excited
state at 557.7 nm. In experiments at HAARP, the emissions were observed to
grow for tens of seconds after pump-on, which is slow compared to the ∼0.7 s lifetime of the source exited state . The
slow growth was attributed to larger-scale transport processes under
self-focusing to produce intensified pumping and the electron acceleration
needed to excite the O(1S) state. We note that the slow temporal
evolution is consistent with the formation of density irregularities that
guide the pump wave in the L-mode, which could facilitate intensified
electron acceleration by the LHCP wave .
Strong self-focusing was observed at HAARP in which the pump-induced
557.7 nm emission region collapsed and intensified from a cone of ∼22∘ to 9∘ in magnetic zenith within tens of seconds after
pump-on . Again the emissions had a growth time at
least 1 order of magnitude longer than the lifetime of the O(1S)
state, indicative of larger-scale plasma structuring. The optical emission
images showed evidence of magnetic field-aligned density striations with
transverse scales of ∼2–6 km. We suggest that such irregularities
guided the pump wave in the L-mode in magnetic zenith, which facilitated
intensified pumping of upper hybrid processes and associated electron
acceleration in an extended height range as well as the self-focusing.
Finally it should be mentioned that the magnetic zenith effect has been
interpreted in terms of self-focusing of the pump wave
. These treatments too are
concerned with large-scale structuring of the plasma by bunching of
small-scale density striations, similar to the formation of ducts discussed
by . However, whereas
propose self-focusing of an
O-mode pump wave, the present results, those of
and suggest the importance of
L-mode propagation deeper into the plasma where an O-mode wave cannot
reach. Further experimental investigations and modelling of the magnetic
zenith effect are needed to find out the importance of O-mode versus
L-mode pumping for the magnetic zenith effect.