Powerful high-frequency (HF) radio waves can be used to efficiently modify
the upper-ionospheric plasmas of the F region. The pressure gradient induced by
modulated electron heating at ultralow-frequency (ULF) drives a local
oscillating diamagnetic ring current source perpendicular to the ambient
magnetic field, which can act as an antenna radiating ULF waves. In this
paper, utilizing the HF heating model and the model of ULF wave generation
and propagation, we investigate the effects of both the background
ionospheric profiles at different latitudes in the daytime and nighttime
ionosphere and the modulation frequency on the process of the HF modulated
heating and the subsequent generation and propagation of artificial ULF
waves. Firstly, based on a relation among the radiation efficiency of the
ring current source, the size of the spatial distribution of the modulated
electron temperature and the wavelength of ULF waves, we discuss the
possibility of the effects of the background ionospheric parameters and the
modulation frequency. Then the numerical simulations with both models are
performed to demonstrate the prediction. Six different background parameters
are used in the simulation, and they are from the International Reference
Ionosphere (IRI-2012) model and the neutral atmosphere model (NRLMSISE-00),
including the High Frequency Active Auroral Research Program (HAARP; 62.39
The ultralow-frequency (ULF) waves with a frequency in the range of
0.1–10 Hz, which exist extensively in the terrestrial space, are associated
with numerous intriguing space physical problems, including
magnetosphere–ionosphere–atmosphere coupling and radiation belt modeling.
As a transitional region from atmosphere to magnetosphere and also an
anisotropic medium with background parameters changing rapidly with height,
the ionosphere has significant effects on the ionospheric propagation of ULF
waves, which therefore is frequently investigated to reveal the mechanism of
relevant problems. Tepley and Landshoff (1966) first proposed the waveguide
theory for ionospheric propagation of ULF waves, which assumes that ULF waves
propagate as shear Alfvén waves along the magnetic field line from low to
high latitudes or propagate as compressional waves from high to low
latitudes. Greifinger (1972) and Greifinger and Greifinger (1968, 1973)
developed the theory of ionospheric waveguide, investigating the coupling,
transmission, reflection and cutoff of ULF waves and the effects of
propagation direction. The shear Alfvén waves and compressional waves
propagate independently in the magnetosphere, while in the ionosphere they
are coupled through Hall conductivity, which can affect the reflection and
penetration of ULF waves (Yoshikawa and Itonaga, 1996, 2000; Yoshikawa et
al., 1999). Since the ionosphere is not an absolutely perfect conductor
itself, ULF waves can penetrate through the ionosphere into neutral
atmosphere then propagate as electromagnetic waves which can be observed on
the ground. The 90
Apart from research on the propagation of naturally excited ULF waves, the generation of ULF waves by ionospheric modulated heating is considered a physical problem of great importance and interest as well. A strong horizontal electric current driven by an atmospheric dynamo electric field and a magnetospheric electric field flows in the D or E region of the polar ionosphere, which is called the auroral electrojet. Similarly, the equatorial electrojet flows in the lower equatorial ionosphere, which is associated with Cowling conductivity and a tidal electric field. Modulated heating of the lower-ionospheric region where these currents flow with powerful high-frequency (HF) pump waves makes the ionospheric conductivity of the region change periodically, which in turn modulates the preexisting currents in the heated area (Moore, 2007). In the meantime, these oscillating currents form an electric dipole antenna radiating low-frequency waves in the ionosphere. This hypothesis was first suggested by Willis and Davis (1973) and was then proved when artificially excited low-frequency signals were detected in an experiment for the first time (Getmantsev et al., 1974). A series of experiments of generating low-frequency waves following this mechanism were carried out at the European Incoherent Scatter Scientific Association (EISCAT) and the High Frequency Active Auroral Research Program (HAARP; Cohen et al., 2012; Agrawal and Moore, 2012; Moore et al., 2007; Ferraro et al., 1984; Papadopoulos et al., 2003), and this mechanism was named PEJ (polar electrojet) (Stubbe and Kopka, 1977; Barr et al., 1991). The method of artificially generating low-frequency waves by modulating the lower ionosphere is completely dependent on the existence of quasi-stationary ionospheric currents, which to some extent limits the location of the heating facility to the high and equatorial latitudes and also makes the generation of ULF waves more unpredictable (Papadopoulos et al., 2011b). Moreover, some experimental observations such as ULF artificial excited signals at frequencies of 3.0, 5.0 and 6.25 Hz at Arecibo in 1985 still cannot be explained by classic ionospheric current modulation mechanism (Ganguly, 1986), which makes it necessary to develop new theories and experimental methods.
In a series of experiments conducted from 2009 to 2010 at HAARP, artificial ULF and lower ELF signals generated by the modulated heating ionospheric F region in the absence of electrojets were received on the ground far away from the heating facility, and the dependence on the heating conditions differs from the low-frequency waves generated by modulating the ionospheric currents (Papadopoulos et al., 2011a, b; Eliasson and Papadopoulos, 2012). This artificial generation of ULF waves relates to the oscillating diamagnetic drift current in the upper ionosphere due to the modulated heating, which is based on the ICD (ionospheric current drive) theory proposed by Papadopoulos et al. (2007). By modifying the model developed by Lysak (1997), Papadopoulos et al. (2011b) built a new model to study the ICD in the polar ionosphere by F region heating in cylindrical geometry. Eliasson et al. (2012) performed a theoretical and numerical study of the ICD based on a numerical model of the generation and propagation of ULF and ELF waves. The simulation results agree with the HAARP experimental measurements. Utilizing the ICD method, similar experiments conducted at SURA also received artificially generated ULF waves by modulated heating the F region. A comprehensive investigation of ULF wave properties and their dependence on modulation frequencies, polarization, beam inclination, receiving location and the geomagnetic activity was carried out by Kotik et al. (2013, 2015).
In this paper, we focused on the study of the effects of the background ionospheric parameters and the modulation frequencies on the process of modulated HF heating in the F region and the following generation and propagation of artificial ULF waves by using two mathematical models describing the above physical process. In Sect. 2, we first briefly introduce the physical mechanism of the ULF wave generation in the F region by modulated HF heating proposed by Papadopoulos et al. (2011a) and Eliasson et al. (2012). Then we introduce the HF heating model and the following model of ULF wave generation and propagation. In Sect. 3, firstly we discuss the possibility of the effects of the background ionospheric parameters and the modulation frequency, based on a relation among the radiation efficiency of the ring current source, the size of the spatial distribution of the modulated electron temperature and the wavelength of ULF waves; secondly, we run the simulation with the HF heating model to investigate the electron temperature response to the modulated heating under different ionospheric conditions with a modulation frequency sweep; thirdly, we run the simulation with the model of ULF wave generation and propagation in the same way to study the radiation efficiency of the ring current source, the propagation loss and the ground ULF wave magnitude. In Sect. 4, conclusions based on the simulation results and the corresponding analysis are summarized.
The radial electron pressure gradient caused by the HF heating in
ionospheric F region can drive a local diamagnetic ring current
perpendicular to the ambient magnetic field given by
The plasma transport model for the F region ionospheric heating model can be
described as follows (Bernhardt and Duncan, 1982; Shoucri et al., 1984; Hansen
et al., 1992b):
Equation (4) is the steady-momentum equation under the assumption of
ambipolar diffusion and quasi-neutrality, and electron inertia can be
neglected for the time- and space scales under consideration. The diffusion
coefficient
Equation (5) is the continuity equation along the direction of the geomagnetic
field line for ionospheric electrons, where
Equation (6) is the electron energy conservation equation along the
geomagnetic field line, which includes the effects of convection and pressure
flux and heat conduction. Also note that our simulation is based on the
assumption that ion temperatures of O
The wave field at altitude of
If ohmic heating is considered as the only mechanism when calculating the
absorption of HF pump power by the ionosphere, the energy deposition of the
ionosphere when the X mode is used as the pump wave is approximately 4 times
larger than that of the O mode (Löfås et al., 2009). This is because the
absorption of HF power is dependent on the imaginary part of the refractive
index
In order to achieve a better HF heating effect, the pump wave of the O mode is
utilized in our simulation and the frequency of the HF wave is adjusted so that
the reflection point is near the F2 peak. At the reflection point in
our simulation, the absorption of HF power is calculated as (Meltz et al.,
1974; Perkins and Valeo, 1974)
In our simulation, the generation model of ULF waves proposed by Eliasson et
al. (2012) is used to calculate the following propagation of ULF waves
excited by modulated HF heating. The model is built under the following
assumption: firstly, the frequency of the artificially generated ULF wave is
far less than the electron cyclotron frequency; secondly, O
In the ionosphere, the propagation of artificially generated ULF waves is
calculated by the following equations:
In this model, the modulated HF heating effect is estimated by Eq. (21), in which
In this paper, simulations with both models introduced previously in
Sects. 2.2 and 2.3 are conducted in a two-dimensional computational domain, with
Heating parameters used in the model.
The heating parameters for the modulated HF heating are listed in the
Table 1, including
Now we introduce the setting of the simulation domain. In the simulation with
the HF heating model, the spatial grid size in the
According to the physical mechanism of the generation of ULF waves in the ionospheric F region, a diamagnetic ring current source of ULF radiation is driven by the modulated HF heating, which is of crucial importance in the whole wave generation process. So, the relation between the wave generation and the source of ULF radiation due to HF heating should be qualitatively discussed before presenting the simulation results.
The background ionospheric electron density and temperature profile used in our numerical simulation.
Since in the simulation with the model of ULF wave generation and
propagation, the electron temperature response to HF heating is estimated
with Eq. (25), it is natural that both the amplitude of the electron
temperature oscillation and the spatial distribution of the
Similarly, we can conduct the deduction in the vertical direction and find that the vertical radiation efficiency is dependent on the ratio of the
wavelength
However, what is truly uncontrollable is the effects of the background
ionospheric profiles on the generation and propagation of artificial ULF
waves. Firstly, during the process of modulated HF heating, both the
modulation frequency and background ionospheric profile are expected to have
an impact on
These factors jointly contribute to the distribution of ground magnetic field intensity, which makes it difficult to find an exact function to describe the relation among them. However, the effects of the background ionospheric parameters and the HF heating modulation frequency can be investigated with the following simulation results.
Contours of electron temperature changes with modulation frequency of 0.5 Hz at heating time of 0.01, 1.0 and 2.0 s in the nighttime ionosphere.
Contours of electron temperature changes with modulation frequency of 0.5 Hz at heating time of 0.01, 1.0 and 2.0 s in the daytime ionosphere.
This section is dedicated to studying the effects of the background
ionospheric parameters and the modulation frequency on the electron
temperature response due to modulated heating. In this simulation, the
parameters of the HF power absorption Eq. (17) are given by
To begin with, we focus on the spatial distributions of electron temperature
change
Temporal evolution of electron temperature change at the reflection point.
Figure 2d, e and f show the change in the spatial distribution of
Now, we extend the discussion in Sect. 3.1 about the relation between the
radiation efficiency of the ULF ring current source and the size of the
Since
The variation of the average electron temperature oscillation amplitude with different modulation frequencies.
Since in the ionospheric F2 layer the electron cooling time is tens of
seconds due to the dramatically decreasing collision rates and the dominating
transport process (Gurevich, 1986), the electron temperature deviation from
the initial background value cannot return to zero in the cooling phase of a
modulation period. Moreover, the oscillation of
According to Sect. 2.1, the HF heating model is a self-consistent simulation
model. Also, the background parameters such as plasma number density and
temperature affect the electron temperature change jointly. So it is not
advisable to directly relate the evolution of
In this section, we discuss the effects of modulation frequency and
ionospheric parameters on the propagation and generation of ULF waves based
on the simulation results from the model of ULF wave generation and
propagation introduced in Sect. 2.2. In our simulation, the parameters of the
electron temperature deviation Eq. (25) are
The magnitude of the total magnetic field vector of the artificially
generated ULF waves at
The magnitude of total magnetic field vector of the artificially
generated ULF wave at
Comparing the nighttime case and the daytime case, we find that the
amplitude of the magnetic field of the ULF waves in the heating region is larger in the daytime ionosphere than in the nighttime ionosphere, despite the effect of the dip angle. Since all the cases contain the same
Now we focus on how the background parameters and the modulation frequency
affect the propagation of ULF waves and their penetration to the ground.
Although we can draw some conclusion from the simulation with the realistic
geomagnetic dip angles and the ionospheric profiles varying together, there is
no doubt that the joint effects of these two factors can make the problem
more complicated and puzzling. In order to simplify the problem without
omitting the parameters we are interested in, we can focus on the HAARP case
but with the dip angle assumed to be 90
The Pederson conductivity profiles in the daytime and nighttime ionosphere at HAARP used in our simulation.
In order to investigate the effects of the ionospheric profiles on the
propagation loss of the ULF waves, we introduce the magnetic energy of the
ULF waves at a certain height within the range from
Temporal evolution of the magnetic energy of the artificially generated ULF wave at the modulation frequency of 2.0 Hz at a height of 90 and 200 km in the daytime and nighttime ionosphere.
Ratio between the magnetic energy of the artificial ULF wave at 90 and 200 km in the nighttime and daytime ionosphere at the modulation frequency of 2.0, 4.0 and 8.0 Hz.
Finally, we discuss the feature of the artificially excited ULF waves penetrating into the ground. The ground magnitudes of the ULF waves at the modulation frequency of 2.0, 4.0 and 8.0 Hz in the daytime and nighttime ionosphere are demonstrated in Fig. 10. We find that both in the daytime and nighttime ionosphere, the amplitude of the magnetic field of the ULF wave decreases when the modulation frequency is enhanced from 2.0 to 8.0 Hz. According to the analysis in Sect. 3.1, the wavelength is shorter when the modulation frequency is raised, which makes the radiation efficiency of the ring current source lower. Moreover, the higher modulation frequency causes more propagation loss in the ionosphere as indicated in Table 2. Both factors contribute to the smaller ground magnetic field amplitude at the higher modulation frequency. When the modulation is fixed, the ground magnitude of the ULF magnetic field is larger when the wave generation and propagation happen in the nighttime ionosphere than in the daytime ionosphere. Also, this difference of the ground amplitude of the ULF wave due to the nighttime and daytime ionospheric profiles expands when the modulation increases.
The ground magnitude of magnetic field of the artificially generated ULF waves at the modulation of 2.0, 4.0 and 8.0 Hz in the daytime and nighttime ionosphere.
Based on the HF heating model and the model of ULF wave generation and
propagation, we investigate the effects of the background profiles and the
modulation frequencies on the process of modulated HF heating in the
ionospheric F region and the subsequent generation and propagation of the
artificially generated ULF waves. Some conclusions can be drawn, as follows:
The magnitude of the artificially generated ULF wave is related to the
intensity of the ring current source driven by F-region-modulated HF heating
and its radiation efficiency. The source intensity depends on both the
spatial distribution size and the oscillation amplitude of the modulated
electron temperature, The size of the spatial distribution of The background ionospheric profiles can affect the absorption of the pump
wave and the cooling rate of the electron temperature during the modulated HF
heating, thus determining the oscillation amplitude of The radiation efficiency of the ULF ring current source is larger in the
nighttime ionosphere than in the daytime ionosphere regardless of different
geomagnetic field dip angles, while the energy conversion efficiency from
electron temperature oscillation to ULF waves is lower in the nighttime
ionosphere with a fixed The daytime ionosphere produces more energy dissipation during the propagation of artificially generated ULF waves due to Joule heating, and this
propagation loss is larger when the modulation frequency is raised. The ground magnitude of the magnetic field of the artificial ULF wave is
larger in the nighttime ionosphere than the daytime ionosphere, and the difference
between daytime and nighttime conditions expands as the modulation
frequency increases. Also the ground ULF wave amplitude decreases when
the modulation frequency increases.
Background parameters of our numerical simulation used in this paper are from
the International Reference Ionosphere (IRI-2012) model and the neutral
atmosphere model (NRLMSISE-00). These data can be accessed at the following websites:
This work was supported by the National Natural Science Foundation of China (NSFC grant No. 41204111, 41574146). Chen Zhou appreciates the support by Wuhan University “351 Talents Project”. Topical Editor K. Hosokawa thanks three anonymous referees for their help in evaluating this paper.