Geophysical Research Letters

Reply to comment by N. A. Gondarenko et al. on “Simulation study of the interaction between large-amplitude HF radio waves and the ionosphere”


[1] In their comment [Gondarenko et al., 2007], the authors have commented on several things in our recent article [Eliasson and Thidé, 2007].

[2] The first claim is that in our Figure 6d, the second branch of the X mode (referred to as the Z mode), is below the reflection point of the ordinary O and the first branch of the X mode. This is not true. The reflection point of the Z mode is always at a higher altitude (i.e. in a denser plasma) than the reflection points of the fast X mode and the O mode. It should be noted that the vertical axis of Figure 6d does not show the altitude but the frequency of waves with given wavenumbers. The authors also claim that the dispersion curves (in Figure 6d) is for the top side of the ionosphere. Again this is not true, and we believe that the authors mistakenly assume that the vertical axis of Figure 6d is the altitude, while it in reality is the frequency axis. The results in Figure 6d are calculated for a constant plasma frequency (5 MHz) with an electron cyclotron frequency of 1.4 MHz and a geomagnetic dip angle of 13°. The Z mode evident in the figure below 5 MHz corresponds to the electrostatic Langmuir/Upper Hybrid branch of the dispersion curve for waves having large wavenumbers.

[3] The next comment is on our discussion of linear mode conversion and generation of electrostatic waves. The authors point out that ”This process takes place near the reflection point of the O mode at the reflection region which is omitted in their discussion.” We would like to discuss this point shortly. In the original paper by Eliasson and Thidé [2007], the electrostatic oscillations (in Figure 6c) are at an altitude of z ≈ 276.7–276.8 km, i.e. near the reflection point of the O mode at z ≈ 277 km (see Figure 3b). The distance from the reflection point of the O mode and the resonance of the Z mode can be expressed as Δzce2sin2(θ)/[ωpe2ωce2cos2(θ)], where L = 1/(∂lnn0/∂z) is the local length scale of the ion density profile. At z = 277 km, we have L = 22 km, which gives Δ z ≈ 100 m. As pointed out by Gondarenko et al. [2007], this length should not exceed two wavelengths of the heater wave in order for the O mode to be transformed into a wave of X mode polarization. In our case, the separation between the O mode reflection and the resonance of the Z mode wave is of the order one wavelength. Mode conversion will thus be present, but the effect will be weak. In addition, the amount of mode conversion possible is limited by the finite pulse length employed by Eliasson and Thidé [2007]. In the work of Gondarenko et al. [2003], continuous wave transmissions are assumed and therefore an effective collision frequency is needed to limit the singularity.

[4] In our original manuscript [Eliasson and Thidé, 2007], we have discussed shortly the case of oblique incidence, commented by the authors. Specifically, we write, starting 13 lines from top in the second column on page 5, that “The mode conversion of the L-O mode into electrostatic oscillations are relatively weak in our simulation of vertically incident EM waves, and theory shows that the most efficient linear mode conversion of the L-O mode occurs at two angles of incidence in the magnetic meridian plane, given by, e.g., equation (17) of Møjlhus [1990].”

[5] The authors' last comment refers to the inclusion of thermal effects into the model. It is indeed true that thermal effects could be important for electrostatic waves with short enough wavelengths so that thermal dispersive effects become important. In our case, seen in Figure 3c of Eliasson and Thidé [2007], the wavelength of the electrostatic oscillations are ∼33 m, which is much larger than the electron Debye length (which is a few millimeters for our plasma parameters). Hence the cold plasma model should be valid in our case since thermal dispersive effects are extremely small.

[6] The authors finally suggest that we should decrease the grid size to resolve smaller scales for waves. We indeed want to resolve also the short-scale electrostatic oscillations in future simulations, and we are designing new algorithms for this purpose [Eliasson, 2007]. We thank the authors for pointing out some references that we had overlooked. Specifically, the reference to Gondarenko et al. [2003] should have been quoted in the original publication by Eliasson and Thidé [2007].


[7] This work was supported by the Swedish Research Council (VR).