Interaction of a high-power UHF beam with the ionosphere

Authors


Abstract

[1] In 1992 a rocket was launched into a high-power radio beam to study its interaction with the ionosphere. The frequency of the beam, 5.1 MHz, was optimized for such interactions since the frequency used was below the maximum plasma frequency and hence was reflected in a manner that optimized such an interaction. Fortuitously, the rocket passed quite close to the diagnostic Arecibo UHF (430 MHz) radar beam and remarkably, as reported here, we find that there was an interaction as well with the UHF beam. In retrospect, however, we see that the energy density of the UHF radar was more than an order of magnitude higher than the plasma energy density. And, although the quiver velocity of the electrons in the beam is only 4% of their thermal speed, the ponderomotive force is quite a bit larger than the other forces in the medium. This force creates a drift velocity perpendicular to the magnetic field at the beam edge which, we show, is unstable to the drift wave instability and is likely to create the heated ions and fluctuating electric field and plasma density we observe. These results suggest that any transmission of high-power radio waves from a solar power satellite to the ground will interact with the ionosphere in a manner that must be studied before such an expensive project is initiated.

1. Introduction

[2] For decades it has been known that high-power radio waves launched from the ground with frequencies less than the maximum ionospheric plasma frequency can interact very strongly with the plasma (e.g., see special section of Radio Science, 9(11), 1974). The interaction can, among many other effects, lead to thousands of plasma filaments only a few meters in size perpendicular to the magnetic field but elongated along the magnetic field (B) for many km [Kelley et al., 1995; Peria et al., 1999] and to enhanced light emissions at 630 nm, 557.7 nm, and infrared wavelengths [Bernhardt et al., 1988; Djuth et al., 1999; Kagan et al., 2000, 2005]. Recently, artificial aurora at kilorayleigh intensities, in principle visible to the naked eye, was created over the High Frequency Active Auroral Program transmitter [Pedersen and Gerken, 2005].

[3] Other high-power radio wave sources exist in conjunction with military and civilian scientific radars but, with the exception of over-the-horizon radars, are operated at frequencies well above any possible plasma frequency in the ionosphere. The interaction of a radio wave with a plasma to first order scales as the frequency squared, so, for example, a 430 MHz (UHF) radar, such as the Arecibo scientific radar discussed in this paper, has four orders of magnitude less effect on the medium than a 5.1 MHz (HF) system. This has led to the notion that there is no effect of importance due to such high-power systems and, indeed, over decades of use and comparisons with satellite data and numerical models, it is clear that UHF scientific radars properly measure the properties of the medium using theories that assume no beam-plasma interaction.

[4] However, this observation only indicates that the radio wave–plasma interaction in the center portion of the beam is weak and does not preclude interactions at the edges of the beam and in the surrounding medium. This is, in fact, exactly what we report in this paper: the medium surrounding the Arecibo beam is highly disturbed by the intense radio wave power.

[5] This result is not merely of scientific interest since there is continuing discussion of the use of high-power microwaves to beam power from solar collectors in space to the ground. An understanding of the interaction of such beams with the environment is thus of relevance to such proposals.

[6] The data described here were somewhat fortuitous since the NASA rocket project was designed to study the interaction of a high-power HF radio wave with the ionosphere. The rocket was launched on 6 June 1992 from a temporary launch site on the northern coast of Puerto Rico into the beam of the high-power facility operated by the National Astronomy and Ionosphere Center. In addition to the rocket instruments, the Arecibo 450 MHz radar was used as a diagnostic of the ionospheric effects of the HF beam. The flight was very successful and a number of papers were published concerning the primary goal of the project [Kelley et al., 1995; Franz et al., 1999; Peria and Kelley, 2001]. By chance, the rocket payload passed quite close to the radar beam on its way to the HF interaction zone, and a number of surprising phenomena were detected by the instruments onboard. Conditions were not perfect for the observations since the attitude control system was performing its tasks prior to the HF beam penetration (during which it was disabled), but we believe that the data are convincing evidence that the UHF beam does interact in a significant way with the medium.

2. Data Presentation

[7] The geometry of the rocket passage from west to east past the incoherent scatter radar (ISR) beam is shown in Figure 1, which is a view projected on the plane perpendicular to the beam. The circle of radius 2.5 km, centered on the ISR beam, intersects the payload trajectory twice. The main beam itself is only 500 m across, so the payload did not actually penetrate it but a very strong radar echo from a sidelobe of the radar was detected at this time, indicating that the trajectory data used to construct Figure 1 was accurate.

Figure 1.

Geometry of the ISR pass. The rocket traveled from right to left. The ISR beam points out of the paper. The velocity of the payload perpendicular to the ISR was 350 m/s, while the total velocity was 1714 m/s.

[8] Before describing the rocket data, it is fairly easy to eliminate electromagnetic interference (EMI) as the source of the ISR effects. First, the maximum effects were not seen at the closest approach to the beam. Second, the ISR is pulsed at a fairly low duty cycle: a 52 μs pulse is emitted every 11 ms, so the ISR is usually off. If the interaction of this wave power with the ionosphere can be neglected, then the time signature of the ISR should be quite clear in data from this payload, which had dozens of channels with bandwidth in excess of 11 ms or 91 Hz, and there is no such indication. The ISR effects occur on timescales of seconds, with no evident 11 ms pulsing. If, on the other hand, the data near the ISR indicate not plasma effects but EMI, which has been somehow smoothed by the ionosphere, then that in itself is an interesting and unexpected interaction of the ionosphere with the ISR. Any mechanism capable of storing the electromagnetic energy of the ISR for a full 11 ms and smoothly releasing it at an intensity capable of overpowering the outputs of two entirely different species of electronics while carefully covering its 90 Hz tracks would be remarkable indeed.

[9] The most convincing indication of the ISR-plasma interaction comes from the superthermal ion detector data from which Figure 2 is reproduced. The detector was turned on between the two crossings of the 2.5 km circle in Figure 1. The second crossing in Figure 1 occurred near 210 km on the eastward edge. At this time an intense burst of superthermal ions was detected with a nearly flat energy distribution up to the detector limit at 50 eV. Other features in the plot attest to the proper function of the detector. For example, the thermal ions are accelerated into the instrument due to the negative vehicle potential, which was verified by the floating potential of the double probe electric field detectors. This potential shifts when the rocket enters the HF beam due to heating of the plasma electrons. Later, when the rocket leaves the HF beam, a trail of heated superthermal ions exists until the end of the plot, ions clearly heated by the HF-plasma interaction. In a previous publication, Peria and Kelley [2001] showed that the heated volume creates its own internal convection. Here we see heated ions downstream from the heated volume.

Figure 2.

Ion survey spectrogram. Hot ions are seen crossing the edge of the heated region at 210 km and downstream above 280 km.

[10] As shown in Figure 3, on first approach to the ISR beam at its eastward edge and at a distance of 2.5 km from the beam center, oscillations in the electric field and the electron density probe current were observed at 24 Hz, a period of ∼40 ms. The signal-to-noise ratio in this plot is clearly poor due to the firings of the aspect control systems. As noted above, the ion detector was not yet activated. The payload reached its point of closest approach, 2.2 km, about 3 s later. Saturation of many electron channels was seen at this time. As the payload receded from the beam, again at a distance of 2.5 km, more oscillations were observed, this time at a frequency of 10 Hz as shown in Figure 4. The disappearance of these waves was followed immediately in time by the burst of superthermal ions discussed above. The ISR pass covers the altitude range of 198–208 km and the time interval of 120–125 s after launch.

Figure 3.

Electric field and plasma current waveforms for the first ion wave event.

Figure 4.

Electric field and plasma current waveforms for the second ion wave event.

[11] For the purpose of discussing these events efficiently, we use the following terms: “ISR electrons” for the saturated signal seen by all of the electron detectors near 122 s, “ISR ions” for the burst of superthermal ions, and “ion waves” for the low-frequency electric field and density perturbations which, it will be argued, energize the superthermal ions.

[12] By calling both sets of wave observations near 2.5 km “ion waves,” implicitly we have interpreted them to be the same wave mode. There are several reasons why this is plausible. First, they are both observed at the same distance from the beam center. This suggests that they are a spatial phenomenon, in steady state, and that their source is stationary with respect to the ISR beam. If so, then their frequency difference has a reasonable interpretation as Doppler shift due to spacecraft velocity, which is of the same order of magnitude as the ion acoustic speed. In addition, the thickness of the cylindrical shell where each wave event occurs is 68 m in each case. In both cases, the density fluctuations were 90 degrees out of phase with the electric field, which is the case for ion acoustic waves. Another way to represent these data is provided in Figure 5. The power spectral density (PSD) electric field and density data are plotted versus time along with the output of the superthermal ion detector. The 10 Hz waves are collocated in the two PSDs and adjacent to the heated ions. These facts, taken together with the damping/disappearance of the wave in a region of elevated ion energy, suggest an ion-acoustic or drift wave mode.

Figure 5.

Power spectral density of the electric field and Langmuir probe signals along with the superthermal ion detector output.

[13] The wavelength cannot be uniquely determined using the frequency measured in the moving reference frame, but some limits can be estimated. If the wave vector is perpendicular to both B and the radar beam, as it might be for waves rotating about it, then the wavelength is a few tens of meters. An upper limit is 170 m for waves parallel to the rocket velocity, which is unlikely.

[14] The normalized cross spectrum of the electric field and the plasma density instrument (V1–2) shown in Figure 6 shows a high level of broadband coherence at the time when the spacecraft is near the ISR. Such high coherence is unusual, though not unique, in the data. The presence of coherence between two instruments lends plausibility to weak signals that might otherwise be considered instrumental noise. The time of high coherence, at the low frequencies associated with the ion waves, spans the interval between the ion wave events, and the coherence drops rather sharply before and after this interval.

Figure 6.

Coherence spectrum between the electric field and current to the Langmuir probe.

[15] The waveforms for the two “ion wave” events (at 120.6–121.0 s and 125.1–125.4 s) have in common their distance from the ISR beam, their phase relation between field and density, and the approximate length of time for which they are observed. They differ significantly in their location along the length of the ISR beam and in their apparent period.

[16] The fact that similar ion wave phenomena are observed at the same distance from the beam axis (2.5 km) but at different points along the beam (separated by 10 km) suggests a cylindrical symmetry for these phenomena. It is not likely that our spacecraft happened to encounter two preferred azimuthal locations at the 2.5 km radius. Therefore, the observations are indicative of a cylindrical shell of ion waves near a radius of 2.5 km. Thus, the length of time for which these waves are observed is an indication of the thickness of the shell (≈68 m) over which they have measurable amplitude.

3. Discussion

[17] The ratio of the energy density of the UHF beam to the plasma energy density,

equation image

can be estimated from the power transmitted and the antenna gain and range to the rocket to be the order of 5. This is quite impressive. The quiver velocity of the electron in the electric field of the beam (eE/) is 3600 m/s, which exceeds the ion thermal speed.

[18] With such a modest quiver velocity, the most likely interaction mechanism of the beam and the medium is through the ponderomotive force [Landau et al., 1984; Istomin, 2002]. This is the force which, for example, causes collection of sand grains at the nodes of a vibrating drumhead. Analogous to the force, −∇p, where p is both the pressure and the energy density, the ponderomotive force is given by

equation image

where ωp is the plasma frequency and ωR is the radar frequency. This force clearly maximizes at the edge of the beam where we see the perturbations. The Arecibo antenna beam is only 500 m in diameter at the encounter altitude. The beam can be modeled by the square of the J0 Bessel function. The gradient scale length is then found to be 50 m, close, in fact, to the 68 m region where the ion waves were seen. Since the energy density exceeds nkT and the gradient scale length is much less than for any ambient gradients, the associated force is quite significant.

[19] We now explore two potential sources of the irregularities. In the presence of a force with a component perpendicular to the magnetic field, the ions will drift according to the expression

equation image

where the factor of n in the denominator determines the force per particle, and νin is the neutral ion collision frequency. This is a drift speed that has the potential for generating drift waves.

[20] The growth rate for the drift wave instability can be written [Ellis and Marden-Marshall, 1979] in the form

equation image

where b = (kρi)2, k is the perpendicular wave number, l is the mean free path, and L is the gradient scale length. For λ = L/3, ρi = 5 m, L = 50 m, l = 800 m, and γ = 1.9 s−1. The only other observation of drift waves in the ionospheric medium occurred during the same rocket flight when 10 m scale, 10% density depletions were detected in the HF beam [Kelley, 2004].

[21] Parallel to the magnetic field, the pressure will drive a current carried by the electrons. In a steady state, their parallel drift velocity will be limited to the sound speed at the electron temperature. The field-aligned current is thus 10 μA/m2. This value is large, even by auroral zone standards, and could be unstable to ion acoustic waves. Nakamoto [2007] has simulated the effects of a ponderomotive force and finds that ion acoustic waves are indeed excited.

[22] The optimum power density for a space-based power system has been quoted as 230 W/m2, which is 50 times that of the Arecibo beam at the rocket penetration point. On the other hand, the size of such a beam is expected to be several km across, which yields gradient scale lengths that are a factor of 5 larger. The result is that stronger drift waves are to be expected at the edge of such a beam than we have observed. Furthermore, GPS signals are occasionally interrupted by ionospheric irregularities of natural origin that cause them to scintillate in intensity on the ground. The associated variation in the ponderomotive force as amplitude fluctuations develop in the beam may well cause these natural structures to be unstable and hence to grow, further disrupting the beam. Finally, the HF beam was found to have an internal convection of the plasma driven, presumably, by the ponderomotive force on a larger scale [Peria and Kelley, 2001]. If this occurs in a space-based power beam, the region may develop a turbulence level that is disruptive.

Acknowledgments

[23] Research at Cornell University was sponsored by the Office of Naval Research under grant N00014-07-1-1079.