Recent ionospheric modification experiments with the 3.6 MW transmitter at the High Frequency Active Auroral Research Program (HAARP) facility in Alaska led to discovery of artificial ionization descending from the nominal interaction altitude in the background F-region ionosphere by ∼60 km. This paper presents a physical model of an ionizing wavefront created by suprathermal electrons accelerated by the HF-excited plasma turbulence.
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 High-power HF radio waves can excite electrostatic waves in the ionosphere near altitudes where the injected wave frequency f0 matches either the local plasma frequency fp ≈ 9 kHz (the density ne in cm−3) or the upper hybrid resonance fuhr = (fc is the electron cyclotron frequency) [e.g., Gurevich, 1978]. The generated waves increase the bulk electron temperature to Te = 0.3–0.4 eV, while some electrons are accelerated to suprathermal energies ɛ = mv2 up to a few dozen eV [e.g., Carlson et al., 1982; Rietveld et al., 2003]. Upon impact with neutrals (N2, O2, O), suprathermal electrons excite optical emissions termed Artificial Aurora (AA) [e.g., Bernhardt et al., 1989; Gustavsson and Eliasson, 2008].
 Heating-induced plasma density modifications are usually described in terms of chemical and transport processes [e.g., Bernhardt et al., 1989; Djuth et al., 1994; Dhillon and Robinson, 2005; Ashrafi et al., 2006]. However, Pedersen et al.'s [2009, 2010] discovery of rapidly descending plasma layers seems to point to additional mechanisms. Pedersen et al. [2010, hereafter P10] suggested that the artificial plasma is able to sustain interaction with the transmitted HF beam and that the interaction region propagates (downward) as an ionizing wavefront. In this paper, the formation of such downward-propagating ionizing front is ascribed to suprathermal electrons accelerated by the HF-excited plasma turbulence.
2. Ionizing Wave
 The descending feature is evident in Figure 1, which is representative of P10's Figure 3 with the regions of ion-line (IL) radar echoes from the MUIR incoherent scatter radar located at HAARP (courtesy of Chris Fallen) overlaid [cf. Oyama et al., 2006]. Shown are sequential altitude profiles of the green-line emissions (λ = 557.7 nm, excitation potential ɛg ≈ 4.2 eV) observed from a remote imager looking over HAARP on 17 March 2009. Here, the O-mode radio beam was injected into the magnetic zenith (MZ), i.e., along the magnetic field B0, at the effective radiative power P0 [MW] ≈ 440 and frequency f0 = 2.85 MHz (2fc at h2fc ≈ 230 km). The contours of fp = f0 or ne = nc ≈ 105 cm−3 (cyan) and fuhr = f0 (violet) are inferred from ionograms acquired from the HAARP site at 1 min intervals (P10, Figure 3). The regions of enhanced IL are shown in green color. As seen from another imager located at HAARP, the blue-line emissions at 427.8 nm (not shown) coincided with the green-line emissions (see Figure 1 of P10); remote-location 427.8 nm optical data are not available.
 During the first 2 min in the heating, the artificial plasma is confined to the bottomside of the F layer at altitudes h > 180 km. The corresponding descent of the IL scatter is similar to that described by Dhillon and Robinson  and Ashrafi et al. . A sudden brightening of AA and increased speed of descent of the artificial plasma ‘layer’ (patch) in the HF-beam center occurs near 180 km, while its peak plasma frequency foFa reaches f0. In fact, the optical data shows [P10] that this patch is fairly uniform near ∼180 km but then becomes a ∼20-km collection of (∥ B0) filaments a few km in diameter. While the degree of inhomogeneity of the descending patch increases, its speed, Vobs ≃ 0.3 km/s, appears to be constant until ≈160 km. Then, the artificial plasma slows down, staying near the terminal altitude hmin ≈ 150 km before the emissions retreat in altitude near the end of 4-min injection pulse. During a continuous ‘on’ period, the artificial plasma near hmin was quenched several times, initiating the process over again from higher altitudes.
 Hereafter, we focus on the descending feature at h ≤ 180 km where foFa ≥ f0 or ne ≥ nc. Enhanced 427.8-nm emissions indicate the presence of electrons with energies ɛ > ɛb ≈ 18.7 eV, exceeding the ionization energies of N2, O2, and O. The ionization rate qa is given by
where νion is the ionization frequency, and 〈…〉 means averaging over the accelerated distribution of the density na. Hereafter, we employ Majeed and Strickland's  electron impact cross-sections and Hedin's  MSIS90 model for the densities [N2], [O], and [O2] on 17 March 2009.
 At each time step ti, artificial ionization occurs near the critical altitude hc(ti), defined from the condition ne(hc) = nc. The density profile just below hc is represented as follows
Here x = ξ/L∥, ξ = (hc − h)/cos α0 is the distance along B0, α0 is the conjugate of the magnetic dip angle (≈15° at HAARP), and L∥ is the (∥B0) extent of the ionization region. Ψ(x) is a monotonic function satisfying the conditions Ψ(0) ≥ 1 and Ψ(x) ≪ 1 at x > 1, since the ambient plasma density n0 ≪ nc at h ≤ 180 km. As the ratio δe(ɛ) of inelastic (νil) to elastic (νel) collision frequencies is small, the accelerated electrons undergo fast isotropization due to elastic scattering and thus L∥ ≃ 〈lion〉, where lion = v/νion [cf. Gurevich et al., 1985].
 Evidently, as soon as at some point xi ≤ 1 the density ne(xi,ti + Δt) ≃ qa(ξi) · Δt reaches nc, the critical height shifts to this point, i.e., hc(ti+1) ≃ hc(ti) − L∥ · x. These conditions define the ionization time, Tion−1 ≃ qa/nc, and the speed of descent
 Note, equation (3) contains no dependence on the total neutral density Nn and hence predicts Vd ≃ const(h), if the same distribution of accelerated electrons is created at each step. As 〈δe1/2v〉 ≃ 1.5 · 106 m/s, we get from equation (3) that the value of Vd (3) matches Vobs at na = na(d) ≃ 6 · 10−4nc or na(d) ≃ 60 cm−3.
3. Discussion and Conclusions
 We now turn to justify this acceleration-ionization-descent scenario. Enhanced IL echoes, like in Figure 1, usually result from the parametric decay instability (PDIl) and oscillating two stream instability (OTSI) of the pump wave near the plasma resonance [e.g., Mjølhus et al., 2003]. The latter develops if the relative pump wave energy density 0 = ∣E02∣/8πncTe exceeds th ≃ + , where k is the plasma wave number, νT is the collision frequency of thermal electrons, and Ln−1 = ∣∇ln ne∣. The free space field of the pump wave is Efs ≈ 5.5/r ≈ 0.65 V/m at r = 180 km (at the HF-beam center) or fs ≃ 5 · 10−4 at Te = 0.2 eV. For incidence angles θ < arcsin ( sin α0), the amplitude in the first Airy maximum is EA ≈ (2π/sin α0)2/3 (f0Ln/c)1/6Efs [e.g., Mjølhus et al., 2003] or A ≈ 0.1(Ln/L0)1/3, where L0 = 30 km. For injections at MZ, following Mjølhus et al.  one gets A(mz) ≈ A/4.
 As A(mz) ≫ μ (the electron-to-ion mass ratio), we get k ≃ rD−1 (μA(mz))1/4 [e.g., Alterkop et al., 1973] or krD ≃ 1/40 (rD is the Debye radius) yielding th ≃ 10−4(L0/Ln). The ‘instant’ gradient-scale of the artificial layer is Ln ≃ 3 → 1 km at 180 → 150 km (see below) gives th ≈ (1 → 3) · 10−3. Thus, OTSI can easily develop in the first Airy maximum. In turn, PDIl can develop in as many as ≃30 Airy maxima over a distance la ≃ 1 km [cf. Djuth, 1984; Newman et al., 1998]. At Te/Ti < 4, PDIl is saturated via induced scattering of Langmuir (l) waves, piling them up into ‘wave condensate’ (k → 0) [e.g., Zakharov et al., 1976]. The condensate is subject to OTSI, thereby leading to strong (cavitating) turbulence and electron acceleration [e.g., Galeev et al., 1977].
where pa ≃ 0.75–1. The density na and ɛmin are determined by the wave energy Wl trapped by cavitons and the joining condition with the ambient electron distribution Fa∥ (ɛmin) = F0(ɛmin). If F0 is a Maxwellian distribution, this gives ɛminm ≈ 10Te and nam ≈ 10−4ne. When background suprathermal (s) electrons of the density ns are present, then F0(ɛ ≫ Te) → Fs(ɛ) and ɛmin ≃ 30(nsTe/Wl)2/5 eV [e.g., Mishin et al., 2004], yielding ɛmin ≤ 10 eV at ne = nc, l ≃ 10−3, and ns ≤ 10 cm−3. In the ionizing wave, a natural source of the s-electrons is ionization by those accelerated electrons that can propagate from ξ ∼ 0 to ξ ∼ L∥ (see Figure 2).
 We can now evaluate the excitation and ionization rates. The column 427.8-nm intensity in Rayleighs (R) is given by
Here σb is the excitation cross section of the N2+(1N) state, Ab ≈ 0.19, Φa = Fa is the differential number flux, and Fa(ɛ) ≃ navmin−3 is an isotropic distribution to which the accelerated distribution Fa∥ (4) is transformed at distances ∣ξ∣ > v/νel due to elastic scattering [cf. Gurevich et al., 1985].
 Integrating equation (5) over the energy range ɛb ≤ ɛ ≤ 102 eV at pa = 0.85 yields the brightness of a Δh-km column ΔI(hc) ≈ 2.5 · 10−12na[N2(hc)] · Δh R near altitude hc, given that Δh ≪ Hn ≃ 8 km (the atmosphere scale-height). Note, using pa = 0.75 (0.95) increases (decreases) ΔI by ≈ 10% (15%). The total intensity I is defined by the vertical extent of the (excitation) layer Δb, where ɛ(ξ) ≥ ɛb. It can be evaluated using the Majeed and Strickland  loss function L(ɛ) = Lj(ɛ) with j designating N2, O2, and O. Outside the acceleration layer, i.e. ∣ξ∣ > la, the energy of an electron of the initial energy ɛ0 at a distance ξ from the origination point h0 is
Figure 2a presents the results of calculations of equation (6) for ɛ0 = 10, 15, … 102 eV and h0 = 150, 160, 180, and 200 km. The altitude profiles at ɛ ≥ 5 eV and hence the layers of excitation/ionization are nearly symmetric about h0 at h ≤ 180 km. Figure 2b shows the half-widths Δg and Δb of the green- and blue-line excitation layers about hc = 180 and 160 km as function of ɛ0. The half-width of the ionization layer Δion (not shown) is ≈Δb at ɛ0 > 20 eV. Since Δb < Hn, we can estimate the 427.8-nm intensity at hc = 180 → 160 km as I∣hc ≃ 5 · 10−12na · [N2(hc)] 〈Δb(hc)〉 ≃ (0.16→0.2) · na R. Comparing I∣hc with the spatially-averaged intensities ≈ 10→5 R (P10, Figure 1) yields a ≃ 60→25 cm−3. Note that a ≈ na(d) at 180 km, in agreement with a uniform structure, while spatial averaging underestimates na inside the ∼km-scale filaments at 160 km.
 Calculating the ionization frequency in equation (1) with Fa(ɛ) gives 〈νion〉 ≈ κion* · ([N2] + [O] + 0.95[O2]) s−1, where κion* = 〈vσion〉/na ≈ 1.8 · 10−8 cm3s−1 is the coefficient of ionization of N2. The total ionization rate qa(d) ∼ 104 cm−3s−1 greatly exceeds recombination losses ≈ 10−7nc2 ≈ 103 cm−3s−1 (the main ion component at these altitudes is NO+). This justifies the use of equation (1) for evaluating the artificial plasma density. Taking an average energy loss per ionization ∼20 eV results in the column dissipation rate <0.1 mW/m2 or <10% of the 440-MW Poynting flux, consistent with P10's estimates.
 As Figure 3 shows, the coefficients of ionization and blue-line excitation by accelerated electrons decrease by a factor of ∼2 (10) between ɛmax = 102 and 50 (30) eV. The Liouville theorem predicts F(ɛ0 − Δɛ(ɛ0, ξ), h0 + ξ) = F0(ɛ0, h0), where Δɛ (ɛ0, ξ) is given by the integral in equation (6). Thus, the gradient scale-length Ln of the artificial plasma is about the distance ξ50, defined by the condition Δɛ(102, ξ50) ≈50 eV. Numerically, we get ξ50 ≈ Δb(50) or Ln ≈ 3→1.5 km near hc = 180→160 km and qaLn/nc ≃ Vobs, as predicted by equation (3). Note that the artificial plasma density profiles derived from ionograms indeed have ∼1-km gradient scale-lengths near 150 km (cf. P10, Figure 2).
Figure 1 shows that the descent slows down below 160 km and ultimately stops at hmin ≈ 150 km. The presence of IL and bright green-line emissions indicate that plasma turbulence is still excited and efficiently accelerates electrons above 4 eV. However, the blue-line emissions almost vanish [P10], thereby indicating only few accelerated electrons at ɛ ≥ ɛb. That this is in no way contradictory follows from the fact that inelastic losses increase tenfold between 10 and 20 eV. Acceleration stops at ɛ = ɛmax ≪ 100 eV when νil(ɛmax) exceeds the acceleration rate mD∥ (umax)/8πɛmax, where D∥(u) ≈ and k∥ = ωp/u [Volokitin and Mishin, 1979]. The critical neutral density is roughly estimated as ∼5 · 1011 cm−3, i.e Nn at ∼150 km. The fact that the artificial plasma stays near hmin indicates that ionization is balanced by recombination or qamin ∼ 10−7nc2 ≈ 0.1qa(d), which at na ∼ na(d) corresponds to ɛmax ≈ 30 eV (Figure 3).
 A mechanism for generating km-sized filaments below 180 km could be the thermal self-focusing instability (SFI) near hc, resulting in a broad spectrum of plasma irregularity scale sizes [e.g., Guzdar et al., 1998]. Significantly, ∼km-scale plasma irregularities grow initially but within 10s of seconds thermal self-focusing leads to smaller (10s to 100s meters) scale sizes. During descent, the critical altitude moves downward by several km within 10 s, thereby precluding further development of SFI, while the ∼km-scale irregularities have sufficient time to develop. When the descent rate drops, small-scale irregularities can fully develop and scatter the HF beam, thereby impeding the development of OTSI/PDIL and hence ionization. As soon as the artificial plasma decays, SFI falls away and hence irregularities gradually disappear. Then, the artificial plasma can be created again. This explains why the artificial layer ceases and then reappears (Figure 1).
 In conclusion, we have shown that the artificial plasma sustaining interaction with the transmitted HF beam can be created via enhanced ionization by suprathermal electrons accelerated by Langmuir turbulence near the critical altitude. As soon as the interaction region is ionized, it shifts toward the upward-propagating HF beam, thereby creating an ionizing wavefront, which resembles Pedersen et al.'s  descending artificial ionospheric layers.
 This research was supported by Air Force Office of Scientific Research. HAARP is a Department of Defense program operated jointly by the U. S. Air Force and U.S. Navy. We thank Chris Fallen for providing the MUIR ion line data.