Artificial Aurora Experiments and Application to Natural Aurora
- Space Vehicles Directorate, Air Force Research Laboratory, Albuquerque, NM, United States
A review is given of the effects observed during injections of powerful electron beams from sounding rockets into the upper atmosphere. Data come from in situ particle and wave measurements near a beam-emitting rocket and ground-based optical, wideband radiowave, and radar observations. The overall data cannot be explained solely by collisional degradation of energetic electrons but require collisionless beam-plasma interactions (BPI) be taken into account. The beam-plasma discharge theory describes the features of the region near a beam-emitting rocket, where the beam-excited plasma waves energize plasma electrons, which then ignite the discharge. The observations far beneath the rocket reveal a double-peak structure of artificial auroral rays, which can be understood in terms of the beam-excited strong Langmuir turbulence being affected by collisions of ionospheric electrons. This leads to the enhanced energization of ionospheric electrons in a narrow layer termed the plasma turbulence layer (PTL), which explains the upper peak. Similar double-peak structures or a sharp upper boundary in rayed auroral arcs have been observed in the auroral ionosphere by optical, radar, and rocket observations, and called Enhanced Aurora. A striking resemblance between Enhanced and Artificial Aurora altitude profiles indicates that they are created by the above BPI process which results in the PTL.
Aurora, also known as polar or northern lights (aurora borealis) or southern lights (aurora australis), is a natural airglow in the Earth's sky, such as shown in Figure 1. As auroras were formerly thought to be the first light of dawn, the name “Aurora” came from the Latin word for “dawn, morning light,” while “Borealis” was coined by Galileo in 1619 from the Roman goddess of the dawn and the Greek name for the north wind (Siscoe, 1986). Aurora is seen mainly at high latitudes in the auroral zone, the position of which is controlled by the geomagnetic activity (e.g., Meng et al., 1991). It is produced when fluxes of energetic electrons precipitate along the magnetic field into the upper atmosphere at altitudes below ~130 km.
Figure 1. Examples of auroral displays: (a) Corona and (b) rayed arcs (https://en.wikipedia.org/wiki/Aurora).
It is thus straightforward to employ electron beams injected from a space vehicle with controlled parameters to explore Artificial Aurora (AA) generated in the upper atmosphere. Such (active) AA experiments have been conducted from sounding rockets and the Spacelab (e.g., Davis et al., 1971, 1980; Hess et al., 1971; Cambou et al., 1975, 1978, 1980; O'Neil et al., 1978a,b; Maehlum et al., 1980a; Jacobsen, 1982; Obayashi et al., 1984; Neubert et al., 1986; Kawashima, 1988; Goerke et al., 1992; Burch et al., 1993). Besides exploring Artificial Aurora, active electron beam experiments, beginning with the Echo 1 experiment (Hendrickson et al., 1971), used injected beams as probes for studying the remote natural processes along the magnetic field. Comprehensive reviews of the “Electron Echo” series and similar experiments have been given by Winckler (1980, 1992) and Kellogg (1992).
The present survey mainly focuses on the AA experiments with primarily downward electron injections. The early experiments were focused on the optical features of Artificial Aurora, then investigation of electron beam-plasma interactions became the main driving force. Because of the limited scope of this review, the setup of different experiments, as well as the electron and ion injectors and diagnostic suites onboard and on the ground, are described only schematically. The presentation is also limited to sounding rocket experiments at altitudes at and below ~200 km to avoid the effects of return currents caused by a positive potential of beam-emitting vehicles (e.g., Linson, 1982; Obayashi et al., 1984; Managadze et al., 1988; Frank et al., 1989). The main conclusion of these experiments is that the overall dataset cannot be explained solely by collisional degradation of the beam electrons and requires collisionless beam-plasma interactions (BPI) be taken into account. This stimulated numerous laboratory experiments and theoretical studies discussed during international symposiums on active experiments in space (e.g., Reme, 1980; Grandal, 1982a; Burke, 1983).
This chapter is organized as follows. The salient features of the “classical aurora” limited to collisional impact processes are summarized in section 2. Section 3 gives a review of the effects observed during injections of powerful electron beams from sounding rockets in the ionosphere. Data come from in situ measurements of the luminescence, thermal and suprathermal populations, and beam electrons near a beam-emitting space vehicle, as well as from ground-based optical, radar, and radioemission observations. A brief survey of the BPI theory, which was developed to address the observed unexpected effects, is presented in section 4.
The processes in the near-rocket region are explained by the beam-plasma discharge (BPD) theory (Galeev et al., 1976; Mishin and Ruzhin, 1980a, 1981; Rowland et al., 1981a; Papadopoulos, 1982, 1986; Mishin et al., 1989; Sotnikov et al., 1992) outlined in section 5. The AA rays far from the rocket reveal a special regime of strong Langmuir turbulence in which the wave spectrum in the beam-plasma system, and thus acceleration of suprathermal electrons, is controlled by collisional damping (Izhovkina and Mishin, 1979; Volokitin and Mishin, 1979; Mishin et al., 1981, 1989). The developed theory explained several puzzling features of natural aurora, which is dubbed Enhanced Aurora by Hallinan et al. (1985). Enhanced Aurora (EA) is discussed in the final section. As a rule, only the basic concepts on a semi-qualitative level are given, just sufficient for understanding experimental results. Details and rigorous derivations can be found in the referenced original papers, reviews, and textbooks. Plots and images have been adjusted and sometimes additionally annotated with respect to the originals.
Before presenting the principal experimental results, it is instructive to discuss briefly the “classical” auroral features that follow from collisional interaction of energetic electrons with the neutral atmosphere.
2. Beam-Atmosphere Interaction: “Classical Aurora”
The collisional or single-particle approach (SPA) considers processes of ionization, dissociation, and excitation of atmospheric constituents (N2, O, and O2) by electron impact (e.g., Rees, 1989). In each ionization event precipitating (primary) electrons with energies εb ~ 1–10 keV lose energy, Δεion = εion + εs, where εion is the ionization energy and εs is the energy of the new-born (secondary) electron. Degradation of primary and secondary electrons along the path is usually calculated using Monte Carlo technique. The energy dissipation rate can be estimated from Bethe's formula
Here lε ≈ (υ/νion)ε/ 〈Δεion〉 and νion is the mean free path and ionization frequency of electrons with the initial energy , respectively; 〈Δεion〉 ≈ 32 eV is the average energy loss in air; v is the electron speed; and N(h) is the neutral gas density at a given altitude, h. Equation (1) is valid as long as Δεion ≪ ε.
The altitude profile of optical emissions at a wavelength λ is determined by the volume emission rate (VER). For the prompt emissions, for which quenching is negligible, the VER reduces to the excitation rate
Here ελ and σλ are the excitation energy and cross-section, respectively, [X] is the density of the neutral species, is the differential omnidirectional number flux, me is the electron mass, and F(ε) is the distribution function.
The aurora's color is determined by the wavelengths, λ, of electromagnetic radiation emitted by atoms and molecules in the upper atmosphere, mainly atomic oxygen (O) and molecular nitrogen (N2), impacted by energetic electrons. The excitation energy is a good indicator of the electron energy distribution. For example, ελ for the green- (λ = 557.7 nm), blue- (427.8), and violet-line (391.4) emissions are about 4.2, 18.9, and 20 eV, respectively. As the excitation cross-sections are small at ε > 500 eV, the auroral glow is mainly determined by suprathermal, Te ≪ ε < 500 eV, electrons with the distribution function Fs(ε). Here Te is the electron temperature, which usually does not exceed ~0.3 eV.
The suprathermal population is created due to degradation of secondary electrons. In the local approximation, the suprathermal (omnidirectional) flux, , can be approximated by a power law function
with the spectral index ps ≈ 3.5, the density of the secondary electrons ns ~ 10 · nb (the density of the primary electron flux), and eV. At ε < εc ≈ 6 eV, the distribution is very sensitive to the neutral composition because of considerable differences between cross-sections for various components. The local approximation is valid until the atmosphere scale height, HN, greatly exceeds v/νil, where νil(ε) is the frequency of inelastic collisions. Note that the spectral index for the (directional) magnetic field-aligned flux is ps − 1 ≈ 2.5.
Figure 2 shows a typical altitude profile of auroral luminosity calculated for the initial energy εb = 7.2 keV using Monte Carlo method (Izhovkina and Mishin, 1979). Apparently, above the peak, at h > hm ≈ 110 km, the brightness is proportional to the neutral density N, which is consistent with Equation (1). The peak altitude, hm, and thickness, Δhm, can be estimated from the conditions and Δhm ~ HN(hm), respectively. Both hm and Δhm decrease with increasing εb, since the primary electrons penetrate the denser and cooler atmosphere. These features, together with the spectrum Φs(ε) (3) and the associative VER (2), constitute the “classical aurora” paradigm that is widely used for calculating the auroral E-region conductivity and power released by precipitating electrons.
Figure 2. Auroral altitude profile for εb = 7.2 keV primary electrons. The dashed line shows the relative neutral density from the MSIS model. Adapted from Izhovkina and Mishin (1979). Reprinted by permission from Geomagnetism and Aeronomy.
The next section presents the “anomalous” features of Artificial Aurora that were unforeseen by the collisional approach.
3. Artificial Aurora Experiments
We start with the observations during the Zarnitza-2 experiment carried out in September 1975 (Cambou et al., 1975; Dokukin et al., 1981; Ivchenko et al., 1981). It is worth noting that Zarnitza 1 and 2 together with the ARAKS (Artificial Radiation and Aurora between Kerguelen and Soviet Union) “North” and “East” experiments constituted the French-Soviet program led by F. Cambou and R. Sagdeev. The electron beam and cesium plasma injectors were put by a rotation-stabilized meteorological rocket into a ballistic trajectory with a 155 km apogee (Figure 3). Ground-based diagnostic instruments, including a low-light TV camera, a dual frequency (22.5 and 33.8 MHz) radar, and a broadband (27–51 MHz) VHF radio receiver, provided enough information to describe the effects of injected electrons.
Figure 3. Cartoon depicting the Zarnitza-2 rocket trajectory with electron and plasma injections. The numbers 136, …80 indicate the altitude in kilometers. After Dokukin et al. (1981). Reprinted by permission from COSPAR.
Electron injections were started at h ≈ 109 km, with the beam energy and current of 9.3 keV and 0.27 A, respectively, and switched to 7 keV and 0.45 A at h ≈ 136 km. The injection duty cycle comprised of 0.67 and 0.04 s pulses with 100% modulation at 2 kHz and 0.75 s gaps between the pulses. The beam was primarily directed downwards with the initial cone angle of 1°. Because of the rocket's spin with Tspin ≈ 3.4 s, the injection angle, θ0, to the magnetic field B0 varied between the extrema, i.e., θmin ≤ θ0 ≤ θmax, with θmin (θmax) changing periodically between 40° and 28° (70° and 92°) in 58 s due to the rocket's axis precession.
3.1. Artificial Aurora
In the course of the experiment, a remote low-light TV camera recorded 350–700 nm emissions at 5 frames/s and exposition time of 0.17 s (Ivchenko et al., 1981). All typical auroral lines have been identified in the emission spectrum. Left frame in Figure 4 is made up of two of about eighty nearly-identical AA images during injections near apogee (Mishin et al., 1981). The luminosity profiles were obtained using microphotometric analysis of the optical emissions along the AA rays and taking the aspect angle condition into account. Each profile features a bright glow near the beam-emitting rocket and two luminosity peaks far from the rocket. The agreement between the observed and calculated AA lower boundary indicates that the beam energy is close to the nominal (cf. Davis et al., 1971; Rees et al., 1976). That is, the rocket potential is small, which agrees with the measurements onboard (Dokukin et al., 1981).
Figure 4. (Left) An example of the near-rocket glow and Artificial Auroral rays in Zarnitza 2 (see text). (Right) The altitude-profile of the leftmost AA ray with a Monte Carlo profile superimposed. After Mishin et al. (1981). Reprinted by permission from COSPAR.
The AA brightness agrees with Monte Carlo calculations below 120 km (cf. Figure 2), but above the observed luminosity substantially exceeds the collisional level. Besides, the lower peak is slightly wider than the SPA profile, indicating some additional (~10%) scatter of the beam energy. A slight increase of the energy of some part of the beam electrons indicated by the lowest portion of the profile can possibly be explained by Kainer et al.'s (1972) mechanism.
Now we turn to describe the characteristics of the near-rocket glow (NRG), suprathermal electrons, VHF radioemission, and fast scattering of the beam electrons dubbed “prompt echoes.”
3.2. Near-Rocket Glow and Suprathermal Electrons
Figure 5 shows the AA radiation from the near-rocket glow (NRG) in the course of the Zarnitza 2 and Polar 5 (Maehlum et al., 1980b,c; Grandal, 1982b) experiments, respectively. The variation of the relative radiation flux, FR/F0, from the near-rocket glow (NRG) with altitude and injection angle (Figures 5A–C) does not follow the SPA predictions (Ivchenko et al., 1981). Here F0 ≈ 2.5·1018 photon/s is the radiation flux from a point source at altitude 100 km, which produces the same flux density, 2·103 photon/cm2s, on the ground as the faintest detectable star of the 9th stellar magnitude. On average, the NRG radiation barely changes near apogee. The scatter of the values between 190 and 220 s is due to unstable electric power supply that resulted in the data loss during 220–250 s. Note that fluxes at altitudes ~150 and 115–120 km are of the same order, FR/F0 ~ 10–15, while the neutral density changes by more than a factor of ten.
Figure 5. (A) The radiation flux in the units of F0 from the NRG in Zarnitza 2 averaged over 3–4 neighboring frames (circles). The dashed (solid) line shows the trend of FR (the neutral density, N, in cm−3). (mid) Variation of the flux with the rocket spin phase for the intervals 150–290 s (the solid line) and 150–220 s (dashed) averaged over (B) 7 or 14 frames taken at ≤0.6 s from the start of long pulses and (C) 3 or 8 frames taken within 0.2 s. The phases for θmin and θmax are indicated. After Ivchenko et al. (1981). (D) The beam-induced luminescence in photon/s at λ = 391.4 nm during Polar 5. The dashed line shows 1/N scaled. After Maehlum et al. (1980b) and Grandal (1982b). Reprinted by permission from Geomagnetism and Aeronomy and Plenum Press.
The presence of two almost equal maxima of FR during one rocket rotation at the extrema of the injection angle, and , also contradicts to the SPA predictions. Taking the average photon energy of 2–3 eV (mainly 391.4-nm photons) gives the radiated power of ~30–45 W. That is, the NRG radiates about one percent of the beam power. These values are of the same order as in the Zarnitza 1 experiment (Cambou et al., 1975) and much larger than the collisional limit. The latter is true for the flux during the whole flight.
Quite similar results have been obtained in the Polar 5 “mother-daughter” rocket experiment (Maehlum et al., 1980b,c; Grandal, 1982b) conducted in February 1976. An electron accelerator on the “daughter” payload produced a ~10 keV electron beam with the maximum current of 0.13 A, which was pulsed at a repetition period 0.4 s. Each pulse comprised five 2-ms sub-pulses separated by 2 ms gaps. The “mother” payload carried a 391.4 nm phometer with the sampling rate of 2.5 kHz and diagnostic instruments for monitoring scattered and secondary electrons, as well as wave effects. The payloads separated slowly, so their distance across B0 reached about 80 m in the end of flight.
Figure 5D shows the luminescence at 391.4 nm detected by the photometer during beam injections. The observed light level follows the neutral density below 130 km but is fairly constant in the altitude range from 150 km to apogee at 220 km and much larger than that produced by the beam electrons. The latter agrees well with the observations of the electron population in the NRG (Figure 6) with many more suprathermal electrons, the source of airglow, than produced by direct impact.
Figure 6. (A) Suprathermal and beam electron spectra in Polar 5. The dashed line shows the SPA spectrum multiplied by 250. After Maehlum et al. (1980b) and Grandal (1982b). Suprathermal electron spectra in (B) Echo 5 with/without (the dashed/solid line) neutral gas injections, and (C) SCEX III. After Arnoldy et al. (1985) and Bale et al. (1995). Reprinted by permission from Elsevier, Plenum Press, and the American Geophysical Union.
Indeed, the suprathermal flux at energies less than 1 keV in Figure 6A greatly exceeds the SPA spectrum and has a power law spectrum, Φ(ε) ∝ ε−1.3, i.e., with the spectral index ~ ps/3 (Equation 3). The same is true for suprathermal electron spectra observed during the Echo 5 (Arnoldy et al., 1985; Winckler, 1992) and the Several Compatible Experiments (SCEX) III (Goerke et al., 1992; Bale et al., 1995) experiments in November 1979 and February 1990, respectively. During Echo 5, three electron guns injected a 25 keV and 0.6 A electron beam. Each 4-ms injection comprised 0.5 ms turn-on and turn-off pulses and three 1-ms pulses repeated every 20 ms in a 90 pulse “fast” series. Particles were measured every 200 ms aboard the same payload. Due to the electrode voltage sweep failure of the particle detectors at 132 s flight time, only 0.5 and 8 keV particles were measured at 80° and 0° pitch angles, respectively. The suprathermal electron fluxes (Figure 6B) observed earlier in the flight without (the solid line) and with (dashed) cold nitrogen gas injections have the power law spectrum, Φ(ε) ∝ ε−1, until the flux drops at about 100 eV as the neutral density increased near the rocket. Note beforehand that the latter is in good agreement with the BPI theory prediction (section 4.5).
The SCEX III rocket with a 375 km apogee carried two payloads with a variety of scientific sensors (e.g., Goerke et al., 1992; Bale et al., 1995). An electron gun was located on the aft payload injecting electrons at various energies up to 6 keV and currents from 1 to 60 mA. The neutral density measured on the aft and forward payload showed a significant enhancement over atmospheric models probably caused by severe outgassing. The plots in Figure 6C show suprathermal populations obtained during two 0.16 s sweeps of the retarding potential analyzer (RPA) aboard the aft payload near apogee at 315 s flight time. The “pre-discharge” and “discharge” curve corresponds to the beam current below and above 10 mA, respectively. Above 10-20 mA, the measured (quasi-directional) electron flux averaged over electron energy and 391.4 nm luminosity averaged over 200 s of photometer data (Bale et al., 1995, Figures 2, 4) grow nonlinearly with the beam current. The flux's spectral index is ≈2.3 (close to the SPA's) during the pre-discharge regime and decreases to ≈1.2 at greater currents.
The concurrent optical and radar observations in Zarnitza 2 established that the near-rocket glow near apogee had a cylindrical shape with the dimensions of ~10 m across and ~300 m along B0 (Dokukin et al., 1981). Similarly, the Polar 5 (Grandal, 1982b), Electron 2 (Jacobsen, 1982), and the U.S./Canadian electron accelerator experiment (Duprat et al., 1983) with mother-daughter payload configurations measured the dimensions of the hot electron/plasma cloud to be ~100 m along B0 and several beam Larmor radii transverse to B0.
As 391.4 nm emission indicates ionization of nitrogen, the airglow data, consistent with suprathermal electrons at ε > εion, unequivocally point to enhanced ionization taking place in the near-rocket region. This conclusion is supported by concurrent observations of the radar backscatter and intense very high frequency (VHF) radioemission from the near-rocket region at frequencies greatly exceeding the plasma frequency of the ambient plasma (Mishin and Ruzhin, 1980b; Dokukin et al., 1981; Goerke et al., 1992) presented next.
3.3. VHF Radioemission From the Near-Rocket Region in Zarnitza 2 and ARAKS
Figure 7 illustrates the evolution of the VHF spectrum with the injection height and pitch angle during 0.67 s pulses in Zarnitza 2 and the temporal development during 20 ms pulses in ARAKS. In Zarnitza 2, a broadband continuous spectrum of beam-induced VHF electromagnetic waves was detected by a ground-based radio spectrograph with a 27–51 MHz bandwidth (Dokukin et al., 1981). It is seen in Figures 7A,B that the radioemission appears during each 0.67 s injection pulse and is modulated by the rocket's spin. This modulation is due to the variation of the injection pitch angle (cf. Figures 5B,C) and also clearly depends on the spin phase. The radio burst near 50 MHz of a 5–10 MHz width at the beginning of the injection pulse is a rapid drift from lower to higher frequencies within the spectrograph sweeping time of 20 ms.
Figure 7. VHF radioemission in Zarnitza 2 and ARAKS: Variation of the broadband spectrum in Zarnitza 2 with (A) altitude and (B) the rocket's spin (one long pulse per 2 revolutions). Arrows indicate the specral maxima at (s + 1/2)fce. Adapted from Dokukin et al. (1981). (C) Delay of radioemission at 50 MHz relative to the start of 20 ms pulses in ARAKS and (D) dependence of radioemission at 75 MHz on the phase of the rocket's rotation. The dashed curve shows the beam pitch angle θ0. After Mishin and Ruzhin (1980b). Reprinted by permission from COSPAR.
During the first injection regime, the maximum frequency averaged over several long pulses between 120 and ≈130 km decreased with altitude as N1/4. After transition to the second regime and until the plasma generator was turned on, fmax is approximated as follows
Here VR⊥ is the rocket's speed across the magnetic field, which differs significantly between the upleg and downleg parts of the trajectory. The dependence of the NRG plasma growth on VR⊥ was predicted theoretically by Galeev et al. (1976).
Assuming that fmax (4) is the increased plasma (Langmuir) frequency, kHz, gives the plasma density in the NRG, ne ∝ IbN/vbVR⊥. The spectral density of the electromagnetic flux was at least 10−20 W/m2Hz, which exceeds more than ten times the detection threshold. Assuming a point source at about 300 km distance gives ~100 W of the total radiated power for a 10 MHz band emission, i.e., ~3 percent of the beam power, which is of the same order as the radiated optical power. As shown in Figure 7B, the spectrum has maxima (buldges) centered at half-integral harmonics of the electron gyrofrequency, fce, i.e., fs ≈ (s + 1/2)fce, with integers s ≥ 20 to ≈ 30 (Dokukin et al., 1981, Figure 10). This “gyro structure” is clearly seen only in a certain height range from 110 to 128 km and 105–115 km in the first and second injection regime, respectively. Near apogee, the radioemission at ≥27 MHz appears only twice during one rocket's rotation as a brief pulse. At the same time, the VHF radar data show radioemission at the radar frequency of 22.5 MHz during the whole injection pulse, i.e., two rotations of the rocket.
The temporal development of radioemission and its dependence on the phase of the rocket' spin was studied in details during the ARAKS “East” experiment using five narrowband receivers located at the launching site (Mishin and Ruzhin, 1980b). A 0.5 A and 27 or 13 keV electron beam was injected at various angles, φ, with respect to the axis of the rocket. As in Zarnitza 2, the spectral density of the VHF electromagnetic flux was at least 10−20 W/m2Hz. Figures 7C,D illustrates the features of 50 and 75 MHz emissions generated by 20 ms injections of 13 keV electrons at φ = 30° (pitch angles θ ≈ 0°–60°) in the altitude range of 111.2–103.7 km.
One can see the time delay of a few milliseconds with respect to the start of 20 ms pulses. The time delay for 75 MHz emissions is greater than that for 50 MHz by a few ms (Mishin and Ruzhin, 1980b, Figure 6). The generation of the higher-frequency emission depends on the phase of the rocket's rotation, ψ, which is counted off from the axis aligned with VR⊥. This dependence results from rotation of the beam guiding center with the spinning rocket, ΔV⊥ ~ 2πrcb/Tspin, where rcb = vb sin θ/ωce is the beam Larmor radius (Mishin and Ruzhin, 1980a). The total speed of the guiding center across B0 amounts to V⊥ = VR⊥ + ΔV⊥(ψ). It is minimized at the “optimum” phase, ψ → ψopt, when the guiding center moves against VR⊥. In the ARAKS experiment, ΔV⊥(ψ)/VR⊥ reached up to 30%.
3.4. Prompt Electron Echoes
Besides the enhanced number of suprathermal electrons in the NRG, strong scattering of beam electrons occurs in the vicinity of a beam-emitting payload (Hendrickson et al., 1971; Winckler et al., 1975; Gringauz et al., 1980; Lyakhov and Managadze, 1980; Maehlum et al., 1980c; Winckler, 1980, 1992; Arnoldy et al., 1985; Wilhelm et al., 1985). This effect is dubbed prompt electron echoes (PEE) as the backscattered electrons are detected within ≤100 ms even during upward beam injections. Figure 8 shows the results from the Echo 5 and ARAKS experiments (Gringauz et al., 1980; Arnoldy et al., 1985). Clearly, above 140 km the scattered flux is almost independent of the neutral density, while the SPA predicts the decrease by a factor of 30. By the same token, the Polar 5 data reveal (Maehlum et al., 1980c) that an initially-collimated beam significantly broadens over pitch angles in less than one gyroperiod, i.e., ~10−6 s. Furthermore, in addition to the beam core, a noticeable part of beam electrons is scattered over large pitch angles up to ~180°. At altitudes 150 to 180 km, the flux of these “halo” electrons varies with the distance, d⊥ (in meters), between the mother and daughter payloads as
which is about 102 times greater than collisional scattering can produce.
Figure 8. Variation of the scattered beam electrons in the ARAKS (squares) and Echo 5 (triangles) experiments. The solid line shows the model value of N−1 in cm3. After Grandal (1982a) and Arnoldy et al. (1985). Reprinted by permission from COSPAR and American Geophysical Union.
In summary, the observed near-rocket glow, suprathermal electrons, VHF radioemission, and prompt electron echoes, as well as the fine altitudinal structure of AA rays, point to much stronger interaction of injected electrons with the upper atmosphere than provided by electron collisions. Next, a brief survey is presented of the theory of collisionless beam-plasma interaction (BPI) resulting in the beam-plasma discharge (BPD) near beam-emitting payloads and the double-peak structure of artificial and natural aurora rays.
4. Beam- Ionospheric Plasma Interaction
The upper atmosphere is, in fact, a weakly-ionized plasma, the ionosphere, with the plasma density ne ≪ N. Conventionally (e.g., Ichimaru, 1973), ionized gases can be regarded as plasma if their behavior is dominated by the collective response of charged particles due to the long-range Coulomb force. Charged particles in motion generate electromagnetic fields that affect motion of other particles, thereby making a fast remote response to local perturbations. The distance over which charges in plasma are shielded is the electron Debye radius, rD = vTe/ωpe, where ωpe = 2πfpe (the Langmuir frequency) and vTe is the electron thermal velocity. The number of particles in the Debye sphere in plasmas is large, . In collisional plasmas, the plasma frequency is supposed to significantly exceed the collision frequency of plasma electrons, νe.
Henceforth, the density, mass, electric (magnetic, B0) fields, and frequency, f = ω/2π, are taken in cm−3, grams, V/m (Gauss), and Hz, respectively. Temperature, Te,i, is taken in units of energy, electronvolts (1 eV = 11,605 K). We consider only one singly-charged ion species with the ion-to-electron mass ratio and 6 · 104 in the F- and E-region ionosphere at altitudes around ~200 km and ~ 100–130 km, respectively.
4.1. Plasma Waves
A symbiotic relationship between plasma particles and fields results in a wide variety of collective motions, i.e., plasma waves. Of those, the most important for the BPI are high-frequency (HF) plasma modes. In a weakly-magnetized (ωce ≪ ωpe) plasma, their frequencies away from the electron gyroharmonics, sωce, are
with the wavenumber k, the propagation angle α = arccos(k·B0/kB0), and . It reduces to the Langmuir (L) branch, at α = 0 (k = k∥) and to the upper hybrid (UH) branch, at α = π/2 (k = k⊥). The spectral energy density of a broad Langmuir spectrum, is .
The other important branch of electrostatic (E = −∇ϕ) HF waves is the electron Bernstein (EB) mode with frequencies approaching sωce at both and ≪rce (the electron Larmor radius). Near k⊥rce ~ 1, they have a wide maximum around half-integral gyroharmonics, ωs ≈ (s + 1/2)ωce, where the group velocity tends to zero (e.g., Mikhailovskii, 1974). It is worth noting that in the magnetospheric community such waves, routinely observed in the plasma sheet region associated with diffuse aurora (e.g., Ashour-Abdalla and Kennel, 1978; Khazanov, 2011), are called electron cyclotron harmonics (ECH).
It is instructive to recall the well-known wave-particle quantum-mechanical analogy (e.g., Ichimaru, 1973), which helps to understand the wave properties in an inhomogeneous plasma. Since ωk(r, k) is constant in stationary media, we have or
That is, the wave vector changes in such a way that the frequency is preserved. Equations (7) are the Hamilton equations for unit-mass particles (plasmons) with the “energy” ωk and “momentum” k, moving with the (group) velocity vg. It is also convenient to introduce the number of plasmons as Nk = Wk/ωk.
Let us consider Langmuir plasmons moving in a one-dimensional density depletion (cavity), n(x) = n0(1 − |δn(x)|) centered at x = xc, with the width (kc = k(xc)). Expanding ωpe(n) gives , so the Hamiltonian can be represented as the sum of the kinetic energy, , and potential, . As it follows from (7), (“acceleration”) and (“deceleration”) for plasmons moving toward and from the cavity's center, respectively. Evidently, the cavity plays a role of the potential hole for plasmons that are trapped inside if the Hamiltonian is negative, i.e., −U(xc) > εk(xc) or
and move freely otherwise.
4.2. Resonance Wave-Particle Interaction
Let us consider plane Langmuir waves, , moving along the magnetic field (∥z) much faster than the bulk of electrons, i.e., vTe ≪ ωk/kz = vph (the phase velocity). Thus, only a small group of fast particles can be in resonance with the waves, i.e., v∥ = vres = (ωk − sωce)/k∥, with s = 0, ±1, ±2, etc. It is called the Cherenkov resonance at s = 0 and the cyclotron resonance otherwise. It is instructive to give an example of the resonance wave-particle interaction in isotropic plasmas. The equation of motion of an electron with the unperturbed velocity v0 = const reads
(e is the elementary charge). Linearizing in the wave field yields the quiver velocity
where is the Doppler-shifted wave frequency. The work of the electric field, , upon non-resonance particles, , vanishes as the positive and negative contributions on average cancel each other. For resonance particles, , the linearization procedure is invalid, and Equation (9) must be solved explicitly. Taking k along the z axis, in the reference system of the wave, , yields the equation of motion in a periodic wave potential
Here ξ = kz′ is the relative phase, ϕk, ω is the amplitude of the potential, and . Nearly at the resonance, ξ ≪ 1, Equation (11) reduces to a classic (mechanical) oscillator with ξ ≈ ξ0 cos(ωtrt). That is, particles in the resonance zone, , where
are trapped and oscillate around the minimum potential energy, maintaining the constant phase relative to the wave for many wave periods (e.g., Galeev and Sagdeev, 1979). The particles exchange energy with the wave
after reflection from a moving potential barrier. That is, slow () particles are “kicked” along by the wave and gain energy, while fast () particles push on the wave and lose energy. The net energy exchange is defined by the difference, , between the population of the two groups with the distribution function F0(v). It is negative in a Maxwellian plasma, so the waves are damped. This resonance, collisionless damping is named the Landau damping. In a magnetoactive plasma, oblique waves are subjected to the cyclotron damping as well. Therefore, in thermal equilibrium waves exist at the thermal noise level, W ~ neTe/ND.
In non-equilibrium plasma, the population of fast particles can dominate in a certain velocity domain so that waves in resonance with these particles will gain energy and grow. This process (inverse Landau or cyclotron damping) is called plasma instability.
4.3. Beam (Bump–in-Tail) Instability
Let a collimated, u = v∥ ≫ v⊥, “warm” and tenuous, , electron beam with the beam density, nb ≪ ne, and the mean energy, εb ≫ Te, precipitates into the ionosphere along the magnetic field. Such distribution function is known as a “bump-in-tail,” meaning the tail of the whole electron distribution with the bulk, secondary, and beam electrons. As ∂Fb/∂u > 0 at ub − Δub < u < ub, Langmuir waves with phase velocities within this range will grow at a rate (e.g., Mikhailovskii, 1974)
Here Wr is the spectral energy density of the beam-resonant waves, k∥ = kr, γnl is the rate of spectral transfer due to nonlinear mode coupling (see below), and at Te < 0.4 eV and at 0.4 < Te ≤ 100 eV below ~ 200 km. Calling for Γr > 0 at γnl = 0 gives the limiting neutral density
Taking cm−3, Te ~ 0.1 eV, nb ~ 1 cm−3, and Δvb/vb ~ 0.1 yields for the standard neutral atmosphere that the instability develops at altitudes above hmin = h(Nmax) ~ 105 km.
The wave excitation goes at the expense of the beam energy leading to widening of the beam distribution and thus decrease of γb. In a steady state, the dissipation rate is determined by the energy flux balance
where < … > b means averaging over the beam distribution. The beam speed greatly exceeds the wave group velocity, vg ≈ 3Te/meub, so in the absence of nonlinear interactions Wr is greater than nbεb by a factor of vb/vg ~ εb/Te.
The relaxation length, lrel, is a distance from the beam entry into the plasma over which the instability stabilizes at some Δub(lrel) = Δu∞. It can be estimated from Equation (16) as follows
Here Λ ~ ln (ND) ~ 10 is a numerical coefficient accounting for the growth of the waves from the thermal level. In order to determine the level of the beam-excited waves, Wr, one should allow for nonlinear wave interactions resulting in the energy transfer from the resonance region at a rate γnl. The efficiency of this nonlinear damping is governed by the parameter of nonlinearity, w = W/n0Te ≪ 1.
4.4. Nonlinear Effects
Disregarding wave-wave interactions and using the statistical description of waves with random phases, results in the quasilinear approximation (Vedenov et al., 1962). It is valid only for very tenuous beams irrelevant to our problem. The next step in w is taking account of the induced scattering, in which electrons interact with beats of different randomly-phased modes (e.g., Galeev and Sagdeev, 1979). This weak turbulence (WT) approximation is valid until the beam density exceeds
The SLT regime is inherently tied to the tendency of Langmuir plasmons to accumulate inside density depletions or cavities, δns = ne/n0 − 1 < 0. Namely, the waves of wavelengths ~ k−1 are trapped if (Equation 8). The resulting excess of the wave pressure, , exceeds the thermal pressure imbalance, δpe = n0Teδns, if . In this case, the ponderomotive force, −∇δWl, pushes plasma out of the cavity, which further deepens and traps yet more plasmons in a positive-feedback loop. As a result, initial modulations grow with time. At Wl/n0Te ≫ Wth, the growth rate of this modulational instability (MI) is
As trapping inside a cavity leads to strong correlation of the wave phases, such that the WT condition of random phases (e.g., Galeev and Sagdeev, 1979) is violated, this regime has been termed strong Langmuir turbulence (SLT).
Cavities with trapped strongly-correlated Langmuir oscillations are termed cavitons and subjected to collapse (Zakharov, 1972). Their evolution depends on the dimension, d, and can be understood from simple arguments (e.g., Sagdeev, 1979). The conservation of the plasmons' number in a cavity of the size, l, yields |E2(t)| ∝ l−d(t). The wavelengths of the trapped plasmons are also of the order of l, i.e., k ~ 1/l. The trapping condition yields , indicating that a deepening cavity narrows, collapses, as time progresses. Since and |E2| ∝ l−d, the thermal pressure will ultimately balance the HF pressure for d = 1, thus forming one-dimensional cavitons. In two (three) dimensions, the speed of collapse persists (accelerates) with time.
In a weakly-magnetized plasma, ωce ≪ ωpe, the cavitons at are pancake-like, with the dimensions
(e.g., Rowland et al., 1981b; Shapiro and Shevchenko, 1984; Robinson, 1997). The basic signatures of the SLT development in various beam-plasma systems have been observed in laboratory experiments (e.g., Cheung et al., 1982; Karfidov and Lukina, 1997; Robinson, 1997; Vyacheslavov et al., 2002).
The phase velocity of plasmons in collapsing cavitons, ~ ωpe/k(t), decreases with time, so eventually plasmons are absorbed by plasma electrons due to Landau and transit-time damping. As a result, a small group of suprathermal electrons gains energy, while the HF pressure in the caviton drops and collapse is arrested due to the wave energy “burnout.” Ultimately, a dynamic equilibrium is reached between the pumping energy into cavitons in the long-scale source region, , and short-scale transfer by collapsing cavitons (Wcav) into the absorption interval, k ≥ ka (e.g., Galeev et al., 1977). The energy density in the source region, , comprises the MI-excited (non-trapped) long-scale waves.
In collisionless isothermal plasmas one gets at γb ≫ μωpe (Galeev et al., 1977)
In collisional plasmas, Equations (18) and (21) hold for νe/ωpe < 3Te/2εb. In the opposite case, the MI threshold is and the threshold beam density becomes (Volokitin and Mishin, 1979)
If , the MI growth rate is of the same order as γmi (19). However, as follows from eq. (21), γmi(WL) < νe at
collisional damping is faster than collapse. Since the nonlinear transfer rate due to collapse reduces, the level of plasma waves in this “collisional SLT” regime increases over that in Equation (21) and becomes (Volokitin and Mishin, 1979; Mishin and Telegin, 1989)
Now the relaxation length can be estimated using Equations (17), (21), and (24)
In addition, in the presence of short-scale, q ≫ kL, density irregularities, , long-scale plasmons are transferred into the short scales via conversion, (Galeev et al., 1977). For a wideband random-phase oscillations, , the conversion rate is
Here νl(k) is the total (collisional + Landau) damping rate and is the phase-averaged spectral energy. The conversion process dominates at γconv > γmi(wL). Applying a similar procedure to the electromagnetic version of the Zakharov equation (e.g., Shapiro and Shevchenko, 1984), one can describe resonant scatter of radio waves on ion density oscillations (e.g., Mishin et al., 1992).
The value of Te in Equation (25) is the average energy of the bulk electrons, Te = Th, heated by the beam-excited turbulence at a rate
At altitudes below ~130 km the growth of Te is limited mainly by inelastic losses, νil(Te) = δil(Te)νe(Te). The coefficient of inelastic losses at h = 150-180 km, calculated using the Majeed and Strickland (1997) tabulations, is at Te ≈ (0.2 → 0.45) → 0.6 → 5 → 10 eV. Assuming the ambient temperature T0 = 0.2 eV and -10−2 in a steady state, one gets the temperature of heated electrons Th ≈ T0(1 + 2wl/3δe(Th)) ≈ 0.3–0.5 eV.
4.5. Acceleration of Suprathermal Electrons
The SLT acceleration of suprathermal (tail) electrons is, probably, the most important consequence of the BPI for artificial and natural aurora. In brief, the short-scale, k > ka, plasmons in collapsing cavities are absorbed by a small group of plasma electrons. Their distribution function along the magnetic field can be found from the kinetic equation
As a result, a suprathermal tail, ε ≫ Te, is formed, with a power-law distribution
In a Maxwellian isotropic plasma (F0 = FM), theoretical estimates give the spectral index pt ≈ 7/4 − 9/4 and the minimum energy, ; while the matching condition, Ft(εmin) = F0(εmin), yields (Galeev et al., 1977; Pelleiter, 1982). One-dimensional numerical simulations yield pt ≈ 3/2 (Galeev et al., 1983; Wang et al., 1997). Figure 9 illustrates the wave spectrum and electron distribution in the developed strong Langmuir turbulence.
Figure 9. Cartoon depicting the wave spectrum and electron distribution in the developed strong Langmuir turbulence. The wave energy in the long-scale source (WL at ωl/k ≥ ωpe/kL), transfer (Wcav at ωpe/ka < ωl/k ≤ ωpe/kL), and absorption (Wa at ωl/k ≤ ωpe/ka) intervals are indicated by the striped rectangle and solid black curves, respectively. The blue and red solid lines indicate the bulk and accelerated tail populations, respectively. After Shapiro and Shevchenko (1984). Reprinted by permission from Plenum Press.
Substituting the accelerated flux Φt(ε) into Equation (2) with σλ = σion gives the ionization rate, which can be approximated as (Mishin and Telegin, 1989)
A remark is in order. In the presence of the ambient (“seed”) suprathermal population, such as secondary electrons with the distribution Fs(ε) ≫ FM(ε) at , the absorption rate increases and collapse is arrested at greater scales than in a Maxwellian plasma. That is, and thus many more energetic electrons are accelerated (Mishin and Telegin, 1986). Another effect of electron-neutral collisions is that εmax depends on inelastic losses of the accelerated electrons, ~ νion(ε), that maximize at εm ~ 100 eV. Evidently, as soon as the rate of inelastic losses, νil(εL) at , exceeds the acceleration rate, meD(uL)/8πεL, the expansion of the tail, , stops (cf. Figure 6B). In the SLT regime (24), it occurs at cm−3 (Volokitin and Mishin, 1979; Mishin, 2010).
4.6. SLT Acceleration in High-Power Radio Wave Experiments
It seems relevant to briefly discuss the SLT acceleration of suprathermal electrons producing artificial aurora and ionization in active space experiments with high-power radio waves (Mishin and Pedersen, 2011; Eliasson et al., 2012, 2015; Mishin et al., 2016). Here Langmuir waves are parametrically driven by ordinary (O) pump waves near the reflection altitude, h0, where the pump frequency, fo, matches the local plasma frequency, fpe(h0) (the interested reader is referred to Streltsov et al., 2018 review). Figure 10 exemplifies the results of the Eliasson et al. (2012, 2015) full-wave one-dimensional simulations with various input pump amplitudes, Ein, for radio beam pointings at and between the geographic zenith (vertical, V) and the geomagnetic field direction (magnetic zenith, MZ) at the High-frequency Active Auroral Research Program (HAARP) facility at Gakona, Alaska, USA. The simulation details are given in Eliasson et al. (2012, 2015). Note only that the nonlinearity parameter, , exceeds the thershold for the SLT regime to develop.
Figure 10. Time-vs.-altitude color-coded plots of (a) log10(|Ez[V/m]|) and (b) log10(|δns[m−3]|) for Ein = 1 and 2 V/m at V and MZ, as indicated in plots; (c) turbulent electric fields, Ez, (d) the distribution function, Ft(ε) = Ft(u)du/dε; and (e) time-vs.-altitude plots of the plasma density at V and 10.5° S calculated for various Ein and Te indicated in frames. Adapted from Eliasson et al. (2012, 2015). Reprinted by permission from the American Geophysical Union.
Figures 10a,b illustrates the development of the longitudinal (Langmuir) electric field, Ez, and cavitons, δns, for vertical and MZ injections with Ein = 1 and 2 V/m. Omitting the features of their spatial distribution related to the radio wave propagation, we point out that in 1–2 ms the initial (Airy) structure starts breaking into small-scale turbulence. In saturation, solitary wave packets in the SLT region are trapped in density cavitons. It is seen that the SLT region of the altitudinal extent, lLT, is sandwiched between the WT regions with turbulent electric fields but without cavitons. The appearance of the electromagnetic waves near h0 at MZ is due to conversion on short-scale ion density oscillations (Equation 26) in the SLT region. Figures 10c,d show the turbulent electric fields, δEsat, and the electron energy distribution, Ft(ε) = Ft(u)du/dε, at the end of the simulation runs.
At each injection angle, the simulated spectral width, Δk, as well as δEsat and lLT, increase with Ein. These factors and the input value of Te lead to considerable differences in Ft(ε). Overall, the main part of Ft(ε) at εmax ≥ ε ≥ εmin can be fitted by a power law, , with the relative tail density, , between 2 and 6 and pt between ≈1.5 and 2. The maximum energy, εmax, at altitudes h ≥ 170 km depends mainly on the transit time, τ∥ ~ lLT/umax, while inelastic losses dominate below 170 km. In particular, Ft(ε) at 10.5° S is more enhanced than at vertical due to greater lLT. At MZ for Ein = 2 V/m, Ft(ε) is close to that at vertical for Ein = 1.5 V/m (Eliasson et al., 2012, Figure 8). This explains the differences in the patches (layers) of artificial plasma descending from the initial interaction altitude at various input parameters shown in Figure 10e.
The downward propagation of the artificial plasma produced by the accelerated electron tail is due to the fact that the electrons propagating along the geomagnetic field create the new plasma resonance condition for the incident radio wave below the initial resonance. This way, an ionizing wavefront created by the SLT-accelerated electrons is formed (Mishin and Pedersen, 2011; Eliasson et al., 2012). Furthermore, the presence of the ambient suprathermal population (photoelectrons) facilitates the SLT acceleration (Mishin et al., 2004, 2016; Eliasson et al., 2018), quite similar to the effect of secondary electrons in auroral plasmas (Mishin and Telegin, 1986). The consequences of the photoelectrons in the sunlit ionosphere are the decreased threshold, the greater downward speeds, and the decay of the persistent artificial ionization at the terminal altitude after sunlit-to-dark transition.
Next we explore the effect of transition from the “collisionless” to “collisional” SLT regime at νe > ν* (23).
4.7. Plasma-Turbulence Layer
At ν > ν* (23), the plasma turbulence level increases as (24). Thus, the condition νe(h*) = ν* defines the upper boundary, h*, of the layer of enhanced plasma turbulence termed the Plasma Turbulence Layer or the PTL (Mishin and Telegin, 1989; Mishin et al., 1989). Balancing the heating rate (27) by inelastic losses gives
As follows from (31), for the temperature Te reaches ≈0.3-0.45 eV in the PTL and does not exceed ≈0.25 eV above h*. Since (30) increases with Te, the auroral luminosity is peaked inside the PTL and greatly enhanced over the collisional (SPA) limit, qb ~ nbνb. This regime continues until νe(h) increases to . Below , deep cavities are not created and , so collapse and concomitant suprathermal electron acceleration are inhibited. For typical auroral beam-plasma parameters, and Δu/ub ~ 0.2, the value of is of the order of 3ν*. This means that for the standard neutral atmosphere scale height, HN ~ 5 km, the overall PTL thickness is of the order of 5 km.
Figure 11 illustrates a scenario (Mishin et al., 1981; Mishin and Telegin, 1989; Mishin, 2010) of the formation of a double-peaked ionization/luminosity profile of auroral rays due to the PTL (cf. Figure 4). The lower peak () is caused by the collisional ionization of neutral gas by the primary (beam) electrons, while the upper layer, i.e., the PTL, is due to accelerated suprathermal electrons. For a few keV beams, both peaks will overlap, so that the observer would see only one thick layer with a sharp upper boundary.
Figure 11. Schematic representation of the Plasma Turbulence Layer (PTL) indicated by the black rectangle and a double-peaked ionization profile. The dotted curve presents the collisional (SPA) ionization profile, The dashed curve shows the electron temperature profile of the heated plasma. The solid curves show the altitudinal profiles of the wave energy density, W, and ionization rate of the accelerated electrons, . The dashed horizaontal line indicates the PTL upper boundary. After Mishin (2010). Reprinted by permission from the American Institute of Physics.
This scenario agrees well with the altitude profile of artificial auroral rays far from the beam-emitting rocket (Figure 4) and natural auroral rays (section 6). Note that artificial beams expand across B0 due to collisional diffusion, so that the beam density far beneath the rocket in Zarnitza 2 was ~ 1 cm−3 (Izhovkina, 1978), i.e., close to that of natural beams. Also, one should bear in mind that beams lose only ≤20% of their energy in the BPD region, acquiring the velocity scatter Δu/ub ~ 0.1–0.2 (Mishin and Ruzhin, 1980a, 1981).
A remark is in order. So far our consideration was limited to collisionless interaction of a warm, tenuous (bump-in-tail) beam pertinent to natural and artificial auroral rays. With regards to the near-rocket plasma, this approximation becomes applicable after the plasma density significantly increases over the background in the beam-plasma discharge, which is described below. In addition to the beam instability, highly oblique EB/ECH waves can also be excited for electron injections at large pitch angles due to the non-equilibrium beam distribution over transverse velocities (e.g., Mikhailovskii, 1974). In the following, both the Langmuir- and EB/ECH-related processes are outlined.
5. Beam-Plasma Discharge
It has long been known that injection of powerful electron beams in neutral gas may result in the avalanche-like ionization accompanied by strong plasma oscillations (e.g., Getty and Smullin, 1963; Vlasenko et al., 1976a; Bernstein et al., 1978, 1979; Szuszczewicz et al., 1979). This phenomenon is termed the Beam-Plasma Discharge (BPD) to emphasize the chief role of the beam-excited waves. As any discharge, BPD develops under certain breakdown conditions that can be readily obtained in a simplified form.
5.1. Qualitative Considerations
At first glance, BPD can be treated similar to the classical high-frequency (HF, ω0 ≫ νe) discharge (e.g., MacDonald, 1966), in which the pump waves are excited by the injected beam. In the HF discharge theory, the key parameter is the pump threshold amplitude, Ehf, as a function of the applied frequency (ω0), gas density (N), and size (L) of the discharge gap. The Townsend criterion requires that an electron must acquire enough energy to produce at least one ionizating impact before disappearing from the gap due to recombination and diffusion. Replacing Wl in Equation (27) by gives the time of the electron heating up to the energy εh ≥ εion. In HF discharges is much greater than τion, so the breakdown criterion reduces to
In the BPD, the pump waves are generated via the beam instability. Therefore, the first step is to find the critical beam density, , necessary for the instability to develop. Let ncr be the minimum plasma density for which the instability can develop at given N and γb, similar to the reverse condition (15). As the pre-discharge ionization is created solely by the beam electrons at a rate qb ~ νbnb (νb = νion(εb)), the instability criterion follows from the ionization balance (Lebedev et al., 1976)
Conditionally, the BPD problem may be divided into the “beam” and “discharge” parts. The former considers the beam ralaxation to find the input parameters, i.e., the excited wave spectrum and the size of the discharge “gap,” for the latter. Then, the energization (heating and acceleration) of plasma electrons with subsequent ionization is calculated. The solution of the first part critically depends on the plasma density and temperature that vary during the breakdown. Nonetheless, the two parts can be considered independently because the BPI timescale is much shorter than τion. That is, the beam relaxation in the course of the breakdown comes about as in a stationary plasma with the density ne = ne(t) and temperature Th(t).
The avalanche starts at some point, t*, when the ionization by plasma electrons, qion = νion(Th)ne(t*), becomes greater than νbnb. Therefore, the BPD threshold is the Townsend condition (32) with the left-hand side replaced by t*. If suprathermal electrons are disregarded, t* is of the order of the heating time of the bulk electrons, τheat. The latter can be estimated from Equation (27) substituting Wl in a generic form Wl = abnbεb, where ab is a coefficient defined by the beam relaxation regime. This yields the criterion for a self-sustained discharge
Here we accounted for the fact that N s−1 for 3–10 keV electrons is of the order of at Th ≥ 1 eV (e.g., Majeed and Strickland, 1997). The condition (34) is satisfied automatically at if , which is valid already for rather tenuous (“weak”) beams, .
For injections at h > 100 km, the requirement (33) becomes obsolete as the beam instability develops already in the ambient ionospheric plasma of the density n0. A finite cross-section of injected beams reduces the growth rate but not quenches the instability (e.g., Alekhin et al., 1972). Furthermore, the values of τheat and τloss at the beginning of the BPD significantly differ from that for weak beams. The main difference stems from the beam energy density, nbεb, being much greater than the gas kinetic pressure of the ambient plasma, n0T0. This makes the BPI/BPD regime at the start of the breakdown drastically differ from the presented above (Volokitin and Mishin, 1978; Mishin and Ruzhin, 1980a, 1981).
5.2. Initial Stage of the BPD
5.2.1. Beam Instability
Following Alekhin et al. (1972) and Gendrin (1974), let us consider a cylindrical (“pencil”) beam injected with the beam current, Ib ≪ Icr, divergence angle, and initial radius, r0. Here the limiting current, [A], with , defines the injection current at which the beam is locked by the space charge. The initial beam density, , greatly exceeds cm−3 for currents Ib > 0.1 A and εb < 10 keV (). Therefore, the beam expands radially due to electrostatic repulsion. For ωpe(n0) = ωp0 > ωce and injections at small pitch angles θ0 < θ*, the beam quickly (in ) expands to
so its density reduces to cm−3 and the velocity/pitch-angle scatter increases to . For ωp0 < ωce, the beam expands to rb*(ωp0/ωce) and its density becomes (Gendrin, 1974).
At injection angles θ0 > θ*, the beam executes a Larmor spiral with a hollow radial cross-section bounded by the beam gyroradius, rcb = vb sin θo/ωce (cf. Winckler, 1992, Figure 2). As for small angles, electrostatic repulsion makes the radial beam thickness of , so its density nears to n0. A helical structure rapidly transforms into a pencil-like (cf. Winckler, 1992, Figure 2) as the excited EB/ECH oscillations scatter beam electrons, thus broadening their pitch-angle distribution and enhancing radial diffusion (see shortly).
A generic form of the distribution function of a cylindrical beam injected at θ0 > θ* can be represented as
with the beam density, , and the radial thickness, r⊥. Here ub = vbcos θ0, vb⊥ = vb sin θ0, Δu0 ≪ ub, Δv⊥0 ≪ vb⊥, , and F∥, ⊥(x) has a maximum (“bump”) at x → 0 and tends to 0 at |x| → ∞. Taking r⊥ ~ rcb = vb sin θ0/ωce, gives cm−3. Using a hollow-cylinder beam does not change the basic results concerning the instability development.
In a uniform beam-plasma system, a “cold,” , beam excites Langmuir oscillations, ωk0 ≈ ωp0 ≈ k0ub, at the growth rate (e.g., Mikhailovskii, 1974). For a bounded beam of a radial extent r⊥, the growth rate depends on whether the inhomogeneity parameter, ξ0 = k0r⊥, is smaller or greater than the root of the first kind, first order Bessel function, ξ1 ≈ 3.75. That is, short-scale waves, ξ0 ≫ 1, develop as for an unbounded beam, in accordance with general considerations. For θ0 < θ*, the radius r⊥ is ≈ rb* (35) and . For a “tenuous” beam, , the growth rate becomes (Alekhin et al., 1972)
For a “dense” beam, , waves at grow at a rate
The radial extent of the wave excitation region, and thus of the discharge,
significantly excees the beam gyroradius, particularly, at small injection pitch angles. In fact, the radial size is even greater because the wave amplitudes outside Rd (39) decrease as (Alekhin et al., 1972). This agrees with the laboratory (e.g., Fainberg, 1962; Kharchenko et al., 1962; Bernstein et al., 1978; Jost et al., 1982) and mother-daughter (Maehlum et al., 1980b,c; Grandal, 1982b; Jacobsen, 1982; Duprat et al., 1983) measurements.
As already noted, the instability due to the bump in transverse velocities is important at θ0 ≫ θ*. At Δv⊥0 → 0, the distribution function, tends to the Dirac delta function, δ(v⊥ − vb⊥), known and as a “ring” or “oscillator” distribution (e.g., Mikhailovskii, 1974). In a uniform beam-plasma system, EB/ECH oscillations can develop with almost any possible ratio of ξ⊥ = k⊥vb⊥/ωce. Similar to the bump-in-tail instability, the beam radial inhomogeneity is less significant for short-scale, ξ⊥ ≫ 1, oscillations. For those, the maximum growth rate is reached at ωk ≈ ωuh ≈ kzub + sωce
If kz → 0, the maximum growth rate at ωk ≈ ωuh ~ sωce (s ≥ 2) reduces to and at s ≫ 1 tends to , where as = 1/2 at and 2/5 otherwise (e.g., Mikhailovskii, 1974).
5.2.2. Relaxation of Cold Beams
As the excited spectrum is narrow, Δk ≪ γc/ub, and width of the resonance region, |u − vph| ~ γc/k0, is greater than Δu0, it is safe considering interaction with a quasi-monochromatic Langmuir oscillation. Henceforth, γc stands for or , whichever applicable. The wave growth slows down when the beam electrons become trapped by the wave potential and change the relative phase bouncing back and forth in the potential hole. The beam velocity scatter, Δutr/ub, increases over the saturation time ~10/γc to ~ γc/ωp0 at the wave amplitude (e.g., Onishchenko et al., 1970; van Wakeren and Hopman, 1972; Abe et al., 1979)
That is, the instability is saturated along the relaxation length, –300 m.
The saturation of the ring/oscillator instability also occurs due to trapping of the beam electrons at the wave amplitude (41) with γc and cosθ0 replaced by γosc or γs and sin θ0, respectively (e.g., Kitsenko et al., 1974; Aburjania et al., 1978). In the saturated state, the scatter of perpendicular velocities is of the order of γo, s/ωuh ~ 0.2–0.3. Since the wave frequency exceeds the cyclotron frequency, the trapped beam electrons are unmagnetized and pulled by the wave across the magnetic field, ultimately filling the void in the center and expanding over the beam gyroradius. This is consistent with the data concerning the beam structure (Bernstein et al., 1979), as well as the distortion of single particle trajectories for beam currents above the threshold (Maehlum et al., 1980c).
5.2.3. Electron Heating and Ionization
If the beam is relatively weak and , the electron heating rate is given by equation (27) with the coefficient of inelastic losses, δil(Th), adjusted to higher values of Th > 1 eV. However, Wtr > n0T0 for Ib ≥ 0.1 A and εb ≤ 10 keV, so the quiver velocity, vE (10), for the wave (41) is greater than the thermal electron velocity and rE = vE/ωp0 > rD(T0). This results in excitation of secondary Langmuir waves, Ep, and low-frequency, , density oscillations, δnp, via an aperiodic parametric instability, , with the maximum growth rate, , at (Kruer and Dawson, 1971; De Groot and Katz, 1973). Trapping of thermal electrons by the secondary waves makes the electron orbits intersect at μs. This leads to the fast, less than , heating of the bulk electrons up to (De Groot and Katz, 1973). Substituting (41) into vE (10), yields
That is, the collisionless heating time, , is much faster than the collisonal time. For the ring/oscillator beam, the value of Th follows from . It is worth noting that the fast heating was observed in the Bauer et al. (1992) laboratory experiment. High electron temperatures in the near zone were reported by Gringauz et al. (1981, up to ~100 eV), Jacobsen (1982), and Arnoldy et al. (1985).
At cm−3 and , the ionization rate, , exceeds at
or h < hhf ≈ 110 - 120 km. Here the BPD criterion is alike the HF discharge (32), while at higher altitudes it becomes . The lifetime of the heated electrons is determined mainly by transverse diffusion, . However, the time of injection into the same magnetic tube is limited due to the transverse speed of the beam guiding center, τR ~ rcb/V⊥, with V⊥ = VR⊥ + ΔV⊥(ψ) (see section 3.3). It is worth noting that Vlasenko et al. (1976a) have observed that the BPD is inhibited at some critical speed of the gas flow across the electron beam.
At high altitudes, the BPD condition reduces to , which yields (Mishin and Ruzhin, 1980a)
For injection currents ~0.5 A, , and VR⊥ ~ 0.3 km/s, the BPD condition (44) yields h(Nmin) = hmax ~ 160–170 km.
A few remarks are in order. Interaction of beam electrons with short-scale, k ≫ ωpe/vb, oscillations results in fast pitch-angle scattering with the effective “collision” frequency (Mishin et al., 1989; Mishin et al., 1994; Khazanov et al., 1993)
which greatly exceeds the collisional frequency, ~ νb, at altitudes above ~120 km. Numerical simulations (Khazanov et al., 1993; Mishin et al., 1994) have shown that this process suffices to explain the basic features of the prompt electron echo (section 3.4).
Thus far, only perpendicular diffusion was considered. However, at injection angles close to π/2 the field-aligned extent of the discharge gap, , is so small that the parallel diffusion becomes dominant and limits the discharge ignition. Therefore, besides parallel injections, the optimal BPD conditions are achieved at injection angles ≤ 80° (cf. Figure 5).
Next, the conversion rate (26) increases to for (Volokitin and Mishin, 1978). In the heated plasma, the low-frequency density oscillations, , are saturated at (De Groot and Katz, 1973), thus yielding . If ( or γs), the beam (ring) instability is suppressed. That is, the heated plasma is “cleared” for the beam propagation and the BPI starts in the adjacent region. This way, the heated region will move away from the rocket at a speed (Mishin and Ruzhin, 1980a, 1981).
The short-scale density oscillations in the “cleared” region decay due to various dissipative processes including diffusion and induced scattering on ions within the decay time . As soon as drops below γc (γo or γs), the BPI resumes in the initial region and is suppressed again after the heating time, . The obvious corollary is that the BPI in each individual gap, , proceeds in a quasi-periodic series of short, , pulses of enhanced wave activity and particle energization repeated at ~ τosc. Such behavior is typical of laboratory experiments with intense cold beams (e.g., Kharchenko et al., 1962; Cabral, 1976; Vlasenko et al., 1976b) and has also been observed in active experiments (e.g., Gringauz et al., 1981; Kawashima, 1988). Evidently, at altitudes above hmax this “oscillatory” regime persists over the duration of injection pulses.
During the oscillation period, τosc, the newly-born plasma cools off due to thermal conduction and inelastic losses down to Te ~ 1 eV and the ionization rate decreases. However, as the diffusion time is greater than τosc, the plasma density, ne, in the heated region increases with the average rate . As long as remains greater than ne, the “initial stage” regime holds. When ne rises to at the time ms, electrostatic repulsion ends and the beam preserves its initial snape. However, the instability development proceeds as before and even faster because of the increase of ωpe. After a few τ0, the plasma density, ne, significantly exceeds so that the “warm”-beam approximation (section 4) becomes applicable. Actually, that can happen even earlier due to radial diffusion of beam electrons scattered off persisting short-scale oscillations at the rate (45), which is indicated by the prompt electron echo (section 3.4).
5.3. Stationary BPD
There are the principal differences between the stationary and initial BPD regimes. First, a cold beam excites convective modes with the group velocity vg ~ ub, while a warm beam excites Langmuir waves (6) with vg ≪ ub. As result, the energy density of the excited waves remains very high even for nb ≪ ne, as well as the electron temperature. Next, in addition to ionization by the heated thermal plasma electrons, accelerated suprathermal electrons can contribute significantly to the BPD ignition when strong Langmuir turbulence determines the beam relaxation (Mishin and Ruzhin, 1980a, 1981; Rowland et al., 1981a; Papadopoulos, 1982, 1986; Sharp, 1982; Omelchenko et al., 1992; Sotnikov et al., 1992). If the SLT development is inhibited, the bulk electron heating is the only source for the BPD. Here the BPD development is similar to that of the HF discharge, as discussed in section 5.1.
As the neutral density in the NRG region varies during the flight, the beam relaxation regime changes accordingly. Let us first consider the region where (22). At νe < ν* (23), as follows from the heat balance (31) with , the electron temperature is Th ~ 1–5 eV. The ionization by the thermal bulk electrons is determined by a Maxwellian tail, i.e., . However, the main contribution comes from suprathermal electrons (29). Comparng the ionization rate (30) with τR yields the maximum plasma density in a stationary discharge of the order of
This dependence is similar to the observed (4).
As soon as or N > Nmd, the electron temperature increases but the acceleration of suprathermal electrons is inhibited. Here the palsma density is determined by the balance between ionization by thermal electrons and radial diffusion to give and then ∝ N3/2, as collisional damping reduces the beam spreading and hence the excited wave energy. The lower BPD boundary is determined by the neutral density, Nmax, at which collisional damping inhibits the development of the cold-beam instability (Mishin and Ruzhin, 1980a; Dokukin et al., 1981).
These results pertain to the beam instability. As far as the ring/ocillatory instability is concerned, its development at ωpe/ωce ~ s ≫ 1 proceeds even faster than at the initial stage. As a result the beam distribution over transverse velocities widens such that the wave energy grows to ~ (0.1 − 0.3)nbεb. Here, the strong electron heating is the main contributor to the BPD development. Since the group velocity at ωk/ωce ≈ s + 1/2 tends to zero, these waves are most enhanced (cf. Ashour-Abdalla and Kennel, 1978; Ashour-Abdalla et al., 1980), which explains the gyrofeatures in Figure 7B. As the ring instability growth rates are smaller than γc, it is suppressed at higher altitudes. Figure 12 illustrates the BPD regimes vs. altitude and the range of altitudes (neutral gas densities) where the various BPD features were observed.
Figure 12. (A) The different stationary BPD regimes vs. altitude defined by the beam relaxation regimes. Adapted from Mishin and Ruzhin (1980a). (B) Altitude and neutral density range over which BPD is expected. The first stripped column indicates the range expected from Mishin and Ruzhin's analysis. The second stripped column indicates the parameter range over which BPD has been observed in the large tank at the Jonson Space Center. The vertical line on the right indicates the altitude range over which the EXCEDE and PRECEDE experiments with currents far beyond the BPD thereshold were conducted. Adapted from Linson (1982). Reprinted by permission from Plenum Press.
Finally, using the heated bulk and accelerated tail electrons it is easy to show that the total power of optical emissions radiated from the NRG is of the order of a few per cent of the beam power (Ivchenko et al., 1981; Mishin and Ruzhin, 1981). The power of VHF radioemission estimated assuming conversion of Langmuir waves on density oscillations inherent in unstable beam-plasma systems also reaches a few percent of the beam power (Galeev et al., 1976; Mishin and Ruzhin, 1981).
6. Enhanced Aurora
The distribution of precipitating electrons, Fb(v), varies significantly in time and space creating various auroral forms with latitudinal scale lengths from tens of kilometers down to hundred meters (e.g., Meng et al., 1991). Some of the measured distributions of auroral electrons do exhibit the bump-in-the-tail feature. Its origin is beyond the scope of this survey.
6.1. Auroral Electrons
Figure 13 exemplifies auroral beam and suprathermal electron spectra observed over auroral arcs (e.g., Reasoner and Chappell, 1973; Arnoldy et al., 1974; Feldman and Doering, 1975; Bryant et al., 1978). In Figure 13B, the primary flux is approximated by a Gaussian distribution of the density nb = 0.6 cm−3, energy scatter Δεb ≈ 2.9 keV, and εb ≈ 10.2 keV (the dashed line). These beam parameters easily suffice the BPI conditions described in sections 4.3 and 4.4. Therefore, the beam relaxation can be described by the BPI theory outlined there. In particular, the relaxation length, lb (25) at νe < ν* (23) exceeds the distance between the acceleration region of auroral beams (e.g., Meng et al., 1991) and the E-region ionosphere. This explains why the bump-in-tail distributions, such as in Figures 13A,B, are preserved along the path (Galeev, 1975; Papadopoulos, 1975).
Figure 13. Differential number fluxes over auroral arcs with the ‘bump-in-the tail' distribution of primary electrons and flat power-law spectra of secondary electrons. Dots and circles show the observed fluxes, while dashed and solid lines show (B) a Gaussian approximation and (C) power-law trends. Adapted from (A) Arnoldy et al. (1974). (B) Bryant et al. (1978), and (C) Feldman and Doering (1975). Reprinted by permission from the American Geophysical Union.
As in Figures 6A,B, the suprathermal spectrum in the range ≥6–1,000 eV is well approximated by a power law Φ(ε) ~ ε−1. It is considerably flatter than the SPA spectrum (3) shown by the solid line in Figure 6B. In frame c, a SPA-like spectrum over the class II arc changes to a flatter one at ε ≥ εmin ≈ 20 eV, i.e., . The overall observations show that the spectrum of suprathermal electrons over arcs is not formed solely on account of the collisional interaction but can be explained in terms of the SLT acceleration (Papadopoulos and Coffey, 1974; Galeev, 1975; Matthews et al., 1976; Mishin and Telegin, 1986). It is worth to note that recent incoherent scatter radar observations (Isham et al., 2012; Akbari et al., 2013) do reveal the signatures of strong Langmuir turbulence in auroral plasma, quite similar to that in high-power radio wave experiments.
6.2. Luminosity and Ionization Profiles
A typical representation of the altitude-profile of auroral luminosity/ionization is illustrated by Figure 2. However, Donahue et al. (1968) reported on rocket measurements of auroral emissions at 557.7 and 391.4 nm, both having narrow local maxima at 115 and 130 km. Similarly, ground-based optical imagers detected either double-peaked auroral rays of about the same thickness, displaced in altitude by about 5–15 km, or one thick layer with the sharp upper boundary below about 130 km, with the characteristic scale length of only a fraction of HN (Oguti, 1975; Stenbaek-Nielsen and Hallinan, 1979; Dzyubenko et al., 1980; Hallinan et al., 1985). This phenomenon was called “Enhanced Aurora.” Similar layers of auroral ionization were also detected from sounding rockets (Swider and Narcisi, 1977; Morioka et al., 1988), the EISCAT UHF incoherent scatter radar (Wahlund et al., 1989; Schlesier et al., 1997), and a dual-altitude 90-MHz radar system (Timofeev and Miroshnikov, 1982). There were efforts to explain such double-peak profiles by the collisional interaction invoking two precipitating electron populations, i.e., a monoenergetic field-aligned beam and an isotropic beam of a higher energy. However, these efforts failed to fit the upper peak and sharp upper boundary.
Figures 14A,B shows double-peaked auroral rays observed near Tixie Bay by a side-looking low-light TV camera, the same as used in Zarnitza 2, and their luminosity profiles (Dzyubenko et al., 1980). The upper peaks are by a factor of two narrower than the minimum possible from the SPA, while the lower peak matches the SPA predictions (cf. Figure 4). Shown below (Figure 14C) is an example of a rayed arc with the sharp upper boundary (Hallinan et al., 1985).
Figure 14. (A) Auroral rays along the magnetic field indicated by the arrow and (B) their luminosity profiles. Adapted from Dzyubenko et al. (1980). (C) A rayed arc with the sharp upper boundary. After Hallinan et al. (1985). Reprinted by permission from the American Institute of Physics and American Geophysical Union.
More than fifty narrow layers of the enhanced electron temperature co-located with the plasma density peaks in the altitude range ≥ 115–150 km have been found in the EISCAT UHF radar database (Schlesier et al., 1997). One sample is shown in Figures 15A,B, where the thin layers in Te and ne are emphasized by thick lines. Note that the ion temperature is significantly smaller than the peak value of Te ≈ 3, 000 K and that the overall density profile has two peaks. A similar double-peaked ionization profile (Figure 15C) was observed in pulsating aurora (Wahlund et al., 1989). Dashed lines show the SPA profiles calculated for εb = 3.8 and 10 keV. As for auroral rays, the difference with the SPA profile for the upper peak is evident.
Figure 15. Thin layers of the (A) elevated electron temperature and (B) electron density indicated by thick lines (after Schlesier et al., 1997); and (C) a double-peaked ionization profile in pulsating aurora. Dashed lines show the SPA profiles calculated for εb ≈ 3.8 and 10 keV. After Wahlund et al. (1989). Reprinted by permission from the American Geophysical Union.
A striking resemblance between the Enhanced and Artificial Aurora (Figure 4) profiles is evident. Given that the parameters of electron beams far beneath the rocket are close to that of natural beams, it is safe to conclude that their generation mechanisms have much in common. It is obvious that the sought-for mechanism is the one that creates the plasma turbulence layer.
The effects of powerful electron beams injected from sounding rockets into the upper atmosphere to create artificial aurora are outlined. Data come from in situ measurements of the luminescence, thermal and suprathermal populations, and beam electrons near a beam-emitting space vehicle, as well as from ground-based optical, radar, and radioemission observations. The overall dataset cannot be explained solely by collisional degradation of energetic electrons but demands collisionless beam-plasma interactions (BPI) be taken into account. A brief survey of the BPI theory in a weakly-ionized plasma is presented. The basic processes of the near-rocket region are described in terms of the beam-plasma discharge (BPD) ignited by plasma electrons energized by the beam-excited plasma turbulence. Depending on the ambient plasma and atmospheric densities, there are several regimes of the BPD development. The observations of artificial auroral rays far beneath the rocket indicate that turbulence regime and thus the relaxation of radially expanded beams are strongly affected by collisions of plasma electrons. As a result, the energy density of plasma waves and concomitant energization of plasma electrons are enhanced in a narrow layer termed the plasma turbulence layer (PTL). The PTL formation results in an upper peak in a double-peak structure of artificial auroral rays. Some examples of optical and incoherent scatter radar observations of the luminosity and ionization profiles of rayed auroral arcs exhibiting two peaks or a sharp upper boundary are presented. Such auroral forms have been called Enhanced Aurora. An evident resemblance between Enhanced and Artificial Aurora points to their common generation mechanism, which is the one that creates the plasma turbulence layer.
The author confirms being the sole contributor of this work and has approved it for publication.
This work was supported by the Air Force Office of Scientific Research LRIR 16RV COR277 and 19RV COR038.
Conflict of Interest Statement
The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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B0 - the ambient magnetic field
L - Langmuir waves
EB - electron Bernstein waves
FM - the Maxwellian distribution
Fs - the distribution function of secondary electrons
Ft - the accelerated tail distribution function
MI - modulational instability
Primary waves -the waves excited by the beam
SLT- strong Langmuir turbulence
SST - superstrong (Langmuir) turbulence
Tspin - the rocket's rotation period
WT - weak turbulence
Wk - the wave spectral energy density
- the plasma density scale height
- the density of the ionizing (ε > εion) electrons
rD - the Debye radius
rcb − the Larmor radius of the beam electrons
w = W/n0Te - the dimensionless parameter of nonlinearity
wth - the modulational instability threshold
γmi - the modulational instability growth rate
- the relative density of ionizing (ε > εion) electrons
εion - the ionization energy
εmin (εmax) - the minimum (maximum) energy of the accelerated electrons
θ - pitch angle
λT - the mean free path of thermal electrons
μ = me/mi - the electron-to-ion mass ratio
νil - the frequency of inelastic collisions
νion - the ionization frequency
Keywords: active experiments, artificial aurora, electron beam-plasma instability, Langmuir turbulence, Enhanced Aurora
PACS: 94.20.dg, 94.20.Tt, 94.20.wf
Citation: Mishin EV (2019) Artificial Aurora Experiments and Application to Natural Aurora. Front. Astron. Space Sci. 6:14. doi: 10.3389/fspas.2019.00014
Received: 20 December 2018; Accepted: 28 February 2019;
Published: 05 April 2019.
Edited by:Ioannis A. Daglis, National and Kapodistrian University of Athens, Greece
Reviewed by:Alla V. Suvorova, National Central University, Taiwan
Konstantinos Papadopoulos, University of Maryland, College Park, United States
Copyright © 2019 Mishin. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Evgeny V. Mishin, firstname.lastname@example.org