Nonlinear Plasma Effects in Natural and Artificial Aurora

.

Nonlinear Plasma Effects in Natural and Artificial Aurora E.V. Mishin Space Vehicles Directorate, Air Force Research Laboratory, Bedford, MA 01731, USA

Abstract. This report describes common features of natural (‘Enhanced’) aurora and ‘artificial aurora’ (AA) created by electron beams injected from sounding rockets. These features cannot be explained solely by collisional degradation of energetic electrons, thereby pointing to collisionless plasma effects. The fundamental role in electron beam-ionosphere interactions belongs to Langmuir turbulence. Its development in the (weaklyionized) ionosphere is significantly affected by electron-neutral collisions, so that the heating and acceleration of plasma electrons proceed more efficiently than in collisionless plasmas. As a result, a narrow layer of enhanced auroral glow/ionization is formed above the standard collisional peak. Keywords: Enhanced Aurora, beam-plasma instability, Langmuir turbulence PACS: 94.20.dg, 94.20.Tt, 94.20.wf

INTRODUCTION During magnetospheric perturbations intense fluxes of 10-keV electrons precipitate into the polar ionosphere to create spectacular auroral displays. Optical emissions are stimulated by impact of energetic electrons on the ambient species (N 2 , O, O2 ). The excitation energies  are good indicators of the electron energy distribution. For example,  of the O1 S, N2 1PG, and N2 1N G states that yield the green ( 557.7 nm), red (676.5), and blue (427.8) line emissions in the E region (altitudes h  150 km), are  g 4.2, r 7.4, and b 18 eV, respectively. As the electron temperature is 3000 K and the excitation cross-sections are negligible at electron energies  500 eV, the observed auroral spectrum is shaped by suprathermal, 3  500 eV, electrons. The suprathermal electron population can be created via ionization of neutral gas (secondary electrons) and/or acceleration of the ambient electrons by excited plasma turbulence (accelerated electrons).

This paper outlines the common features of natural and artificial aurora and theory of electron beamionosphere interaction. We describe the underlying physical processes and basic limitations on a semiqualitative level that is sufficient to allow comparison with the observations. SINGLE-PARTICLE APPROACH The single-particle approach (SPA) relies on processes of ionization, dissociation, and excitation of neutral particles by collisional impact of precipitating or primary electrons with energies b  12 m b2 1-10 keV (e.g., [1]). In each ionization event electrons lose energy i  ion  s , where i on is the ionization energy and s is the energy of the new-born (secondary) electron. As long as the losses are small, the energy dissipation rate of the primary electron is given by Bethe’s formula db  b lb ∝ N z dz

(1)

Here lb   b  b b  i  is the mean free path, i   2i on 30-35 eV is the average energy loss,  b 1.5107 N is the ionization frequency, N z is the neutral gas density, and the z-axis is along the geomagnetic field B. The distribution function of secondary electrons (DFSE) in a steady state can be determined from z

d f s  z  qs  z  St  f s  dz

(2)

[2]. Plots and images are adjusted and annotated. In general, the SPA profile peaks at the altitude h m b  estimated from the condition lb N h m   Ha , where Ha is the atmosphere scale altitude. The thickness of the peak h m b  is also of the order of Ha h m . Both h m and h m decrease with increasing b , as electrons penetrate the denser atmosphere. Apparently, above the peak, i.e. at h  h m , the brightness monotonically increases with N , consistent with eq. (1).

Here qs  z   i on 0 zconst  2  is the production rate of secondary electrons, St  f s    i n   f s  z at energies   1 eV is the collision integral,   is the frequency of inelastic and  in   j j collisions with neutrals ( j designates the j-channel of inelastic losses including excitation and ionization). If  s  i n  Ha , the approximation of local losses, d f s dz  0, can be used. Then, from eq. (2) it follows f s  x  qs  x in 

(3)

The source qs  z retains the similarity of the spectrum with the change of the energy of primaries at 0 1 keV. As  i n   152 in the energy range c   100 eV (c 5 eV), eq. (3) yields a power law spectrum    ps c f s   const  (4)  with ps 3.5-4. At   c , DFSE is very sensitive to changes in the neutral composition because of considerable differences between cross-sections for various components. For a given spectrum of primary electrons in the topside ionosphere, the altitude profile of aurora is determined by the energy loss per unit volume. Then, the volume emission rate  is eq

  A  [X  ]  A

Q L   A

(5)

Here [X  ] stands for the density of the excited neutral species in cm3 ; Q  and L  are the production and loss rates, and A is the Einstein transition probabilities in s1 . The rates of electron impact excitation are   Q e  [X]  4   s d (6) 

Here s   m22 f s  is the differential omnidirectional number flux,  and   are the excitation energy and cross-section, respectively. The dissipation rate of the primary electrons can be calculated from the electron kinetic equation or applying the Monte Carlo technique. Figure 1 shows a typical (Monte Carlo) altitude-profile of auroral luminosity

FIGURE 1. Auroral altitude-profile calculated for 0 7.2 keV by Monte Carlo method (adapted from [2]). The dashed line shows the relative neutral density from the MSIS model.

OBSERVATIONS The distribution of precipitating electrons f b varies significantly with time and space, as does aurora. The horizontal (latitudinal) scales vary from 100 km (the so-called ‘inverted V’ events) down to 0.1 km (auroral rays). Sometimes, the primary population has a ‘bumpin-tail’, like shown in Figure 2 adapted from [3]. The origin of auroral electron beams is beyond the scope of this paper. Suprathermal electrons Figure 3 gives two examples of suprathermal electron spectra over auroral arcs from (a) [4] and (b) [5] In panel a, the primary flux is approximated by a Gaussian (Maxwellian) distribution of the density n b 0.6 cm3 , energy scatter b 2.9 keV, and b 10.2 keV (dashed line). As in Figure 2, the suprathermal spectrum in the range 6-1000 eV is well approximated by a power law    po with po 1. It is considerably flatter than the SPA spectrum (4)

shown by the solid line. In panel b, a SPA-like spectrum over the class II arc changes to a flatter one at    20 eV. The overall observations

gas injection. Note that the flat suprathermal spectra resemble those in natural aurora.

FIGURE 2. A ‘bump-in-tail’ distribution observed over the II class auroral arc (adapted from [3]). Reprinted by permission from the American Geophysical Union.

suggest (as first noted by [6]) that the spectrum of suprathermal electrons over arcs does not form solely on account of SPA. FIGURE 4. Suprathermal electron spectra in (a) Polar 5 and (b) Echo 5 with/without (dashed/solid line) neutral gas injections (see text). Reprinted by permission from the American Geophysical Union.

Auroral atitude-profiles FIGURE 3. Differential number fluxes of primary and secondary electrons over auroral arcs adapted from (a) [4] and (b) [5] (see text). Reprinted by permission from the American Geophysical Union.

Figure 4 shows suprathermal electron spectra observed during active rocket experiments (a) Polar 5 and (b) Echo 5 adapted from [7] and [8], respectively. During the Polar 5 experiment, measurements were performed onboard the subpayload separated by tens of meters across B from the beam-injecting payload, while during Echo 5 it was done aboard the same payload. Shown in panel a is a typical spectrum for Polar 5, which can be approximated as o  3108 1 cm2 s1 sr1 keV1 at  1 keV. For comparison, the dashed line shows the SPA spectrum multiplied by 250. By the same token, the Echo 5 spectra (panel b) behave quite similarly until about 100 eV, where the suprathermal population drops (the dashed line) due to neutral

A typical representation of the altitude-profile of auroral luminosity/ionization is illustrated by Figure 1. However, [9-13] reported on thin layers of auroral luminosity at altitudes below about 130 km with the characteristic gradient scale of only a fraction of Ha . This phenomenon was termed ‘Enhanced Aurora’ (EA) [13]. In short, EA consists of two peaks of about the same widths, displaced in altitude by about 5–15 km, or of one thick layer with a sharp upper boundary. Similar layers of auroral ionization were also detected from sounding rockets [14, 15] and by the EISCAT UHF incoherent scatter radar [16]. Figure 5 shows double-peaked auroral rays observed by a side-looking low-light TV camera near Tixie Bay [11]. The upper peaks are by a factor of two narrower than minimum possible from SPA, while the lower peak matches the SPA predictions.

FIGURE 5. (left) Auroral rays and (right) their luminosity profiles (adapted from [11]). The magnetic field direction is indicated by a thick arrow.

More than fifty narrow ‘layers’ of the electron temperature (Te ) co-located with the plasma density (n e ) peaks in the altitude range 115-150 km have been found in the EISCAT UHF radar database [17]. One sample is shown in Figure 6a-b, where the layers are indicated by thick lines. Note that the ion temperature is well below the Te peak. Shown in panel c is a double-peaked ionization profile in pulsating aurora adapted from [16] (c.f., Figure 5). Dashed lines show the SPA profiles calculated for b 3.8 and 10 keV. As above, the difference with SPA is evident.

FIGURE 7. (left) Image of two AA rays and (right) the altitude-profile of the left most ray with a Monte Carlo profile superimposed.

One should bear in mind that initially monoenergetic and monodirectional beams lose only 10%-20% of their energy in the BPD region, acquiring the energy scatter b 0.2b [19]. As follows from Monte Carlo simulations, due to collisional diffusion the beam significantly spreads across B. As the beam density far beneath the rocket is of the same order as of natural beams [2], the beam dynamics should be similar. We conclude the observational section by stating that SPA is unable to explain the flat spectra and fine altitudinal structure of Enhanced and Artificial Aurora. Therefore, [10, 2, 22] suggested that collisionless beam-plasma interaction (BPI) creates the EA feature.

COLLISIONLESS INTERACTION

FIGURE 6. Samples of EISCAT data showing thin layers in (a) electron temperature and (b) electron density indicated by thick lines and (c) a double-peaked ionization profile in pulsating aurora. Dashed lines show the SPA profiles calculated for b 3.8 and 10 keV by [16]. Reprinted by permission from the American Geophysical Union.

Figure 7, adapted from [12], shows two of about eighty nearly-identical AA rays observed in the course of the Zarnitsa-2 active rocket experiment by a 20-ms time-resolution low-light TV camera. A bright glow near the beam-emitting rocket is created by intense radiation from the region of beam-plasma discharge (BPD) [18-21]. Again, the SPA predictions agree with the lower peak but fail to explain the upper one.

A great number of experimental and theoretical studies of BPI over almost five decades is nearly impossible to mention. For the subject of interest, key references, besides cited above, are [23-29]. As first discussed by [6, 30, 23], the strong Langmuir turbulence (SLT) regime of collisionless electron beam-ionosphere interactions should be taken into account. Then, [22] found a specific regime of the SLT development, significantly affected by collisions of the ambient electrons. In this regime, the latter are heated/accelerated more efficiently than in collisionless fully-ionized plasmas. As a result, a narrow layer of enhanced auroral glow/ionization is formed above the SPA layer, so the overall profile resembles EA (see details in [31, 32]). Let an electron beam with 1 b b  n b n13 , as in Figures 2 and 3, intrudes the ionosphere. As  f b    0 in the range  b   b      b , Langmuir (l) waves with phase velocities

 b   b  l kr   b will grow with the rate

1 dWr  b  (7) Wr dt  2 b is the growth rate in colHere  b   p nn b  b  lisionless plasmas, l   p 1  3k 2r D 2  c  p 2 , r D is the Debye radius, the plasma frequency  p  9 n kHz greatly exceeds the electron gyrofrequency 56 c ,  1.8107 N Te s1 (at Te 0.3 eV) is the collision frequency of ionospheric electrons at h 150 km, and Wr is the spectral energy density of the beamresonance waves, k  kr . Calling for b  0 gives  56   n 01 N  Nmax  3  1015 b cm3 (8)  p Te 105 b 

Taking n  105 cm3 , Te 0.1 eV, n b 1 cm3 , and  b  b 0.1 yields for the standard neutral atmosphere that the instability develops at altitudes h  h min  hNmax   105 km

(9)

Figure 8 shows an example of the EISCAT UHF radar observations of plasma and ion lines (courtesy of Tom Grydeland) indicating that Langmuir and ionacoustic waves are excited well over the thermal noise at h 105 km.

FIGURE 8. Range-time plots of the plasma and ion line intensities from the EISCAT UHF radar (courtesy of Tom Grydeland). Color codes are given in linear scale.

The wave excitation goes at the expense of the beam energy leading to the energy spreading out (widening

of the bump-in-tail) and thus decrease of b . This way, an unstable B-P system relaxes towards an equilibrium state. The dissipation rate of the beam energy is given by nb

d  d b   W  b Wr k k dt dt

(10)

where    means averaging over velocities. The relaxation length, lr , is defined as a distance from the boundary (z  0) where the instability is stabilized, i.e. b     0. If    c   p n b n, the ultimate beam scatter is     b  c 12 , otherwise     b . From eq. (10) it follows lr 

  n b b  Wr b

(11)

where Wr has yet to be found. If the beam density exceeds the critical value   2 b  (12) n b  106 n 1  3 p Te the relaxation process is dominated by SLT. In brief, the ponderomotive force, W , pushing plasma out, depletes (n  0) regions where spontaneous modulations 2 , Langmuir waves of W  0 occur. At n n  3k 2r D 1 wavelengths  k are trapped inside a density cavity, 2 nT , a posthereby increasing W . If W  Wth  3k 2r D e itive W  n loop leads to the initial modulations growth. As trapping inside a cavity leads to correlation of the wave phases and hence violation of the weak turbulence condition of random phases [33] this regime is termed STRONG (Langmuir) turbulence. The auroral values of n b 0.5-3 cm3 satisfy the SLT condition (12) if n (1-3)105 cm3 (at h 120130 km). The characteristic growth rate of the modulational instability (MI) at W  Wth is  W (13)  md W    p 3nTe ( 2105 at h 150 km). The next key point is collapse of a cavity with trapped waves, i.e., increasing the magnitude along with decreasing spatial dimensions, predicted by [34]. Trapped waves acquire wavelengths of the order of the cavity dimension R, so collapse leads to the wave energy transfer toward short scales. As the phase velocity l k ∝ Rt decreases, collapse is arrested when the ambient electrons absorb the trapped waves. For a continuously acting source of the pump k  kr  waves, the wave energy in a steady state is localized in a large number of chaotically distributed cavities at different stages of collapse. The energy density

W L of the short-scale, k L  1r D W L 3nTe 12  kr , waves greatly exceeds Wr . The rate of the energy spectral transfer is determined by the effective collision frequency  e f   p Wca 3nTe

(14)

Here Wca is the energy density in the collapsing cavities, and b  p  3Te b   is implied. The energy balance in a steady state d Wr  b  e f Wr dt

and  e f Wr   md W L Wca (15)

Here Wk is the spectral density of the wave energy in the absorption region determined by

    2 2 4p dk d p Wk  k Wk   f Wk at dk dt n k3 k (spectra of waves and particles are isotropic). Here kt  t0  t2 is determined by the collapse law in the absorption region. These equations yield a power law spectrum

yields b Wca 3 nTe p

and

W L  03

Wr2 nTe

 Wr (16)

The key problem of SLT is the determination of the dependence Wca W L . In collisionless isothermal plasmas Wca  W L . Then, if 2 p  3Te b Wr  Wr  3



b p

12

nTe

(17)

c  2 p nTe and Otherwise, the MI threshold is Wth th th c n b  n b 2b 3Te  p . If W L  Wth , the MI growth rate is of the same order as given by eq. (13). However, if  md W L    or

12       b  p 

(18)

the trapped waves collisionally damp before cavities collapse. As  e f ∝ Wca  0, eq. (15) predicts the c increase of Wr and W L . If b   and Wr  Wth , in  the ‘collisional’,    , SLT regime one gets Wca    2 and W L  3 WL 3 Wr    nTe p nTe 



 p

2

(19)

 If       p 01, deep cavities are not created  2 and Wr  W L  1 bp nTe . Resonance absorption of plasma waves in collapsing cavities accelerate plasma electrons. In isotropic plasmas, their stationary distribution, f a , is found from the kinetic equation     4p Wk  f a 1  dk  St  f a   2  mn  p  k 3 

fa 

na 32

8  min



 min

 pa

at min    max (20)

where pa 1.75. In a weakly-magnetized plasma, the exponent of the power law is 3/2. The lower boundary, min , and the tail density, n t , are determined by the ‘boundary’ conditions:   f a min   f 0 min  and  md Wkl m  km (21) where km   p  min and f 0 is the ambient electron distribution at   min . In Maxwellian plasmas, f 0  f M , one has min 10Te and n am 0.312 n. In the ionosphere, f 0 min   f s min  and at     [35] 

ns



nTe WL

25

c min

 c

n c t

 n t   min   03n s  10n b

12 n

 20 eV

(22)

The upper boundary of the tail max is defined by inelastic losses St  f a    in  f a that maximize at 14 74 m 150 eV. If  i n  L   Te  L  W L n L   p 10 3 5 or N  N L 210 n10 cm at  L  104 W L n eV ( m ), the tail’s growth slows and the power law (20) breaks down (c.f., Figure 4b).

CONCLUSION The observations and theory of Enhanced and Artificial Aurora are outlined. Their common features are explained in terms of the SLT regime of collisionless beam-plasma interaction affected by collisions of the ambient electrons. ACKNOWLEDGMENTS This work was supported by the Air Force Office of Scientific Research. REFERENCES

1. M. Rees, Physics and Chemistry of the Upper Atmosphere, Cambridge University Press, New York, 1989. FIGURE 9. Schematic of the Plasma Turbulence Layer and formation of a double-peaked EA profile.

2. N. Izhovkina, and E. Mishin, Geomagn. Aeronomy, Engl. Transl. 19, 398–399 (1979).

3. R. Arnoldy, P. Lewis, and P. Isaacson, J. Geophys. Res. 79, 4208–4221 (1974).

4. D. Bryant, D. Hall, and D. Lepine, Planet Space Sci. 26, 81–90 (1978).

Plasma Turbulence Layer When     (18) the level of plasma turbulence increases as W L   2 . Thus, the equality     defines the upper boundary, h  , of the layer of enhanced plasma turbulence or Plasma Turbulence Layer. Its ultimate lower boundary is determined by suppression of the beam instability, that is, h min . However, with regards to aurora, its lower boundary is near     . The electron temperature in PTL becomes

Te 



3ion

5. P. Feldman, and J. Doering, J. Geophys. Res. 80, 2808–2812 (1975).

6. K. Papadopoulos, and T. Coffey, J. Geophys. Res. 79, 674–676 (1974).

7. B. Maehlum, B. Grandal, T. Jacobsen, and J. Troim, Planet. Space Sci. 28, 279–289 (1980).

8. R. Arnoldy, C. Pollock, and J. Wincler, J. Geophys. WL n

Res. 90, 5197 (1985).

(23)

As min (max ) decreases (increases) with W L , the suprathermal tail in PTL expands, thereby increasing  4 b Te . Figthe ionization rate qit on  10Te n b i on  b ure 9 shows schematically our scenario of the formation of a EA-like double-peaked auroral ionization/luminosity profile due to PTL. The lower peak c ) is caused by the collisional ionization of neutral (qion gas by the primary (beam) electrons, while the upper layer, i.e. PTL, is due to accelerated electrons. If the beam energy is below 5 keV, both peaks tend to overlap, so that the observer would see only one layer with the sharp upper boundary.

9. T. Oguti, J. Atmos. Terr. Phys. 37, 1501–1504 (1975). 10. H. C. Stenbaek-Nielsen, and T. J. Hallinan, J. Geophys. Res. 84, 3257–3272 (1979).

11. N. Dzyubenko, V. Ivchenko, G. Milinevsky, and E. Mishin, JETP Lett. 31, 607–610 (1980).

12. E. Mishin, V. Ivchenko, and G. Milinevsky, Adv. Space Res. 1 (1), 163–165 (1981).

13. T. Hallinan, H. Stenbaek-Nielsen, and C. Deehr, J. Geophys. Res. 90, 8461–8475 (1985).

14. W. Swider, and R. Narcisi, Planet.Space Sci. 25, 103– 106 (1977).

15. A. Morioka, H. Oya, H. Miyoka, T. Ono, T. Obara, H. Yamagishi, and H. Fukunishi, J. Geomag. Geoelectr. 40, 923–937 (1988).

16. J. Wahlund, H. Opgenoorth, and P. Rothwell, J. Geophys. Res. 94, 17223–17233 (1989).

17. 17. A. Schlesier, E. Mishin, and K. Schlegel, Geophys. Res. Lett. 24, 1407–1410 (1997).

18. 18. A. Galeev, E. Mishin, R. Sagdeev, V. Shapiro, and V. Shevchenko, Sov. Phys. Doklady 21, 641–643 (1976).

19. 19. E. Mishin, and Y. Ruzhin, Adv. Space Res. 1 (1), 47–59 (1981).

20. K. Papadopoulos, Theory of Beam Plasma Discharge, in Artificial Particle Beams in Space Plasma Studies, edited by B. Grandal, Plenum, New York, 1982, pp. 505–524.

21. K. Papadopoulos, J. Geophys. Res. 91, 1627–1631 (1986).

22. A. Volokitin, and E. Mishin, Sov. J. Plasma Phys. 5, 654–656 (1979).

23. A. Galeev, Plasma Turbulence in the Magnetosphere With Special Regards to Plasma Heating, in Physics of the Hot Plasma in the Magnetosphere, edited by B. Hultqvist, and L. Stenflo, Plenum Press, New York– London, 1975, pp. 251–270.

24. D. Matthews, M. Pongrats, and K. Papadopoulos, J. Geophys. Res. 81, 123–129 (1976).

25. A. Galeev, R. Sagdeev, V. Shapiro, and V. Shevchenko, Sov. Phys. JETP 45, 266–271 (1977).

26. R. Sagdeev, Rev. Mod. Phys. 51, 1–20 (1979). 27. A. Galeev, R. Sagdeev, V. Shapiro, and V. Shevehenko, Beam Plasma Discharge and Suprathermal Electron Tails, in Active Experiments in Space (Alpbach, Austria), SP-195, ESA, Paris, 1983, pp. 151–155.

28. Grandal, B. (editor), Artificial Particle Beams in Space Plasma Studies, Plenum, New York, 1982.

29. V. Shapiro, and V. Shevchenko, Strong Turbulence of Plasma Oscillations, in Handbook of Plasma Physics, Vol. 2, Basic Physics II, edited by A. Galeev, and R. Sudan, Elsevier, New York, 1984, vol. 2, pp. 123– 182.

30. K. Papadopoulos, Phys.

Fluids 18, 1769–1777

(1975).

31. E. Mishin, Y. Ruzhin, and V. Telegin, Interaction of Electron Fluxes With the Ionospheric Plasma, in Russian, Hydrometeoizdat, Leningrad, 1989.

32. E. Mishin, and V. Telegin, Geomagn. Aeronomy, Engl. Transl. 29, 1–13 (1989).

33. R. Sagdeev, and A. Galeev, Nonlinear Plasma Theory, Benjamin, New York–Amsterdam, 1969.

34. V. Zakharov, Sov. Phys. J.E.T.P., Engl. Transl. 35, 908 (1972).

35. E. Mishin, and V. Telegin, Sov. J. Plasma Phys. 12, 509–510 (1986).