Aftereffect in modified ionospheric plasma

Advances in Space Research 38 (2006) 2490–2494 www.elsevier.com/locate/asr

Aftereffect in modified ionospheric plasma A.V. Kochetov a

a,*

, G.I. Terina

b

Plasma Physics and High Power Electronics, Institute of Applied Physics of RAS, UlÕjanova St., 46, Nizhny Novgorod 603950, Russia b Radiophysical Research Institute, 25 BolÕshaya Pechrskaya s., Nizhny Novgorod, 603950, Russia Received 30 October 2004; received in revised form 12 January 2005; accepted 19 January 2005

Abstract Experimental and theoretical results of study of ‘‘aftereffect’’ phenomena arising in the modified ionosphere after the action of powerful radio emission are presented. The experimental results were obtained by the method of ionosphere sounding by short probing radio pulses. The theoretical model is based on the numerical solution of modified nonlinear Schro¨dinger equation with a driven extension. The qualitative agreement of theoretical and experimental results is obtained. Ó 2006 Published by Elsevier Ltd on behalf of COSPAR. Keywords: Ionosphere sounding; Radio wave scattering; Nonlinear dynamics; Artificial turbulence

1. Introduction

2. Experimental results

Under sounding of an artificial ionospheric turbulence by short probing radio pulses of ordinary polarization two types of scattered signals were observed: a ‘‘caviton’’ signal (CS) and a ‘‘plasma’’ signal (PS), which appeared with the heating transmitter switching on and disappeared after its switching off (Terina, 1995, 1996). The scattered signal of PS type was revealed also after the heating switching off. It was an ‘‘aftereffect plasma signal’’ (AEPS) (Terina, 2000). This signal had large time and spatial delays and appeared mostly when corresponding PS had envelope fluctuations. The aftereffect phenomenon was expressed at time on CS by amplitude increasing at once after the heating transmitter turning off. In this paper, aftereffect phenomena of the scattered signals in modified ionospheric plasma are considered. The theoretical model of this phenomenon is proposed (Kochetov et al., 2001, 2002a,b).

The experiments were carried out in Nizhegorodsky region at the heating facility ‘‘Zimenki’’. The heating transmitter operated at frequencies 4.6, 5.455, 5.75, and 5.828 MHz with the effective radiated power (ERP) 10–20 MW and was switched on for 0.3–60 s and off for the same duration. The probing transmitter radiated pulses of duration 50 ls with the pulse power 100 MW in the frequency range 5.5–5.9 MHz. The transmitters were able to radiate radio waves of ordinary (o) and extraordinary (x) polarization. A recorder registered the amplitude of observed scattering signals from 10 virtual heights simultaneously. AEPS was observed when the heating and probing transmitters radiated radio waves of ordinary polarization and corresponding PS had envelope fluctuations – signals of types Ia and II (Dmitriev et al., 1995). In the height-amplitude scanning, it was situated at the virtual heights exceeding the reflection height of probing radio pulses by 100 km and more and occupying the height range of 300–1000 km. The appearance time of AEPS amplitude maximum was several seconds. The relaxation time changed from several seconds up to

*

Corresponding author. Tel.: +7 8312 164836; fax: +7 8312 160616. E-mail address: [email protected] (A.V. Kochetov).

0273-1177/$30 Ó 2006 Published by Elsevier Ltd on behalf of COSPAR. doi:10.1016/j.asr.2005.01.047

A.V. Kochetov, G.I. Terina / Advances in Space Research 38 (2006) 2490–2494

10 min and essentially increased with increasing of virtual heights of scattering. The rising and relaxation times depended also on the probing and heating frequencies, ionospheric conditions and the shape of PS envelope. The examples of the time dependencies of PS and corresponding to it AEPS are presented in Fig. 1. The aftereffect phenomena manifested itself on CS by the increasing of its amplitude during milliseconds after the heating transmitter turning off. CS occurred, when the heating and probing transmitters radiated both the ordinary and extraordinary polarizations. CS aftereffect was observed seldom mainly with the small heater duration. The example of CS aftereffect phenomenon is presented in Fig. 2.

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Fig. 2. An example of the time dependency of CS amplitude (in a.u.) with aftereffect: fh = 4.6 MHz (x), fpr = 5.62 MHz (x). h 0 = 230 km. ERP = 20 MW. Arrows mark the moment of the heating turning on and turning off.

3. Theoretical results field and the limited depth of penetration yield in dimensionless variables:

3.1. Theoretical model We assume that the half-space x > L is filled with the plasma with unperturbed density, n0(x) = (1 + x/ L)Nc, where Nc = mx2/4pe2, x is the wave frequency, m, e are the electron mass and charge, respectively. The plasma layer is irradiated by the normally incident electromagnetic wave with a given amplitude E0(t). The electromagnetic field in vacuum x 6 L combines the incident and reflected wave with an amplitude Er. The density of plasma is modified in the field by MillerÕs force as, n(x) = n0(x)exp(|u|2), u2 ¼ E2 =E2p is the complex amplitude of the wave in square, normalized to plasma field E2p ¼ 16pN c T , T is the temperature of electrons (Litvak, 1986). We seek an electric field in the layer in the form E(x,t) = E(x,t)exp(ixt). For the description of the field evolution in plasma the modified NSE, written in dimensionless variables with units t = 2/x, x = 1/k0 = c/x, c is the light velocity, n = Nc, u = Ep is used 2

iut þ uxx þ ð1  nðx; juj ÞÞu ¼ 0:

ð1Þ

The standard boundary conditions of the continuation of the tangential components of electric and magnetic

ux ¼ iu þ 2iu0 ðtÞjx¼l ;

ð2Þ

u ¼ 0jx¼1 :

ð3Þ

The typical laws of the smooth turning on (at t = 0) and turning off (at t = t1) of the incident wave are as follows: ( u0 ð1  expðt2 =T 20 ÞÞ; T 0 P 1; u0 ðtÞ ¼ ð4Þ 2 u0 expððt  t1 Þ =T 21 Þ; T 1 P 1: We assume that there is no initial electric field in the layer u(x, t = 0) = 0. The prescribed density depletion of Gaussian form moderates the initial density profile as n00 ðxÞ ¼ 2 n0 ðxÞ þ n1 ðxÞ, where n1 ðxÞ ¼ n2 hðtÞ expððx  x0 Þ = 2 2r Þ and h(t) is prescribed function 8 t 6 t2 ; > < 0; h ¼ ð1  expððt  t2 Þ=T 2 ÞÞ; t2 6 t 6 t3 ; ð5Þ > : expððt  t3 Þ=T 3 Þ; t P t3 ; with the specific parameters of turning on and turning off t2, t3, T2, T3 correspondingly and n2, x0, r are the density depletion parameters.

Fig. 1. Examples of the time dependencies of PS and AEPS amplitude (in a.u.): (a) fh = 5.75 MHz (o), fp = 5.6 MHz (o); (b) fh = 5.455 MHz (o), fp = 5.6 MHz (o), h 0 = 345 km, ERP = 10 MW. Heating duration 50 s. Arrows mark the moments of heating turning on and turning off.

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Fig. 3. The temporal dependencies of electric field modulus at the plasma resonance point and the reflection signal for linear inhomogeneous plasma layer l = 70, u0 = 0.25, t1 = 150.

3.2. Simulation results The simulations allow us to studying the spatial structures of electromagnetic field u(x, t), including the phase dependencies at any point of the plasma layer, the plasma density n(x, t), the amplitude and the phase of the reflected wave ur(t) = u(l, t)  u0, their time and spectrum characteristics at the formation (t < t1) and relaxation (t > t1) states. The obtained results show that under the action of the powerful wave, the formation of soliton structures in the reflection region and their penetration in the overdense plasma take place. In the initial stage, quasi-periodic structures are formed and then they transform to chaotic ones (Kochetov et al., 2001, 2002b). At the relaxation stage solitons, which velocity at the moment of heating turn off was enough high, continue to propagate into the overdense plasma increasing in amplitude, decreasing in width and decelerating. Then they reflect and move into the underdense plasma, decreasing in amplitude, increasing in with and acceler-

ating. In Fig. 3, the example of time dependencies of the electric field at the plasma resonance point and the reflected signal for linear inhomogeneous plasma layer is presented. The formation of the density depletion on the linear plasma profile lower the plasma resonance region essentially changes the spatial and temporal structures of the electric field and the plasma density. The time dependencies for the linear inhomogeneous plasma layer with the fixed density depletion for the same field and plasma layer parameters as in Fig. 3 are presented in Fig. 4. The calculation results show that for definite values of the electric field amplitude, the plasma density gradient and the density cavity parameters the trap of electromagnetic field in the cavity takes places. Thus the relaxation time of soliton structure is defined by the lifetime of the density depletion. Just that case is presented in Figs. 4 and 5. In Fig. 5, the spatial amplitude structure of the electric field and the electron concentration are shown at various time moments of formation and relaxation stages.

Fig. 4. The temporal dependencies of electric field modulus at the plasma resonance point and the reflection signal for linear inhomogeneous plasma layer: l = 70, with density depletion: n2 = 0.7, x0 = 10, r = 1, t2 = 100, t3 = 450, incident wave u0 = 0.25, t1 = 150.

A.V. Kochetov, G.I. Terina / Advances in Space Research 38 (2006) 2490–2494

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Fig. 5. The spatial structures of electron density and electric field squared for linear inhomogeneous plasma layer with density depletion at the formation (t = 136) and relaxation stages (t = 208 and t = 360) for the same parameters as in Fig. 4.

4. Conclusion The results obtained for linear inhomogeneous plasma layer and for plasma one with density depletion allow us to interpret the aftereffect of CS and PS qualitatively (Kochetov and Terina, 2004a,b). The field amplitude increase at relaxation stage displayed at calculations allows us to interpret of CS aftereffect. The big time delays of AEPS can be explained as a result of powerful radio waves trapping in the forming at the plasma resonance regions density depletions, which are able to keep their shape for a long time. It should be noted that PS and CS are analogous to different components of the stimulated electromagnetic emission (SEE) (see, e.g., Mjølhus, 1998; Isham et al., 1999): ‘‘broad continuum’’ (BC) and narrow continuum’’ (NC) accordingly. AEPS is corresponded to Diagnostic SEE at the relaxation stage. The obtained results allow us to clarify some features of the physical processes, arising after the action of the powerful radio emission into the ionospheric plasma. However, many questions have not been answered yet. For the further study of the considered phenomena with

the purpose of their quantitative interpretation, it is necessary to take into account a number of factors, first of all, a plasma waves excitation (Mjølhus et al., 1995; Kochetov et al., 2003) and an external magnetic field action.

Acknowledgments This work was support by the Ministry of Education of Russia (Grant E02-3.2-90) and in part by the Russian Foundation for Basic Research (Grants 05-02-17370, 03-02-16309). The authors thank S.A. Dmitriev and L.M. Elkhina for the help in carrying out the experiments and V.N. Bubukina for the help in the manuscript preparation.

References Dmitriev, S.A., Terina, G.I., Tushentsova, I.A. Some characteristics of ‘‘Plasma’’ signal, scattered by artificial ionospheric turbulence. Geomagnet. Aeronomia 35, 123–127, 1995, In Russian.

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Isham, B., La Hoz, C., Rietveld, M.T., Hagfors, T., Leyser, T.B. Cavitating Langmuir turbulence observed during high-latitude ionospheric wave interaction experiments. Phys. Rev. Lett. 83, 2576–2579, 1999. Kochetov, A.V., Mironov, V.A., Terina, G.I., Bubukina, V.N. Eelectromagnetically driven solitons in inhomogeneous overdence plasma. Physica D, Nonlinear phenomena 152–153, 723–730, 2001. Kochetov, A.V., Mironov, V.A., Terina, G.I. Strong turbulence effects in artificially disturbed ionosphere. Adv. Space Res. 29 (9), 1369– 1373, 2002a. Kochetov, A.V., Mironov, V.A., Terina, G.I. Dynamic self-action of driven electromagnetic fields in inhomogeneous overdense plasma. In: Litvak, A.G. (Ed.), Proceedings of the International Conference Progress in Nonlinear Science Frontiers of Nonlinear Physics, vol. II. Institute of Applied Physics, RAS, University of Nizhny Novgorod, Nizhny Novgorod, Russia, pp. 376–381, 2002b. Kochetov, A.V., Mironov, V.A., Terina, G.I., Shaleev, M.V. Selfconsistent electromagneticaly driven Langmuir turbulence in overdence plasma. In: Litvak, A.G. (Ed.), Proceedings of IV International Workshop Strong Microwaves in Plasmas. Institute of Applied Physics, RAS, Nizhny Novgorod, Russia, pp. 505–510, 2003. Kochetov, A.V., Terina, G.I. Aftereffect in modified ionospheric plasma, in: Abstracts of 35th COSPAR Scientific Assembly, July

18–25, 2004, Paris, France, P-0079, COSPAR04-A-01885, C5.1/ D4.1-0041-04. Available from: . Kochetov, A.V., Terina, G.I. Aftereffect in modified ionospheric plasma, in: Abstracts of 31th EPS Conference on Plasma Physics, June 28–July 2, 2004, London, England, P2-078. Available from: . Litvak, A.G., Dynamic nonlinear electromagnetic phenomena in plasmas, in: Leontovich, M.A. (Ed.), Reviews of Plasma Physics, vol. 10, Consultants Bureau, New York, 1986. Mjølhus, E., Hanssen, A., DuBois, D.F. Radiation from electromagnetically driven Langmuir turbulence. J. Geophys. Res. 100, 17527–17541, 1995. Mjølhus, E. Theoretical model for long time stimulated electromagnetic emission generation in ionospheric radio modification experiments. J. Geophys. Res. 103, 14711–14721, 1998. Terina, G.I. Characteristics of signals scattered by artificial ionospheric turbulence. J. Atm. Terr. Phys. 57, 273–278, 1995. Terina, G.I. The investigation of the artificial ionospheric turbulence by the method of probing radio wave pulses, Izv. VUZov, Radiofizika, 39, 203–208, 1996 (in Russian). Terina G.I., An ‘‘After-Effect in Artificially Disturbed Ionospheric Plasma, Izv. VUZov, Radiofizika, 43, 958–961, 2000 (in Russian).