Power Spectra of Ionospheric Scintillation

Transcription

1 ower Sectra of Ionoheric Scintillation G. V. Jandieri and A. Ihimaru Deartment of hic Georgian Technical Univerit Tbilii Georgia Deartment of Electrical Engineering Univerit of Wahington Seattle Wahington USA Abtract - eculiaritie of the atial ower ectrum (SS) of cattered radiation in magnetized turbulent aniotroic lama are invetigated b mooth erturbation method taing into account diffraction effect. Second order tatitical moment: broadening wave tructure function angle-of-arrival cintillation index are calculated numericall for both aniotroic and ower-law correlation function of electron denit fluctuation uing exerimental data. New feature of the evaluation of a double-humed hae of the SS for different arameter of aniotro and angle of inclination of rolate irregularitie with reect to the external magnetic field taing into account geometr of the ta are revealed for the firt time. The ga increae in roortion to the aniotro factor. The ower ectra and cintillation level of cattered ordinar and extraordinar wave have been calculated taing into account movement of ionoheric irregularitie. Keword: atial ower ectrum double-humed effect cintillation magnetized lama. Introduction Statitical characteritic of cattered electromagnetic wave in randoml tatiticall iotroic media have been intenivel tudied []. However in man cae irregularitie are aniotroic and are oriented along a certain direction. In the uer atmohere ionization become ignificantl aniotroic becaue electron can move eail along the magnetic field line than acro them. There i therefore a tendenc for all irregularitie to become aligned along geomagnetic field [3]. Aniotroic irregularitie in the ionohere lead to the daming and amlification of the amlitude of radio wave fluctuation of the hae and variation of the angle-of-arrival; ionoheric cintillation i a reult of comlex action of all thee effect. For relativel mall irregularitie diffraction effect are imortant. The feature of the SS of cattered radiation in magnetized aniotroic lama in the comlex geometrical otic aroximation uing the erturbation method have been invetigated in [-7]. The Double-humed effect in turbulent aniotroic magnetized lama ha been dicovered recentl uing the mooth erturbation method taing into account diffraction effect [8]; ome eculiaritie of tatitical characteritic of cattered radiation have been reorted in [9]. Thi aer i devoted to the invetigation of econd order tatitical moment of the SS of cattered electromagnetic wave in turbulent colliionle magnetized lama with electron denit fluctuation. New eculiaritie of the Double-humed effect are revealed analticall in the SS of a multile cattered radiation at oblique illumination of magnetized lama with rolate irregularitie b mono-directed incident radiation uing the mooth erturbation method taing into account diffraction effect. Numerical calculation are carried out for both aniotroic Gauian and owerlaw correlation function of electron denit fluctuation aling exerimental data. It wa hown that the SS ha a double-eaed hae for the ower-law correlation function the ga increae in roortion to the aniotro factor location of it maximum weal varie and width ubtantiall broaden with increaing ditance travelling b electromagnetic wave in randomlinhomogeneou magnetized lama. Formulation of the roblem Conider a lane wave roagating in the z direction and the unit vector τ of an external magnetic field lie in the YZ coordinate lane ( z H ÎYZ - rincile lane) / l l i the radio wavelength in free ace. Abortion in the laer i negligible for high frequenc incident wave and comonent of econd-ran tenor e of the colliionle magnetized lama are []: i - - e xx -v( - u) e -v(-u in a)( - u) ezz u u - -v(- co a)( - ) - % ex - % ex v u co a (-u)

2 - % exz - % ezx - v u in a (-u) ; where a i the angle between and H vector; / w () r [ N() r e / m] i the lama frequenc u( r) [ eh ( r)/ mcw] and v( r) w ( r )/ w are the magneto-ionic arameter W H ( r) eh( r )/ mc i the electron grofrequenc. Dielectric ermittivit of turbulent magnetized lama i () i () () i i + i e () r e e () r e ( r ) <<. The firt term i the regular (unerturbed) comonent of the dielectric ermittivit connecting with the ionization ditribution in the uer atmohere at different altitude above the Earth urface; the econd term i a random function of the atial coordinate caued b electron denit fluctuation in the ionohere; v( r) v [ +n( r )]. The electric field E atifing wave equation æ -Ddi - ei ( r) E ( ) ç xi x r () introduce a E( r ) E ex( ) i + i z ( << ); comlex hae fluctuation () are of the order ~ () e i ~ e i. Wave field arameter m / decribing diffraction effect i calculated in zero-order aroximation [8]. The irregular lama tructure in the cattering medium imoe a random hae on the tranmitted radio wave. hae fluctuation in the econd order aroximation atifie differential equation + ir + i + ( G ) -R z x z x æ i -R - G + z ç x é æ æ ù ig ê ç +ç ú () ê x ú û where olarization coefficient are []: u ( -v )coa R u in a ± u in a + u ( -v ) co a v u ina +R u vinacoa G -. (3) -u - v + u v co a The uer ign (index ) correond to the extraordinar wave and the lower ign (index ) correond to the ordinar wave. Ordinar and extraordinar wave in magnetized lama generall are elliticall olarized. The nowledge of the olution of two-dimenional ectral comonent of the hae fluctuation atifing tochatic differential equation (for z comonent) allow u to calculate variance of the hae fluctuation for arbitrar correlation function of electron denit fluctuation: ( r) L 5 dx d é ò ò x G - - < > W - + æ ig -G3 + R ( - ) + ir x ù û Vnç x () G v u where: W 5 (in a + R u in a coa - (-u ) 3 u u - G ina co a -R G ina co a + u u +R in a co a +G co a) x are the atial wavenumber comonent in direction X and Y reectivel; L i the hical ath through the inhomogeneou lama G are comlicated function of i magnetized lama arameter and The nowledge of the correlation function of the hae taing into account that the obervation oint are aced aart at a ver mall ditance ρ { r r } erendicular to the rincile lane allow u to calculate the width of the atial ower ectrum in the XZ and YZ lane reectivel: <D > % - x W x x h W h <D > % - x x h (5) wave tructure function of the amlitude hae and mutual correlation function []: ( )( ) D ( r r ) < ( r )- ( r ) ( r )- ( r ) > ( ) D ( r r ) < ( r )- ( r ) > Dc ( r r ) ( D+ Re D) DS( r r ) ( D-Re D) Dc S Im D. (6) where: x rx h r.

3 Tranvere correlation function of a cattered field W ( ρ) < E( r) E ( r+ ρ ) > i [8]: EE ( ) W ( ρ ì é ) E ex Re ( ) ( ) EE í ê < >+< + > î r r ρ +< ( r) ( r+ ρ ) >+ < > ù û} ex( -ir ) (7) where E i the intenit of incident radiation. SS of cattered field in cae of incident lane wave W ( ) i eail calculated b Fourier tranformation from the tranveral correlation function of cattered field []: W( ) ò dr W ( r )ex( ir ). (8) - EE When the angular ectrum of an incident wave ha a finite width and it maximum coincide with z axi SS of cattered radiation i given: ò (9) - I( ) d W( )ex(- b ) where b characterize the dieral of an incident radiation (diorder of an incident radiation) i a tranvere comonent of the wavevector of cattered field []. Intenit of cintillation i determined b index S characterizing ower of a receiving ignal. The atial relationhi between the ower ectrum of the twodimenional fluctuating received ower ( ) S x L and the oberved ower ectrum of the hae fluctuation for a wea cattering medium i given b [] where x + % S( x ) % ( x )in () ç f L W L f / ( / ll) i the Frenel wavenumber. The inuoidal term in () i reonible for ocillation in the cintillation ectrum. For the cintillation level S (zeroth moment) we have: S d d % ( L). () ò ò - - æ x S x A cintillation ectrum with Frenel ocillation i interreted for both Gauian and ower-law wavenumber model. Equation () and () decribe two dimenional diffraction attern at the ground and alo illutrate the trong attenuation of the interference attern. If rigid irregularitie are moving at the ra ath along the Y direction with aarent velocit V the reultant temoral ectrum i given b a tri can integration along the X axi ( L ) d x W æ x n V L n % ò ç V æ n S( n L) ( n L)in ç n f The Frenel frequenc n f /. () V /( lz) i directl roortional to the drift velocit V tranvere to the radio ath and inverel roortional to the Frenel / radiu ( l z) z i the mean ditance between the oberver and the irregularitie. The intenit fluctuation are everel attenuated for irregularitie larger than thi radiu or frequencie le than the Frenel frequenc. The ocillation minimum aear with ratio : : 3 : Obervable ower ectra ( n L) allow u to calculate the ectral width ( t and quare root nd moment) which i a meaure of the cintillation rate. 3 Numerical calculation Numerical calculation are carried out for MHz ( 8 m - ) incident electromagnetic wave; Frenel radiu at the altitude 3 m i equal to.5 m. lama arameter are: u. v.33. We ue both Gauian and ower-law ectra. Aniotroic Gauian correlation function in the rincile YZ lane i [5] 3/ l l V% n( x z) n 8 æ x l l z l ex zl (3) ç where: - (in g + c co g ) [ + (- c ) in gco g / c ù û (in g + c co g )/ c 3 (- c )ingco g /c n i variance of electron denit fluctuation. Thi function contain aniotro factor of irregularitie c l / l (ratio of longitudinal and tranvere linear cale of lama irregularitie) and S

4 inclination angle g of rolate irregularitie with reect to the external magnetic field. Meaurement of atellite ignal arameter aing through ionoheric laer and meaurement aboard of atellite how that in F-region of the ionohere irregularitie ha the ower-law ectrum with different atial cale. We utilize 3D aniotroic ower-law ectrum of electron denit irregularitie. The correonding ectral function atial ower-law ectrum for > 3 ha the following form [5] N 5/ 5 ( 3) V% æ æ - é - ù n( x z) Gç G ç in ê ú û 3 l c é l ( ) ) x l ù z û / () The value of deend on the ecific condition of develoment of the turbulence in articular the intabilit roce involved the latitude the altitude and o on. A oberved b meaurement with atellite ETS- the ectral index i uuall between and [3]. Correlation function of the hae fluctuation caued b electron denit fluctuation for aniotroic Gauian correlation function (3) ha the following form x +R ( m + ) 5 ò ò ( d+ x ) - - W% ( x h L) W % d dx ìï é + í - T + + ïî x ( d3 d x ) ê c ( d + x ) d3 + d x ù ïü + 3 ex( ix x ih ) ú ý - - (5) d + x û ïþ where: x x % W5 T 5 B W c B TL n c T l d -R G m -R G d3 R ( R m -G m +R -3 G m -G ) m d R ( + ). Knowledge of thee function allow u to calculate wave tructure function and angle-of-arrival in the XZ lane uing (6): D ( x h L) W % T d dx + co( x + h) ò ò - - é T ù ex ê- ( m5 x + b6 x + b7) ú û where: + v é u u (-u) [ ] (6) W + - (ina - coa + u in a co a ) ù û WT W % B c m5 [( + m ) R +G ] G ( ) m6 + m 3 b7 + ( m + 3) + ( + m + 3m) b6 + m5m6 + 3m5. c Figure how the broadening of the SS veru aniotro factor c (left figure) for rolate electron denit irregularitie; characteritic longitudinal linear cale l m electromagnetic wave roagate with reect to the external magnetic field at the angle a. Numerical calculation how that maxima of the SS are at c 5 and c 6 in the XZ lane for g and g 3 reectivel. Increaing angle a maximum of the SS dilaced to the right c» 8 (for g 3 ) and not dilaced for g. The broadening of the SS of cattered ordinar and extraordinar wave aroximatel i the ame for L m. External magnetic field ha a ubtantial influence on the broadening of the SS and narrow in the rincile lane which i in agreement with [8]. Deformation of the SS deend on the angle a and the ditance travelling b electromagnetic wave in turbulent magnetized lama; excet the cae g (rolate irregularitie are tretched along the external magnetic field). lot of the hae wave tructure function D of cattered ordinar wave a a function of h for g are reented on the right figure in the 5 direction erendicular to the rincile lane. Numerical calculation how that maxima of the D function i at h 3 if g ; and at h 59 if g 5 ; hae wave tructure function tend to aturation at h 5.

5 Anali how that the angle-of-arrival in the XZ lane i in the interval.5. 5 ( 3) where: Q % æ æ - é in - ù Gç Gç ê ú û. Square of the cintillation index i roortional to the thicne of a laer and the root-mean-quare deviation of mall-cale electron denit irregularitie n which are reonible for ignal fading. From equation () (7) and () for the SS of ower-law correlation function of electron denit fluctuation in turbulent non-magnetized lama we obtain: æ W ( x h L) ç EE 3/ T v Q ex( - ihm) exç L E ç æ ç c G ç - ( + C ) - ( -)/ ì æ - æ cx í- G ç ò d + ç (8) î T ex( -ih) æ cx ü ï +F ý - +F ïþ ò d K ( )/ [ () - - ç ] [ () ] T where: T é 3 æ ù F ( ) ê + m + ç + m ú c û Figure. Broadening of the SS of cattered radiation in the XZ lane a a function of the arameter c at a and different angle of inclination of rolate irregularitie with reect to the external magnetic field g 3 (to figure). hae tructure function a a function of the ditance between obervation oint h at. c a for ( n L) (bottom figure). S Scintillation index S for ower-law correlation function in the YZ lane i given b % % S dx d 8W ( ) 5 Q x +R m + ò ò ( x + d) - - -/ ì ï é x + ( d x + d3) ùüï í+ T ê + úý ïî ê c ( x + d) úûïþ in él( x + ) ù û (7) Q Q% T C ( + c m c ) G ( x) i the gamma n 5/ function Kn ( x) i the McDonald function. Figure illutrate the evaluation of a ga in the SS of cattered ordinar wave in turbulent aniotroic colliionle non-magnetized lama with rolate irregularitie of electron denit fluctuation having characteritic longitudinal linear cale l m; ectral index i equal to 3.. Numerical calculation how that electromagnetic wave having arameter m.5 a b travelling ditance m in the ionohere broaden on 56% increaing aniotro factor of rolate irregularitie from c 5 u to 35. When the cattering i wea ocillation are oberved in the ower ectra. Thee ocillation are attributed to a Frenel filtering effect. Thee ocillation are ued to calculate the velocit etimate the irregularit cale ize aniotro factor and angle of inclination of rolate irregularitie with reect to the external magnetic field. The rate of ocillation i deendent on the irregularit velocit. The ower ectra

6 S ( n L) for the ordinar and extraordinar wave have different minima and allow u to calculate correonding f and n f. are obtained for arbitrar correlation function of electron denit fluctuation. Numerical calculation are carried out for both aniotroic Gauian and ower-law correlation function. New eculiaritie of the Doublehumed effect have been revealed firt time analticall in the SS of multile cattered high frequenc electromagnetic wave at oblique illumination of magnetized lama with rolate inhomogeneitie b mono-directed incident radiation uing the mooth erturbation method. It wa etablihed that the SS ha a double-eaed hae the location of it maximum weal varie and width ubtantiall broaden with increaing ditance travelling b electromagnetic wave in turbulent aniotroic magnetized lama. Aniotro factor and the angle of inclination of rolate irregularitie have a ubtantial influence on the ga of the SS. The ower ectra for the ordinar and extraordinar wave have different minima allowing determining the Frenel frequenc. The ower ectral anali of cintillation obervation offer a new and imortant method of analzing the mall-cale tructure in the ionohere. The obtained reult will have alication in communication acoutic at obervation of electromagnetic wave roagation in the uer atmohere and remote ening. Figure Deict SS of cattered ordinar wave veru for m.5 a b at fixed B 33 lama arameter: 3. l m and different aniotro factor c 5 35 (to figure); The ower ectra S ( n L) for the ordinar and extraordinar wave a a function of non-dimenional frequenc arameter n / n f at c 5 T 5 the bottom figure. Concluion a g are lotted on Second order tatitical moment of cattered radiation: correlation function of the hae fluctuation broadening of the SS angle-of-arrival and the cintillation index caued b electron denit variation 5 Reference [] Ihimaru A. Wave roagation and Scattering in Random Media Vol. Multile Scattering Turbulence Rough Surface and Remote Sening IEEE re icatawa New Jere USA 997. [] Rtov S. M. Yu. A. Kravtov and V. I. Tatarii rincile of Statitical Radiohic. vol.. Wave roagation Through Random Media. Berlin New Yor Sringer 989. [3] Gerhman B. N. L. M. Eruxhimov and Yu. Ya. Iahin Wav henomena in the Ionohere and Comic lama Mocow Naua 98 (in Ruian). [] Jandieri G. V. V. G. Gavrileno A. V. Saroin and V. G. Jandieri Some roertie of the angular ower ditribution of electromagnetic wave multil cattered in a colliional magnetized turbulent lama lama hic Reort Vol [5] Jandieri G. V. A. Ihimaru V. G. Jandieri A. G. Khantadze and Zh. M. Diaamidze Model comutation of angular ower ectra for

7 aniotroic abortive turbulent magnetized lama rogre In Electromagnetic Reearch IER Vol [6] Jandieri G. V. A. Ihimaru N. N. Zhuova T. N. Bzhalava and M. R. Diaamidze On the influence of fluctuation of the direction of an external magnetic field an hae and amlitude correlation function of cattered radiation b magnetized lama lab rogre In Electromagnetic Reearch B IER B Vol. B 3. [7] Jandieri G. V. A. Ihimaru and V. G. Jandieri Deolarization effect of incoherentl cattered electromagnetic wave b inhomogeneou magnetized lama lab Journal of Electromagnetic Anali and Alication Vol [8] Jandieri G.V. Ihimaru A. Mchedlihvili N.F. Taidze I.G. Satial ower ectrum of multile cattered ordinar and extraordinar wave in magnetized lama with electron denit fluctuation rogre In Electromagnetic Reearch M (IER M) Vol [9] Jandieri G.V Zhuova N.N. Diaamidze Zh.M Diaamidze M.R. Angular ower ectrum of cattered radiation in ionoheric lama with both electron denit and magnetic field fluctuation WORLDCOM (The World Congre in Comuter Science Comuter Engineering and Alied Comuting) CSC (the 9th International Conference of Scientific Comuting): Numerical method Aroximation and etimation technique Otimization method Jul 6-9 La Vega Nevada USA 39. [] Jandieri G.V. Ihimaru A. Mchedlihvili N.F. Angular ower ectrum of cattered electromagnetic wave in randoml inhomogeneou lama with electron denit fluctuation ISA ( International Smoium on Antenna and roagation) October 9-November Nagoa Jaan [] Ginzburg V. L. roagation of Electromagnetic Wave in lama. New Yor: Gordon and Beach 96. [] Rufenach C.L. A radio cintillation method of etimating the mall-cale tructure in the ionohere J. Atmoh. Terr. h. Vol [3] Afraimovich E.L. Zherebtov G.A. Zverzdin V.N. Frane S.J. Characteritic of mall-cale ionoheric irregularitie a deduced from cintillation obervation of radio ignal from atellite ETS- and olar Bear at Irut Radio Sci. Vol. 9 No