Indian Journal of Radio & Space Physics Vol. 1, June 1971, pp. 192·194 Dependence of Whistler Activity on Geomagnetic Latitude* MANORAN]AN RAO. LALMANI, V. V. SOMAYA]ULU & B. A. P. TANTRY Electronics & Radio Physics Laboratory, Department of Physics, Banaras Hindu University, Varanasi 5 ManuscriPt received 16 March 1972 It is shown that the couplin~ between the ordinary and extraordinary magneto-ionic waves in the lower ionospheric regions should also be considered as one of the factors which control the dependence of whistler activity on the ~eoma~netic latitude. Introduction In this communication we wish to point out that the coupling between the ordmary and extraordi• nafY magneto-ionic waves in the lOWEr ionsphelic latitudinal variation of the whi:;tler occur• layers siouid also ie considered as one of the factors OUR knowledge of the diurnal, seasonal and rence is derived mainly from the synoptic which control the dependence vf whistler activity observations made at a chain of stations under on the geomagnetic latitude. We also show t.rat the whistler-eastl and whistler-west .networks2,3 the dependmce of the coupling parameter 011 the during the IGY and IGC periods. An important latitude satisfaCtorily exphJins the observed whistler feature of the latitudinal variation of the whistlel activity. Towards this end ",e first derive the ex• activity if:: the high whistler rate occurrence ob· pression for the coupling parameter following the selVed at high geomagnetic latitudes in contrast to treatment given by Budden9 and tben briefly dis• the low rate at low geomagnetic latitudes4•5• A cuss the physical mechanism of the coupling pheno• part of the observed latitudinal variaticn in wbistlEr menon. Tbis is followed by some numerical cal• activity probably results from the difference in tbe culations, the results of which are discussed in the equiprrJents and in the local noise levels. On the last section. otber hand. the major part of the 'Variation should be attrituted to, or interpreted in terms of: (i) tbe The Coupling Parameter glObal morphology of the tbWlderstorm occurrence Mode couplin!! in the ionosphere can be described and (ii) the conditions conducive to the whistltr by using Forsterling's coupled equations for vertical mode propagation below, througt and ahove the incidence in an inhomogeneous anisotropic medium9: ionosphere6• Though we know trat lightning dis• charges dre almost non-existent in Arctic and An• tarctic regions v,hile being quite prevalent in F~+Fo(n2+1ji2)F:+Fx(n;+1ji2) = Iji'Fx+2IjiF~}Iji'Fo+2IjiF; ...(1 ) tropics?, the meagreness of the world.vide data for• where Fo and Fx are proportional to fields in the bids us to attempt an acceptable interpretation of tbe ordinary and extraordinary modes respectively. the latitudinal dependence of the whistler activity in terms of thundtrstorrn occurrence. Thus, most The prime denotes ~. where nc6.l is the wave• of the attempted explanations of the latitude-wise 0: k= occurrence of whistlers consider mainly the condi• number, z is the vertical coordinate; no and nx are tions that are important fortrapping and propagation refractive indices for 0 and x modes and Iji is the of whistler mode signals. For example, Helliwel13 coupling parameter - so called because when Iji attributES the high level of '\\histler lates observed = 0 the equations are independent and the two within a broad lCmge of hish latitudes centred modes propagate independently. If Iji# 0, the equa• around 500 geomagnetic north to: (i) the reduced tions are coupled and there is an interaction between level of atmosphEric noise, (ii) the tendency of whist• the modes. The parameter Iji is dven by lers to propagate a\\-ay from the equator after exiting from the duct, and (iii) the low enhance• Iji Po Px ... (2) = P2_1o = P2_1x mEtlts of ionization required to trap the whistler energy in the ducts. TI- e decrease in whistler acti• where P is the polarization defined in terms of the vity at very high latitudes ~700N) is attributed components of the electric field which lie in the to the low thunderstorm activity and to the low wavefront. Tbe polarization equation of the mag• gyrofrequEncies, encountered at the top of the neto-ionic theory is given by whistler paths, which make trapping in the crests of enpanced ionization very difficu1t8. Further, ac• cording to He1liwe1l3, the coupling of whistler energy Po,x= 2Ydl-X-iZ)±iiy2 [ 4Yi(1-;-iZ)2+1y4 ] ...(3) into and Gut of ducts of enhanced ionization is most ",here we pave followed the notation recommended favourable whel1 tre source (or receiver) is located by URSI (see Ratcliffe10). on the high latitude side of the ducts. From relations (3) and (2) we get *Paper presented to the Physics Section of the 59th tiYfYL . Session of the Indian Science Congress, held at Calcutta in ~= /1 "'{T _·J"7\'lTT?' 'I,..,.&' (X'-tZ') ... (4) February 1972. 192 RAO et al.: DEPENDENCE OF WHISTLER ACTIVITY ON GEOMAG. LATITUDE "WHISTLER" Eq. (3)&hows that if Z = 0 both values ot Pare MODE purely imaginary. The condition that the two solu,. X tions of Eq. (3) shall be equal is X-I+Y -'- ---- Y}++Yf(1-X-iZ)2 = 0 •.. (5) ---- II when X and Z are real, and Eq. (5) is satisfied I only if / I?fo Yi• I; ... (6) / \ I X .= 1 and Z = Zc = 2YL I\ I The second condition can also be written as ,,, &in26 ... (7) lx v = Vc= (i)H'--6cos , )(-0 +-- where Vc is known as the critical collision frequency, I CJ)H is the gyrofrequency and 6 is the angle between , the wave normal and the magnetic field. The con· I dition (6) is known as tbe critical coupling condi• I tion since it makes IJI in Ielation (4) tend to infinity. 0'" ~lC In the vlf range and for the generally accepted "INCIDENT WAVE" _ -V- models of electron density and collision frequency -MAIN" ECHO in the lower ionosphere, the critical condition given Fig. 2 - Schematic representation of the reflection of vlf in (6) is never satbfied and "Wealways get finite waves including the possible effects of coupling value& of IJI. Some Numerical Results and Discussion of the coupling phenomenon iil relation to the Given the electron density and collision frequency whistler mode of propagation. In the usual theory profile3, the coupling parameter IIJII can be calcu• of whistlers, very low frequency (vlf) wave propa~ lated from (4) at all hei1:)hts for variou~ latitudes. gat ion in a homogeneoui'>ionized medium permeated Since IIJII show!;a peak usually around X = llevel9, by a static magnetic field i!>consideled. ,The a&• it would be sufficient, for our pre&ent purpose to sumption of homogeneity of the medium ib jqstified demonstrate how this peak value varies "With the latitude. To do this, we have considered the elec• only in the magnetosphere, wbere the paIam€.ters of tbe medium are belie"ed to vary sufficiently tIon density (night-time) and collision frequencv slowly in the space of one wavelength. HOweveI, profilei'>used by Ilelliwtll3 and nave evaluated Ilji I in the lowel ionosphere, the parameters of, the at X - 1 for various latitudes for a frequency of medium change very rapidly and hence the propa• 10 kHz. The result& are shown in Fig. 1. The gation of vlf wave&in an inhomogeneous medium, shaded area in this figure shows regions wheie must be considered. Thelefore, it -i&no longer pos~ quasi-Iongitud,inal conditions do not prevail. The sible to consider a vlf wave as' a purely'progx:essive height scale for the &haded area is shown on wave, for each point in the mediUm gives ri8e to a, the right hand side of Fig. 1. It must be remem• forward and a backward wave, and these must be bered that the heights sho"n in the figure have no cOnsidered in describing the propagation. ,Further, relevance for th e coupling para meter Ilji I. the two magneto-ionic "aves no longer propagate Before discussing the &ingnificance of Fig. 1, we indepmdently and we mu:,t consider coupliJlg not shall now hriefly dwell on the physical significance only between the magneto-ionic waves tut also be• tween the progressive wave of one component and the backw&.ld wave of the other. '-10 kHz Following Belrosell, a &chematic representation of the reflection of vlf waves including the, possible 90 effects of coupling is pIesented in Fig. 2. At the bottom of the ionosphere (X=0) the two dr• culary polarized 0- and x-components travel in• \ dependently at different speeds. At the 1e"el ,of coupling, the upgoing x-wave gives ri~ to a back• scattered o-wave. The progresshe x-wave is the whistler mode vlf wave·. Similarly, the upgoing o-wave gives rise to a back-scattered x-wave. These 70 back-scattered 0- and x-waves combine to produce a 'coupling echo' and the polarization of 'the coupling echo' would be fairly constant since the amplitudes of the back-scattered 0- and x-waves should be in proportion. However, the amplitude 60 90 of the coupling echo depends on how clo&ely the .Some authors, e.g. Budden', define the progressive 0• Fig. 1-Latitudinal variation (evaluated) of IIjII[f= 10 kHz wave as the whistler mode. This change in notation does and X=l] not, however, affect our argument. INDIAN J. RADIO SPACE PHYS., VOL. 1, JUNE 1972 x = 1 level coincides with the level '1= Vc' When (geomagnetic), although our explanation ]s over• these two levels are very close, the 'coupling echo' simplified. is strong and there will be very little energy left in Conclusion the progressive x-wave to proceed in the whistler mode.