EFFECTS IONS IONOSPHERIC REFLECTION COEFFICIENTS FOR VLF RADIO WAVES.

Transcription

1 Title EFFECTS IONS IONOSPHERIC REFLECTION COEFFICIENTS FOR VLF RADIO WAVES Author(s) ARAKI, Tohru Citation Contributions of the Geophysial In (1971), 11: 1-10 Issue Date URL Right Type Departmental Bulletin Paper Textversion publisher Kyoto University

2 Contributions, Geophysial Institute, Kyoto University, No. 11, 1971, 1-10 EFFECTS OF IONS ON IONOSPHERIC REFLECTION COEFFICIENTS FOR VLF RADIO WAVES By Tohru ARAKI (Reeived September 16, 1971) Abstrat Effets of positive ions on the ionospheri refletion oeffiients for very low frequeny radio waves are examined with speial attention to the lower hybrid resonane in whih ions play the prinipal role. The ionosphere is assumed to be uniform and sharply bounded and impressed with a horizontal stati magneti field. The refletion oeffiients are alulated for VLF radio waves whih are inident perpendiularly to the stati magneti field with their eletri field in the plane of inidene. It is shown that ions should be taken into onsideration on the nighttime refletion oeffiients for grazing inidene. 1. Introdution Round, Ekersley, Tremellen and Lunnon (1925) examined the results of the field strength measurements of VLF radio waves propagating in the earth-ionosphere wave-guide and suggested that VLF radio waves suffered less attenuation if they were propagated from west to east instead of from east to west. Crombie (1958) re-examined the results of Ro4nd et al. in addition to his own observations and onluded that the evidene strongly supported their suggestion. In order to interpret this non-reiproal property of VLF radio wave propagation, Barber and Crombie (1959) alulated the refletion oeffiient for VLF radio waves whih are inident perpendiularly to the horizontal magneti field on a sharply bounded ionosphere and found that the refletion oeffiient for waves inident from the west, is greater than that for waves inident from the east, when the angle of inidene is large and the wave eletri field is in the plane of inidene. Though there are several kinds of ions in the ionosphere Barber et al. (1959) onsidered eletrons only as harged partiles. It is well known (Stix, 1960) that for waves propagating perpendiularly to the magneti field in the plasma the lower hybrid resonane ours for whih ions play an essential role. Though this resonane would be smeared beause of ollisions with neutral partiles dominant in the lower ionosphere from whih VLF radio waves are refleted, it is important to estimate the effets of this resonane on VLF refletion oeffiients. In setion 2 of this paper, general expression for ondutivity tensor is derived

3 2 T. ARAKI taking into onsideration the presene of eletrons, ions, and neutral partiles and their mutual ollisions. By the use of this general ondutivity tensor, the refletion oeffiients from sharply bounded ionosphere are alulated for VLF radio waves propagating perpendiularly to the horizontal magneti field in setion 3. The results of numerial alulation of refletion oeffiients are presented in setion 4 and disussed in setion Condutivity Tensor in Partly Ionized Plasma We onsider a partly ionized old plasma whih is omposed of eletrons of harge -e, positive ions of harge Ze and neutral partiles and immersed in the stati magneti fields B 0. Equations of motion for three partiles are (in CGS Gaussian Unit) dv. e v. ~d-=--( +- 1\ Bo)- Vet (Ve- V,)- Ven (Ve- Vn), t me dvt Ze Vt ~d-=-( +- 1\ Bo)- Vte (Vt- Ve)- Vin (Vt- Vn), (1) t m, dvn dt- = - Vni (Vn- Vt)- Vne (Vn- Ve), where Ve,i,n and me,i," are veloity and mass of the three partiles and E is the eletri field and v,~ is effetive ollision frequeny for momentum transfer of partile a to partile S. Sine there is no loss of total momentum in ollisions among the partiles, (2) Here the stati magneti field B 0 is taken to be parallel to x-axis and harmoni time variation e-iwt is assumed. After linearization of equation (I) and elimination of V., we reah following equations, (3) where ex is a unit vetor of x-diretion and C1= f, {n - Vtn Vnt rn 7r rn - Ven Vne rn (4)

4 IONOSPHERIC REFLECTION COEFFICIENTS 3 C - rn re + lint lien 3- ' rn ( re = liet + lien - ~(1), r; = Ji,. + litn - l(j), Tn =.Vnr + Vnl! - iw, em. ~~e- ' n -~)!2t = ZeBo mt, In the derivation of equations (3) and (4), equation (2) and a relation of harge neutrality, n.=zn; are used. From equation (3), three omponent of v. and V; are derived as a funtion of E, and urrent J is alulated as follows; ZD6- D4 ix =en. (Vtx- V.x) = en - -D -Ex /y =en. (V;y- Vey) =en I ' [(D1+D3) (ZD6-D4)+Dz Ds (Z-1)] Ey+[Ds (D1+D3) (Z-I)-Dz(ZD6-D4)] Ez J J z = en. ( V; z - V e z) == en. (5) [ -Ds(DI +D3) (Z-l)+Dz(ZD6-D4)] Ey+[(DI +D3)(ZD 6~I!_4)+D2_}-Js(Z- I )]J, where J D - Q, Q, 3-3 ' D 4 = e Zm. C 3 - mt C 1 mtmec3 ' (6) m = m. J m;. Generally urrent J is given by a produt of a ondutivity tensor [O"] and an eletri field vetor E ( 0"11, 0, 0 l (Ex l J=[O"] E= O,O"_i,O"H EY 0,-0"R>O" _j_, (7)

5 4 T. ARAKI By omparison of equation (5) and (7), elements of the ondutivity tensor are given by (J 11 = ene (J-'- = ene ZD6- D4 D1 (D1 + D3) (ZD6 - D4) + D2 Ds (Z- 1) j D 5 (D1 + D3) (Z- 1) -D2 (ZD6- D4) j (8) 3. Refletion Coeffiients. We onsider a situation that in a half spae z>o, there is a uniform ionosphere having a horizontal magneti field in x-diretion. This ionosphere is haraterized by the ondutivity tensor (7). We derive a refletion oeffiient for a plane eletromagneti wave inident from below perpendiularly to the magneti field on a sharp boundary at z=o. A set of governing equations for this problem is 1 ab r 1\ E =- -- at' I ae p 1\ B = 4nJ + -- a/-, (10) The inident and refleted waves below the boundary (z=o) and the transmitted waves above it an all be assumed to vary with spae and time in a manner exp (ky y + kz z - wt). (11) By substituting equation (11) into (10), the following omponent equations are obtained, (1) kyt E z - kzt E z = - Bx, (1) kztex=-by, (1) - k, 1 Ex = -- Bz, (1) ky, B, - k,, By =- - - CEx, (1) (1) kztbx =- -AEY- -BEz, (12-1) (12-2) (12-3) (12-4) (12-5)

6 IONOSPHERIC REFLECTION COEFFICIENTS 5 where a) a) -k.v,bx=~be.v-~aez, A= i_±:co"j_ + 1, a) C=i~nO"u +1, a). 4nO"H B = z----, a) (12-6) and suffix t denote a transmitted waves. It is evident from equations (12-1)-(12-6) that two modes of waves are de-oupled in this ase. Equations (12-1), (12-5) and (12-6) show waves with a transverse magneti field (TM-wave) and equations (12-2), (12-3) and (12-4) show waves with a transverse eletri field. The latter is independent of the stati magneti field and exluded from present onsideration. From the former, refrative index in the ionosphere is obtained,, n2 = 2 (k.v,2 + k::_2) w2 A2 + B2 ----~~- A (13) Eletromagneti field in a half spae z<o is determined by equation (10) putting O" 1, = O" j_ = O" H = 0. If suffies i and r are used to express inident and refleted waves, bounddary onditions at z=o are given by Ey, + E.vr = E.v,, Bxi + Bxr = Bxt. (14) By the use of equation (10), (12), (14) and relation k.v;=k.vr=k.vt and kzr= -kz,, the refletion oeffiient at the boundary z=o for TM-wave is obtained as Bxr IIRII=-B xi (An 2 - B) k.v; + An 2 kz1 - kzt A (An 2 - B) k.v; - An 2 kz1 - kz1 A. (15) For a given angle of inidene(}, and frequeny w, k.v,, kz1 and kzt are determined by k a) 0 y; = --- Sill(};, a) k z i = -- COS (}I ' (16) kzt = ( ~~- n2- k.v 12) Y2. 4. Numerial Results We onsider NO+ as positive ions and the stati magneti field is taken to be 0.3 Gauss with the value at the equator in mind. In the lower ionosphere, eletron-ion (or ion-eletron) ollision an be negleted in omparison with eletron-neutral (or

7 6 T. ARAKI ion-neutral) ollision beause of dominant neutral partiles. For the same reason, neutral partiles an be onsidered to be unmoved. Therefore, ve1, v,e, Vne and vn, may be put to zero. lf to' :'.: Imk(el/ /Imk(e i).. --::> / 10 _./ w (rod.se- 1 ) I / 10' 10' "'VV 10~ Fig. l. Frequeny dependene of the real part of the refrative index (solid line) and the imaginary part of wave number (dotted line) for a wave propagating perpendiularly to a stati magneti field in a partly ionized plasma. The wave eletri field is assumed to be perpendiular to the stati magneti field. Letters, e and e+i, in the braket show that effets of eletrons only and of eletrons and ions are taken into onsideration, respetively. - w{rodse"') 10' 10' Fig. 2. Frequeny dependene of a ratio ' of the refrative index with onsideration for ions (n (e+i)) to that without ions (n (e)). The lower hybrid resonane frequeny is shown by ''JLH on the absissa. Calulated results of the real part of the refrative index and the imaginary part of the wave number in the ionosphere are shown in Figure 1. The ollision frequeny is taken to be 10 5 se- 1 for eletrons and 10 3 se- 1 for ions and eletron density to be 10 3 m- 3 Figure 2 shows a frequeny dependene of a ratio of the refrative index with onsideration for ions, n(e+i), to that without ions, n(e). It is evident that the ratio for the real part of the refrative index has a lear peak at the lower hybrid resonane frequeny and this peak beomes sharp as eletron density dereases. Figure 2 also shows a general tendeny that ions redue the refrative index at lower frequeny, though they do not play an important role in higher frequeny.

8 IONOSPHERIC REFLECTION COEFFICIENTS 7 uj 10 4 rod se"' 1 ~~~----~e~-=~~ e +i I,R,I 08 10~-----e~-===~~ e+i IOn,one _e e+l ne=i04m 3 e+l Q Cl' 3() 6CI' e, w = 10 5 rod se"' ne =I O'm' 9CI' Cf 3Cf 6CI' 9CI' (1' o 9; 9; w = 10 6 rod se"' 10 ne = 10 4 m" 3 \,,R"I (e = e+ i)! ( e = e + i) 0.5 o e, e, Fig. 3. Modulus of the refletion oeffiients for the angle of inidene. The solid line shows the ase that the waves inident on the sharply bounded ionosphere with a horizontal stati magneti field from east to west and the dotted line shows inidene from west to east.

9 8 T. ARAKI 10[?\Z[~"""!,. /-- ' oa I.. R I..,.. J../ " "10 em 10' 10, 10' 10' w (red se ) Fig. 4. Frequeny dependene of the modulus of the refletion oeffiients for the grazing inidene. The solid line shows refletion from east to west and the dotted line the refletion from west to east. The vertial dotted line shows the lower hybrid resonane frequeny. Re n!e 11 ~ "~" 1o' CITf' lm nle il ::~mnlel 10 1 ~\ -, 05 "'(rod sec) Fig. 5. Frequeny dependene of a ratio of a refrative index with onsideration for ions (n (e+i)) to that without ions (n (e)). The lower hybrid resonane frequeny is shown by "'LH on the absissa. 10' Fig. 6. Frequeny dependene of the modulus of the refletion oeffiients for the grazing inidene. The solid line shows refletion from east to west and the dotted line shows the refletion from west to east. The vertial dotted line shows the lower hybrid resonane frequeny "'Lrr-

10 IONOSPHERIC REFLECTION COEFFICIENTS 9 Figure 3 shows the modulus of the refletion oeffiients for the TM-wave, 1 11 R 11 1, alulated from eq. (15). From this figure, we an see that ions make \ 11 R 11 : smaller than when eletrons only is taken into onsideration. This tendeny is notable for the grazing inidene in the neighbourhood of the lower hydrid resonane frequeny. The frequeny dependene of 1 11 R 11 I for the grazing inidene (8,=89 ) are shown in Figure 4. It should be noted that a differene between I,, R 11! and 1 11 R 11 I +' beomes marked at frequenies lower than the lower hybrid resonane frequeny. The ratio n(e -H)/n(e) for (v., v,) = (10 5, 10 4 ) se- 1 is shown in Figure 5. In this ase the peak of Re n(e+i)/re n(e) broadens beause the lower hybrid resonane is smeared by inreased ollisions for ions. Therefore, effets of ions on refletion oeffiients beome small exept for the grazing inidene. The modulus of the refletion oeffiients is plotted versus frequenies in Figure 6. It is interesting that 1 11 R,,I +' is different from 11 R 11 le at the both sides of the lower hybrid frequeny in ontrast to the previous ase (Fig. 4). 5. Disussions VLF radio waves propagating obliquely in the earth-ionosphere wave-guide is onsidered to be refleted at the height of 70km in daytime and 90km in nighttime. The ollision frequeny at 70 km height is of the order of 10 6 for eletrons and 10 5 for ions (for example, Belrose et al. (1964)). Calulations for these values of ollision frequeny show that the refrative index n(e+i) is nearly equal to n(e) at any frequenies. So it may be said that the presene of ions does not affet daytime propagation of VLF radio waves. At nighttime refletion level (90km), the order of the ollision frequeny is 10 5 for eletrons and 10 4 for ions. In this ase, presene of ions hange the values of the refletion oeffiients at least for the grazing inidene at the neighbourhood of the lower hybrid resonane frequeny as evident from figure 6. ELF radio waves whih have longer wave-length may penetrate deep into the ionosphere without fatal attenuation where ollision frequeny is smaller than the lower region. Figure 1-6 suggest that the frequeny range in whih ions play an important role extends to lower frequeny as the ollision frequeny beomes smaller. Therefore, ELF radio waves propagating perpendiularly to the geomagneti meridian might be affeted by ions but assumptions used here (sharp boundary and homogenous ionosphere) limit further disussion. In order to make onsideration for waves with greater wave-length, it is neessary to solve a wave equation in an inhomogeneous ionosphere. In onlusion it is said that ions should be taken into onsideration on the nighttime refletion oeffiients for grazing inidene of VLF radio waves. The author is indebted to Professor Susumu Kato, Ionosphere Researh Laboratory, Kyoto University and Professors Ken-ihi Maeda and lwane Kimura, Department of Eletronis, Kyoto University, for drawing their attention to this problem.

11 10 T. ARAKI Referenes Barber, N. F. and D. D. Crombie, 1959; V. L. F. refletions from the ionosphere in the presene of a transverse magneti field, J. Atmosph. Terr. Phys., 16, Belrose, J. S. and M. J. Burke, 1964; Study of the lower ionosphere using partial refletion, J. Geophys. Res., 69, Crombie, D. D., 1958 ; Differenes between the east-west and west-east propagation of VLF signals over long distanes, J. Atmosph. Terr. Phys., 12, Round, H. J., T. L. Ekersley, K. Tremellen and F. C. Lunnon, 1925 ; Report on measurements made on signal strength at great distanes during 1922 and 1923 by an expedition sent to Australia, J. lnst. Ele. Engrs, 63, Stix, T. H., 1962; The theory of plasma waves, MGraw-Hill, New York, 283 pp.