Disruption of reciprocity principle during daytime propagation of superlong radio waves around eart

Baybulatov, R. B.

Krasnushkin, P. E.

English

NASA Technical Reports Server

National Aeronautics and Space Administration 
Goddard Space Flight Center 
Contract No.NAS-5-12487 
ST -RWP -AM -MAT -10717 
ON THE DISRUPTION OF THE RECIPROCITY PRINCIPLE 
DURING THE DAYTIME PROPAGATION OF SUPER LONG RADIOWAVES 
AROUND THE EARTH 
GPO PRICE $ 
CFSTI PRICE(S) $ 
Hard copy (HC) 3=@ 
P. E. Krasnushkin 
R. B. Baybulatov 
Microfiche (MF) I 4 5 -  
ff 653 July 65 
.. 3 6 I 
(USSR) 
24 MAY 1968 
.. _ _  
, 
https://ntrs.nasa.gov/search.jsp?R=19680016172 2020-03-12T10:55:34+00:00Z
ST -RWP -AM -MAT 10717 
ON-THE- DISRUPTION OF THE RECIPROCITY PRINCIPLE 
DURING THE DAYTIME PROPAGATION OF SUPER LONG RADIOWAVES 
T H E - W T H  
Doklady A.N. SSSR, 
Geof izika 
Tom 1 7 1 ,  No.2, 340 - 343  
I z d a t e l ' s t v o  "NALJKA", 1966 
by P. E .  Krasnushkin 
& R. B. Baybulatov 
SUMMARY 
The d i s r u p t i o n  of t h e  r e c i p r o c i t y  p r i n c i p l e  dur ing  t h e  daytime propaga- 
t i o n  of super-long radiowaves around t h e  Ea r th  is  d iscussed  on t h e  b a s i s  of  
t h e  so  c a l l e d  va lve  effect  t ak ing  p l a c e  i n  daytime ,near  t h e  e q u a t o r i a l  reg ion .  
A s  i n  t h e  preceding  work on t h e  genera l  boundary va lue  problem, t h e  p r i n c i p a l  
a u t h o r  bases  t h i s  work on ear l ie r  ones,  mostly by h imsel f .  However, h e r e  some 
problems of  aeronomy are involved. 
* 
* *  
1. Experiments [l - 41 have e s t a b l i s h e d  t h a t  t h e  damping of super-long 
Th i s ,  s o  c a l l e d  ' 'valve e f f e c t ' '  is p a r t i c u l a r l y  g r e a t  i n  
waves ( s l w )  on courses  proceeding from east t o  w e s t  is  g r e a t e r  than  i n  t h e  
o p p o s i t e  d i r e c t i o n .  
dayt ime cour ses ,  c l o s e  t o  t h e  geomagnetic equator .  
a n i s o t r o p y  [5 - 81 and a l s o  by the  magnetized t r a n s v e r s e  magnetic f i e l d ,  ana la-  
gous ly  t o  t h e  va lve  e f f e c t  t ak ing  p l a c e  i n  shf-waveguides wi th  f e r r i t e  [9]. 
I n  the waveguide theory of s . 1 . w .  i t  w a s  d i s r ega rded  [ L O - 1 2 1 .  Th i s ,  however, 
may b e  done i n  a n a t u r a l  f a sh ion  i f  du r ing  t h e  c a l c u l a t i o n  of ionosphere impe- 
dances by t h e  method of [13], e n t e r i n g  i n t o  t h e  equa t ions  f o r  wave numbers 
of  normal waves, w e  t ake  i n t o  account no t  only t h e  v e r t i c a l  component of t h e  
E a r t h ' s  magnetic f i e l d  H r ,  but  a l s o  t h e  h o r i z o n t a l  ones,  He (a long t h e  course)  
and H+, ( ac ross  i t ) .  The s c a r c e  da ta  on t h e  va lve  e f f e c t  i n  s.h.w. do n o t  per- 
m i t  t h e  a p p l i c a t i o n  of t h e  method of d a t a  coord ina t ion  on t h e  f i e l d  and t h e  
medium - 121. This  is why we s h a l l  t a k e  fer a f i r s t  approximation t he  pro- 
f i l e s  of e l e c t r o n  concen t r a t ion  Ne(h) and t h e  c o l l i s i o n  f requencies  V e f f ( h ) ,  
o b t a i n e d  wi thout  t ak ing  i n t o  account t h e  valve e f f e c t ,  co r rec t ed  f o r  t h e  equa- 
t o r i a l  zone by aeronomical c a l c u l a t i o n s  [14]  by in t roducing  them concomitant ly  
w i t h  H e ,  H+ and Hr i n t o  t h e  tensor  of ionosphere d i e l e c t r i c  cons t an t  (E). 
I t  is  caused by ionosphere 
(*) 0 NARUSHENII PRINTSIPA VZAIMNOSTI P R I  RASPROSTRANENII SVERJLHDLINNYKH 
U D I O V O L N V O K R U G  ZmI V DNEVNOYE VREMYA 
The components of t e n s o r  Ejk ( i ,  j, k being t h e  o r t s  w i th  r e s p e c t  t o  8 ,@ and r )  
are 
where u = 4nNe(h)e2/mo2; Z = 1 + iveff(h)  l o ;  Uj = - e H j / m c o ,  3 is  o r t  8 ((I o r  r) , 
6 = Uii + Ujj + Ukk; Ujk iS  t h e  p r o j e c t i o n  of 6 on t h e  p l ane  wi th  o r t s  j ,  k ;  t h e  
s i g n  + is taken whgn i, j i n  ~ i j  s t a n d  i n  t h e  o r d e r  9, $, r; He, H 
t h e  components of Ho i n  a system of coord ina te s  lir,ked wi th  t h e  course of t h e  
wave: i t s  o r i g i n  i s  on t h e  p o l a r  a x i s .  
and H r  are 
4j 
2 .  For a course proceeding along t h e  geomagnetic equa to r ,  only He is n o t  
z e r o  and t h e  system of Maxwellian equa t ions  f o r  t h e  ionosphere ( 4 )  of [13]  
b reaks  up i n t o  pu re ly  TH- and purely TE-waves.  
t o  us t h e  impedance Eq. (9) of [ 1 3 ]  assumes t h e  simple form: 
For t h e  TH-waves of i n t e r e s t  
where A = &eo2+ &erz, The las t  term of (2 )  i s  r e s p o n s i b l e  f o r  t h e  d i s r u p t i o n  of 
t h e  r e c i p r o c i t y  p r i n c i p l e  and t h e  va lve  e f f e c t  l i nked  wi th  i t .  I n t e g r a t i o n  of 
( 2 )  over  L from rm = c + h,, where 2 assumes t h e  a d i a b a t i c  va lue  
e t o  t h e  p o i n t  r = c ,  where u ( c )  gives  t h e  impedance Zy 
t h e  equa t ion  
= i u ( c ) / k ,  e n t e r i n g  i n  
of which t h e  r o o t s  are t h e  wave numbers of type-TH normal waves. It is ob ta in -  
ed from (14) of [13] on t h e  condi t ion t h a t  Xe = 0. The e x c i t a t i o n  c o e f f i c i e n t s  
are determined from formula (13) of [12] .  
3 .  We s h a l l  demonstrate t h a t  t h e  c a l c u l a t i o n  of TH-wave parameters  f o r  any 
daytime courses  on Ea r th  may be conducted w i t h  s u f f i c i e n t  p r e c i s i o n  u s i n g  f o r -  
mulas of t h e  preceding s e c t i o n  2 .  To t h a t  e f f e c t  w e  s h a l l  break down t h e  in-  
t e g r a t i o n  i n t e r v a l  ( r m , c )  of Eqs.(9) of 1131 i n  two : (r,,d) where t h e  a d i a b a t i c  
approximation and ( d , c ) ,  where s to rage  of radiowave r e f l e c t i o n s  t a k e s  p l a c e ,  
are v a l i d .  
of Eq.(9) from [13]  w i t h  t h a t  of t h e  a d i a b a t i c  approximation U(r)  of Eq.(lO) of 
r e f .  [ I31  ; r = d depends on v ,  80 and oti p r o f i l e s  of Xe(h) and Vef f (h ) .  
c a l l  t h e  Ne(h) p r o f i l e  as d i u r n a l  i f  f o r  v near ka 
d i t i o n  Z(d) > U is  s a t i s f i e d .  On t h e  s t r e n g t h  of a d i a b a t i c i t y  of ( r m , d ) ,  w e  
s h a l l  t r a n s f e r  t h e  o r i g i n  of  i n t e g r a t i o n  from roD t o  A. Eq.(lO] of [13] ,  d e t e r -  
mining G(d) i s  approximated by a b i q u a d r a t i c  equa t ion  when t h e  d i u r n a l  p r o f i l e  
c o n d i t i o n  i s  f u l f i l l e d .  One of i t s  r o o t s  c o i n c i d e s  wi th  ue, determinable  from 
(3) a t  r = d. 
The p o i n t  r = d may be def ined by comparison of hodograph of u(r) 
we s h a l l  + 
and any IHo I Q 0.5 oe t h e  con- 
3 
Since  t h e  p r o f i l e  of V e f f  has t h e  form 
(5) veff = ~010s exp [-0,148 ( h  - 89)], 
where S O  = 5 - 10 ,  h = r - a i n  km, i t  fo l lows  t h a t  f o r  Z(d) > U t h i s  inequa- 
l i t y  i s  a l s o  f u l f i l l e d  f o r  a l l  r < d. 
impedances Zye of TH-waves a t  any H e ,  H+ and H r  \< 0.5 oe  is  approxmiated by 
( 2 ) .  Confirmation of  t h i s  important r e s u l t  s imp l i fy ing  t h e  c o r r e c t i o n  of t h e  
theory  [ l o  - 121, is given i n  Fig.1,  where hodographs u ( r ) ,  ob ta ined  by i n t e -  
g r a t i o n  of (9)  from r e f . [ l 3 ]  f o r  f = 1 5  khz, v = 2000 are p l o t t e d  f o r  t h e  pro- 
f i l e  of  Ne(h) of  middle l a t i t u d e s  (curve 1 of F ig .1) .  S u b s t i t u t i n g  Ne(h) and 
dograph u ( r )  may b e  represented  by 
jump a t  each  s t e p  
r e f .  [13]  
By v i r t u e  of t h i s ,  Eq,(9)  of [13] f o r  
u e f f ( h )  by echelon p r o f i l e s  w i th  jumps a t  p o i n t s  ho, h l ,  ..., h,,  h,+l,hd ho- piecewise-continuous curve undergoing a 
h, a s s u r i n g  t h e  c o n t i n u i t y  of Zye according t o  E q . ( l l )  of 
Between s t e p s ,  t h e  
hodograph moves along a 
c i rcumference ,  of which 
t h e  r a d i u s  depends on 
t h e  s t o r e d  r e f l e c t i o n  
f a c t o r  i n  t h e  ove r ly ing  
l a y e r s .  Hodograph A is  
cons t ruc t ed  f o r  H e  = ll+ = 0 
and H r  = 0,445 oe. 
graph B i s  p l o t t e d  f o r  
iie = = ti, = 0. Accord 
i n g  t o  t h e  aforementioned 
c o n s i d e r a t i o n s ,  t h e i r  t e r -  
mina l  va lues  u ( c )  co inc ide  
d e s p i t e  t h e  s t r o n g  d i s t i n c t -  
i o n  of t h e  i n i t i a l  ones:  
t h e  accumulation of r e f l c c t -  
t i o n  t a k e s  p l ace  only  a t  t h e  
expense of t h e  f i r s t  term 
of  ( 6 ) .  I n  hodographs r 
and A , H e  = H r  = 0,  and 
H a  = 0 . 4 4 5  oe ,  and t h e  2nd 
t e r m  of (6)  i n t roduces  a 
d i f f e r e n t  e f f e c t  of r e f l e c t -  
on accumulat ion,  as a 
function of t h e  cho ice  
of wave d i r e c t i o n  u > 0 
(W + E )  o r  v < 0 (E + W). 
6 i s  a case s imi l a r  t o  A ,  
b u t  f o r  t h e  o rd ina ry  wave only .  
Hodo- 
L - 
U'- 
Fig .1  
Hodographs u (h )  and p r o f i l e s  of e l e c t r o n  
concen t r a t ion  Ne (h) 
4 
4 .  P l o t t e d  i n  F igures  2 and 3 are t h e  computations of damping c o e f f i c i -  
e n t s  B(TH1) and of d i f f e r e n c e s  i n  t h e  angular  wave numbers Aa(THI) = a(H4) 
- a(O),  performed as a func t ion  of f requency f and , us ing  an e l e c t r o n i c  
computer, f o r  Two types  of p r o f i l e s :  I r e p r e s e n t i n g  t h e  middle  l a t i t u d e s  i n  
summer and I1 r e p r e s e n t i n g  t h e  e q u a t o r i a l  zone (Fig.1)  a t  so = 5 and so = l o>+) .  
Ind ica t ed  on t h e  curves B(f )  and Aa(f)  are t h e  
va lues  of H@, so and t h e  type  of p r o f i l e .  To 
t h e  r i g h t  dampings are given i n  db and p l o t t e d  
i n  o r d i n a t e s  f o r  1000 km. The computations 
were conducted according t o  formulas of sec.2 
rad  
E3 db 
Fig.3.  Parameters B(f) and 
Acr(f) of  the  TH1-wave f o r  the 
p r o f i l e  I, so = 1 0  (dashed 
curves)  and p r o f i l e s  11, so = 
( s o l i d  l i n e s ) .  The va lues  of 
equal  t o  0.445 and 0 are 
i n d i c a t e d  on t h e  curves  
F ig .2 .  Parameters  B(f)  and Aci(f) of t h e  wave 
THi  f o r  t h e  Ne(h) p r o f i l e  I o f  middle l n t i t u -  
d e s  a t  so = 5 
b u t ,  on t h e  s t r e n g t h  of t h e  a s s e r t i o n  of  sec .3 ,  they  are a p p l i c a b l e  f o r  any 
d i u r n a l  courses .  P r o f i l e  I is app l i cab le  f o r  l a t i t u d e s  > 4 0 " ,  and pro- 
f i l e  I1 f o r  I @ /  < 20". I n  t h e  in te rmedia te  zone 20" < 1 @ 1  < 4 0 " ,  f3 and Aa are 
e s t i m a t e d  by mean va lues .  The va lues  of a ( 0 )  may be borrowed from t h e  co r re s -  
ponding graphs f o r  a ( f )  of r e f .  [ l o  - 121. If Iir = v i i q 2 + I I e 2  i s  t h e  t o t a l  ho- 
r i z o n t a l  component of t h e  f i e l d  a t  t h e  given p o i n t  of t h e  course ,  and $J is 
t h e  ang le  between I& and t h e  course ,  f3 aay be  determined f o r  i t  approximate- 
l y  by formula fi=fi(&)sin9, where p ( f j P )  w i l l  be obta ined  from e i t h e r  Fig.2 o r  
3 by i n t e r p o l a t i o n .  It may be see= frcm Figs .  2 and 3 that  ir: t h e  e q u a t o r i a l  
zone t h e  va lve  e f f e c t  a t t a i n s  h ighes t  va lues .  Thus, f o r  example, f o r  f = 10 
kc / sec  i t  fo l lows  t h a t  on t h e  course Panama Canal - H a w a i i  of 1 . 3 3  rad .  ex- 
t e n s i o n ,  where t h e  mean va lue  H = 0.3 oe  ( p r o f i l e  11, Fig .3 ) ,  B ( W ,  E) = 1 . 2  
n e p e r / r a d ,  and B(E, 14) = 2.9 ne&r / r ad ,  whence t h e  r a t i o  of  f i e l d  i n t e n s i t i e s  
km 
5 
5 
.t . . 
i s  p = e V [ $ ( &  w) - p(w, E110 10, which is c l o s e  t o  t h e  experimental  
va lue  of 12.3 ob ta ined  i n  t h e  work [31. A t  middle  l a t i t u d e s  t h e  va lve  
e f f e c t  is  a t t e n u a t e d  a t  t h e  expen e of t h e  appearance of l a y e r  C induced 
by cosmic r a y s  i l l ,  12 ,  141 and t h e  dec rease  of H@. Over summer t r a n s a t l a n -  
t i c  cour ses ,  where 9 2 0 . 1 5  oe ,  f o r  f = 1 5  kc/sev,  
B(W, E) = 1.4  neper / rad ,  which g ives  P = 1 . 4  f o r  8 = 1 rad.  
t i m e  computation g i v e s  B(E, W >  = 2.8,  
s h a l l  o b t a i n  P = 2.5. 
t h e  round-the world e x p e d i t i o n  of 1922 - 1923 [ 4 ] .  The valve e f f e c t  is  weak- 
ened wi th  t h e  rise of  atmospheric p r e s s u r e  because of veff i n c r e a s e  ( see 
graphs of  F igs .  2-3 f o r  s o  = 5; so = 10) and wi th  t h e  i n c r e a s e  of frequency f .  
The resul ts  of c a l c u l a t i o n s  f o r  t h e  p r o f i l e s  I and I1 are a good corrobora- 
t i o n  of t h e  f a c t  t h a t  t h e  C-layer i s  p r a c t i c a l l y  absen t  i n  t h e  e q u a t o r i a l  
zone,  as t h i s  i s  r equ i r ed  by the  aeronomical theory  of o r i g i n  of  t h e  C-layer. 
a t  t h e  expense of primary cosmic rays .  Had t h e  C-layer e x i s t e d  i n  t h e  equa- 
t o r i a l  zone, and i f  t h e  N e  p r o f i l e  were c l o s e  t o  p r o f i l e  I ,  t h e  c a l c u l a t e d  
P would have been equa l  t o  5 ,  which i s  s i g n i f i c a n t l y  below t h e  experimental  
v a l u e  of 12. 
have t o  be taken  i n t o  account f o r  t h e  r e g i s t r a t i o n  of t h e  va lve  e f f e c t .  
B(E, W) = 1.75 neper / rad ,  
I n  win te r  day- 
B ( W ,  E)  = 2.1, and f o r  8 = 1 rad  w e  
These r e s u l t s  are c l o s e  t o  t h e  experimental  ones of 
- 
I n  n igh t t ime  a l l  t h e  t h r e e  components of t h e  f i e l d ,  He, H$,, H r  
* * * THE E N D  * * * 
V. A. S tek lov  I n s t i t u t e  of  Methematics Manuscript rece ived  on 
of t h e  USSR Academy of Sc. 27 December 1965 
C O N T R A C T  N 0. NAS- 5 - 1 2  48 7 T r a n s l a t e d  b y  
V o l t  T e c h n i c a l  C o r p . ,  
1 1 4 5  1 9 t h  s t .  N.W. D r .  A n d r e  L .  B r i c h a n t  
W a s h i n g t o n ,  D . C .  2 0 0 3 6  
T e l e p h o n e :  223-6700  (x -36-37)  May 2 3 ,  1 9 6 8 .  
References fo l low. . / . ,  
6 
R E F E R E N C E S  
1. D . D .  C R O M B I E .  J .  A t m .  T e r r .  P h y s . ,  1 2 ,  110 ( 1 9 5 8 ) .  
2 .  W.L.  TAYLOR. J .  Res. N .  B, S. 64D,  3 4 9  ( 1 9 6 0 ) .  
3. J . S .  HANSELMAN, C . J .  CASSELMAN e t  a l . ,  J .  R e s .  N . B . S . ,  
4 .  H . J .  R O U N D ,  T . L .  ECKERSLEY e t  a l . ,  J . ,  I n s t .  E l e c t r . ,  
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1 2 .  P . E .  KRASNUSHKIN, Nuovo C i m . ,  2 6 ,  X ,  50 ( 1 9 6 2 ) .  
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No.6  ( 1 9 6 6 ) .  
* * * * * * * * *  


On the disruption of the reciprocity principle during the daytime propagation of super long radiowaves around the earth

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