Use of Fresnel reflection coefficient for studying reflections from mesospher

Manson, A. H.

English

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Electro -magnetic V:FP’JC s of m cZitrm Crequczcy, which are 
Fxtially rcflccted frx3  irregularities in the mesosphere, 
w e t e  first used to m c ~ ~ s - ~ ~ r ~ !  dcctrm.: drtnsStics by Gardner 
and Pawsey in i953 .  
len$h in the original p i ~ c r ,  zn2 h t c r  5y Fcjer and Vice (1959), 
and BeZrose and Burke (i354). 
The -nethsd uzcd is discussed at some 
If t h e  receiver octprrts h r  the ordin-ry 2nd extraordinary 
compomnts are A - the ccmrespond<l#g Fresnel reflection 
coelficients are Ro, Rc; i k  absori>ti;n c9cfiicients arc 
KO, ICe, and the electras dcnaily at hei& h is N(h), then 
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73.c ratio Xi /I?. (5s  dciicezd by G:rrdxr  and Pawsey and 
(KP - X J  e o  
other workera), and -+J~) , m z y  bc cnlcut-ated from 
- clcctro-magnetic thcorr., In the l o w s  wcsusphcre the coliision 
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f;cquencp is of the order cf the wave fren_;tcncy, and it is 
necessary t o  use the gencszlizcd thcury, -<;here the energy 
dependence of the colli-cion ireqrzcizcy is  camsidered (Fhclps 
and Pack, 1959; Sen a id  ?'yllcr, 195::. It may bc shown that 
for a probir,~ frcqucncy of 2.4 ^tlc/s, both R,/R- 2nd 
(Ke - ;io)/N(h) zrc cssc-cially in6epcnZzct c;f X(h) for the 
c onditiono encountered i-n thc mid -li?tittir;n; T: C? sosphere. 
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latter assum?tion dspcnds on the nstuzc af these irregularities 
in the mesosphere. Unfortun-iteiig, rocket measurements of 
relevznt variables from 5r -9:3 k12 2re not gemrally sensitive 
enough to show the amall. changes in relrL:cti.m index which 
are required for the observed rcficctions. It is to be hoped 
that future rocket-born expi'rimcnts will give information a8 
to the change in refractive ind3x sd:h height, 
The n o s t  phucible es:Fl:%xxtion for t17zsz irregularities 
is due to I-Tjncs f?96r ) ,  wlsil d z r c r i b d  than1 in terms of 
internal atxnosphcric grsviiy i-.-zvcs. Ec cuzzestcd that the 
partid renections from 613-75 h-n; wcrc duc? to irregularities 
whSn werc caused dircc'lly by thcsz Gravity waves; and 
tlbovc 80 km were due to txz'sulencc c-~uszi? by the waves. 
Ohscsvatiuno of tho pzrti:.'l rcflcctizas sccir  to bear out this 
hy2othesis. 
occurrezce, and slovr, hlc;ilk,r c o r r c h t z d  ( c l ~ ~ e n d c n t )  fhding 
of thc two reflected corap3:icDts at a give2 height; while the 
The lowcat cd i t ics  chow sc:~s:3nzl vlriations in 
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C O P Y  
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reflccted wave spectra f u r  or6inary a d  extraordinary components. 
Thio is a reasonable asswnption if the irregularities in refractive 
index are clue to turbulence. 
Expcrimen"a1 evfr?mcc obt.iincd by using a gated integration 
device on the two reflected compooents, has shown that the 
ineasured amplitude r a t i D  of dcpcndent and independent fading 
signals i s  the same within c!spcrixentsZ error. 
justilied with preocnt expzrim ental and theoretical evidence to 
use  the Fresnel rcflectbn codficicnt f=lr studies of the partial 
reflections from the rnesospherc. 
It thereiore seems 
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Returning 
tends to unity, 
R( and 
Since n 2 is a function of electron density X(h), and collision 
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~rcc,u-ncy 3, , then 
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and 
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The d e f i n i t i o n  of R used by previous workers assumed t h a t  t he  change i n  
c o l l i s i o n  frequency, g> , was zero.  However, i f  t he  echoes 
a r e  due t o  i r r e g u l a r i t i e s  i n  t h e  atmospheric d e n s i t y  p r o f i l e ,  which 
are caused by i n t e r n a l  g r a v i t y  waves, t he re  w i l l  be an a s s o c i a t e d  
p res su re  change and hence a change i n  c o l l i s i o n  frequency within each 
i r r e g u l a r i t y .  
b 
The changes i n  log, (Re/Ro) f o r  e l ec t ron -dens i ty  i r r e g u l a r i t i e s ,  and 
combined e l ec t ron -dens i ty  and c o l l i s i o n  frequency i r r e g u l a r i t i e s  
(F ig .  1) a r e  shown i n  f i g u r e  1. A change i n  N(h) of 1-10 per cen t  i s  required 
f o r  t h e  observed echoes, and changes i n  
t h e o r e t i c a l l y  p red ic t ed ,  so these curves a r e  q u i t e  r e a l i s t i c  f o r  t he  
lower mesosphere. 
dependent upon t h e  r e l a t i v e  magnitudes of &$ m/ 
and hence r e q u i r e s  a knowledge of the physical  n a t u r e  of t he  i r r e g u l a r i t y .  
This  w a s  c l e a r l y  unnecessary with the e a r l i e r  t reatment ,  when the  
independence of (Re/Ro) upon the s i z e  of t h e  e l e c t r o n  d e n s i t y  
3 of 1-10 per  cen t  are 
It i s  evident  t h a t  t he  value of (Re/R,) i s  s t r o n g l y  
4 and d N ( h ) / N ( h ) ,  
XERO 
C O P Y  
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(Figure 2) 
irregularity enabled ;ur explicit expression €or N(h) to be obtained. 
It has also been found that the dependence of R,/R, on $4 =/ 4 
docreasas with height, a d  becornos quite small above 80 b. At 
these heights the error introduced into electron doneity calculations 
- 
by observational techniques would twually bo larger than that due 
to the omission of the collision frequency term fzom equation 7. 
.-’ i The error introduced by ignoring the collision frequency 
irregularities at the lower heights (60-80 km) is eipificant however. 
This is darnonatrated by figure 2, which presents electron denaity 
measurements mado at Bird’ling’a Flat, New Zealand, during the 
winter of 1964. The thres curves were obtained from the same 
cqcrisnental data, by substituting three different value8 of the 
collision frequency irregularity ( i) m/ 9 m) hto the expraesfon 
for the reflection coefficients. Further theoretical and experimental 
work is intended, t o  help clarify the baoie of the reflection mech;r#fsm. 
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. Acknowledgment 
I would like to thank Prof, C. 0. Nine8 for bio helpful 
comments OA the manuscript. 
Thia work was supported in part by the University of 
Canterbury, Christchurch, New Zealand, during study for the 
degree of Doctor of Philosophy; and more recently by the 
National Aeronautic8 and Space Administration under grant 
NsG 467. 
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