Effect of negative ions on diffusion of charged particles in lower ionospher

Ginzburg, E. I.

English

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National Aeronautics and Space Administration 
Goddard Space Flight Center 
Contract No.NAS-5-3760 
E F F E C T  OF NEGATIVE IONS ON THE D I F F U S I O N  OF CHARGED 
PARTICLES I N  THE LOWER IONOSF'HERF, 
bY 
E. I. Ginsburg 
[USSR J 
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S T -  A I -  E- 10385 
EFFECT OF N X G A T N E  IONS ON TJ3E D I F F U S I O N  OF CHARGED 
PARTICLES I N  THE LOWER IONOSPHERE * 
I V U Z . ,  Radiof ie ika 
T o m  8, No. 3, 
I e d ,  Gorlkovskogo Universteta ,  
Gor k i y  , 1965 
626- 7, 
by E. I. Ginaburg 
S U M M A R Y  
The so lu t ion  of t h i s  problem is  a r r ived  a t  by a method analogous 
t o  t h a t  expounded in [31 and is based upon the  f a c t  t h a t  the  d i f fus ion  
process i n  a plasma i n  the  presence of a magnetic f i e l d  takes place at 
the  ra te  of t he  ve loc i ty  of slower p a r t i c l e s  ( e l e c t r o n s  and p o s i t i v e  i o n s ) ,  
inasmuch as the  e l e c t r i c  f i e l d ,  emerging on account of t he  d i f f e rence  in 
the  d i f fus ion  r a t e s  of  e l ec t rons  and ions ,  hampers a f u r t h e r  separa t ion  
of these  p a r t i c l e s  and t h i s  i s  evidence t h a t  t he  presence of negat ive i o n s  
may s u b s t a n t i a l l y  modify the character  of the  d i f f u s i o n  process. 
* 
* * 
I n  t he  condi t ions of the  l o w e r  ionosphere the  inf luence  of negat ive 
ions  is  s i g n i f i c a n t  t o  he ights  of the order  of 80 km [l]. However, in t h e  
works c2, 31 on the  d i f fus ion  i n  the ionosphere t h e  inf luence  of negat ive 
ions  on the  d i f fus ion  process  w a s  not taken i n t o  account. 
The method, appl ied  below, is  analogous t o  t h a t  proposed in c31: 
i n  the  case,  when the concentration of p a r t i c l e s  v a r i e s  l i t t l e  over t h e  
length of the  f r e e  path and when for t he  desc r ip t ion  o f t h e s e ' p a r t i c l e s *  
motion au r ing  the  f r e e  path time, macroscopic equat ions can be appl ied  
(in our case i t  concerns e l ec t rons ,  negat ive and p o s i t i v e  ions) .  The l i n e a r -  
i zed  system of these equat ions i s  resolved alongside with t h e  equation for 
the  long i tud ina l  e l e c t r i c  f i e l d  by way of expansion of t h e  func t ions  searched 
f o r  i n t o  the  Four ie r  i n t e g r a l  by the coordinates  = San(r)e-"'djr 
* VLIYANIYE 0 T R I T S A T E L " Y K H  IONOV NA D I F F U Z I Y U  ZARY.AZHENiqYKH QHASTITS V 
11 IZHNEY IONOSFERE . 
2. 
A t  the  same time we obtain f o r  the  Fourier-components of the  func t ions  
the  equat ions 
Here De = x Te/m Yem i s  the coef ' i c ien t  of long i tud ina l  d i f fus ion ,  oe=ezn&vem 
is the  conduct ivi ty ,  uHe = eHO/mc i s  the  gyrofrequency f o r  e l ec t rons ,  
' H e  '[I -t ( f o ~ p / Y d C O S 2 ~ l ~ 1 +  ( W H e / v e m ) 2 ] - 1 ,  fJ is the angle between k and Ho, D1, Db 'Ji9 @HI* "'HI* 
a H I  a r e  t5e  corresnonding q u a n t i t i e s  f o r  the  ions ,  ;ne,  ant, an] is t h e  
r e s i d u a l  concentrat ion r e spec t ive ly  f o r  the e l ec t rons ,  p o s i t i v e  and nega- 
t i v e  ions ,  
( a n  << no, n , , + n ~ j  = ~ O I ) , W  MI, Mi are the masses of e l e c t r o n s  and ions, 2 is t h e  
charge of the  e l ec t rons ,  T e ,  T i  a r e  the  temperatures r e spec t ive ly  of 
e l e c t r o n s  and ions,  )c is the  Boltzmann constant ,  vem, vim, vjm a r e  tbe  fre- 
quencies of e l ec t rons '  and ions'  c o l l i s i o n s  with n e u t r a l  p a r t i c l e s ,  E is 
the  e l e c t r i c  f i e l d  s t r eng th ,  Ho i s  the constant  Ear th ' s  magnetic f i e l d ,  
We s h a l l  wr i t e  the  s o l u t i o =  of the system (1) 
nee, nol,in,,j is the mean concentrat ion of these p a r t i c l e s  
in t he  form 
where 4 1 9  
1 . ~  s h a l l  l i m i t  ourselves  t o  the case,  when the  masses and t h e  col-  
l i s i o n  frequencies  f o r  var ious  kinds of i ons  are i d e n t i o a l  ( f o r  the  lower 
ionosphere i t  is r e a l i z e d  i n  the presence of molecular oxygen ions  only). 
A t  the  same time, M I  = Mj = M ,  Y l m = v j m  and 
q, - aHIDtk*,  trig - 0. (31 
If the  c h a r a c t e r i s t i c  dimensions of the  per turbed region a r e  l a r g e  by 
Comparison w t h  the Debye r d ius  RD, 
I ! 
th.en w e  shall have for the  remaining q u a n t i t i o s  i n  ( 2 )  
where 
iinj:)/nOi = - 5nnfi)/noj = Bnl?,)/(n,i + no/), 
i,iz!i) = i d 3 )  la - (n,lanla(0) + nO,~n lk (~ )J / (n , i  + no/). 
Here enk,(oh bn,,(O) are the Fourier  components of t he  i n i t i a l  d i s tu rb -  
ence of the  dens i ty  of e l ec t rons  and ions.  
One of the c h a r a c t e r i s t i c  r a d i c a l s  (ql i n  our case)  descr ibes  t h e  
spreading out  of t he  i n i t i a l  charge i n  the  plasma, as should have been 
expected L31. Inasmuch as q1 i s  s i g n i f i c a n t l y  greater than q2 
the  process of d i f fus ion  takes  place mair,lg a t  compensated plasma charge 
(anbipolar  d i f fus ion) .  A t  the sane t i n e  Sn%=s,L') . The e l e c t r o n s  and the 
noncompensated ion cilcrre,  equal. t o  e(iin# ik = e6ne,(0) , take p a r t  in the 
ambipolw 2iffusipr. procesr; dcrcribcd by the  r a d i c a l  92. The compensated 
i o n  charce spreads out with t l e  ion  d i f f u s i o n  rate descr ibed by t h e  r ad i -  
c a l  q3. In  the f i r s t  ap7roxinGtion by kF l~  the  e l e c t r o n s  do not  take par t  
in t h i s  process. The c o e f f i c i e n t  of ambipolar d i f f u s i o n  is 
a n d  q3,  
(8) W) = f T i )  (imvemlaHr f MvlmlaHl )-I , 
wkere = (nOl + nc,,)/noe. 
;:ate t:;at f o r  t k e  l oxe r  ionosphcre 1 may be s i g n i f i c a n t l y  greater 
than the  unity.  That i s  why the  anisotropy of the  d i f f u s i o n  process  may be 
manifest  a t  very s m a l l  h e i r h t s  i n  t5c ionosphere. A t  he igh t s  where 
(oHe/vem)z  << 1 0 (9) 
t he  charac te r  of the  d i f fus ion  i s  i s o t r o p i c  r e g a r d l e s s  of the  form of the  
inhomogeneity. The dependence of inhomogeneity )s spreading our process  
on i t s  i n i t i a l  s t r u c t u r e  war; discussed a t  l eng th  i n  t h e  work [3]. Here 
w e  s h a l l  note  only  t h a t  if i t  i s  not  too  s t rong ly  s t r e t c h e d  out  a long  t h e  
magnetic f i e l d  ( see  C331, t he  d i f fus ion  i so t ropy  may take place t o  he igh t s ,  
4 
I 4. 
where t h e  condit5.m ( 9 )  i s  disruyted.  To t h a t  e f f e c t  i t  i s  s u f f i c i e n t  
t h a t  we have (ut,i ivim)a.2;1. 
The c o e f f i c i e r t  of i s o t r o p i c  d i f f u s i o n  i s  
If we neglec t  t he  inf luence  of neeativc i o n s  on the  d i f fus ion ,  
we s h a l l  have r l  and the  d i f f u s i o n  c o e f f i c i e n t  w i l l  be s u b s t a n t i a l l y  
underrated.  
* * * *  T H E  END * * * *  
Novosibirsk I n s t i t u t e  of Radio 
Engineering and Comriunications 
Contract  No.NAS-5-3760 
Consul tan ts  & Designers, Inc. 
Arl ington,  V i r g i n i a  
Received on 
15 December 1964. 
Trans la ted  by ANDRE L.BRICHANT 
on 13 September 1965 
R E F E R E N C E S  
[1].- Yh. L. AL'FEHT.- Rasprostraneniye radiovoln v ionoefere  (Radiowave 
Propagation i n  t he  Icnosphere) . - Isd.Al?SSSR, 1960. 
[2].- B.N. GERSHMA1J.- Radiotekhnika i e lek t ron ika ,  1, 720, 1956. 
V. P. Dokuchayev. I W Z ,  Radiof ie ika,  3, 50, 1960. 
>,'' ST - A I  - PF - 10 385 ( 6 pp. 80 C C )  
GODDARD SPACE F.C. 
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Effect of negative ions on the diffusion of charged particles in the lower ionosphere

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