THERMAL CONDUCTION AND ION TEMPERATURES IN THE IONOSPHERE

EARTH AND PLANETARY SCIENCE LETTERS 1 (1966) 270-275. NORTH-HOLLAND PUB. COMP., AMSTERDAM

T H E R M A L C O N D U C T I O N A N D I O N T E M P E R A T U R E S I N T H E I O N O S P H E R E

P e t e r M. BANKS

Institut d 'A~ronomie Spatiale de Belgique, B r u x e l l e s 18, Belgium Received 5 August 1966

An analysis is made of the ion energy balance equation for the ionosphere including the effects of O +, He +, and H + ions, thermal conduction, and the cooling by atomic hydrogen and lium. It is shown that thermal conduction strongly affects the ion temperature profile for conditions of moderate and low elec- tron densities and that the high altitude ion temperature can be significantly less than the electron tem- perature. In addition, H + in concentrations as low as 10~o of the total ion density is found to be a major recipient of heat from the ionospheric electron gas and has an important influence upon the total ion en- ergy budget.

1. I N T R O D U C T I O N

T h r o u g h n u m e r o u s e x p e r i m e n t s it has b e e n d e t e r m i n e d that the e l e c t r o n t e m p e r a t u r e above 150 km i s c o n s i s t e n t l y h i g h e r than the t e m p e r a - t u r e of the n e u t r a l a t m o s p h e r e . To explain t h i s s t a t e of t h e r m a l n o n e q u i l i b r i u m , a n u m b e r of t h e o r e t i c a l s t u d i e s h a v e b e e n m a d e of the e l e c - t r o n heat budget e q u a t i o n u s i n g p h o t o i o n i z a t i o n as the p r i n c i p a l e l e c t r o n gas e n e r g y s o u r c e [1-5].

T h e m o s t r e c e n t of t h e s e a n a l y s e s [5] g i v e s r e - s u l t s in g e n e r a l a g r e e m e n t with c u r r e n t m e a s - u r e m e n t s but, b e c a u s e the e l e c t r o n t e m p e r a t u r e i s v e r y s e n s i t i v e to m i n o r c h a n g e s in the s o l a r EUV flux, the e l e c t r o n d e n s i t y , and the m a g n i - tude of the a s s u m e d m e c h a n i s m s of e l e c t r o n e n - e r g y l o s s , a high d e g r e e of c o r r e s p o n d e n c e c a n - not be e x p e c t e d at the p r e s e n t t i m e .

The p r i m a r y s o u r c e of e l e c t r o n e n e r g y l o s s a b o v e 300 k m a l t i t u d e o c c u r s by m e a n s of e l a s - tic c o l l i s i o n s b e t w e e n e l e c t r o n s and the a m b i e n t ions. T h e ions, in turn, t r a n s f e r t h i s e x c e s s t h e r m a l e n e r g y to the n e u t r a l g a s e s of the a t m o - s p h e r e . Hanson [3] w a s the f i r s t to point out that, b e c a u s e the d e n s i t y of the n e u t r a l a t m o s p h e r e d e c r e a s e s m u c h m o r e r a p i d l y than that of the e l e c t r o n gas, the ion t e m p e r a t u r e should have a p r o n o u n c e d a l t i t u d e d e p e n d e n c e in r e s p o n s e to the e l e c t r o n heating, i n c r e a s i n g g r a d u a l l y f r o m the n e u t r a l gas t e m p e r a t u r e n e a r 300 km to the e l e c t r o n t e m p e r a t u r e above 800 kin.

E x p e r i m e n t a l s u p p o r t f o r the t r a n s i t i o n b e - h a v i o u r of the ion t e m p e r a t u r e can be i n f e r r e d f r o m s a t e l l i t e m e a s u r e m e n t s [6] and i n c o h e r e n t

r a d i o b a c k s c ~ t t e r data [7, 8]. It i s n e c e s s a r y to point out, h o w e v e r , ~hat although the r e s u l t s of Hanson [3] i n d i c a t e that the e l e c t r o n and ion t e m - p e r a t u r e s should be a p p r o x i m a t e l y e q u a l at high a l t i t u d e s , in fact, in the a v a i l a b l e e x p e r i m e n t a l data [6-9] t h e r e a p p e a r to be s i g n i f i c a n t d e v i a - t i o n s of the ion t e m p e r a t u r e t o w a r d s v a l u e s which a r e c o n s i s t e n t l y l o w e r than the e l e c t r o n t e m p e r a t u r e , even in the a t m o s p h e r i c r e g i o n s w h e r e the i o n - n e u t r a l e n e r g y l o s s e s a r e not e f - f e c t i v e in c o o l i n g the 1on gas. F u r t h e r , in the r e g i o n s 4ud-600 km it i s d i f f i c u l t to m a t c h the c a l c u l a t e d v a l u e s of ion t e m p e r a t u r e with t h o s e a c t u a l l y m e a s u r e d u n d e r c o n d i t i o n s of low e l e c - t r o n density.

T o r e c o n c i l e the d i f f e r e n c e s b e t w e e n t h e o r y and e x p e r i m e n t , a r e a n a l y s i s h a s b e e n m a d e of the ion e n e r g y b a l a n c e e q u a t i o n s to i n c l u d e the p r e v i o u s l y n e g l e c t e d e f f e c t s of ion t h e r m a l c o n - duction, the p r e s e n c e of He + and H + ions, and the c o o l i n g by a t o m i c h y d r o g e n and h e l i u m . T h e r e s u l t s , p r e s e n t e d in t h i s p a p e r , i n d i c a t e that ion h e a t conduction can p l a y an i m p o r t a n t p a r t in d e t e r m i n i n g the p r o f i l e s of ion t e m p e r a t u r e , l e a d i n g to v a l u e s which a r e c o n s i d e r a b l y below the e l e c t r o n t e m p e r a t u r e . It i s a l s o shown that H + i o n s a r e i m p o r t a n t in the o v e r - a l l ion e n e r g y b a l a n c e , e v e n in c o n c e n t r a t i o n s l e s s than 10% of the t o t a l ion density.

2. ION E N E R G Y B A L A N C E

T h e t i m e - d e p e n d e n t e n e r g y b a l a n c e equation

for the ion g a s e s of the i o n o s p h e r e is:

avi

at - P i " Li " V ' ¢ i ' (1) w h e r e U i = ~ n i k T i 3 i s the ion t h e r m a l e n e r g y p e r u n i t v o l u m e , n i = n ( O + ) + n ( H e + ) + n ( H +) is the total ion n u m b e r d e n s i t y , k i s B o l t z m a n n ' s c o n - stant, T i i s the ion t e m p e r a t u r e (for a d i s c u s s i o n of ion t e m p e r a t u r e coupling, s e e [10]), P i is the r a t e of ion gas e n e r g y p r o d u c t i o n , L i i s the r a t e of e n e r g y l o s s to the n e u t r a l a t m o s p h e r e , and FTi i s the ion heat flux a r i s i n g f r o m conduction and diffusion effects.

U n d e r the i n f l u e n c e of t h e r m a l conduction and the n o n - l o c a l h e a t i n g effects of p h o t o e l e c t r o n s , it i s found [5,7] that the e l e c t r o n t e m p e r a t u r e above 300 k m i s s i g n i f i c a n t l y g r e a t e r than the t e m p e r a t u r e of the n e u t r a l a t m o s p h e r e , thus p r o v i d i n g a heat s o u r c e for the ion gases. By m e a n s of e l e c t r o n - i o n c o l l i s i o n s , the e l e c t r o n gas of t e m p e r a t u r e T e and d e n s i t y n e t r a n s f e r s e n e r g y to the i o n s at the r a t e s :

Pi(O +) = 4 . 8 x 10 - T n e n ( O +) [T e - T i ] T e - 4 , (2a) P i ( H e +) = 1.9 × 10 -6 hen(He+ ) [T e - Ti] T e - ~ , (2b) Pi(H +) = 7.7 × 10 -6 hen(H+)

3

× [ T e - T i ] T e - ~ eV c m - 3 sec -1 , (2c) which a r e in the r a t i o s 1:4:16. Thus, the h e a t i n g r a t e s for He + and H + a r e equal to the O + r a t e when n ( H e + ) / n ( O +) = 0.25 and n(H+)/n(O +) = 0.063, r e s p e c t i v e l y , i m p l y i n g the e l e c t r o n e n e r - gy t r a n s f e r to the He + and H + ions p l a y s an i m - p o r t a n t p a r t i n the o v e r a l l ion e n e r g y b a l a n c e .

The r a t e s of ion e n e r g y l o s s to n e u t r a l g a s e s by m e a n s of e l a s t i c c o l l i s i o n s have b e e n d i s - c u s s e d r e c e n t l y [10, 12] and these r e s u l t s a r e adopted for this study. B r i e f l y , for ions i n p a r - ent g a s e s the p r o c e s s of r e s o n a n c e c h a r g e ex- change i s d o m i n a n t , while for ions in u n l i k e g a s - es the p o l a r i z a t i o n i n t e r a c t i o n alone is a s s u m e d to be acting. F o r H + and O + in a t o m i c oxygen and hydrogen, the effects of a c c i d e n t a l l y r e s o n a n t c h a r g e exchange have b e e n included.

The heat flux, qi, can be e v a l u a t e d for a m a g n e t i c f i e l d - f r e e m e d i u m as, n e g l e c t i n g t h e r m a l diffusion [13],

qi = - K i V T i + ~ n i k T i C i , (3) w h e r e K i i s the ion t h e r m a l conductivity and Ci i s the ion diffusion v e l o c i t y r e l a t i v e to the m a s s velocity of the c o m b i n e d ion gas and the n e u t r a l a t m o s p h e r e . T h e e v a l u a t i o n of the two t e r m s in

(3) shows that heat conduction i s g e n e r a l l y d o m i - nant, but that t h e r e a r e s o m e c i r c u m s t a n c e s , e s p e c i a l l y for low t e m p e r a t u r e s and l a r g e ion d e n s i t i e s , when the diffusion c o n t r i b u t i o n r e s u l t - i n g f r o m a downward flux of ions cannot be n e - glected. However, b e c a u s e the c a l c u l a t i o n of C i r e q u i r e s the s o l u t i o n of the coupled ion t e m p e r a - t u r e and d e n s i t y equations for c o n d i t i o n s of c h e m i c a l and diffusive e q u i l i b r i u m , it is difficult to adopt r e l i a b l e v a l u e s . Hence, in this a n a l y s i s we take C i = 0 and deal only with the heat flux a r i s i n g f r o m ion t e m p e r a t u r e g r a d i e n t s in an e q u i l i b r i u m d i s t r i b u t i o n of ion gases.

T h e c a l c u l a t i o n of K i for a s i n g l e ion gas fol- lows f r o m the work of C h a p m a n [14] as:

5 1

K i = 4 . 6 x 1 0 4 T i i / A i ~ e V c m - l s e c - l O K -1 , (4) w h e r e A i i s the ion m a s s in a t o m i c u n i t s . Unlike the e l e c t r o n t h e r m a l conductivity, it is not n e c - e s s a r y to i n c l u d e a t h e r m o e l e c t r i c r e d u c t i o n f a c t o r or, for a l t i t u d e s above 300 km, to c o n - s i d e r the effects of i o n - n e u t r a l c o l l i s i o n s [16].

F o r the ion gas of the i o n o s p h e r e , an e x t e n - sion of (4) m u s t be made to i n c l u d e the effects of d i f f e r i n g c o n d u c t i v i t i e s for each i o n s p e c i e s . An exact e x p r e s s i o n i s difficult to obtain and f o r the p r e s e n t a n a l y s i s an a p p r o x i m a t e , d e n s i t y w e i g h t - ed, c o n d u c t i v i t y has b e e n u s e d in the f o r m g i = 1.15 x 104 Ti~[n(O+)+ 2n(Se+)+4n(H+)]/n e

X eV c m -1 sec -1 OK-1 . (5) When the effect of the e a r t h ' s m a g n e t i c field is c o n s i d e r e d it i s found [13] that t h e r e i s heat flow only along the l i n e s of g e o m a g n e t i c force.

To i n c l u d e the i n f l u e n c e of the i n c l i n a t i o n of the field l i n e s upon v e r t i c a l p r o f i l e s of ion t e m p e r a - t u r e , we i n t r o d u c e the m a g n e t i c dip angle, I, and r e w r i t e (1) as

aUi - ~ [ K dTi] (6)

at = P i - Li + s i n 2 I i d z J ' w h e r e z i s a v e r t i c a l c o o r d i n a t e .

The solution of (6) for the ion t e m p e r a t u r e p r o f i l e r e q u i r e s a knowledge of the e l e c t r o n and ion d e n s i t i e s i n the u p p e r i o n o s p h e r e . F o l l o w i n g r e c e n t work [10, 17], we adopt a state of O + dif- f u s i v e e q u i l i b r i u m above 340 k m while t a k i n g H + and He + to be in c h e m i c a l e q u i l i b r i u m with N2, O2, and O t o an altitude of 500 km, above which a condition of t e r n a r y ion diffusive e q u i l i b r i u m i s applied [17].

T h e n u m e r i c a l solution of (6) r e q u i r e s a choice of ion t e m p e r a t u r e b o u n d a r y c o n d i t i o n s which r e l a t e to the i n f l u e n c e s of ion e n e r g y p r o - duction outside the r e g i o n of a n a l y s i s . F o r the

272 P . M . BANKS l o w e r b o u n d a r y c o n d i t i o n i t i s a s s u m e d t h a t c o n -

d u c t i o n i s i n e f f e c t i v e a t 300 k m a n d t h e i o n t e m - p e r a t u r e i s t a k e n a s t h e s o l u t i o n t o (6) w i t h K i = 0. A t t h e u p p e r l i m i t (z = 1500 k m ) i t i s c o n v e - n i e n t to t a k e d T i / d z = 0 a n d n e g l e c t t h e h e a t c o n - d u c t e d d o w n w a r d s f r o m h i g h e r r e g i o n s .

3. B E S U L T S

T h e i o n e n e r g y b a l a n c e h a s b e e n s o l v e d n u - m e r i c a l l y f o r s t e a d y - s t a t e c o n d i t i o n s ( a U i / a t = 0) u s i n g t h r e e a t m o p s h e r i c m o d e l s of N i c o - l e t [18] t o r e p r e s e n t t h e e f f e c t s of c h a n g i n g a e r o - n o m i c c o n d i t i o n s . T h r o U g h o u t a l l c a l c u l a t i o n s t h e e l e c t r o n t e m p e r a t u r e h a s b e e n t r e a t e d a s a p a r a m e t e r w h i c h h a s t h e s a m e v a l u e f o r a l l a l t i - t u d e s .

S e v e r a l p o i n t s of i n t e r e s t h a v e b e e n f o u n d . F i r s t , i t a p p e a r s t h a t t h e i o n t h e r m a l c o n d u c t i o n c a n p l a y a n i m p o r t a n t p a r t i n d e t e r m i n i n g t h e

:I :11

T Ti 1 Ti T e

O* O* H* O*

He, H He, H no He, H

-- goc /

--

Ti . /

70~ I . O , no conduction

/ - ' ' J r T = IO00eK

SO0 / . " / Te = 2500°K

/ , ' / ' / n = 2 x IOScm "3 at 360 kn'

,~

3o~ I I

lOgO 1500 2000

TEMPERATURE (OK)

Fig. 1. Ion t e m p e r a t u r e s with an e l e c t r o n t e m p e r a t u r e of 2500OK and n e u t r a l gas t e m p e r a t u r e of 1000OK, for a m a g n e t i c dip angle of 90o with an e l e c t r o n density of 2 x 105 c m - 3 at 340 km. Curve 1 includes O + ions and t h e r m a l conduction but n e g l e c t s cooling by He and H.

In c u r v e 2 the s a m e conditions a r e u s e d with no t h e r - m a l conduction. Curve 3 includes O + ions, t h e r m a l conduction, He and H. Curve 4 r e p r e s e n t s the final r e -

sult with O +, H +, He, H and t h e r m a l conduction.

s h a p e of t h e i o n t e m p e r a t u r e p r o f i l e a t h i g h a l t i - t u d e s , y i e l d i n g , f o r a c o n s t a n t Te, i s o t h e r m a l v a l u e s w h i c h a r e s i g n i f i c a n t l y l e s s t h a n t h e e l e c - t r o n t e m p e r a t u r e . T h i s e f f e c t i s s h o w n i n c u r v e 1 of fig. 1 w h e r e a 1000OK n e u t r a l a t m o s p h e r e h a s b e e n u s e d w i t h o n l y O + i o n s p r e s e n t . T h e e l e c - t r o n t e m p e r a t u r e w a s t a k e n a s 2500OK, 1= 9 0 °, a n d t h e e l e c t r o n d e n s i t y d e t e r m i n e d f r o m t h e b o u n d a r y c o n d i t i o n n e = 2 × 105 c m - 3 a t 340 k i n . F o r c u r v e 1 t h e c o o l i n g e f f e c t s of a t o m i c h y d r o - g e n a n d h e l i u m h a v e n o t b e e n i n c l u d e d . T o s h o w t h e i m p o r t a n c e of t h e r m a l c o n d u c t i o n , c u r v e 2 ( b r o k e n l i n e ) h a s b e e n c a l c u l a t e d w i t h K i = 0.

S i n c e t h i s c h o i c e f o r K i i s e q u i v a l e n t t o t h e c o n - d i t i o n s f o u n d a t t h e g e o m a g n e t i c e q u a t o r , i t i s s e e n t h a t f o r i d e n t i c a l a e r o n o m i c p a r a m e t e r s t h e i o n a n d e l e c t r o n t e m p e r a t u r e s e p a r a t i o n w o u l d h a v e a r a n g e of 350OK b e t w e e n t h e g e o m a g n e t i c e q u a t o r a n d p o l e s .

A s e c o n d e f f e c t o c c u r s w h e n a t o m i c h y d r o g e n a n d h e l i u m a r e i n c l u d e d i n t h e O + e n e r g y l o s s . C u r v e 3 of fig. 1 s h o w s t h a t , f o r t h e m o d e l c h o s e n h e r e , t h e h i g h a l t i t u d e c o o l i n g , a l o n g w i t h t h e r m a l c o n d u c t i o n , r e d u c e s t h e i s o t h e r m a l v a l u e of t h e i o n t e m p e r a t u r e t o 1550OK. T h e i n -

150~

gO0

700

T : IO00°K Te = 2500°K I : 90 °

t ~ 2S~

/

2x105 / /

5x105 lx|O~

/ ,

TEMPERATURE (°K)

Fig. 2. Effects of changing e l e c t r o n density boundary conditions upon ion t e m p e r a t u r e s with the e l e c t r o n

density v a r y i n g f r o m 105 to 106 c m - 3 .

t r o d u c t i o n of H + as p a r t of the ionic c o m p o s i t i o n r e v e r s e s t h i s s i t u a t i o n , h o w e v e r , by p r o v i d i n g an i m p o r t a n t s o u r c e of ion h e a t i n g at high a l t i - tudes. A s shown by c u r v e 4 of fig. 1, t h i s r e - s u l t s in an i n c r e a s e of 450OK in the i s o t h e r m a l ion t e m p e r a t u r e . In fact, the p r o f i l e obtained f o r the ion t e m p e r a t u r e o m i t t i n g the e f f e c t s of H + i s v e r y s i m i l a r to the p r o f i l e found when H +, He, and H a r e included. T h e b a s i s f o r this n e a r e q u a l i t y l i e s in the c o u n t e r b a l a n c i n g of the s u p e - r i o r h e a t i n g r a t e of H + by the l a r g e H + c h a r g e e x c h a n g e e n e r g y l o s s r a t e to a t o m i c h y d r o g e n and an i m p r o v e d ion t h e r m a l conductivity. The i m p o r t a n t point to note i s that f o r the adopted model, the ion t e m p e r a t u r e is c a l c u l a t e d to be about 500OK l e s s than the e l e c t r o n t e m p e r a t u r e . T h e e f f e c t s of He + , which a r e not shown h e r e , do not a p p e a r to be l a r g e and can be n e g l e c t e d in a f i r s t a n a l y s i s .

T h e v a l u e of the e l e c t r o n d e n s i t y is i m p o r t a n t in d e t e r m i n i n g the ion t e m p e r a t u r e p r o f i l e . At high a l t i t u d e s , w h e r e ion c o o l i n g by the n e u t r a l g a s e s i s i n e f f e c t i v e , conduction m u s t c a r r y away

the heat obtained f r o m the e l e c t r o n gas. T h e c h a n g e s b r o u g h t about by v a r y i n g the e l e c t r o n d e n s i t y boundary condition at 340 km a r e shown in fig. 2 f o r n e = 1 × 105 , 2 × 105 , 5 × 105 , a n d l

× 106 c m -3 with T--- 1000OK, T e = 2500OK, and both O + and H + i o n s b e i n g included. It is s e e n that ion h e a t conduction is g e n e r a l l y i m p o r t a n t d u r i n g c o n d i t i o n s of low e l e c t r o n d e n s i t y or, m o r e e x a c t l y , when the high a l t i t u d e e n e r g y p r o - duction r a t e i s s m a l l . F o r e n h a n c e d e l e c t r o n d e n s i t i e s at high a l t i t u d e s , the ion c o n d u c t i v i t y is not l a r g e enough to t r a n s p o r t downwards the e n - e r g y p r o d u c e d in the ion gas following m o d e r a t e s e p a r a t i o n s b e t w e e n the ion and e l e c t r o n t e m - p e r a t u r e s .

Changes in the n e u t r a l a t m o s p h e r e a f f e c t the ion t e m p e r a t u r e p r o f i l e s by shifting the r e g i o n of i o n - n e u t r a l t e m p e r a t u r e d e c o u p l i n g with r e - s p e c t to the e l e c t r o n d e n s i t y p r o f i l e . T h i s e f f e c t is shown in fig. 3 w h e r e m o d e l a t m o s p h e r e s c o r - r e s p o n d i n g to n e u t r a l t h e r m o s p h e r i c t e m p e r a - t u r e s of 800 o, 1000 o, and 1394OK h a v e b e e n u s e d with T e = 2500OK and n e = 2 × 105 c m -3. T h e r e -

1,o~

A 2[

v

<

700

3o0

ne : Z xl0Scm "3 at 340 km T : 1394°K MODEL J1.55D

1000°K MODEL J 1.53 O 800°K MODEL J 1.53 D (NICOLET, [IS] )

T = I ~ * K

ION TEMPERATURE (OK)

"re

2500

Fig. 3. Effects of different models of the neutral at- mosphere upon ion temperatures. The chosen models have thermospheric temperatures of 8000, 1000o, and

1394OK.

g ~ I I I

I

i / • Data from EVANS [7]

,m for 1200 EST, Sept. 1963 / rt e = 3AxlOScm J at 300 km

T = lO00°K Te = 2600°K

3o~ I I I

to0o 1soo 2ooo 2SOO

ION TEMPERATURE (°K)

Fig. 4. Comparison of calculated and measured ion temperatures. The solid curve was calculated using a 1000OK model neutral atmosphere and the experimen- tal parameters of Evans [7]. The squares indicate the

measured values.

274 P.M. BANKS sult, which i s due to a c o m b i n a t i o n of t h e r m a l

c o n d u c t i o n and change in the ion h e a t i n g r a t e , i s that f o r g i v e n v a l u e s of e l e c t r o n t e m p e r a t u r e and d e n s i t y , the high a l t i t u d e ion t e m p e r a t u r e d e - c r e a s e s s l i g h t l y with i n c r e a s i n g n e u t r a l g a s t e m - p e r a t u r e s .

A s a f i n a l point, a c o m p a r i s o n has b e e n m a d e b e t w e e n the t h e o r e t i c a l c a l c u l a t i o n s b a s e d upon (6) with O + and H + ions, and the r a d a r o b s e r v a - t i o n s of E v a n s [7]. By c h o o s i n g n e = 3 . 4 x 105 c m -3 at 300 km, T e = 2600OK, and T = 1000OK to m a t c h the o b s e r v e d p a r a m e t e r s f o r 1200 EST, S e p t e m b e r , ]963, the r e s u l t s shown in fig. 4 h a v e b e e n obtained. T h e s q u a r e s r e p r e s e n t the e x p e r i m e n t a l data, w h i l e the s o l i d c u r v e r e p r e - s e n t s the t h e o r e t i c a l r e s u l t .

T o e v a l u a t e the i n f l u e n c e of diffusion (see d i s c u s s i o n f o l l o w i n g (3)), which has not b e e n i n - cluded h e r e , the d i v e r g e n c e of the s e c o n d t e r m in (4) has b e e n c o m p u t e d u s i n g the final r e s u l t s of the ion t e m p e r a t u r e and e l e c t r o n d e n s i t y p r o - f i l e s . F o r the diffusion e f f e c t to h a v e an i m p o r - t a n c e equal to that of t h e r m a l conduction, it is found that the ion diffusion v e l o c i t y , Ci, would h a v e to be about 7 x 103 c m s e c -1 which, f o r the c o n d i t i o n s i n d i c a t e d by E v a n s ' data, a p p e a r s to be too l a r g e to r e p r e s e n t the t r u e p h y s i c a l s i t u a - tion.

A s a t e s t f o r the e x i s t e n c e of l a r g e ion diffu- s i o n v e l o c i t i e s which could a l t e r the ion t e m p e r - a t u r e p r o f i l e , it is noted that a net m o t i o n of 7 x x 103 c m s e c -1 would y i e l d a d o p p l e r shift of n e a r l y 200 c / s at a r a d a r f r e q u e n c y of 430 M c / s . H e n c e , a l o n g with an a s y m m e t r y in the c h a r a c - t e r i s t i c e l e c t r o n t e m p e r a t u r e p e a k s t h e r e should o c c u r a d e t e c t a b l e shift in the r a d a r s p e c t r a half p o w e r points.

4. CONCLUSIONS

F r o m the p r e s e n t a n a l y s i s it i s c o n c l u d e d that t h e r m a l c o n d u c t i o n within the ion g a s e s of the i o n o s p h e r e can be i m p o r t a n t in m a i n t a i n i n g the high a l t i t u d e ion t e m p e r a t u r e at v a l u e s l e s s than the e l e c t r o n t e m p e r a t u r e . F u r t h e r , an ion e n e r g y budget which d o e s not i n c l u d e both H + (and p e r h a p s He + ) and the p r e s e n c e of a t o m i c h y d r o g e n and h e l i u m cannot be e x p e c t e d to y i e l d t e m p e r a t u r e p r o f i l e s which a g r e e with e x p e r i - m e n t a l data. T h e e f f e c t of ion c o o l i n g at high a l - t i t u d e s by m e a n s of d o w n w a r d s diffusion, a l - though not i n c l u d e d h e r e , m a y a l s o be i m p o r t a n t u n d e r p a r t i c u l a r c o n d i t i o n s in f u r t h e r i n c r e a s i n g the s e p a r a t i o n b e t w e e n the ion and e l e c t r o n t e m - p e r a t u r e s .

C h a n g e s in the p a r a m e t e r s of the c h a r g e d and n e u t r a l a t m o s p h e r e s a f f e c t the i m p o r t a n c e of t h e r m a l conduction in the ion e n e r g y b a l a n c e . In- c r e a s e s in the a t m o s p h e r i c t e m p e r a t u r e lead, f o r i d e n t i c a l e l e c t r o n t e m p e r a t u r e s and c h a r g e d p a r t i c l e d e n s i t i e s , to a d e c r e a s e in the high a l t i - tude ion t e m p e r a t u r e . L i k e w i s e , i n c r e a s e s in the o v e r - a l l e l e c t r o n d e n s i t y can be e x p e c t e d to i n c r e a s e the ion t e m p e r a t u r e and d e c r e a s e the ion and e l e c t r o n t e m p e r a t u r e s e p a r a t i o n .

S i n c e the e f f e c t i v e n e s s of the ion h e a t c o n d u c - tion t e r m d e p e n d s upon the dip a n g l e of the e a r t h ' s m a g n e t i c field, the s e p a r a t i o n of t e m p e r - a t u r e s at high a l t i t u d e s should be l a r g e r f o r h i g h e r g e o m a g n e t i c l a t i t u d e s . T h u s , when the d a t a of F a r l e y [8], taken at the g e o m a g n e t i c e q u a t o r , is c o m p a r e d with the r e s u l t s of E v a n s [7], and D o u p n i k and N i s b e t [9], t h e r e i s s o m e i n d i c a t i o n that t h e r e a r e i n c r e a s e s in the t e m p e r a t u r e s e p a r a t i o n s f o r the h i g h e r l a t i t u d e s i t e s .

A C K N O W L E D G E M E N T S

T h i s w o r k was s u p p o r t e d u n d e r g r a n t ONR(G)- 00009-66 f r o m the Office of N a v a l R e s e a r c h , Washington, D.C.

R E F E R E N C E S

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