Presunrise heating of ambient electrons in ionosphere due to conjugate point photoelectron

Kwei, M. W.

Nisbet, J. S.

English

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ABSTRACT 
Ck377 
/ I  
"Presunrise  Heating of the Ambient Electrons in the 
Ionosphere due to Conjugate Point Photoelectrons" 
M. W. Kwei and J. S .  Nisbet 
Iono spher e Res ear  ch Labor ator y 
The Pennsylvania State University 
University Park,  Pennsylvania 
In winter, as has previously been, reported, the electro 
a t  Arecibo s ta r t s  to increase prior to local sunrise following illumination of 
the conjugate ionosphere. 
The mechanism of this increase is examined. The roles  played by 
heat conduction along the field line and by photoelectrons which t raverse  the 
field line %re investigated. 
photoelectron f l G x  f rom the conjugate region including the effect of elastic 
collisions with neutrals in confining the photoelectrons. 
Detailed analyses a r e  made of the escaping 
Comparisons 
between the theoretical heat input and observed energy losses or" arnient 
electrons a r e  presented. 
compared. 
I. INTRODUCTION 
Also the theoretical and measured heat fluxes a r e  
The presuxrise heating of the ambient electrons in the ionosphere 
was f i r s t  noticed by a ser ies  of experiment performed at the Arecibo 
Ionospheric Observatory, Puerto Rico by Carlssn and Nisbet (1965) in 
December 1964. 
Arecibo data, and by Carru,  Peti t  and Waldteufel (1966) using the data obtained 
at  Saint-Santin de Maurs in France.  The observations have indicated an 
increase in the electron temperature during the predawn period in the ionosphere 
Since then i t  has been discussed by Carlson (1966) using 
https://ntrs.nasa.gov/search.jsp?R=19680018397 2020-03-12T10:02:41+00:00Z
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above an altitude which var ies  with latitude and solar cycle. 
sunspot condition at Arecibo this altitude is about 300 km. 
the electron temperature as a function of time at 400 km level. 
Under low 
Figure 1 shows 
Any theory for the photoelectron heating of the conjugate region must 
explain two pieces of data. The f i r s t  is the observed heating of the F-region 
a s  a function of altitude and the time and the second the downward heat fluxes 
f rom the protonosphere, both during the sunrise period and throughout the 
day. 
11. METHOD OF CALCULATING THE DOWNWARD HEAT FLUXES AND 
HEAT INPUT TO AMBIENT ELECTRONS 
The mechanisms relevant to this pre-sunrise heating will be discussed 
below. The continuity equation 
a = P - L - div (nv) a t  
can be written for the photoelectrons produced at the conjugate point, The 
solution of this equation is extremely complicated because in the upper F 
region losses  to the ambient electrons a r e  comparable with those to inelastic 
collisions with neutral particles while the transport  is considerably affected 
by elastic neutral collisions. A t  the higher energy levels electrons may lose 
several  electron volts in a single inelastic collision and the angle between the 
photoelectron velocity and the local magnetic field must be considered. 
In the approach adopted here  the analysis starts with the assumption 
of steady state condition and as  an initial approximation neglects the transport  
term. Based on this approximation it is possible to calculate the photoelectron 
densities as a function of altitude and energy in a manner similar to that 
employed by Hoegy, Fournier and Fontheim (1965). 
this paper is drastically different f rom that implied in previous analyses. 
The approach adopted in 
In 
this paper i t  has been assumed that the elastic collisions with neutral particles 
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play a dominant role  in controlling the diffusion flux of the photoelectrons in 
an upward direction. When a photoelectron moves downwards into a region 
of increasing neutral density, the mean f ree  path between neutral elastic 
collisions is shorter than i t  is in an upward direction. 
upward flux at all altitudes depending upon the photoelectron density at a given 
energy, the velocity of these photoelectrons, the mean f r ee  path required to 
randomize the photoelectrons velocity vector 
There is thus a net 
and the number density and 
gradient of the density of the neutral particles controlling the cd l i s ion  process. 
For  the simple case when the mean f ree  path is much less  than the scale height, 
cos 8 sin I for X << H where H i s  V X  the diffusion velocity redu.ces to 7 = -6 H  
the neutral scale height, X the mean f ree  path of photoelectron in elastic 
collisions with neutral particles, I the magnetic dip angle, 0 the angle between 
the velocity of photoelectron and magnetk field line, and v the thermal velocity. 
Corresponding formulas to that given above have been solved using a digital 
computer for the case where X is comparable or  greater  than H. 
by these calculations that the divergence of n 7  is small  compared to the other 
terms in the continuity equation and hence it is permissible to use the energy 
distribution of photoelectrons determined based on the equilibrium assumption 
to determine the upward-going flux of photoelectrons 
It is found 
The next relevant calculation i s  the amount of heat deposited along the 
field line by this upward flux of photoelectrons above EL height of about 1000 km. 
The photoelectrons lose their energy to the ambient electrons along the field 
line through elastic collisions. The loss  in each energy and angular range can 
be readily calculated. The photoelectron energy flux along the field line is 
given by 
H = z 7 Ex (Eo, 0 )  a (Eo, 0 )  
X 6.J 
Eo 8 
where is the photoelectron flux, and 
x -12 = 2 3 . 9  x 10 
cos e Jo nedX Ex = 0 -  
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Under low sunspot condition, the probability that the incoming photo- 
electrons make a collision with the neutrals above 300 km level is quite small. 
As the incoming photoelectrons spiral  down the field line f rom 1000 km level, 
they will lose their energy through elastic collisions to the ambient electrons 
in the dark ionosphere above Arechibo. The heat input to the ambient electrons 
due to the incident photoelectron fluxes is given by 
1.95 x n @ (Eo, e )  
Ex (Eo, e )  cos 8 
e 
Q i =  2 C 
Eo e 
III. THE ENERGY LOSSES OF AMBIENT ELECTRONS 
The energy losses  of ambient electrons in the dark ionosphere above 
Arecibo a r e  calculated using the following equations: 
4 1 2.3 x 10 
e 72.8 x l o B 6  T - 0.23 - 
525 4- 0.125 T 6 7 . 5  x l o a 6  T," e 72.5 4- 8.65 x l o e 3  Te 
Qpzesent work) 
1 -* 
ID ' {Te - Tn}, (Banks, 1966) -18 zz -3 e 74 x 10 ne r, (0)  Te Qo (elastic) 
Q o (rot .  vib) = -1.31 x 10 -4 n e .n(02) -14T e -8 x 10 -'2}{Te - Tn} 9 
2 
(Hansonn, 1963) 
1 1 
_D 
= -1.21 x 10 -18 nen(02)  {I + 3.6 x P O w 2  Te2} TeZ {Te 1 Tn} 
QoZ(elastic) 
(Banks, 1966) 
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*NZ(rot. ) = - n e n  (N2) 1.57 x - 7.35 x 10 -19T n }{Te- Tn}, 
(Dalgarno, 1963) 
a*% i --e 
(Banks, 1966) 
*; 
3 
3 '' {Te - Ti}, (Hanson and Johnson, 1961), -7 2 Q o t  = -4.82 x 10 n e Te 
neglecting helium ion content at and, below 400 km level. 
IV. THE MODEL ATMOSPHERE AND CROSS-SECTIONS 
For  calculations of production rates of photoelectrons we have adopted 
the photon fluxes, absorption cross-sections and photoinoniaation cross-secfions 
published by Hinteregger e t  al. (1964) (mean solar f l u x  a t  10,7 c m  in July 1963 
was 76 and that in December 1964 was 75.2). 
The composition of the neutral atmosphere was taken from the Harr i s  
and P r i e s t e r  (1964) model. 
The electron density a t  3000 km level above Jicamarca,  Peru,  measured 
4 -3 by Farley-in the ear ly  morning on February 3, 1965, is about 10 c m  
According to Brace and Reddy (1965), the electron density at 1000 km level, 
50's - 50° N meg.. measured by Explorer XXII at night (0000 - 0330 hrs . )  i n  
Nov. - Dec. 1964 is between 10 and a b o u t 2 . 5 ~  10 c ~ n - ~ .  Based on these 4 4 
measurements i t  seems reasonable to a s s m e  the total electron content of a 
13 -2 tube of force above 1000 krn to be 10 c m  . . 
For  the spatial r a t e s  of energy loss of photoelectrons to neutrals we 
used the various inelastic collision c ross  -sections published by Fi te  and 
Brackmann (1959), Boksenberg (1961), Rapp e t  al. (1965), Engelhardt et al. 
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(1964), and Dalgarno (1961). For the arift velocity of photoelectrons we 
employed the total collision c ross  -sections published by Brode (1933), Sunshine 
et al. (1966), and Engelhardt et  al, (1964). 
V. THE RESULTS AND COMPARSIONS WTTH OBSERVATIONS 
Fig. 2 shows the upward-going fluxes of photoelectrons a€ 300 km level. 
ron energy flux along the field line. Fig. 3 shows the variations of the photael 
It can be seen that the energy deposited along the field line above an altitude of 
1000 km is about 2 x 10 ev - cm w sec . The thermal capacity of both the 
ambient electrons and ions along the field line 
heated up rapidly. 
9 -2 -1 
very small so they can be 
The time constant for  thia heating process is about 10 
minutes, thus in l e s s  than about 1/4 of an hour equilibrium would be estab- 
lished. 
For this calculation some approximation must be made +bout the temperature 
gradient at the conjugate region for which no data of this type is available. 
Fig. 4 shows the measured downward heat flux compared with the theoretical 
This heat will  be condycted downwards at both ends of the field line. 
values. 
present at both ends of the field line, and curve B is based on the heat flux 
observed at Arecibo in summer the same length of time after sunrise, When 
the measured heat flux is extrapolated to the 1000 km level, it may be some- 
where in the neighbourhood of curves A and €3, 
Curve A is obtained under the assumption that equal heat fluxes a r e  
Fig. 5 shows the heat input from the photoelectrons to the ambient 
It electrons compared with the total heat losses of the ambient electrons. 
is apparent that estimates of the photoelectron flux is greater by a factor of 
approximately two. The distribution of the heat input as a 
is quite similar for the theoretical and measured profiles. 
function of altitude 
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VI. CONCLUSION 
Jt appears that the assumptions we w e d  and the data agree within a 
factor of two for both the heat f l u x  conducted downwards from the protonosphere 
and the local heating by migrating photoelectrons in the ionqsphere above 
Arecibo. 
in the model used, or in the experimental data, remains to be determined. 
Further measuremeets at Arecibo and other locations will be valuqble in 
studying the relative energy loss along the field line and the time difference 
between local and conjugate point sunrise. 
Whether the e r r o r s  a r e  in the assumptions employed in the analysis, 
ACKNOWLEDGMENTS 
We wish to express our thanks to Dr.  Brace who supplied us with 
electron densities and temperatures f rom Explorer XXII. The electron 
densities obtained at Por t  Stanley were kihdly supplied to us by R. R. S. Slough. 
The authors a r e  grateful to the staff of the Arecibo Ionospheric Observatory 
and Mr. J. Doupnik, Mr. R. Divany, and Mr. R. Warner of the Ionosphere 
Research Laboratory of the Pennsylvania State University for obtaining the 
data on which this work is based. The Arecibo Ionospheric Observatory is  
operated by Cornel1 University with the support of the Advanced Research 
Projects Agency under a research contract with the Air Force Office of 
Scientific Research. 
under NASA Grant NsG134-61. 
Support for obtaining and analyzing the data was provided 
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Carlson, H. C. , and J. S. Nisbet, "Electron Densities and Temperatures in 
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Presunrise Heating of the Ambient Electrons in the Ionosphere Due to Conjugate Point Photoelectrons

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