Vol. 11, April 1982, pp. 71-75
Atomic Oxygen Cooling Rate in the F-region
PKSARKAR
School of Damodar Valley Corporation, Durgapur Thermal Power Station, Durgapur 713207 and
SNGHOSH
Department of Applied Physics, Calcutta University, Calcutta 700009 Received 13 November 1981
Similar to the rate of energy loss due to electron impact induced transitions in the fine-structure levels of atomic oxygen, the cooling mechanism of atomic oxygen arising from momentum transfer elastic collisions with slow ionospheric electrons is an important energy loss process. The calculated average cooling rates are J.J4 x 10\ 7.97 x 103and 2.17 x 103eV cm -3 see -1 at 200, 250 and 300 km, respectively. These results agree well with the experimental values of the total electron cooling due to various neutral and ionic constituents observed at Arecibo on 26 June 1968 at 0757 hrs by W E Swartz and
J
S Nisbet [JGeophys Res (USA), 78 (\973) 5640].
The collision frequency (lOcO) between electrons and oxygen atoms of the F-region isrepresented1s by between electrons and neutrals having different temperatures4 is given by
1
VcO
=
n(0)T:126(0)(~)2
nm* .... (4) ... (2) ... (1)
=
6.21 xlOSn(0)T:12 0"(0)sec-1 where0"(0)Momentum transfer collision cross-section of atomic oxygen with slow ionospheric electrons n(0) Atomic oxygen number density
m* Reduced mass of the system where
mc Electron mass
m Neutral mass Tc Electron temperature Tn Neutral temperature k Boltzmann constant
nc Electron number density
Vcn Electron-neutral collision frequency Sincemc ~ m,Eq. (1) reduces to
QCft
= -
3(mc/m)nck(Tc - T,,)vcn2 Energy Loss Expression
The rate of energy transfer due to elastic collisions 1 Introduction
Hanson1 and Dalgamo et al.2 investigated the thermal balance of F-region and showed that due to photoelectron heating by solar ultraviolet radiations, the electron temperature is greater than the neutral temperature. Geisler and Bowhill3, Banks4,s, Dalgamo et al.6, Herman and Chandra 7,8, Stubbe9, Swartz et al.10, Bailey et al.11 and others, developed theoretical methods for energy balance of the ionosphere to account for different processes of energy loss rates. Energy loss due to fine-structure transitions of atomic oxygen is the dominant cooling mechanism over a wide range of temperature throughout the E- and F-regions of the ionosphere12•13. The cooling of atomic oxygen by elastic collisions with electrons4 is smaller by two orders than that of fine-structure loss . rate12• Swartz and Nisbet14 pointed out that electron cooling rates of atomic oxygen developed by different workers1•3 -10 are different.
Atomic oxygen predominates in F-region as neutral constituent. The contribution of molecular nitrogen (N ~ towards collision frequency in this region is only about one-third of that between atomic oxygen and electron. The collision frequency due to molecular oxygen (O~ is negligible1s. In the present paper a general formula is developed for energy transfer rate of atomic oxygen by elastic collisions of low energy electrons with the help of electron-oxygen atom collision frequency inF-region1s.
71
U~ingEq. (4)the electron-neutral energy transfer rate can be represented as
QeO= - 1.863 x 106'(:e) k(Te - T.In(O)neO'(O)T~12 ergscm -3 sec -1 ... (5) 8.864 x 10 -9(Te - Tn)neveO
eVcm-3sec-1 ... (6) 3 Atomic Oxygen Cooling Rate
The rates of cooling of atomic oxygen arising from different electron temperatures and the corresponding electron-oxygen atom collision frequency in the altitude range 200-500 km are calculated. Different sets of electron temperatures are obtained from the following.
(i) Incoherent scatter observations at Millstone HiII16 on 3 July 1970.
(ii) Thomson scatter results at Millstone HilI17on 6- 8 Apr. 1965 at 1015 hrs EST.
(iii) Rocket-borne spherical ion trap launched from Eglin Air Force Base18 on 3 Aug. 1962 at 1146 hrs CST.
Table I-Atomic Oxygen Density, Electron Density and Neutral Temperature at Different Altitudes Altitude
Neutral AtomicoxygenElectron
km temperaturedensitydensity
K( x 10-3)
atem -3( x 10 -5)Tn=IOOOK
cm-3( X 10 -8) ionosonde Ground-based
200
0.90042.5603.0 210
0.90034.1903.5 220
0.95027.6704.0 230
1.00022.5904.6 240
1.00018.5304.8 250
1.00015.2405.0 260
1.00012.6204.8
Topsidesounder
270
1.00010.4504.5 280
1.0008.6894.2 290
1.0007.2443.9 300
1.0006.0393.5 310
1.0005.0583.4 320
1.0004.2363.2 330
1.0003.5483.0 340
1.0002.9782.9 350
1.0002.5062.7 360
1.0002.1132.5 370
1.0002.31.774 380
1.0002.21.493 390
1.0002.11.258 400
1.0002.01.064 420
1.0000.75861.9 440
1.0000.54321.7 450
1.0000.46991.6 460
1.0000.38991.6 480
1.0000.28051.3 500
1.0000.20231.2
72
(iv) Upleg probe data of NASA 6.04 rocket flight19 at Wallops Island, Virginia, on 26 Mar. 1961at 1156 hrs EST.
(v) Downleg probe data of NASA 6.07 rocket fligheO at Wallops Island, Virginia, on 18Apr. 1963at 1604 hrs EST.
The elastic collision cross-sections of oxygen atom for temperatures given in items (i)-(v) above are obtained from the theoretical results of Mitra etal.21 and the corresponding temperature profiles of electron-oxygen atom collision frequencies are determined 15.The atomic oxygen number density and . the neutral temperature are taken from Jacchia's atmospheric model22. The ground-based ionosonde and topside sounder results for electron number density are taken from Narcisi23. Neutral tempera- tures, atomic oxygen densities and electron densities are tabulated in Table 1. The calculated altitude profiles16 -20 of atomic oxygen collision frequencies and cooling rates arising from elastic collisions with electrons having different temperatures corresponding to items (i)-(v) above are shown in Figs. 1 and 2, respectively. The loss rates compared with that due to fine-structure6 and experimental results at Arecibo14 are also shown in Fig. 2.
4 Discussion
Atomic oxygen cooling rates due to elastic collision with very low energy electrons agree with those of Dalgarno et al.6, Herman and Chandra 7,Stubbe9 and Swartz et a/.10, but do not agree with the results obtained by Banks4.5. The average atomic oxygen energy loss rate in the altitude range 200-300 km obtained by those workers lies between 4.0 x 103 and 4.6 x 102 eV cm -3 sec -1. The average oxygen cooling rates at 200, 250 and 300 km are calculated and found to be 1.14 x 104, 7.97X 103 and 2.17 x 103 eV cm-3 sec -1, respectively. These values agree with the observed values of total electron cooling rates found to be 1.4 x 104,8.0X 103and 4.1 x 103eV cm -3 sec -1 due to various neutral and ionic constituents at Arecibo on 26 June 1968at 0757 hrs14. The experimental values of electron-oxygen atom cooling rates at Arecibo on the same datei4 are also obtained and are found to be slightly lower, viz. 6.0 x 103,3.5X 103 and 1.3 x 103 eV cm - 3 sec -1 at 2OQ,250 and 300 km, respectively. Mitra etal.21 calculated quantum mechanically the collision cross-section of atomic oxygen with slow electrons by employing Hartree's numerical solution. Bates and Massey24 also calculated the collision cross-section of atomic oxygen introducing a polarizability parameter
(p). The values of collision cross-section of atomic oxygen(0'0)obtained from Mitra etal.21, which is of the order of 10-4 cm2, agree closely with those obtained by Bates and Massey24 for p = 18.3 auiS.
..
I
/
Banks4 adopted the expression of momentum transfer cross-section of atomic oxygen with slow electrons after Cooper and Martin2s• The phase shifts computed by these authors2s are not accurate at low energies. They obtained cross-section (0'0) to be (3.4
±
1.0)x 10-16 cm2 which is independent of the electron temperature below 4000 K. Banks used thecross-section of atomic oxygen as 4-5 x 10-16 cm2in one place4 and as I x1O-1S cm2 in someotherplace2o•
No experimental data of0'0below 2 eV are obtained due to chemical affinity of atomic oxygen.
Experiments were performed above 2eV which is much greater than the ionospheric electron energies.
The experimental value of Daiber andWaldron26 is of
400
200 2
10
CURVE 1
2
3
4
5
103
COLLISION FREQUENCY. sec-1
REFERENCE 16 17 18 19
~O
Fig. I-Curves showing the variation of electron-atomic oxygen collision frequency with altitude
.103
COOLING RATE ..•eV cm-3 see-I
400
...
UJ
o
::::>
~
6
300<t
200 2 10
CURVE
1
2 3
4 5
6
REFERENCE 16 17 18 19
20
12 (OUETO\FINE-STRUCTURE; \
14 (EXPTL OS5.1
Fig.2-Curves showing the variation of atomic oxygen cooling rates with altitude
73
the order of 1.7 x 10-15 cm2. However, the values obtained by other investigators27 at above 0.5 eV is
1.5-5.5 x 10-16 cm2.
Baluja et a1.28considered the collision cross-section of atomic oxygen with electrons as 1.8-5.8 x 10-16 cm2 from the theoretical work of Thomas and Nesbet29.
These workers29 expressed the view that their results are not expected to be sufficiently accurate for the experimental as well as theoretical scattering data at low ionospheric energy required for calculation of collision cross-section of atomic oxygen.
The collision frequency of electrons with atomic oxygen ions in F-region has been calculated by Nicolet30 and many others5,31 -35 and its value is found to be 0.5-3.0 x 102 sec-1. Agarwal et al.36 calculated collision frequencies of electron with ions in F-region for quiet sun
(iiz =
10) and active sun(iiz
=
100) and the values are of the order of 102and 103 see -1, respectively (Fig. 6 of Ref. 36). However, they found the average for quiet and active sun as 1- 2 xX103sec-1 (Fig. 7 of Ref. 36) and concluded that the effective collision frequency in F-region is entirely due to collision between electrons and ions, which is not reasonable.
From cosmic radio noise absorption by riometer measurement, Saha and Venkatachari37•38 suggested that the electron-ion collision frequency predominates in F-region. But, their method is not capable of measuring F-region component of absorption for values less than 0.1 dB (for a frequency of 20 MHz). It is capable of measuring the absorption for F2 peak having electron density in the range between 5.0 x105 and 1.0x 106cm-3 and not below. It is, therefore, not possible to detect high values of electron temperature greater than 2000 K (Ref. 39). The electron density profIle ofthe same day and period is required when the absorption is measured by cosmic radio noise technique. However, the density profIle ofF-region on the day of the experiment was not considered. These workers37 obtained the low values of daytime electron temperatures as 600 and 870 K at Delhi, respectively, during 1964-65 and 1967-68 from pulse absorption measurement of cosmic radio noise technique. From these measurements of electron temperature it is inferred that the collision frequency of electron- neutral dominates in F-region rather than that due to electron-ion collision.
Utlaut40 conducted an ionospheric modification experiment using very high power, high frequency transmission in F -region at Boulder and estimated that the electron temperature increased by 30% whereas the amplitude of o-component decreased by about 10dB.
If the collision of electron with ions were dominant, the amplitude must have increased contrary to the observed results. This also suggests that the dominant 74
mechanism of collisions in F-region is due to those of electrons with neutral particles.
The theoretical value of electron-ion collision frequency(0.5-3.0 x102sec-1)becomes less by a factor often than the experimental value of effective collision frequency (2-5 x103sec-1) in F-region41 which is entirely due to electron-atomic oxygen collision. The collision cross-section «(j0)of atomic oxygen should be of the order of 10-14 cm2. The experimental value of collision frequency in F-region41 agrees with that obtained from Eq. (4). The value is larger by two orders than that of Banks4. Values of momentum transfer elastic collision cross-section of atomic oxygen with low energy electrons used in Eq. (4) are two orders larger than that of Banks4• It may be noted that cooling rate is directly proportional to the collision cross-section of the neutral constituent of the atmosphere and hence to electron-oxygen atom collision frequency(veo).This accounts for two orders higher value of cooling rate obtained by us compared to that ofBanks4. Therefore, it may be concluded that predominant mechanism for atomic oxygen cooling rate in the F-region is the elastic collision with thermal electrons.
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