A computer code to accurately compute the fluctuation spectrum for linearly speed dependent collision frequencies was developed. The effect of ignoring the speed dependence on the estimates of ionospheric parameters was determined. It is shown that disagreements between the rocket and the incoherent scatter estimates could be partially resolved if the correct speed dependence of the i-n collision frequency is not ignored. This problem is also relevant to the study of ionospheric irregularities in the auroral E-region and their effects on the radio communication with satellites

Theimer, O.

English

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}SFEED-DEPENDENT COLLISION EFFECTS ON
RADAR BACK-SCATTERING FROM THE IONOSPHERE
(NASA-CR-168746) SPEED-DEPENDENT COLLISION 	 N82-21456
EFFECTS ON RADAR BACK-SCATTERING FROM THE
IONO:iPHERE Annual Report, 1 Sep. 1980 - 30
Nov. 1981 (Neer Mexico State Univ.) 17 p	 Onclas
HC A02/MF A01	 CSCL 20N 63/32 09540
9 ,	 Annual Report
Principal Investigator: Dr. 0. Theimer
Period September 1, 1980 to November 30, 1981
J	
_ Y L -
C' ^V
y4i 4
New Mexico State University
Box RC, Las Cruces, NM 88003
Research Grant #NSG-1622
i 	 r
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k t
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Abstract	 . . . . . . . . . . . . . . . . . . . . . .
I. Introduction	 . . . . . . . . . . . . . . . . . . . . .
II. Results	 . . . . . . . . . . . . . . . . . . . . .
i) i-n collision frequency . . . . . . . . 	 . . . . .
ii) a-n collision frequency . . . . . . . . . . . . . .
III. Future research plans
	
. . . . . . . . . . . . . . . .
Figure 1. The fluctuation spectrum as a function of
normalized frequency Wkve . . . . . . . . . .
Table I. One ionic-species plasmas without drift.. .
Table II. Comparison of results of the minimum-X2
analysis for model spectra computed by
using a semi-linear approximation and
computed numerically using no approximations.
Table III. Critical drift parameters of one ionic-species
plasmas for speed-independent and speed-
dependent i-n collision frequencies; a-n
collision frequency is set equal to zero.	 .
Table IV. Critical drift parameters of one ionic-
species plasmas for speed-independent and
speed-dependent i-n and a-n collision
frequencies; T r is equal to 1.0	 . . . . . .
References	 . . . . • . . . . . . . . . . . . . . . . .
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2ABSTRACT
Rockets and radars are two main instruments available to experimentally
investigate the collision dominated E region. But the estimates of some
ionospheric parameters like density of neutrals and the electron-ion
temperature ratio common to the two techniques are not in agreement.
The reason for these disagreements may lie in the fact that the charge-
neutral collision frequencies are assumed to be speed-independent in the
estimates of ionospheric parameters by the incoherent scatter technique.
However, mobility measurements and calculations indicate that the ion-
neutral collision frequencies are speed-dependent. Under NASA grant
NSG-7622, we have developed a computer code to accurately compute the
fluctuation spectrum for linearly speed-dependent collision frequencies.
We have also determined the effect of ignoring the speed-depenuence on the
estimates of ionospheric parameters. It appears that disagreements
between the rocket and the incoherent scatter estimates would be partially
resolved if the correct speed-dependence of the i-n collision frequency
is not ignored. This theoretical investigation amply justifies the need
to experimentally investigate the problem. This research problem is also
relevant to the study of ionospheric irregularities in the auroral E
region and their effects on the radio communication with satellites.
3I. Introduction
The ionosphere occupies a key position in the earth's atmosphere,
which hosts probably the broadest range of physical processes and
phenomena within any single physical system. The ionosphere is associated
with the problems of practical interest like radio communication, satellite
drag and atmospheric electricity. An accurate estimate of various
parameters in this region is also important with respect to the construc-
tion of neutral atmospheric models (Salah et al., 1975; Stein and Walker,
1965; Wand, 1969). Presently, many different experimental techniques are
available involving rockets, satellites, and ground-based radars to
investigate the ionosphere. Because of the huge number of variables
involved in ionospheric investigations, no single experimental technique
can estimate all the variablea. Therefore, each technique depends heavily
on other techniques in estimating ionospheric parameters and in constructing
ionospheric models (CIRA, 1972; Hedin et al., 1977). Also, the estimates
of the parameters common to more than one technique provide checks on the
accuracy of these techniques. As a matter of fact, disagreements do exist
both with regards to estimates of some parameters (Brace et al., 1969;
Farley, 1970, Giraud et al., 1972; Salah et al., 1975; Smith et al., 1968;
Trinks et al., 1978; Wand, 1976) and with regards to the overall picture
of the thermosphere (Rishbeth and Kohl, 1976). Our research efforts under
NASA grant NSG-7622 have been directed towards some disagreements between
the rocket and the incoherent scatter estimates of the density and
composition of neutral gases and the electron-ion temperature ratio in the
collision dominated E region. Our research is also relevant to the
scintillations of radio signals from satellites by the irregularities in
the auroral ionosphere (D'Angelo, 1968).
4In the E region dominant collisions are between charged particles
and neutral atoms find molecules. To the best of our knowledge, in the
analysis of the incoherent scatter data the collision frequency is assumed
to be speed-independent. However, mobility calculations and measurements
(Dalgarno at al., 1958; McDaniel and Mason, 1973; Eisele at al., 1979,
Perkins at al., 1981) indicate that i-n collision frequencies for i-n
pairs relevant to the E region are in far,: F: )eed-dependent. In our past
work (Bahl, 1977; Theimer and Bahl, 1977, 1980) we found that fluctuation
spectra for linearly speed-dependent and speed-independent collision
frequencies were significantly different. The computer code to compute
speed-dependent plasma functions and spectra has been improved under the
present grant but the above mentioned differences remained significant.
We have also determined the effect of these differences on the estimates of
ionospheric parameters by the incoherent scatter technique. Tne results
of this analysis are presented in Section II. In Section III, we discuss
the future plans of the research.
II. Results
i) i-n collision frequency
To see the effect of the speed-dependence of the i-n collision frequency
we computed fluctuation spectra for constant and linearly speed-dependent
collision frequencies. The computations for values of parameters typical
to the E region are presented in Figure 1. Curve B (y i yiv/vi) has a
narrower and bigger peak at w w 0 than Curve A (yi W yi ) implying that the
collision effects are enhanced by the linear speed-dependence of the
collision frequency. The differences between Curves A and B are larger or
ssmaller in magnitude depending on the value of yi . vin/kvi . We have also
determined by the X2 test the effects of these differences on the estimates
of ionospheric parameters by the incoherent scatter technique. X2 is
defined as (Alder and Roessler, 1972)
X2 '	 (ej-oj ) 2 /ei .3
where e  and of are the values of the jth point of the standard spectrum and
the model spectrum, respectively. A standard spectrum corresponds to
speed-independent collision frequencies and a model spectrum corresponds to
speed-dependent collision frequencies. We choose a set of two parameters,
call them modelling parameters. One of the modelling parameters is the
collision parameter yi ; by varying the two modelling parameters we find the
minimum-X2 model spectrum. By comparing the modelling parameters of the
standard and the minimum-X 2 model spectra we can estimate the effect of
ignoring the speed-dependence of the collision frequency.
We have applied the above procedure to a drift-free, one ionic
species plasmas using the a-i temperature ratio Tr and the ion collision
parameter yi as the modelling parameters. The inaccuracies in estimating
these parameters caused by ignoring the speed-dependence are shown in the
last two columns of Table I. In all the cases considered, the temperature
ratio is not significantly affected, but y is over-estimated by about
40%. Since the collision frequency is proportional to the density of
neutrals, this means that the density of neutrals would be over-estimated
by about 40% by the incoherent scatter technique using constant collision
frequencies. If the collision frequency is proportional to v p instead,
qualitatively speaking, the effects will be smaller if p<1 and larger if
p>l.
6In Table II, we have compared the above results with the results
based on the model spectra computed by applying certain approximations
(Theimer and Bahl, 1980; Theimer, 1980). t The differences in a-i
temperature ratio have been almost completely eliminated, and the differences
in the estimates of yi (i.e., the density of neutrals) have been enhanced
due to the improvements in the accuracy of the computed fluctuation spectra
for speed-dependent collision frequencies. Therefore, all the efforts
directed towards improving the computer code seem to have been worthwhile.
We have also considered one ionic-species plasmas in the presence
of electron drift relative to ions and neutrals. In this case, we computed
the critical drift both for the constant and linear speed-dependent
collision frequencies. The critical drift is that drift at which the value
of the peak corresponding to the ion acoustic line is a maximum. It appears
from the numbers presented in Table III that the critical drift will be
underestimated if the speed-dependence of the collision frequency is
ignored, however, the extent of underestimation would depend on the a-i
temperature ratio. Incidentally, a-i temperature ratios can be quite large
in the auroral E region under disturbed conditions (Ogawa at al., 1980;
Schlegel et al.. 1980) .
ii) a-n collision frequency
The speed-dependence of a-n collisions (ven (v) m v2 ) has been incor-
porated in the computer code during the grant period of this report. The
low frequency fluctuation spectrum of drift-free plasmas does not seem to
be significantly modified even for large values (-5) of T r ; remember that
the contribution of the electron line to the fluctuation spectrum increases
tAnnual report, 1980, NASA grant NSG- 7622
7with increasing value of T r . However, we did observe some modifications
of the critical drift parameter when the speed-dependence of the e-n
collision frequency is included.
We couputed critical drift parameters for four possible combinations
of the speed-dependence: both van and vin constant; van constant, and
vin a v; von s v2 , and vin constant; and both vaA and vin speed-dependent.
The results are tabulated in Table IV. The a-i temperature ratio in all
cases is equal to 1.0. The critical drift parameter is decreased when a-n
collisions are not neglected. A comparison of columns three and five In
Table IV indicates that this decrease is enhanced when the quadratic
speed-dependence of the a-n collision frequency is included. These effects
are smaller or larger depending on the values of ye and yi . However, the
effect of including the speed-dependence of the i-n collision frequency
(compare columns five and six of Table IV) is to slightly increase the
critical drift parameter. These effects need to be investigated more fully
for higher a-i temperature ratios.
The results of this section were presented in the Fall 1981 meeting
of American Geophysical Union at San Francisco.
III. Future Research Plans
Our results based on the exact computations of fluctuation spectra
for the speed-dependent collision frequencies clearly establish that
ignoring the speed-dependence of ion-neutral collisions would significantly
modify the incoherent scatter estimates of the density of neutrals.
However, these results are based on the theoretical analysis, and therefore,
need to be checked experimentally. To perform the radar back-scattering
experiment, we shall need to go to some national lab like the Arecibo
8Observatory in Puerto Rico_ It takes about six months for the approval
for the radar time (Dr. M. Sulzer, the Arecibo Observatory, private
communications), and 3-4 months to analyse the data. This experimental
investigation will help us obtain more accurate estimates of the density
of neutrals and, in all likelihood, will lead to better agreements between
the rocket and the incoherent scatter estimates.
Many theoretical aspects of the problem could also be investigated,
either in lieu of or in oddition to, the above mentioned experimental
investigation. F.r exc:,.c, the phenomenon of ion-acoustic instabilities,
i.e., astimnras of critical drift parametu:rs and the corresponding wave-
lengths, needs to be investigated further through literature survey and
the theoretical analysis of the kind discussed in Section II. Currents
large enough to excite ion-acoustic instabilities do occur in the auroral
E region, and the related problems like scintillations of radio signals
are of practical importance in the radio communication with satellites
(D`Angelo, 1968).
90
0
N
0
0
C;
V
yi	 0.5
mi = 31.5
Te/Ti . 1.0
o
^, o
y o
a0	 Curve A
va
o
U O
O	 curve B
0
0
U^
M
0O
8;00	 0.03	 0.06	 (X . 09
-1 	
0.12
	
0.15
Frequency w/kva
Figure 1. The fluctuation spectrum as a function of
normalized frequency w/kve . Curve A corresponds to a speed-
independent collision frequency and Curve B corresponds to
linearly speed-dependent collision frequency.
i
Table I. One ionic-species plasmas without drift.
Tr
 is the a-i temperatures ratio; y i •
vin/kvi. where k is the wave number and
vi
 is the ion thermal speed.
Standard Spectrum Minimum-X2 Model Spectrum 2 Difference
Tr yi Tr yi Tryi
1.00 0.10 0.98 0.11 2 40
0.30 0.98 0.17 2 4:!
0.40 0.98 0.24 2 40
0.50 0.97 0.30 3 40
1.50 0.50 1.47 0.30 2 40
2.00 0.50 1.96 0.29 2 42
r
11
Table II. Comparison of results of the minimum-X 2 analysis
for Lodel spectra computed by using a semi-linear
approximation and computed numerically using no
approximations.
Standard Spectrum
Difference Between Standard and
Minimum-X2 Model Spectra
Semi-Linear Approx. 	 Exact
Tr gi Tr 71 Tr 91
1.00 0.20 26 25 -2 40
0.30 34 33 -2 43
1.50 0.2C 14 27 -2 45
0.30 19 37 -2 43
2.00 0.20 8 45 -2 45
0.30 12 43 -2 43
12
Table III. Critical drift parameters of one Tonic-species
plasmas for speed-independent and speed-
dependent i-n collision frequencies; e-n
collision frequency is set equal to zero.
Tr
Critical Drift Parameter
y 	 ^ yi 	 yi'gi v/qi
2 Difference
1.0 0.2 1.02 1.02 0
3.0 0.1 0.40 0.44 10
0.2 U.46 0.51 11
0.3 0.51 0.56 10
5.0 0.1 0.23 0.28 22
10.0 0.1 0.08 0.12 50
13
Table IV. Critical drift parameters of one ionic-species
plasmas for speed-independent and speed-
dependent i-n and e-n collision frequencies;
Tr
 is equal to 1.0
7e 7i
Critical Drift Parameters
7e = 7e ^ 7e a 7e . 7e^'e a/°e. Ye=Ye V2 V;.
7i	7i pi-'i V/vi 7i	 71 7i-7i V/^i
0.00 0.3G 1.04 1.07 1.04 1.07
0.11 0.30 0.98 1.01 0.95 0.97
0.00 0.50 1.09 1.12 1.09 1.12
0.18 0.50 1.00 1.03 0.95 0.98
0.00 0.80 1.14 1.17 1.14 1.17
0.29 0.80 1.01 1.06 0.93 0.96
14
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16
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Speed-dependent collision effects on radar back-scattering from the ionosphere

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