Electron temperatures determined by electrostatic probe, diffuse resonance, and radar backscatter techniques in an isotropic two temperature plasma are presented. Plasma models corresponding to the addition of a minor component of energetic electrons, and models corresponding to a process that cools a fraction of the ionospheric electrons are considered. The diffuse resonance temperature is found to lie between the probe and radar backscatter temperatures. The isotropic models corresponding to the addition of energetic electrons cannot support the reported discrepancies between radio wave and probe electron temperature measurements. Temperature differences similar to the observed differences can be produced by models with a fraction of the electrons at a temperature cooler than that of the main component of electrons

Benson, R. F.

Hoegy, W. R.

English

NASA Technical Reports Server

~-~ ~.~ ~ - -. <(\'~ -c-~ _~' lz: -~; '-~ ~ '--: ..>-%- -'--k..-62t- - - : .:.-7 .-24 . '.c 
~''. '~.-~':~-,~'<'., V_-:-~:..,~~-' X~~,,<- :~ ~ -'  - _~-~'' -K '~.,-'/' ~<:5~--s:.-.P'R: -P: / .k' 
- ~.~' '~ -c ',-'... ~-'-.... :"-'' . : ~ ,'--.' . · - ' ~~. > ~-- 'v -'~ - ~ : :' . ' .<· 
>-.l'? '': .. ~,:.~-, ' -";-. '. '~ ' - '- '-~- ~ '--~./ -. * ~- ->-~ ~ %..~ :,:
,_::.:::,:: : ::  N:N ',EQ I ILK -
._' -q.~~~~~~N -E',
: :.:_>ME/~~:EAS:ORE:ET :STM~~~? .... MM<
:::. -: WALTER :R.: HOE~~~~~~~~~~~~~~-GY r,:z
,.-. . ~: <': ¢ - -. -~ . . . . C_ - , . . - , , + ...
- '-' i~ ~ .. ~:> --..~,~ ~ - :.~ .  ~  ~ ~ ~ ~ ~ ~ ~ ~
,~ .~. ; .k..-q.-~ . ' ' O ' '~' --. > ': -~ ... '" *. : ~ ~'' - .. - .. ~;z' 
: :',,V" . NASA - TM.:'}158 TH EFFCT$.0CC OFAN UN73as4
, >:.-:~.:-> '-.:_~( ~~ ~ ~G3/13 ·53803 ·V>-;
· , .:-. 1~,- '''?~' ~'> - ~ '~- ." ~'"-~- '' ":: -:-~ -. -- ,"- .6: -: .~': ~: '~::-77-7: ..
· ,~ c- I': ~ ~ ~ '-~-,'~" .:~-'":'~:."-*-,"- . . ..-Z' ' :'....<'R- .9<-''/- ~-<'~
';'" -- -"N/ -~.:~ ~~ ~: ;j,: ... ,. .. , ,.~' ~~-~-~~ , ' ' .~" 
Z-~.'tF' "~-' i ... :-- ~ '~ ~ > :~':'-,, ?:.~: - --' % " ~',--~"'-.". ' -""~'-~c,, ,~'-.~-,~ ~' _'~. -~ .- ;/ / < ,/-.,.A
;/ - - ~ I --- '¢ 'MR"C,-E
g~~~~,,~. >*~j~ ~, ~~~t -L " - ~.x. - . 4~'.. t., ~~.~~&/.~-;-.
"-,, ''._' ! :' ' .~- ,-, . " ~ 'i~L_ ;.'x ' ':.-~: .. ,~ .. ('-:~~,-, ,::.:,.;,-.,,t -, 
. ,i -. '> 7--...:' - _-,.-. ':.,-< .'A- '> ---- ' .,-.%:':: ' -- %(*"_:":
, --. - ' , , ',_¢'z ' - - ",.·. . .-- ' , -... r'.L ''""-,P2 -~"".'', "/ :-".·'
·) .,_;'- ...: .q~ .'~.~...~~ ~....
https://ntrs.nasa.gov/search.jsp?R=19730007706 2020-03-23T08:08:12+00:00Z
THE EFFECT OF AN ISOTROPIC NON-EQUILIBRIUM PLASMA ON
ELECTRON TEMPERATURE MEASUREMENTS
Robert F. Benson
Walter R. Hoegy
Laboratory for Planetary Atmospheres
December 1972
GODDARD SPACE FLIGHT CENTER
Greenbelt, Maryland
Preceding page blank 
THE EFFECT OF AN ISOTROPIC NON-EQUILIBRIUM
PLASMA ON ELECTRON TEMPERATURE MEASUREMENTS
Robert F. Benson
Walter R. Hoegy
Laboratory for Planetary Atmospheres
ABSTRACT
The electron temperatures which would be determined (using
the conventional single-temperature analysis) by the electro-
static probe, the diffuse resonance, and the radar backscatter
techniques in an isotropic two temperature plasma are pre-
sented. Plasma models corresponding to the addition of a
minor component of energetic electrons, and models cor-
responding to a process that cools a fraction of the ionospheric
electrons are considered. The diffuse resonance temperature
is found to lie between the probe and radar backscatter tempera-
tures. The isotropic models corresponding to the addition of
energetic electrons cannot support the reported discrepancies
between radio wave and probe electron temperature measure-
ments. Temperature differences similar to the observed
differences can be produced by models with a fraction of the
electrons at a temperature cooler than that of the main com-
ponent of electrons. These models, however, are difficult to
explain in terms of our present understanding of the ionospheric
plasma.
PPEC~,ING PAPP PLAMTt NOT ,",rrT-
iii
INTRODUCTION
A discrepancy has been observed between the electron temperature de-
duced from in situ electrostatic probe measurements and from ground-based
radar backscatter measurements; the probe temperature Tp being greater than
the backscatter temperature Tb (Hanson et al., 1969; Carlson and Sayers, 1970).
A similar discrepancy has been observed in a comparison of simultaneous in
situ Alouette 2 electron temperature measurements based on the rf sounder
stimulated plasma resonances and the cylindrical probe experiment (Oya and
Benson, 1972). The resonance measurements are based on the diffuse reso-
nance which occurs at the frequency fD1 between fH and 2 fH (Oya, 1970), where
f His the electron cyclotron frequency; the probe measurements are based on
the experiment of Findlay and Brace (1969). Again, the radio wave temperature,
i. e., the diffuse resonance electron temperature TfD1 , is less than the probe
temperature Tp.
An assumption inherent in the determination of Tp, Tb, and Tf0 1 is that
the electron velocity distribution function f(v) is Maxwellian. The purpose of
the present paper is to determine the effect of an isotropic non-Maxwellian
velocity distribution on the three temperature measuring techniques. For
illustrative purposes we represent the distorted velocity distribution by a
simple, isotropic two temperature distribution - a superposition of two
Maxwellian distributions. Hoegy (1971) applied this distribution to a study of
the probe-radar temperature difference for distortions in f(v) at high energies
1
(photoelectron distortion) and at low energies (thermal distortion). It was con-
cluded that significant temperature differences could be produced by a thermal
distortion but not by a distortion due to realistic photoelectron populations.
This paper represents an extension of the work of Hoegy (1971) to include the 1
diffuse resonance technique.
Basically, we pose the following question: if an isotropic two temperature
plasma is present, but the data are interpreted in terms of a one temperature
Maxwellian plasma, what temperature will be computed? A description of the
method for obtaining Tp and Tb for such a plasma has been given by Hoegy
(1971); the procedure for obtaining Tfol is given in the Appendix.
ILLUSTRATIVE EXAMPLES
The effect of an isotropic distorted f(v) on the temperatures deduced by
the probe, radar, and diffuse resonance techniques is illustrated in Figure 1
for a wide range of conditions. In all cases the bulk of the electrons are con-
sidered to be at 3,000"K and the perturbing electron component extends over a
range of temperatures above (top row) and below (bottom row) this value. By
convention, T ! denotes the temperature of the cooler electron component re-
gardless of its role as the major or minor constituent. The three columns of
figures from left to right in Figure 1 represent perturbing electron populations
of 10%, 20%, and 30%, respectively.
2
The following trends are evident from Figure 1: . , ,,,. ..
(1) T 1 is between Tp and Tb in allcases.,
(2) A larger perturbation in the .irobe temperature can be obtained when
a fraction of the electrons are warmer than the main component,
rather than cooler than the main component; the converse is true
in the case of the diffuse resonance and radar backscatter tempera-
tures (compare Figure la with ld, lb with le., or lc with if).
(3) All three techniques give very similar results when warmer electrons
(at T2 ) are present up to T2 10,000°K; when electrons with
T2 > 10, 000°K are present the radio wave temperatures (Tf 10 and
,Tb) are greater than the probe temperature (see Figures la, lb,
and 2c).
(4) The radio wave temperatures are always less than the probe tem-
peratures (Tb <. TIO < Tp) when cooler electrons are present (see
Figures ld, le, and if).
The following comments should be kept in mind when interpreting Figure 1.
(1) The actual temperature values for Tp and TfD, depend on the simulated ex-
perimental conditions - the voltage interval for the probe and the ambient plasma
conditions for the diffuse resonance. (2) There is a double-valued behavior of
Tp as a function of the perturbing temperature because the perturbing current
can be recognized and rejectted in the temperature reduction process when the
perturbing temperature differs by, a large amount from.the temperature of the
3
major component of electrons. (3) The peak observed in TfD, in the top row of
Figure 1 corresponds to the conditions giving the maximum distortion in the two
temperature dispersion curves (see Figure Al of the Appendix).
DISCUSSION
Hanson et al. (1969) observed Tp to be as much as 70% greater than Tb,
and Oya and Benson (1971) found Tp to be typically 20% to 30% greater than
TfD 11 . It is clear that these discrepancies cannot be explained in terms of an
isotropic plasma with a component of hot electrons present (see comment 3 of
the previous section).
If an isotropic plasma exists with a fraction of the electrons at a tempera-
ture cooler than the main component, then it is possible to produce a temperature
difference resembling the observed discrepancies (see comment 4 of the previous
section). For example, consider the case of a 10% perturbation (Figure ld) with
T 1 = 1, 200°K; the two temperature model then gives the following values:
TP = 2930°K, TfD -- 2740°K, and Tb = 2610°K. The calculated ratios for
Tp/TfE0 and Tp/Tb (1.07 and 1.12, respectively) are smaller than the observed
ratios, but larger values can be obtained by using a lower T, and/or a higher
minor constituent population (see Figures id, le, and if).
In order to maintain such large distortions of the low energy electron
population, there must exist heating and cooling processes with rates comparable
in magnitude to the electron-electron energy exchange rate. Since this time is
three orders of magnitude smaller than the electron-ion or electron-neutral
4
energy exchange time, the main effect of Coulomb collisions with cooler particles
is to modify the average energy of the electrons rather than to modify their
Maxwellian velocity distribution. Other processes, however, may be important
enough to modify this picture-such as non-local processes or wave-particle
interactions which could enhance the selective heating and cooling mechanisms
at the expense of the electron-electron equilibration. This possibility merits
future investigation.
The present work has treated the isotropic case. Recent observations by
Clark et al. (1973) indicate that significant anisotropies, with the electron tem-
perature parallel to the earth's magnetic field vector B greater than the tem-
perature perpendicular to B, are common in the upper ionosphere. Such
anisotropies could contribute to the observed discrepancy between radio wave
and probe measurements (for example, TODi corresponds to electron motion
perpendicular to B, whereas Tp is not very sensitive to direction). Thus, in
addition to considering mechanisms which could produce a distortion in the
isotropic distribution of electron velocities, future work should consider the
anisotropic case.
APPENDIX
TfDo IN A TWO TEMPERATURE PLASMA
In order to determine Tfo I in a two temperature plasma it is necessary
to derive the two temperature dispersion relation for plasma waves propagating
perpendicular to the earth's magnetic field vector B. (The diffuse resonance
5
experiment is interpreted in terms of perpendicular propagation (Oya and
Benson, 1972).)
The dispersion relation for longitudinal plasma waves with the wave vector
k perpendicular to B is obtained by setting the expression for the dielectric
constant (Elong) equal to zero, ie.,
+co nvL aF(v) 2 tkv\
2 ~ ~ ~~v cov Ip J. '-fi-'0 lo(n) 1 +4remk2 27rv I dv L E n aV conv 1
where ink 2 J 0 w=~ (Al)
where
+xo
F(vL) = f dv, f(v)
-00
is the distribution function for electron motion perpendicular to B, e and m are
the electron charge and mass, vi and vI are the components of electron velocity
v parallel and perpendicular to B, w= 2rf, = 21rfH, k= IT, f (v) is the electron
velocity distribution function, and J, is the Bessel function of order n (e. g.,
see the review by Dougherty and Watson (1971)). Inserting the isotropic two-
temperature velocity distribution function
f(v) = (1 - p) N (2 ) 3/2 exp ( mv 2 )2p) NT 2KTI
+ pN (2 T)3/2 exp ( 2KT ) (A2)27rKT2 (~- 2KT2
into A1 (where p represents the population of electrons at T2 ) gives the two
temperature dispersion relation
6
O0 ....; co ; C
1 -'t 4 eXI (AX) ___ e __ 0_2)
= ,22 + .
(d") Al 1- (w)22 1 (°) 2-1
WN =4 ir Ne 2/m (A3)
T KT k 2
Al =m 2ma 2
KT2 k2
;2 mr2.
The standard single-temperature dispersion relation is obtained by setting
p=O or 1 or by setting T, = T2 in (A3). Note: When very energetic electrons
are considered, large X2 values are encountered and the second summation
term in (A3) converges very slowly. A much faster convergence is obtained by
making use of the identity
+00
E e-XIn (X) = 1
n=-oo
in order to make the following replacement
co e AIn GO e-I.n(X) e-XIo (W)-1
I ~~~= 2+
= = 1 -(n)2 2
n=I ~~~n=1
The dispersion curves based on (A3) are presented in Figure A1 in the
form of the frequency f, normalized by the electron cyclotron frequency fH,
versus the wave number k normalized by l/R. where R represents the electron
cyclotron radius. In Figures la-c, R is expressed as R=R(T) = (KT/m(2rfH)2)1/2cyclotron radius. In Figures la-lc, R is expressed ag R= R(T,) = tKT, /m(27rf,))
7
where T, is the temperature of the major component; in Figures ld-lf it is ex-
pressed as R=R(T2 ) = (KT2 /m(2rfH)2) /2 where T2 is the temperature of the
major component. The first case (Figures l(a)-l(c)) corresponds to the ad-
dition of energetic photoelectrons, while the second case (Figures 1 (d)-i (f))
corresponds to a process that cools the ionospheric electrons. The solid line
in each figure corresponds to the single temperature dispersion relation that
was used by Oya and Benson (1972) in the determination of TfDI .
The procedure for determining Tfo I from a single-temperature dispersion
relation in a two temperature plasma is as follows: Select the two temperature
parameters p, TI, and T2 , and the ionospheric parameters wN,, , k, that
correspond to the conditions of the observations. Then determine the nor-
malized diffuse resonance frequency from the two temperature dispersion re-
lation (A3). Finally, use the standard single temperature dispersion relation
to obtain X = (kR)2 and hence Tf = XmD22 /Kk2.
ACKNOWLEDGE MENTS
We are grateful to Mr. L.H. Brace, Dr. S.J. Bauer, and Dr. E.J.R.
Maier for many helpful discussions. We are also grateful to the referees for
their critical comments.
REFERENCES
Carlson, H.C., and J. Sayers, Discrepancy in electron temperatures deduced
from Langmuir probes and from incoherent scatter radars, J. Geophys.
Res., 75, 4883-4886, 1970.
8
Clark, D. H., W. J. Raitt, and A. P. Willmore, A measured anisotropy in the
ionospheric electron temperature, J. Atmos. Terr. Phys., 35, 63-76, 1973.
Dougherty, J. P., and S. R. Watson, The interpretation of plasma resonances
observed by ionospheric topside sounders, Advances in Plasma Physics,
Vol. 4, edited by A. Simon and W. B. Thompson, p. 1, John Wiley and
Sons, Inc., New York, 1971.
Findlay, J. A., and L. H. Brace, Cylindrical electrostatic probes employed on
Alouette II and Explorer XXXI satellites, Proc. IEEE, 57, 1054-1056, 1969.
Hanson, W. B., L. H. Brace, P. L. Dyson, and J. P. McClure, Conflicting
electron temperature measurements in the upper F region, J. Geophys.
Res., 74,400-401, 1969.
Hoegy, W. R., Probe and radar electron temperatures in an isotropic non-
equilibrium plasma, J. Geophys. Res., 76, 8333-8340, 1971.
Oya, H., Sequence of diffuse plasma resonances observed on Alouette 2
ionograms, J. Geophys. Res., 75, 4279-4285, 1970.
Oya, H., and R. F. Benson, A new method for in-situ electron temperature
determinations from plasma wave phenomena, J. Geophys. Res., 77,
4272-4276, 1972.
9
FIGURE CAPTIONS
Figure 1. The electron temperature Tp, Tb, TfD1 deduced from a single
temperature analysis using a two temperature plasma for the
electrostatic probe, the radar backscatter, and the diffuse reso-
nance techniques, respectively. T versus T2 with T2 >T1 = 3,000°K
in the top row, and T versus Tl with T, < T2 = 3,000 °K in the
bottom row. The left column corresponds to the condition when
10% of the electrons deviate from the model temperature of 3,000°K,
the center column corresponds to a 20% perturbation, and the right
column to a 30% perturbation. Note the abscissa scale change be-
tween the top and bottom rows. In each column, the bottom figure
represents an enlarged extension of the top figureto the temperature
range below 3,000°K. The Tp values correspond to the 0.3 to 1.3v
interval of the probe current-voltage curve; the TfoD values cor-
respond to the plasma conditions given in the caption of Figure Al.
Figure Al. Dispersion curves based on the two-temperature dispersion equation
(A3) for plasma models with T 2 >T 1 = 3,0000 K (a), (b), and (c); and
for models with T1 < T2 = 3, 000°K (d), (e), and (f). The parameter
p represents the fraction of electrons at T 2 . The solid curves
(p=0 and 1) correspond to the single temperature dispersion curve.
The plasma conditions used in these models correspond to a typical
observation from the Ottawa data sample of Oya and Benson (1972)
(fN=caN/2r=3.475 MHz and fH=l. 178 MHz so that fN/fH=2. 95; the
corresponding value for kR when the temperature is taken as
3, 000°K is 0.97).
- 10 -
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
~~~~~~~~~~~~~~~~~~~~~~~I
~~~~~~~~~~~~~~~~~~~I,
I,
~~~~~~I 
I C i
i I
0itD
0t
0
00
I'D
':2
0
o C 0 0
o 0 0 0
CD 00 to 
C) N Cs "
- 11 _
0)
CD
C0
CV)
0
0
C\j
0
0
0
0
0
0 I
C)
c'J
-4
a)
o) 0 0 0 0 o 00 ( 0-0 0o COJ 0D s ~ 
m m - m m 
ol
0 0
CD
0 O
_ LOCD
-N0
0
C\J
._-
2'
I I I
o.0
II11o
0O 0
Co O
00 
11
0 ~c5
C\J0
6
R 11goI:a
m-" I /,II
- C
Co 
n I,
I1 X
,X '~~~~~~~~C
I l I
o
11
''°loo00", lll, r0 =
11
II
'V. Ic
°I.,oO ,~~I
cc
o. .
II
fi IiiJ
(.. , I , I I I I [ , Ic- C
o 0 0 X - C
CNi -4 4 *-4
o
O-4
o
U
L-
I
u'C
z
©-4
a)
Ci
o. 00 tD -,¢ CDN~i _-1 _s4 _§ _4 1o
CN4
m
C"J
0 0
- /:a -


The effect of an isotopic non-equilibrium plasma on electron temperature measurements

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server