The ISEE-3 SBH radio receiver has provided the first systematic observations of the quasi-thermal (plasma waves) noise in the solar wind plasma. The theoretical interpretation of that noise involves the particle distribution function so that electric noise measurements with long antennas provide a fast and independent method of measuring plasma parameters: densities and temperatures of a two component (core and halo) electron distribution function have been obtained in that way. The polarization of that noise is frequency dependent and sensitive to the drift velocity of the electron population. Below the plasma frequency, there is evidence of a weak noise spectrum with spectral index -1 which is not yet accounted for by the theory. The theoretical treatment of the noise associated with the low energy (thermal) proton population shows that the moving electrical antenna radiates in the surrounding plasma by Carenkov emission which becomes predominant at the low frequencies, below about 0.1 F sub P

Couturier, P.

Hoang, S.

Meyer-Vernet, N.

Steinberg, J. L.

English

NASA Technical Reports Server

MEASUREMENT OF MACROSCOPIC PLASMA PARAMETERS WITH A RADIO EXPERIMENT :
INTERPRETATION OF THE QUASI-THERMAL NOISE SPECTRUM OBSERVED IN THE SOLAR WIND.
P. Couturier, S. Hoang, N. Meyer-Vernet and J.L. Steinberg
D_partement de Recherche Spatiale, Observatoire de Paris-Meudon
92190 Meudon, France
ABSTRACT
The ISEE-3 SBH radio receiver has provided the first systematic observations
of the quasi-thermal (plasma waves) noise in the solar wind plasma. The
theoretical interpretation of that noise involves the particle distribution
function so that electric noise measurements with long antennas provide a fast
and independent method of measuring plasma parameters: densities and temperatures
of a two-component (core and halo) electron distribution function have been
obtained in that way. The polarization of that noise is frequency dependent and
sensitive to the drift velocity of the electron population. Below the plasma
frequency, there is evidence of a weak noise spectrum with spectral index -I
which is not yet accounted for by the theory. The theoretical treatment of the
noise associated with the low energy (thermal) proton population shows that the
moving electrical antenna radiates in the surrounding plasma by Cerenkov emission
which becomes predominant at the low frequencies, below about 0.I f
p"
Introduction
Using the SBH radio experiment on ISEE-3 (Knoll et al, 1978), we have
observed systematically the noise spectr_n associated with the quasi-thermal
fluctuations of the solar wind plasma (Hoang et al., 1980; see also Grigorieva
and Slysh, 1970). From the theoretical interpretation of the measured spectra
(Andronov, 1966; Meyer-Vernet, 1979), using a bi-maxwellian model, we were able
to deduce the density and temperature of the two electron components (Couturier
et al., 1981, paper A) The results are in excellent agreement with the parameters
measured at the same time on the same spacecraft by the Los Alamos plasma
analyzer. Sentman (1982) investigated the electron quasi-thermal noise in a
magnetized plasma to account for the noise spectrum observed near plasma
resonances in planetary magnetospheres.
The purpose of the present paper is to introduce the physics involved in the
plasma and antenna description in order to make clear some fundamental points to
solar wind physicists who may not be familiar with the subject developed at
length in the quoted literature.
The antenna as a thermometer and densitometer.
Let us first consider a passive receiving antenna in vacuum, in equilibrium
with blackbody radiation at temperature T I. The spectral component e_0 of the
voltage measured at the terminals of that antenna is related to the fluctuations
of the electromagnetic field inducing that voltage; Nyquist's theorem provides a
relation between the output voltage, the antenna radiation resistance in vacuum
Rao and its temperature:
2
e = 4 K TI Rao (I)
377
https://ntrs.nasa.gov/search.jsp?R=19840005028 2020-03-22T07:37:40+00:00Z
For a thin short dipole antenna of half-length %, Rao is given by:
(_o/ Co)½ 2 %2
Ra0_ 2
6 _ c
(2)
Let us now consider the same antenna in equilibrium with blackbody radiation
at temperature TI, but immersed in a lossless dielectric. Equation(i) remains
valid if we replace Rao by the radiation resistance Ra which takes into account
the dielectric permittivity gr which affects the _hase velocity of the radiation;
namely, if the antenna remains short: Ra=Ra0Er _. The plasma surroundin$ the
antenna may be considered as a pure dielectric when 0_)_ n where er=l-(_n/m) _ , _n
is the plasma frequency and we assume there is no static magnetlc f{eld. Thi§
cold plasma approximation breaks down near the plasma frequency and is of no use
for _ since no transverse mode can propagate and couple the antenna to the
blackbody.
Finally, let us consider an antenna immersed in the solar wind, a hot
collislonless electron plasma if we neglect the ions in a first approximation.
Now, longitudinal modes do propagate and contribute predominantly to the voltage
measured at the antenna terminals. In fact, there is a detailed energy balance
which allows a separate calculation of the transverse and longitudinal modes
contributions with appropriate Nyquist's formulas. When _>_ , the transverse
modes couple the antenna to radlo-sources; since the solar windPls optically thin
for this mode, it contributes an output voltage given by: eT2=4KTeffR T where Tef f
is an effective temperature deduced from the integration of the electromagnetic
flux incident on the antenna taking into account its directlvity pattern. RT is
the transverse mode radiation resistance which is the classical radiation
resistance Ra previously mentioned.
The longitudinal modes couple the antenna to the natural electrostatic
oscillations of the plasma. Landau damping provides the thermalisation process
between electric field fluctuations associated with longitudinal plasma waves and
the electrons. The electrons with velocity larger than the plasma wave velocity
are slowed down and transfer energy to the plasma waves; electrons which are
slower than the plasma waves are accelerated and damp the waves. At thermal
equilibrium, electric field fluctuations and the electron temperature are related
by the fluctuation-dissipation theorem (Sitenko, 1967). Thus, the output voltage
these fluctuations is again given by:e_2=4KTLRl ,_ where RL is theassociated with
radiation resistance of the antenna for the longitudinal modes.
The method used to evaluate that radiation resistance will be given later;
we now present some analytical results (paper A) which describe the resonance
peak of the radiation resistance near the plasma frequency fo; a dipole antenna
of half length %_>£D--VT/(2_mp) the Debye length, VT,(2KT/m)_ is the electron
thermal velocity.
For low frequencies _4mp, RL can be analytically approximated by:
(_ _o )_ c %D (_ _o )_ c
4 E° pvT % 4 (2 Go) _ £
For high frequencies, _>>_p, RL decreases with frequency as _-3:
(3)
378
2
_o _ cP (4)
_= 2 _½ 3
O
The resonance peak appears just above the plasma frequency; for m=mp, the
radiation resistance increases rapidly (cut-off) and reaches a maximum value for:
2
(I- ---$-) --~ 3.5 (5)
£D
which corresponds to the antenna in tune with the plasma waves. The constant 3.5
is valid for cylindrical antennas, it would be slightly different for spherical
antennas. So, there is a well defined resonance peak only if %/%D > i. The peak
value is roughly equal to the low frequency asymptotic value (3) multiplied by
(%/%D)2. In the resonant frequency range the transverse mode contribution can be
neglected.
These expressions show that we can deduce the plasma frequency from the cut-
off frequency of the spectrum and the electron temperature from the peak noise
voltage and the width of the resonance peak.
Basic equations for a multicomponent plasma
Using the preceding model results in a good fit to the observations for the
resonance peak position but the predicted values of the noise peak are too low.
The noise peak is produced by plasma waves with frequency close to Up and phase
velocity much larger than vT. The discrepancy between the theoretical predictions
based on a one-component model and the observations must therefore be solved by
using a multicomponent model with cold core and hot halo electrons. We shall
later discuss the limitations imposed by the quasi-thermal assumption on the
distribution functions. Now we summarize the results (paper A) derived from a
plasma model made of two maxwellian isotropic electron populations.
For a multicomponent plasma Nyquist's theorem is not valid, there is no
longer any linear relationship between the output voltage at the antenna
terminals and the antenna resistance; these quantities must be evaluated
separately. The particle distribution functions set the plasma dielectric
properties and are used to evaluate the dispersion tensor Aij(_ , _) and the
dielectric permittivity tensor E..(_, _). The antenna geometry sets the current
13
distribution _(_). The antenna output voltage is related to the fluctuating
electric field:
,t).J(r) (6)V(t) = _ dBr _(_ ÷ +
I
0
Io is the current flowing at the center of the antenna. The plasma _luctuations
give a spectral distribution of the electric field fluctuations [EiE. ], ; this
tensor is deduced from the fluctuation-dissipation theorem (Sitenko, i_6_)_
2 K k.k. T (Im EL) q
[_i_j] _ i 3 E q (7)
E m k2 q [eL ]2
O
379
q is an index for the different componentsof the plasma, e_ is the longitudinal
part of the dielectric permittivity tensor, (Im eL)q is th_ contribution of the
q-componentto its imaginary part.
Calculating the autocorrelation of the output voltage (6) and using
Parseval' theorem ,we obtain:
V2 - 2
8 3 1 2 fd3k Ji (_) [Eigj]k,00 Jj(_) (8)
O
We emphasize that this output voltage at the antenna terminals is not the input
voltage at the receiver.The transfer function from the antenna terminals to the
receiver involves the antenna impedance and the receiver input impedance (paper
A). For ISEE-3, this transfer gain varies with frequency by one order of
magnitude due to the variations of the Debye length. The antenna impedance is
given by:
Z -- 1 "> q_ -> q_
a 2 f d3r E(r).J(r) (9)
I
0
Plasma dielectric properties relate the current distribution to the electric
field so that, by Fourier transform, we obtain:
i ]i(_,_) jj(_) (i0)Z = 3 2 f d3k Ji (_) Ai
a 8_e_l
0 0
For a multicomponent plasma, there is no longer a linear relation between the
longitudinal resistance deduced from (I0) and the output voltage given in (8).
Figure 1 shows the difference between the calculated spectrum of a one-component
plasma with electron density Nc and temperature Tc and the calculated spectrum of
a two-component plasma with a cold (Nc,Tc) and a hot (Nh,Th) electron population.
These spectra have been calculated for the receiver input voltage. As shown by
Fejer and Kan (1969) and in paper A, the hot population plays a dominant role
close to the resonance peak. As compared to the single cold population case, the
peak voltage _s _alt_plied by Th/To, the asymptotic low frequency value by a
factor l+(NhTc_)/(NcTh ) and the hig_ frequency decreasing part of the spectrum
by a total pressure factor (NhTh+NcTc)/NcTc .
Observations and discussion
Figure 1 shows spectra obtained on October 6, 1979 before and after a shock
(figure I is a corrected version of paper A figure ii). The parameters of the two
maxwellian populations used to determine the calculated radio spectrum are given
in table I; figure 2 represents the corresponding electron distribution functions
(thin line) and the distribution function deduced from the Los Alamos plasma
analyzer measurements made at the same time (thick line). The difference between
the two curves is essentially due to our use of a two maxwellian model to
interpret the radio spectrum while the Los Alamos distribution shows evidence of
a hot population with a high energy tail somewhat like a lorentzian (Feldman et
al, 1982). Apart from this tail, the shapes of the two distribution functions are
essentially the same; note also, from the parameters of table I, that we have not
380
used the samenormalization factor for the two distribution functions; the plasma
density given by the radio experiment differs slightly from that given by the
plasma analyzer, this difference is less than the roughly ¥30% uncertainty in
estimating plasma densities from measurementsof solar wind electron velocity
distributions. We have repeated this fitting exercise many times, and in every
case, we obtained the same agreement. We are quite sure that a purposedly
designed radio experiment tracking the plasma resonance "llne" in frequency with
a multichannel receiver would be a fast and efficient means to acquire
macroscopic plasma parameters with a high time resolution.
TABLEI. Summaryof plasma parameters
Parameters Nh/Nc
Oct.6, 1979, 10:28 UT 0.016
Oct.6, 1979, 10:58 UT 0.011
Tc Th Nc (SBH) Nc (LANL)
0.92 105 °K 16 105 °K 22 cm-3 18 cm-3
1.50 105 °K 16 105 °K 29 cm-3 31 cm-3
//
50
I0
.5 ....
.2 I
3O
10 28 UT
Oct. 6 1979
ISEE-3 SBH --
\
/
I I
60 100
Frequency [kHz]
DistributionfunctionLet.crn-3ev-_]
1 I
-1
lO
-2 10 59 UT10
Oct. 6 1979
ISEE-3 BAH
LANL
I0 28 UT
1o
Figure i. Thermal noise spectra at the
receiver input terminals as measured
(closed circles) and computed. The
dotted curves were computed with a
single (cold) electron population; the
solid curves with two populations. In
both cases, the plasma parameters are
those of table i obtained from the
distribution functions plotted on figure
2. The horizontal bars show the
bandwidth of the receiving channels.
10-_ I
lO lOO lOOO
E!.ectron energy [eV]
Figure 2 • Electron distribution
functions on October 6, 1979. The
thick llne is the function measured
with the Los Alamos plasma analyzer.
The thin line is the two-maxwellian
function used to compute the noise
spectra shown on figure i. The i0 28 UT curves are displaced to the right, for
clarity, by the length of the horizontal arrow.
381
However, someconstraints are imposed for such a method to be efficient. We
need an antenna length larger than the Debye length. We need electromagnetic
cleanliness of the spacecraft to achieve a low instrumental noise level(4 10-16 V2Hz-I has been achieved on ISEE-3). The method cannot be used
effectively in the presence of intense radio waves. It is model-dependent and
does not describe distribution functions which would differ widely from a multi-
maxwellian. Finally, the "quasl-thermal" equilibrium between the plasma and the
antenna and the use of the fluctuatlon-dlssipation theorem imply (Sitenko,1967)
that the relaxation time of the observed distribution function towards a mono-
maxwelllan distribution function (exact thermal equilibrium) is long comparedto
the time needed to acquire a complete spectrum. The noise spectrum arising from
an unstable distribution function cannot be interpreted assuming quasl-thermal
equilibrium.
The effect of the antenna velocity relative to the solar wind
Further developments of the theoretical interpretation have been motivated
by the ISEE-3 observations. For _,_p the observed noise spectrum is not flat as
predicted by our models. An electric noise componentwith a spectral index -I has
been identified, a spin modulation of the plasma noise is observed on the
spinning antennas and the anisotropy is clearly correlated with the solar wind
velocity (Hoanget al, 1982). These observations led us to take into account the
thermal ion distribution function and the velocity of the antenna relative to the
solar wind plasma. Longitudinal electron and ion plasma waves are Doppler-
shifted in the antenna frame ; this effect is particularly important for low
frequency waves (_p) which are the slowest. The ion contribution to the noise
calculated in that case yields a bump in the low frequency parE of the spectrum
but it is far from being sufficient to explain the observed f-i noise spectrum.
The anisotropy introduced by the Doppler shift of the waves results in a spin
modulated noise (Couturier et al., 1983) which is frequency-dependent ; the
direction of the minimumelectric field changes by 90° in the plasma resonance
peak region in agreementwith the observations.
A property of this model was predicted earlier by Andronov (1966) : for
typical solar wind parameters, the ISEE-3 antenna resistance may becomenegative
below 0.I fp when the dipole antenna is parallel to the solar wind velocity. In
such a case, we get an unstable situation similar to the beam-plasmainstability;
Cerenkov effect due to the antenna velocity explains this behaviour. Whensuch a
process is predominantj the low frequency electric field measurements are
quantitatively and qualitatively affected since the antenna gain has nothing in
commonwith the gain evaluated in vacuum. Wecannot encounter such a situation on
ISEE-3 because our lowest receiver frequency is 30 kHz.
In conclusion, we wish to emphasize the fact that passive electric field
measurementswith antennas long as compared to the Debye length have been
demonstrated to be useful tools for plasma diagnosis.
REFERENCES
o Andronov, A.A., Antenna impedanceand noise in space plasma (in Russian),Kosm.
Issled., 4, 558, 1966.
o Couturier, P., S. Hoang, N.Meyer-Vernet and J.L. Steinberg, Quasi thermal noise
in a stable plasma at rest : theory and observations from ISEE-3,J.Geophys. Res.
86, ii 127, 1981. (paper A)
382
o Couturier, P., S. Hoang, N. Meyer-Vernet, C. Perche and J.L. Steinberg, Quasi
thermal noise in a stable flowing plasma : theory and observations from ISEE-3.
In preparation for submission to J. Geophys. Res. in 1983.
o Fejer, J.A. and J.R. Kan, Noise spectrum received by an antenna in a plasma,
Radio Sci., 4, 721, 1969.
o Feldman, W.C., R.C. Anderson, J.R. Asbridge, S.J. Bame, J.T. Gosling and R.D.
Zwickl, Plasma electron signature of magnetic connection to the Earth bow
shock: ISEE-3, J. Geophys. Res., 87, 632, 1982.
o Grigorleva, V.P. and V.I. Slysh, Long wave cosmic radio radiation in circumlunar
space (in Russian), Kosm. Issled., 8, 284, 1970.
o Hoang, S., J.L. Steinberg, G. Epstein, P. Tilloles, J. Fainberg and R.G. Stone,
The low frequency continuum as observed in the solar wind from ISEE-3 : thermal
electrostatic noise, J. Geophys. Res., 85, 3419, 1980.
o Hoang, S., J.L. Steinberg, P. Couturier and W.C. Feldman, An electric noise
component with density f-I identified on ISEE-3, J. Geophys. Res., 87, 9025,
1982.
o Knoll, R., G. Epstein, S. Hoang, G. Huntzlnger, J.L. Steinberg, J. Falnberg, F.
Grena, S.R. Mosler and R.G. Stone, The 3-dimensional radio mapping experiment
(SBH) on ISEE-3, IEEE Trans. Geosci. Electron., GE-16, 199, 1978.
o Meyer-Vernet, N., On natural noises detected by antennas in plasmas, J. Geophys.
Res., 84, 1979.
o Sentman, D.D., Thermal fluctuations and the diffuse electrostatic emissions, J__x_"
Geophys. Res., 87, 1455, 1982.
o Sitenko, A.G., Electromagnetic Fluctuations in Plasma, Academic, New York, 1967.
383


Measurement of macroscopic plasma parameters with a radio experiment:  Interpretation of the quasi-thermal noise spectrum observed in the solar wind

Couturier, Pierre

Hoang, Sang

Meyer, Nicole

Steinberg, Jean-Louis

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Measurement of macroscopic plasma parameters with a radio experiment: Interpretation of the quasi-thermal noise spectrum observed in the solar wind

Measurement of macroscopic plasma parameters with a radio experiment: Interpretation of the quasi-thermal noise spectrum observed in the solar wind

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