Antenna response to ambient electron plasma oscillation fields in magnetospher

Fredricks, R. W.

Scarf, F. L.

English

NASA Technical Reports Server

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OSCILLATION FIELDS IN THE MAONETOSPHERE 
F. L. Scarf and R. W. Fredricks 
TRW Space Technology Iaboratories 
Redondo Beach, California 
Recently, Huguenin, Ulley, McDonough and Papagiannis (l) reported 
on 700 kc/s and 2.2 Mc/s radio noise measurements made on 30 July, 1963 
at altitudes between 3000 and 11,000 km from a high-altitude rocket 
probe. 
and several intense noise bursts were also observed. 
They found a relatively high background brightness at 700 kc/s, 
It was suggested 
that non-thermal source mechanisms such as harmonic gyro radiation and 
EM radiation from plasma waves could contribute to the high 700 kc/s 
background, and radiation from relativistic electrons was considered as 
the source of one of the noise bursts (event A which appeared in both 
channels near the geomagnetic equator). However, Huguenin, et.al,, ob- , 
-17 M-l served that event D, the most intense noise burst [bmaF 8 x 10 
(c/s)-', duration 2 800 sec] appeared only in the lower channel and at 
an altitude (h" 4600 1500 km) for which the local electron plasma 
frequency approached 700 kc/s. 
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In this note we wish'to discuss a possible interpretation of event 
D. Specifically, we suggest that the antennas were simply responding to 
the electrostatic fields associated with the thermal or equilibrium level 
of electron plasma oscillations, rather than to any local resonance4 If 
the geomagnetic field is ignored and the distribution functions are - 
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https://ntrs.nasa.gov/search.jsp?R=19650014332 2020-03-17T00:02:17+00:00Z
Maxwellian, the wave fields are described by (2 1 
E = - E @  , 
w k c *  
fb = fbo exp i(k r - urt) , 
with w = y - iw2 and 
w 2 = w 2(1 + 32/52 + ...) 
1 P 7 
O<k<% 
1 
w = (n/8)5 up ( q k ) 3  exp( -%'/2k2) +. . . 
2 
Here w 
represents Landau damping. 
temperature is finite, the thermal motion gives rise to a non-vanishing 
level for the plasma oscillations. 
= 4nNe2/m, ma 2 = 2hT, IC,,' = 2u, 2 2  /a and the imaginary term P P 
If the plasma is in equilibrium and the 
Ro~toker(~) has shown that a form of 
equipartition which takes into account Iandau damping leads to the f o l -  
lowing expression for the equilibrium fields: 
In the presence of a magnetic field, Eqs. (l), (2) &main strictly 
valid only for propagation parallel to B, and hence Eq. ( 3 )  requires 
modification. Harever, Bernstein has dem~nstrated'~) that weak field 
corrections to the dispersion relation involve terms of order (u /u, ) 2 
C P  
and Fig. (3)  of Huguenin, et.al., shows that (w /u )'% 0.08 at the 
i-- 
C P  
peak of 
Eq. (3) 
the noise burst. 
to study event D. 
We therefore neglect this correction andlapply 
/- 
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The two ten-meter antenna elements were coupled to form a bslanced 
dipole and the probe was relatively inefficient as a detector of modes 
with h,,&hoe (10-20) meters. We approxlmate the response by inte- 
grating only over the range 0 L k C  k = 2fi/ho for k parallel to the 
dipole and EQ. (3) becomes 
0 
At the altitude of 4500 km, cu1 2 w C! 2n( 7 x 10 5 ) gives 
P 
2 6 x lo3 ~m'~, and for Te 2 3 x lo3 OK, K D S  0.2 cm'. If ) is Ne 
20 meters, Eq. (5) yields 
E~ 3.4 x 10-9 esu/cm 
100 microvolts/meter 7 
as the predicted equilibrium level of the electron plasma oscillation 
field with k,,< ko. 
latively narrow receiver bandwidth (A)  2 14 kc/s in the 700 kc/s channel) 
and thus Eq. (4) certainly overestimates the background field which should 
be observed. However, E q .  (2 )  may be used to show that the group velocity 
for the electron plasma oscillation is on the order of 
This prediction does not take into account the re- 
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and v can be sufficiently low so that Doppler shifts increase the 
g 
effective bandwidth significantly. Fbr Te 
is very large compared to the probe speed but koa/W 3 0.02, and 
(dw/dk) can then have a maximum value of about 10 
probe orientations. 
3 x 10' OK, a X 300 km/sec 
P 
cm/sec for certain 6 
Sheath effects, and inclusion of geomagnetic field 
corrections to Eq. (3 )  must also be considered, and hence the significance 
of the absolute value for EB is quite questionable. 
In spite of these pncertainties it seems plausible thatjevent D is 
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describable in terms of detection of the ambient electrostatic fields. 
The relationship between f l u ,  bandwidth and Thkrenin open circuit 
voltage (ea) given by Ifuguenin, et.al., is 
and for a solid 
measured. This 
angle near 4n, a flux of 8 x 10 
gives e 6 x volts. With an effective length of 
w M - ~  (c/s)-' was 
a 
10 meters, the indicated electric field in the antenna is thus on the 
order of 6pV/M or a factor of 16 below -the uncorrected equilibrium 
value of Eq. ( 6 ) .  
value for ea is a factor of 4000 smaller than %T/e, a ,reasonable 
estimate of the largest amplitude for an electrostatic wave in a plasma 
under non-equilibrium conditions. This observation is relevant because 
DC electric fields, currents, thermal anisotropies and inhomogeneities 
can all serve to reduce the Landau damping and allow the waves to attain 
Furthermore, it is worth noting that the observed 
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large non-equifibrium amplitudes. 
rnea~urernents'~) on the spacecraft 1964-4s reveal that when finite 
Indeed, recent VLF electric field 
bandwidth corrections, sheath effects and Doppler broadening are taken 
into account, Eq. (3)  does yield an adequate description of the back- 
ground level, assuming that the' waves are electrostatic ion oscillations 
[O <u)(u)  (ion)] b However, VU? field enhancements by factors of (5-50) 
over the background value were customarily encountered, and it therefore 
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seems reasonable to suppose that the rocket probe antennas were simply 
sampling the ambient near-equilibrium values for electron plasma 
oscillation fields during event D. 
ACKNOWLEDGEMENT - This work was supported in part by the National 
Aeronautics and Space Administration under Contract NASy-698. 
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REFERENCES 
1. G. R. Huguenin, A. E, Lilley, W ,  H. McDonough and M. D, Papagiannis, 
Planet. Space Sci., 12, 1157 (1964). 
2. T. H. Stix, The Theory of Plasma Waves , McGraw-Hill Book Co., 
New York (1962). 
3. 
4. 
5 .  F. L, Scarf, G. M. Crook, and R. W. Fredricks, submitted t o  J. 
N. Rostoker, Nuclear Fusion, 1,, 101 (1961). 
I. B. Bernstein, Phys. Rev. 1% 10 (1958). 
Geophys. Res., (Feb. 1965). 
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Direct detection of ambient electron plasma oscillation fields in the magnetosphere, appendix d

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