Volume 5 1A, number 8
PHYSICS LETTERS
5 May 1975
INTERFERENCE STRUCTURE IN THE FAR FIELD OF THE
RESONANCE CONE
R.W. BOSWELL and A. GONFALONE
Space Plasma Physics Division, ESTEC, Noordwijk aan Zee, The Netherlands
Received 28 February 1975
The interference structure of the resonance cone below the electron gyro-frequency (Whistler mode propagation)
has been observed with electric and magnetic antennas in a large volume experimental magnetoplasma at distances
greater than a wavelength from the transmitter.
In a cold magneto plasma, the dispersion characteristics of the whistler wave are a function of the
angle the wave makes with the magnetic field. In particular, at a certain angle Bc, which is dependent on
frequency and density, the group velocity of the wave
approaches zero. If the waves are launched from a
point source, they propagate within a cone of half
angle Bc, hence the name resonance cone.
A temperate plasma has little effect on the actual
cone angle but an interference structure appears within and close to the cone which has been interpreted
by Fisher and Gould [l] and by Kueh [2] as a coupling between the electromagnetic field of the cone
and the electric field of a slow plasma wave. Experiments in the near field have been carried out by Fisher
and Gould [l] and by Gonfalone [3] and in both cases
the interference structure was observed in the near
field with the antennae separation being much less
than a wavelength. These measurements were made
with small electric antennae. Although the theory
given by Kuehl [2] predicts that this interference
should be observed in the far field, it has been suggested
that damping (collisional or collisionless) could remove
the structure. It is therefore, of interest to determine
whether the resonance cone and its structure still exist in the far field.
The experiment was carried out in a large volume
magnetoplasma which has been described elsewhere
by Boswell and Arends [4] . An argon plasma was
formed in a chamber with a diameter of 60 cm and
length 120 cm permeated by a magnetic field uniform
to * 0.6%. Langmuir probes were used to measure the
electron temperature which was of the order of 2.6
eV, in good agreement with other measurements in
similar plasmas [5] . With a neutral gas pressure of 4 X
lOA torr, this resulted in collision frequency u =
0.0005 wc for a gyrofrequency oc = 180 MHz.
By using interferometric techniques, the whistler
wave dispersion relation was obtained, from which the
average electron density was deduced to be 4 X lOlo
cmq3.
The transmitting antenna was a 1 cm diameter loop
which behaved essentially as a point magnetic dipole
and the receiving antenna was an electric probe with
an exposed surface 3 mm long and 1 mm diameter
which gave a greater degree of spatial resolution. Slmilar results were obtained by using an electric probe as
a transmitter as in the experiment by Gonfalone. The
interference structure can therefore be seen to be an
inherent part of the resonance cone and is independent
of the type of antenna used. This is the first measurement, to our knowledge, of the resonance cone and
structure launched by a magnetic dipole.
The cone was observed for all frequencies and the
result presented here was obtained at o = 0.47 oc
where the wavelength was approximately 17 cm. Although the cone and interference structure have been
measured at distances greater than 10 X, the graph
shown in figure 1 was obtained by rotating an electric
probe around the transmitting antenna on a circle with
a radius of 28 cm. i.e. about 1.5 h distant. The asymmetry of the cone is probably due to a slight misalignment in the orientation of the loop of the transmitting
antenna. Following the theory given by Kuehl, and
using his notation, the angle of the resonance cone:
eM = Bc - 1.8 c~~‘~sin~‘~O~/R~‘~
and the angle of the first maximum of the interference
485
Volume 5 1A, number 8
PHYSICS LETTERS
5 May 1975
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Fig. 1. Resonance cone and structure measured at w = 0.47 wc. 8M is the cone angle and Bm is the angle of the first maximum of
the interference pattern.
pattern:
em = Bc - 7.4 a113sin4/3Bc/R2’3
where 19~is the angle of the resonance cone given by
the cold plasma theory, cr is a parameter involving the
frequency and density, and R is the ratio between the
antenna separation and the gyro radius.
Inserting the measured values into these expressions,
yields the angles 19~ = 26.9” and eM - em = 4.4’
From fig. 1 the experimental values are 8 - 27.5
*0.3%ideM-em
= 4 .6 f 0 .3’ and are in Eid agreement with theory.
In conclusion, it has been shown that the resonance
cone and its interference structure exist in the far field,
even when the transmitter is a point magnetic dipole.
The structure was still associated with the cone and
therefore may be regarded as an integral part of it,
rather than as an electrostatic wave with free existence.
The present results demonstrate that energy is convected away from the near field along the resonance
486
cone. In future space experiments designed to launch
waves into the ionospheric or magnetospheric plasmas,
it shotrid be noted that a certain amount of the energy
radiated from an antenna will not appear in the wave
fields, but on the resonance cone.
One of us (R.W. Boswell) would like to thank ESRO
for providing a Research Fellowship. We would like to
express our grateful thanks to H. Arends for his excellent technical assistance.
References
[l]
(21
[3]
[4]
R.K. Fisher and R.W. Gould, Phys Fluids 14 (1971) 857.
H.H. Kuehl, Phys. Fluids 17 (1974) 1275.
A. Co&lone, Journal de Physique 33 (1972) 521.
R.W. Boswell and H.J. Arends, The ESTEC E.P.V. int. report, ESTEC, Noordwijk, The Netherlands.
[5] C. Christopoulos, D. Phil. thesis, University of Sussex
(1974).