We have used the spin modulation of the quasi-thermal noise
spectrum measured between electron gyroharmonics to deduce the
dispersion relation of electrostatic waves propagating roughly normal to the
magnetic field. In the frequency range where this can be
achieved, which covers a large part of the harmonic bands 
and 
, these measured
characteristics are very
similar to Bernstein's dispersion curves.
To our knowledge, this is the first time that such
dispersion relations are measured in space. Whereas they are
relatively easy to measure in the laboratory (see for example
[Harp, 1966] and [Ono, 1993] for electron and
ion
Bernstein waves), these dispersion relations are difficult to
measure in space. Previous space measurements were performed by
comparing the response of two antennas of different lengths
[Filbert and Kellogg, 1988] or by using a single antenna of
suitable length [Paranicas, 1993]. Data were only acquired
on a small set of isolated frequencies, since these experiments measured
narrowband emissions due to instabilities. The present results
were made possible by the high sensitivity of the instrument,
which allowed us to measure the quasi-thermal noise with minima
around 
V 
Hz 
, a level which is still 2 orders
of magnitude above the instrument background.
Some limitations to our measurements prevent us from obtaining
the dispersion curves in the close vicinity of
gyroharmonics: the modulus of the wave vector has to be larger
than the inverse of the antenna length in order for the angular
pattern to be dependent on it (this excludes frequencies just below
gyroharmonics); it must not be too large either, in order that
the Doppler shift due to the plasma bulk velocity be
sufficiently small (which excludes frequencies just above
gyroharmonics). A further limitation is that we only consider
weakly damped electrostatic waves propagating roughly across
. This is expected to be adequate for the present
quasi-thermal noise measurements, except, again, in the
vicinity of gyroharmonics, where there is a strong damping by
thermal electrons.
For most of our dispersion curves, the plasma frequency was measured
independently, allowing us to derive from them the electron temperature with a
good precision, since it was the only unknown parameter. These results are
completely new, compared to the Pioneer and Voyager ones, because it is the
first time one gets in situ measurements of electron temperature and density of
the IPT outside the vicinity of the centrifugal equator (because of the
particular Ulysses trajectory used to drive it out of the Ecliptic plane). They
might remain the sole measurements of this kind for a while (in
particular, the Galileo spacecraft will have, as Vogager 1, a trajectory close
to the torus equator). Densities and comparison with Voyager 1 data were
already published by [Hoang et al., 1993], but we give here many
more temperature results and improve the precision by more than a factor of
2. These improved measurements allow us to mention the polytropic state law
for the electrons in the IPT with an exponent 
. We discuss
and interpret this result in a related paper [Meyer-Vernet, Moncuquet and Hoang, 1995].
Finally, we have verified that the small proportion of hot
electrons known to be present in the IPT has no significant
effect on the dispersion curves considered here. We have also
shown that a moderate departure of the bulk cold population
from a Maxwellian does not change the shape of the
dispersion curves much in the middle of the lowest gyroharmonic bands,
which corresponds to the range studied here. With such non-
Maxwellian distributions, the dispersion curves depend on an
equivalent temperature, which is mainly determined by the less energetic
electrons.
The present study might be generalized in several ways. The
sensitivity of the antenna angular pattern to the bulk velocity (appendix A)
for large values of 
might be used in some cases to measure
that velocity. We have not tried to make use of that property,
because the achieved precision would not be sufficient to detect
the expected small deviation from corotation. One might also try
to measure the dispersion relation when the plasma is at the
threshold of instability, or unstable, which seems to be the
case for a few spectra recorded close to the magnetic equator;
such a study might help determine which free energy source is
at work in that region.
Unfortunately, the limited frequency range of the receiver did not
allow us to fully study the harmonic bands near or above the
upper hybrid frequency in the IPT (except in one case). One
expects in these bands a drop of the plasma quasi-thermal noise
between each 
frequency and the following gyroharmonic due to
the absence of undamped solution of the dispersion equation in
this range. This might be used to detect these
frequencies fairly easily in order to deduce the
electronic densities along another part of the Ulysses trajectory
in the Jovian magnetosphere (M. Moncuquet et al., manuscript in preparation,
1995).