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Significance of the temperature

It is important to discuss the significance of the measured temperature, since the electron velocity distribution is not Maxwellian in the region explored. The electron analyzers aboard Voyager ([Scudder et al. 1981], [Sittler and Strobel 1987]) detected at this Jovicentric distance ( tex2html_wrap_inline1749 ) a suprathermal population 10-30 times hotter than the main (cold) population, and representing a few percent of the total density. The presence of such a population was confirmed by Ulysses data, since it allowed us to interpret quantitatively the suprathermal level of electrostatic fluctuations in Bernstein waves ([Meyer-Vernet et al. 1993]). This minor hot population does not affect significantly the part of the dispersion relation used in our temperature measurements ([Moncuquet et al. 1995] ), so that, if the velocity distribution were a mere superposition of a cold and such a hot population - both being Maxwellian, the measured temperature plotted in Fig.1 would be approximately that of the main (cold) population.

However, the velocity distribution is expected to be more complex than a superposition of two Maxwellians. Firstly, the Voyager electron analyzer results clearly showed that the hot electrons were not Maxwellian distributed ([Scudder et al. 1981]). Secondly, these analyzers had a low-energy threshold of 10 eV, and the spacecraft was negatively charged, thereby yielding a higher effective threshold ([Scudder et al. 1981], [Sittler and Strobel 1987]); since 10 eV tex2html_wrap_inline1751 K in temperature units, this implies that a significant part of the main (cold) population could not be detected, so that the precise shape of the distribution at low energies is unknown. Hence, although the cold electron distribution could be roughly fitted to a Maxwellian, it is not certain that it was precisely Maxwellian. On the other hand, aboard Ulysses, the particle analyzers were unfortunately not operating in the torus, and the frequency range in which we measured the dispersion relation was not large enough to settle that question.

Hence, let us consider a more general case: a non-Maxwellian distribution made of a superposition of several Maxwellians of densities tex2html_wrap_inline1753 and temperatures tex2html_wrap_inline1755 . Since our Bernstein wave measurements were mostly made in the middle of the first gyroharmonic band, it can be shown ([Moncuquet et al. 1995]) that they are not sensitive to the mean energy of the distribution, i.e., to the traditional temperature tex2html_wrap_inline1757 . Instead, our measurements give an effective temperature tex2html_wrap_inline1759 defined by:

  eqnarray92

if the densities and temperatures of the individual populations have similar orders of magnitude, or if the hot population densities are much smaller than that of the coldest one. In this case, the temperature plotted here is thus tex2html_wrap_inline1759 . This effective temperature tex2html_wrap_inline1759 is defined from the mean inverse energy of the particles, and is thus mainly sensitive to the cold electrons; this is reminiscent of the classical Debye shielding, which depends on the same effective temperature, albeit for different reasons ([Meyer-Vernet 1993]).


next up previous
Next: POLYTROPE RELATION Up: ELECTRON MEASUREMENTS FROM Previous: Electron density and

Michel Moncuquet
Mon Feb 2 16:12:15 MET 1998