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3.2. Fitting with both Adjustable Temperature and Density

During the period tex2html_wrap_inline1416 1710 to 18 UT, no measurements of the density are available. Actually, the upper hybrid frequency tex2html_wrap_inline1184 probably falls between the two lowest-frequency channels of the URAP high-frequency receiver (52 and 66 kHz); it is thus no longer possible to identify tex2html_wrap_inline1184 in the HF spectra in order to deduce the density [Hoang et al., 1993]. It also could not be deduced from the onboard particle analyzers, since they were not operational in the IPT.

Nevertheless, we can still determine the plasma dispersion characteristics from the spectrum modulations, since the method is independent of the plasma density. Then, is it possible to determine both the temperature and the density by fitting a solution of the dispersion equation with two adjustable parameters ( tex2html_wrap_inline1478 and tex2html_wrap_inline1118 )? A necessary condition is of course that this solution significantly depends on the plasma frequency. Owing to the expression of the derivative given by (B2) (this derivative, in respect with tex2html_wrap_inline1118 , is plotted on Figure B1), this condition only holds in the upper hybrid band and above. This range includes the so-called tex2html_wrap_inline1126 frequencies at which the wave group velocity vanishes (see upper panel in Figure B1), and there is a frequency gap in the spectrum of Bernstein waves between each tex2html_wrap_inline1126 and the upper consecutive gyroharmonic [Bernstein, 1958].
The nondetection of the upper hybrid frequency during the period 1710 to 18 UT, in the frequency range where the HF receiver has sufficient frequency resolution, implies that our low-frequency spectra indeed includes a part of that upper hybrid band, which is the band tex2html_wrap_inline1534 . There are, however, two problems: (1) the greatest dependence on tex2html_wrap_inline1118 occurs in the range of small values of tex2html_wrap_inline1138 (see Figure B1), which, as we have seen in section 2, are difficult to measure, and (2) our determination of k from the spin modulation only works for frequencies where the dispersion equation has a unique solution in k: this excludes frequencies between tex2html_wrap_inline1184 and tex2html_wrap_inline1126 . With these limitations in mind, we tried to fit the theoretical dispersion curves to the experimental ones using the same method as

   figure302
Figure 6: (top) Part of the spectrum observed at 1714 UT above the second gyroharmonic frequency. The small circles are the measurements and the solid lines are the best fitted antenna response with corresponding values of tex2html_wrap_inline1094 indicated below. The value of tex2html_wrap_inline1126 is that computed from the dispersion curves shown on the bottom panel. (bottom) The points with error bars are deduced from the spectrum and the solid lines are the best fitted solution of Bernstein's waves dispersion equation with two free parameters T and tex2html_wrap_inline1118 . The dashed lines are the solutions of the dispersion equation for the extrema values of tex2html_wrap_inline1118 in its range of uncertainty.

before but with two adjustable parameters: the electron gyroradius tex2html_wrap_inline1478 and the ratio tex2html_wrap_inline1134 . Owing to the above limitations, and also because of the difficulty to numerically separate the dispersion variations due to tex2html_wrap_inline1478 from the variations due to tex2html_wrap_inline1118 , the results of these fits are not very good. The fitting method yields acceptable least tex2html_wrap_inline1368 for only 12 dispersion curves out of 20 available ones, and the uncertainties are about tex2html_wrap_inline1566 for the temperature and tex2html_wrap_inline1568 for the density. These results are added on Figure 5 with error bars in dotted lines.

Despite the large error bars on the density, we may remark that the ratio tex2html_wrap_inline1134 probably does not fall under tex2html_wrap_inline1572 during this period; otherwise, the tex2html_wrap_inline1126 would be in the range of frequencies swept by the receiver (<48.5 kHz with a gyrofrequency about 20 kHz). In this case, one would expect two important qualitative changes in the observed spectra: (1) the quasi-thermal noise should peak at tex2html_wrap_inline1184 and tex2html_wrap_inline1126 , where the group velocity tex2html_wrap_inline1580 vanishes, and (2) the signal should fall abruptly just above tex2html_wrap_inline1126 until the following gyroharmonic, since no weakly damped mode exists in that band. Actually, we show in Figure 6 a spectrum where there is a power jump in the vicinity of the tex2html_wrap_inline1126 (computed from the fitted dispersion curves), which can satisfy our first statement. Owing to the limited frequency range of the receiver, this spectrum is the only one among the 20 available spectra in that period (before 18 UT) to show such behavior. However, since both tex2html_wrap_inline1118 and tex2html_wrap_inline1120 decrease with distance to Jupiter, the two above expected properties are routinely seen on the spectra acquired at later times; this can be used to determine the density (M. Moncuquet et al., manuscript in preparation, 1995).


next up previous
Next: 4. Temperature Measurement in Up: 3. From Dispersion Characteristics Previous: 3.1. Fitting the Temperature

Michel Moncuquet
Tue Nov 18 19:18:28 MET 1997