4.1 Input Parameters

Considering first the radial dependency of the model, we have the following input parameters: the densities of each species at a reference point -e.g. the location of the spacecraft at the time of in situ measurements, the densities $n(0)$ at the centrifugal equator being then extrapolated using (10)- and the values of the parallel and perpendicular temperatures $T_{\parallel}(0)$ and $T_{\perp}(0)$ at the centrifugal equator (or, equivalently, the parallel thermal speed $\Theta_{\parallel}$ and the thermal anisotropy at the equator $A_0$). In this paper, the input densities and temperatures are those used by Bagenal [1994], comprising 48 points between 4 and 12 ${\rm R_J}$ based on the inbound Voyager 1 plasma measurements and the Voyager UVS emissions. The radial profiles along the spacecraft trajectory (illustrated in Figure 1) are shown in Figure 4, and constitute the ``reference data set'' for the radial structure of the IPT.

Figure 4: The reference densities (top) and temperatures (bottom) of the main particle species (from Voyager 1) used to compute our torus model (identical to Bagenal [1994]). The electron parameters are plotted in black, the densities of sulfur ions ($S^{+,++,+++}$) are in red and the densities of oxygen ions ($O^{+,++}$) are in blue; the proton density are plotted in green. The parameters of cold species (core) are plotted as bold lines, the parameters of hot species (halo) are plotted as thin lines (there is no halo for minor species $S^{+++}$, $O^{++}$ and protons). The core and halo temperatures (in pink) are the same for all ions (except for the protons between 5 and 6${\rm R_J}$ which are in green).

In addition, since the latitudinal changes in density (equation 10) as well as in temperature (equations (11) and (12)) are given along the magnetic field lines, their calculations require a reliable model of the Jupiter magnetic field and eventually of the azimuthal current sheet. At first approximation, the Jupiter magnetic field is assumed to be a tilted dipole (sketched in appendix) to which we may add, as Bagenal [1994], non-dipolar contributions from the GSFC $O_4$ or $O_6$ models, with or without current sheet contributions [ Connerney, 1992]. Note also we have simply assumed, to express the centrifugal potential in equation (A2) of the appendix, that all the torus plasmas rigidly corotate with Jupiter, while the bulk plasma speed is indeed slower than the exact corotation speed in the outer IPT [ Hill, 1980, Belcher, 1983], as it was recently confirmed with Galileo plasma measurements[ Frank and Paterson, 2000]. But the consequences on our model of this centrifugal speed variation with radial distance are actually negligible, especially when compared to those due to possible variations of the main unknown inputs of the model -namely the ions' kappa and anisotropy values- which we discuss now.

The choices of kappa and of the anisotropy parameters for the ion species are not well constrained by the observations. Nevertheless, we can eliminate the most extreme values. First of all, the Voyager 1 observations of a non-thermal tail in the ion velocity distributions indicate that the kappa must be finite ($\lesssim 10$). We can also eliminate values $A_{0i} \ge 10$. Although such an anisotropy matches the equatorial confinement observed by Ulysses, the assumption of high anisotropy requires a strong increase in equatorial temperature with radial distance which conflicts with remote sensing observations and with the plasma cooling on expansion.

Unfortunately, the data do not sufficiently constrain the ion temperature anisotropy $A_{0i}$ and the ion kappa values $\kappa_i$. Indeed, among the four in situ data sets available to us, only two can constrain these parameters, namely the electron density at Ulysses (whose confinement requires a significant anisotropy) and the temperature increase with radial distance at Voyager 1 (which is not compatible with such a significant anisotropy if the distributions are Maxwellian). To derive some more precise constraints on $A_{0i}$ and $\kappa_i$, we would need either a simultaneous measurement of the temperature at the equator for Voyager 1 or a measurement of the ion temperature at Ulysses (along the magnetic field), neither of which was obtained. So, the most conservative constraint we can derive is $A_{0i}>1$, probably $< 5$ and $\kappa_i$ is finite, probably $< 6$.

In this paper, we have chosen values for the ion distributions of $\kappa_i = 2$ and $A_{0i}=3$ as a compromise which (1) matches the confinement of the plasma to the centrifugal equator observed by Ulysses, (2) produces a relatively flat (to decreasing) variation of temperature with radial distance (consistent with expectations of plasma cooling by expansion), (3) is consistent with the increase of temperatures with latitude observed by Voyager 1 beyond 8${\rm R_J}$, and, finally, (4) gives an increase in ion temperature with latitude comparable to that observed for the electrons on Ulysses. We discuss below the first three issues in more detail.