5. Summary and Final Remarks

With a kinetic collisionless model assuming bi-kappa velocity distributions for ions and electrons, we have been able to model various aspects of the Ulysses data: the tight confinement of the plasma to the equator and the variation in electron temperature with latitude. Using input parameters based on Voyager 1 conditions [ Bagenal, 1994] enables us to model many features of the density measurements made by Voyager 1, Voyager 2, Ulysses and Galileo. Differences between the model and the observations suggest variations in density of about a factor of 2 with longitude (for V1 inbound data) or with time (between Voyager, Ulysses and Galileo epochs).

The bi-kappa distribution also enables us to explain part of the increase in ion temperature observed by Voyager 1 between 7 and 10 ${\rm R_J}$ where the spacecraft was $\sim$1${\rm R_J}$ below the centrifugal equator. When the ion temperatures are extrapolated to the equator with the bi-kappa model, we find that the temperature increases less rapidly with radial distance (compared to the earlier core-halo fit), which is more nearly consistent with both the plasma cooling quasi-adiabatically as it diffuses radially outwards, and with observations of the vertical distribution of emissions from the torus diminishing with radial distance from Jupiter [ Herbert and Sandel, 1995, Thomas, 1995].

It is noteworthy that the choice of the bi-kappa distribution parameters which enable us to obtain the above results, namely the ion anisotropy $A_{0i}=3$ and the ion kappa value $\kappa_i = 2$, is a working compromise and not the result of any fitting-to-data process. We cannot indeed derive precise values of these parameters, since we lack ion measurements over a significant latitude range. The best constraint we can derive is $1<A_{0i}<5$ and $\kappa_i$ sufficiently moderate so that the bi-kappa is not equivalent to a bi-Maxwellian (say $\kappa_i<6$ for all species in the outer IPT). We may however conclude that a kinetic collisionless model, using a non-Maxwellian anisotropic distribution, provides physical explanations for both the unexpected behavior of the temperature along the magnetic field lines as seen at Ulysses and the misunderstood behavior of the equatorial temperature with distance from Jupiter as seen at Voyager 1 [ Moncuquet, 1997].

From a basic plasma physics point of view, this illustrates an important consequence of the lack of collisions in space plasmas. The particles have non-Maxwellian velocity distributions, so that they cannot be adequatly modelled by (multi) fluid equations, but require instead a kinetic approach. The present results show that kinetic effects play an important role not only on small scales but also for describing large scale structures [ Meyer-Vernet, 2001].