Long-range interactions and probability distribution functions in the 
interplanetary medium

Pronounced core-halo electron and ion velocity distribution characteristics 
are a persistent and ubiquitous feature of astrophysical plasmas, in 
particular manifest in the solar wind by space observations. On the other 
hand, the probability distributions (PDFs) of the differences of any 
physical variable in the intermittent, turbulent interplanetary medium are 
scale dependent and also subject to strong non-Gaussianity for small-scale 
spatial separations, whereas for large scales the differences turn into a 
Gaussian normal distribution. Theoretically the nonextensive character of 
the interplanetary medium, counting for long-range interactions or memory 
and non-locality in turbulence, can be introduced by pseudo-additive 
entropy generalization where a parameter kappa measures the degree of 
nonextensivity in the system. Compatible also with negative values of the 
parameter kappa, generalized thermo-statistics provides via a recently 
introduced single temperature bi-kappa function the observed pronounced 
core-halo solar wind velocity space patterns that are generated 
adiabatically and following density conservation out of the infinite kappa 
Maxwellian state. Similarly, the PDFs of solar wind scalar field 
differences, computed from WIND and ACE data for different time lags, are 
compared with the characteristics of the theoretical bi-kappa functional 
and found also to represent accurately the overall scale dependence of the 
spatial solar wind intermittency. The observed PDF characteristics for 
increased spatial scales are manifest in the theoretical distribution 
functional by enhancing the only tuning parameter kappa where the 
large-scale Gaussian is approached for infinite kappa. It is argued that 
non-thermal core-halo velocity space distributions as well as the 
intermittency of the turbulent fluctuations must be related physically to 
the non-extensive character of the interplanetary medium counting for the 
long-range interactions via the entropy generalization.