Magnetized plasmas in the Universe are turbulent and are characterized by multiple spatial and temporal scales. Within the last two decades or so, major advances have been made in understanding the physics of turbulence in different astrophysical, solar and heliospheric layers. The wealth of data from space experiments as well as the considerable growth of computing power has allowed for a huge progress in our understanding of astroplasma turbulence properties. The importance of turbulent processes in maintaining the larger-scale phenomena has become widely recognized in astrophysics. Nevertheless, our knowledge of the interaction between turbulence and large-scale processes in astroplasma remains rudimentary. This aspect has not received the attention it deserves, in part because current understanding and models have failed to represent adequately the intellectual challenge of a problem that hinges on formulating the inherently nonlinear interactions between large scales and small scales of motions in turbulent flows. This is especially true in many astrophysical plasma studies, namely as example, in studies of the energy flow and links between physical processes in the solar interior and the magnetic-field-dominated regime in the solar atmosphere, and the particle-dominated regime in the heliosphere.
In spite of the large MHD scale turbulence is relatively well studied, the physical picture behind scales smaller than the ion gyroscale remains an open question. Recent solar wind studies showed that energy is dissipated and the fluid description of turbulence fails at these scales. Moreover a second cascade may take place, in the so-called dispersive range. Investigating plasma turbulence at these scales has crucial implications on various processes occurring in astrophysical plasmas : transport and particle acceleration, plasma heating and magnetic reconnection. In many applications of MHD turbulence, one would like to know how the energy is converted into heat or energetic particles at the tail of the cascade. Examples include the solar wind and hot accretion flows. To address this question on an ab initio basis, one has to resort to a kinetic treatment. Apparently, there is a pressing need for new initiatives in the development of the foundations of our current understanding of multi-scale phenomena in turbulent magnetoplasma in astrophysics. We propose a workshop to study the cascade and dissipation at small-scale turbulence in different (astrophysical, interplanetary and near Earth’s) plasmas, with the purpose to suggest novel ways in making substantial progress in the field. The work will be based on the application of the recent achievements on this topic and the synergy between novel data analysis of in-situ multipoint observations (Cluster, Themis) and advanced numerical simulations with MHD, Vlasov, Gyrokinetic and Landau-fluid codes. The nature of the fluctuations below the ion inertial scales, namely whether the fluctuations are dissipative or dispersive or both will be studied. How the cascade proceeds to the electron scales from the proton scales is another challenge. The relative strength of the two kinds of dissipative processes at ion kinetic scales, namely wave particle interactions or current sheets and reconnection sites, are important questions to discuss. The nature of the relations of turbulent cascade in inertial range to the form of modes in which energy is available at the kinetic scales and the relative importance of different dissipative processes will be discussed. It is to be expected that the complementary expertise of the workshop participants having very different views will lead to a better understanding of the challenging problems of astrophysical plasma physics, and open new prospects and avenues in Sun and in Heliosphere research.