Scaling laws for the energy transfer in space plasma turbulence

One characteristic trait of space plasmas is the multi-scale dynamics resulting from non-linear transfers and conversions of various forms of energy. Routinely evidenced in a range from the large-scale solar structures down to the characteristic scales of ions and electrons, turbulence is a major cross-scale energy transfer mechanism in space plasmas. At intermediate scales, the fate of the energy in the outer space is mainly determined by the interplay of turbulent motions and propagating waves. More mechanisms are advocated to account for the transfer and conversion of energy, including magnetic reconnection, emission of radiation and particle energization, all contributing to make the dynamical state of solar and heliospheric plasmas difficult to predict. The characterization of the energy transfer in space plasmas benefited from numerous robotic missions. However, together with breakthrough technologies, novel theoretical developments and methodologies for the analysis of data played a crucial role in advancing our understanding of how energy is transferred across the scales in the space. In recent decades, several scaling laws were obtained providing effective ways to model the energy flux in turbulent plasmas. Under certain assumptions, these relations enabled to utilize reduced knowledge (in terms of degrees of freedom) of the fields from spacecraft observations to obtain direct estimates of the energy transfer rates (and not only) in the interplanetary space, also in the proximity of the Sun and planets. Starting from the first third-order exact law for the magnetohydrodynamics by Politano and Pouquet (1998), we present a detailed review of the main scaling laws for the energy transfer in plasma turbulence and their application, presenting theoretical, numerical and observational milestones of what has become one of the main approaches for the characterization of turbulent dynamics and energetics in space plasmas.