Energy Conversion through a Fluctuation–Dissipation Relation at Kinetic Scales in the Earth’s Magnetosheath

Low-frequency fluctuations in the interplanetary medium represent a turbulent environment where universal scaling behavior, generated by an energy cascade, has been investigated. On the contrary, in some regions, for example, the magnetosheath, universality of statistics of fluctuations is lost. However, at kinetic scales where energy must be dissipated, the energy conversion seems to be realized through a mechanism similar to the free solar wind. Here we propose a Langevin model for magnetic fluctuations at kinetic scales, showing that the resulting fluctuation–dissipation relation is capable of describing the gross features of the spectral observations at kinetic scales in the magnetosheath. The fluctuation–dissipation relation regulates the energy conversion by imposing a relationship between fluctuations and dissipation, which at high frequencies are active at the same time in the same range of scales and represent two ingredients of the same physical process.