Spectral properties and energy transfer at kinetic scales in collisionless plasma turbulence

Abstract

Context. Recent satellite observations in the solar wind and in the Earth’s magnetosheath have shown that the turbulent magnetic field spectrum, which is know to steepen around ion scales, has another break at electron scales where it becomes even steeper. The origin of this second spectral break is not yet fully understood, and the shape of the magnetic field spectrum below electron scales is still under debate. Aims. By means of a fully kinetic simulation of freely decaying plasma turbulence, we study the spectral properties and the energy exchanges characterizing the turbulent cascade in the kinetic range. Methods. We started by analyzing the magnetic field, electron velocity, and ion velocity spectra at fully developed turbulence. We then investigated the dynamics responsible for the development of the kinetic scale cascade by analyzing the ion and electron filtered energy conversion channels, represented by the electromagnetic work J ⋅ E, pressure–strain interaction −P : ∇ u, and the cross-scale fluxes of electromagnetic (e.m.) energy and fluid flow energy, accounting for the nonlinear scale-to-scale transfer of energy from large to small scales. Results. We find that the magnetic field spectrum follows the k−α exp(−λ k) law at kinetic scales with α ≃ 2.73 and λ ≃ ρe (where ρe is the electron gyroradius). The same law with α ≃ 0.94 and λ ≃ 0.87ρe is observed in the electron velocity spectrum, but not in the ion velocity spectrum that drops as a steep power law ∼k−3.25 before reaching electron scales. By analyzing the filtered energy conversion channels, we find that electrons play a major role with respect to the ions in driving the magnetic field dynamics at kinetic scales. Our analysis reveals the presence of an indirect electron-driven mechanism that channels the e.m. energy from large to sub-ion scales more efficiently than the direct nonlinear scale-to-scale transfer of e.m. energy. This mechanism consists of three steps. In the first step the e.m. energy is converted into electron fluid flow energy at large scales; in the second step the electron fluid flow energy is nonlinearly transferred toward sub-ion scales; in the final step the electron fluid flow energy is converted back into e.m. energy at sub-ion scales. This electron-driven transfer drives the magnetic field cascade up to fully developed turbulence, after which dissipation becomes dominant and the electrons start to subtract energy from the magnetic field and dissipate it via the pressure–strain interaction at sub-ion scales.