Eulerian ion energisation in three-dimensional hybrid-Vlasov-Maxwell turbulence

Abstract

In collisionless plasma turbulence, energy is transferred from electromagnetic fluctuations to the particles. However, the relative contributions of different ion energisation mechanisms remain unclear. We investigate ion energisation in three-dimensional hybrid Vlasov--Maxwell simulations of decaying turbulence at $β_{i0}=0.25$ and $β_{i0}=4$, where $β_{i0}$ is the initial ratio of ion thermal to magnetic pressure. Using the exact ion momentum equation, we decompose the ion energisation rate $\mathbf{j}_i\mathbf{\cdot}\mathbf{E}$ into the work done on the parallel, diamagnetic, curvature, agyrotropic and polarisation ion currents. This decomposition requires neither gyrotropy nor scale separation and, therefore, remains valid where guiding-centre theory breaks down. We show that the agyrotropic term, which has no guiding-centre counterpart, accounts for $21\,\%$ of the energisation at $β_{i0}=0.25$ and $91\,\%$ at $β_{i0}=4$. We find that the dominant instantaneous energisation term changes with $β_{i0}$, from the polarisation current at low $β_{i0}$ to the diamagnetic and agyrotropic currents at high $β_{i0}$, at all resolved scales. In addition, we show that reversible exchange with the ion bulk flow dominates the instantaneous rate, so the time-integrated energy transfer is larger at $β_{i0}=4$ even though the instantaneous rate is smaller. Our results provide quantitative evidence that guiding-centre drifts alone cannot describe ion energisation in kinetic-scale turbulence and that the dominant energisation term depends on $β_i$. The results also highlight the key role of non-local thermodynamic-equilibrium effects in energy conversion in collisionless plasma turbulence.