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Role of Parallel Solenoidal Electric Field on Energy Conversion in 2.5D Decaying Turbulence with a Guide Magnetic Field

We perform 2.5D particle-in-cell simulations of decaying turbulence in the presence of a guide (out-of-plane) background magnetic field. The fluctuating magnetic field initially consists of Fourier modes at low wavenumbers (long wavelengths). With time, the electromagnetic energy is converted to plasma kinetic energy (bulk flow+thermal energy) at the rate per unit volume of ${\pp J}\cdot{\pp E}$ for current density ${\pp J}$ and electric field ${\pp E}$. Such decaying turbulence is well known to evolve toward a state with strongly intermittent plasma current. Here we decompose the electric field into components that are irrotational, ${\pp E}_{\rm ir}$, and solenoidal (divergence-free), ${\pp E}_{\rm so}$. ${\pp E}_{\rm ir}$ is associated with charge separation, and ${\pp J}\cdot{\pp E}_{\rm ir}$ is a rate of energy transfer between ions and electrons with little net change in plasma kinetic energy. Therefore, the net rate of conversion of electromagnetic energy to plasma kinetic energy is strongly dominated by ${\pp J}\cdot{\pp E}_{\rm so}$, and for a strong guide magnetic field, this mainly involves the component ${\pp E}_{\rm so,\parallel}$ parallel to the total magnetic field ${\pp B}$. We examine various indicators of the spatial distribution of the energy transfer rate {\bf J$_\parallel\cdot$E$_{so,\parallel}$}, which relates to magnetic reconnection, the best of which are 1) the ratio of the out-of-plane electric field to the in-plane magnetic field, 2) the out-of-plane component of the non-ideal electric field, and 3) the magnitude of the estimate of current helicity.