Parallel electric field generation by Alfvén wave turbulence

Aims. This work aims to investigate the spectral structure of the parallel electric field generated by strong anisotropic and balanced Alfvénic turbulence in relation with the problem of electron acceleration from the thermal population in solar flare plasma conditions. Methods. We consider anisotropic Alfvénic fluctuations in the presence of a strong background magnetic field. Exploiting this anisotropy, a set of reduced equations governing non-linear, two-fluid plasma dynamics is derived. The low-β limit of this model is used to follow the turbulent cascade of the energy resulting from the non-linear interaction between kinetic Alfvén waves, from the large magnetohydrodynamics (MHD) scales with $k_{\perp}\rho_{\rm s}\ll 1$ down to the small “kinetic” scales with $k_{\perp}\rho_{\rm s} \gg 1$, $\rho_{\rm s}$ being the ion sound gyroradius. Results. Scaling relations are obtained for the magnitude of the turbulent electromagnetic fluctuations, as a function of $k_{\perp}$ and $k_{\parallel}$, showing that the electric field develops a component parallel to the magnetic field at large MHD scales. Conclusions. The spectrum we derive for the parallel electric field fluctuations can be effectively used to model stochastic resonant acceleration and heating of electrons by Alfvén waves in solar flare plasma conditions