The Effects of Transverse Magnetic Field and Density Variations on the Particle Energy Spectra in a Reconnecting 3D Current Sheet

Electron and proton acceleration by a super-Dreicer electric field is further investigated in a non-neutral reconnecting current sheet (RCS) with a variable plasma density. The tangential B _z and transverse magnetic field components B _x are assumed to vary with the distances x and z from the X nullpoint linearly and exponentially, respectively; the longitudinal component (a ‘guiding field’) is accepted constant. Particles are found to gain a bulk of their energy in a thin region close to the X nullpoint where the RCS density increases with z exponentially with the index λ and the tangential magnetic field B _x also increases with z exponentially with the index α. For the RCS with a constant density (λ = 0), the variations of the tangential magnetic field lead to particle power-law energy spectra with the spectral indices γ₁ being dependent on the exponent α as: for protons and for electrons in a strong guiding field (β > 10⁻²) and for electrons in a moderate or weak guiding field (β > 10⁻⁴). For the RCS with an exponential density increase in the vicinity of the X nullpoint (λ≥ 0) there is a further increase of the resulting spectral indices γ that depends on the density exponent index λ as for protons and for electrons in weaker guiding fields and as for electrons in stronger guiding fields. These dependencies can explain a wide variety (1.5–10) of particle spectral indices observed in solar flares by the variations of a magnetic field topology and physical conditions in a reconnecting region. This can be used as a diagnostic tool for the investigation of the RCS dynamics from the accelerated particle spectra found from hard X-ray and microwave emission.     

Combining MHD and kinetic modelling of solar flares

Solar flares are explosive events in the solar corona, representing fast conversion of magnetic energy into thermal and kinetic energy, and hence radiation, due to magnetic reconnection. Modelling is essential for understanding and predicting these events. However, self-consistent modelling is extremely difficult due to the vast spatial and temporal scale separation between processes involving thermal plasma (normally considered using magnetohydrodynamic (MHD) approach) and non-thermal plasma (requiring a kinetic approach). In this mini-review we consider different approaches aimed at bridging the gap between fluid and kinetic modelling of solar flares. Two types of approaches are discussed: combined MHD/test-particle (MHDTP) models, which can be used for modelling the flaring corona with relatively small numbers of energetic particles, and hybrid fluid-kinetic methods, which can be used for modelling stronger events with higher numbers of energetic particles. Two specific examples are discussed in more detail: MHDTP models of magnetic reconnection and particle acceleration in kink-unstable twisted coronal loops, and a novel reduced-kinetic model of particle transport in converging magnetic fields.