Energy Deposition by Energetic Electrons in a Diffusive Collisional Transport Model

Abstract

A considerable fraction of the energy in a solar flare is released as suprathermal electrons; such electrons play a major role in energy deposition in the ambient atmosphere and hence the atmospheric response to flare heating. Historically the transport of these particles has been approximated through a deterministic approach in which first-order secular energy loss to electrons in the ambient target is treated as the dominant effect, with second-order diffusive terms (in both energy and angle) being generally either treated as a small correction or neglected. However, it has recently been pointed out that while neglect of diffusion in energy may indeed be negligible, diffusion in angle is of the same order as deterministic scattering and hence must be included. Here we therefore investigate the effect of angular scattering on the energy deposition profile in the flaring atmosphere. A relatively simple compact expression for the spatial distribution of energy deposition into the ambient plasma is presented and compared with the corresponding deterministic result. For unidirectional injection there is a significant shift in heating from the lower corona to the upper corona; this shift is much smaller for isotropic injection. We also compare the heating profiles due to return current Ohmic heating in the diffusional and deterministic models.

Electron Beams Cannot Directly Produce Coronal Rain

“…Such a non-local flux could effectively carry energy to the footpoints of the loop (Karpen & DeVore 1987), providing an additional source of heat that can lead to thermal instabilities, which requires further examination. It has also been suggested that the diffusion of non-thermal elec-trons to greater depths than predicted by the cold thick-target model is non-negligible (Emslie et al 2018;Jeffrey et al 2019). While this diffusion would allow energy to penetrate further shortly after the onset of heating, it is still not clear that the beam itself would last long enough to induce TNE (the heating needs to be on the order of the cooling time, Johnston et al 2019).…”

“…Electron beam heating has been previously implemented in HYDRAD (Reep et al 2013. We use the heating function derived by Emslie (1978), though a recent study suggested a modification to this to include the effect of diffusion in pitch angle, which effectively decreases the height at which electrons deposit their energy (Emslie et al 2018). In this work, we assume an injected electron flux spectrum with a sharp low-energy cut-off:…”

Modeling the Transport of Nonthermal Particles in Flares Using Fokker-Planck Kinetic Theory

“…Battaglia et al (2012) used a stochastic differential equation approach to model the source sizes of X-rays produced by nonthermal electrons injected at the top of loop models. Emslie et al (2018) used a collisional transport model to consider the effects of momentum and pitch-angle diffusion on the energy deposition rate from nonthermal electrons.…”

A fully self-consistent model for solar flares

“…Analytic fast electron models aim to estimate the change of the fast electron energy and pitch angle owing to collisions via analytic means, where it is assumed that these electrons are moving along magnetic field lines. Two types of models are often used in solar physics, one based on the solution of the Boltzmann equation with a Fokker-Planck treatment of collisions (McTiernan & Petrosian 1990;Allred et al 2015;Kerr et al 2016;Brown et al 2018;Emslie et al 2018), the other based on analytic energy loss rates of test electron beams in cold target plasma using a scattering treatment (Brown 1972;Emslie 1978). Analytic fast electron models, together with one dimensional (1D) (M)HD models, have been widely used to study the generation of evaporation of chromospheric plasma due to energetic electron deposition (e.g.…”