Velocity and Dissipation Characteristics of Turbulence in Solar-Flare Plasma: An Application of Stochastic Lagrangian Models

Abstract

Turbulence is one of the products of the magnetic-reconnection process in the solar-flare plasma. It intensely shifts the dynamics of the magnetic-reconnection process and rapidly transfers energy that facilitates plasma heating by over 10 MK and particle energization. In this study, using the results of a Monte Carlo experiment through the Euler–Maruyama approximation of stochastic Lagrangian models for inhomogeneous hydrodynamic turbulence, we present the velocity and dissipation (relaxation rate) characteristics of stochastic motions of particles (particles obeying a Gaussian distribution) in the turbulence of the solar-flare plasma. A Monte Carlo experiment was performed for a turbulent kinetic energy of $10^{30}\text{ erg}$, on a time scale of ten seconds and a length scale of the order of the full loop half-length [$10^{10}\text{ cm}$] of the solar flare. The results of the velocity and dissipation (relaxation rate) are presented and analyzed in both one and two dimensions. We observed that the positive value of relaxation rate of $(1\,\text{--}\,8) \times 10^{-4}\text{ s}^{-1}$ for ≈ five seconds of dispersion time could lead to energy transfer and dissipation of the energy in the turbulence of the solar flare. The Monte Carlo mean relaxation rate of $4.5 \times 10^{-4}\text{ s}^{-1}$ shows that it dissipates $\approx 4.5 \times 10^{27}\text{ erg}$ energy into thermal energy in ten seconds, which is equal to ≈ 0.5% of the total injected kinetic energy. Velocities of the stochastic particles in the turbulence show the random fluctuations, which are unsteadily dispersive in nature. The range and mean values of particle velocities are $\approx (0.5\,\text{--}\,3) \times 10^{6}\text{ cm}\,\text{s}^{-1}$ and $1.5 \times 10^{6}\text{ cm}\,\text{s}^{-1}$, respectively, which indicates low-atmospheric turbulence (chromosphere) in the solar flare. The results obtained are in agreement with observations. Our analysis thus demonstrates that the turbulence in the solar flare dissipates ≈ 0.5% of the injected energy into thermal energy and low-atmospheric turbulence (chromosphere) in the solar flare. We surmise that the rest of the turbulent kinetic energy goes to the non-thermal particle energization (particle acceleration), generation of the termination shock, and other dynamical processes in the solar flare.