Velocity and dissipation characteristics of turbulence in solar flare plasma: An application of stochastic Lagrangian models

Abstract

The 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 transfer energy that facilitates plasma heating by over 10 MK and particle energization. In this study, using results of Monte Carlo experiment through 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 Gaussian distribution) in the turbulence of the solar flare plasma. Monte Carlo experiment was performed for the turbulent kinetic energy of 10 30 erg, at a time scale of 10 sec and length scale of the order of full loop half-length 10 10 cm of the solar flare. The results of the velocity and dissipation (relaxation rate) are presented and analysed in both one and two dimensions. We observed that the positive value of relaxation rate of (1 − 8) × 10 −4 sec −1 for ≈ 5 sec of dispersion time could lead to the energy transfer and dissipation of the energy in the turbulence of the solar flare. The Monte Carlo mean relaxation rate of 4.5 × 10 −4 sec −1 shows that it dissipates ≈ 4.5 × 10 27 erg energy into thermal energy in 10 seconds, which is equal to the ≈ 0.5 % of the total injected kinetic energy. Velocities of the stochastic particles in the turbulence show the randomly fluctuations which are unsteadily dispersive in nature. The range and mean values of particles velocities are ∼ (0.5 − 3) × 10 6 cm sec −1 and 1.5 × 10 6 cm sec −1 respectively which indicate low atmospheric turbulence (chromosphere) in the solar flare. The turbulence onset at the loop top of the flare corona and propagate to lower chromosphere atmosphere of the flare. The obtained results are in the agreement with the observations. Our analysis thus demonstrates that the turbulence in the solar flare dissipate ≈ 0.5% of the injected energy into thermal energy. The rest of energy goes for the non-thermal particle energizing (particle acceleration).