Numerical Simulation to Study Solar Wind Turbulence and Coronal Heating

Abstract

The solar wind turbulence and coronal heating have been an open problem in solar physics in spite of having proposed many theoretical models to explain it. Dispersive Alfvén wave (DAW) is one of the main candidate which is responsible for inhomogeneous heating of solar wind and coronal plasmas. In this thesis, we explore some of the magnetohydrodynamic and kinetic properties of nonlinear Alfvén waves in the context of solar wind, solar corona and the magnetospheric turbulence as well as the heating of the plasma particles. It studies about the formation of coherent, filamentary Alfvénic structures, their decay processes, their role in particle heating and acceleration, and their relevance for creating the power-law spectra of turbulence observed in solar wind and corona. The dynamical equations satisfied by DAWs follow the form of modified nonlinear Schrödinger equation. The equations were numerically solved by pseudo-spectral method of simulation by taking Fast Fourier Transform and forward difference method with predictor corrector scheme. By assuming an energy inputs in the form of pump waves in the kinetic range or electron inertial range, the author studies numerically the evolution of these waves that lead to filamentary nonlinear structures, or to creation of spatio-temporal turbulence. The magnetic filaments of DAWs with high intensity are generated as the waves propagate along the direction of magnetic field. The transverse modulation of Alfvén waves resulting in coherent structures formation has a significant effect on the evolution of the turbulent magnetic spectra and density fluctuations. The perpendicular characteristic scale of the magnetic coherent structurs is of the order of ion Larmor radius for the kinetic Alfvén waves (KAWs) and it is of the order of electron skin depth for the inertial Alfvén waves (IAWs). The applications of the dynamical models and numerical simulations of KAWs at 1AU solar wind parameters and coronal loops, and IAWs at the coronal holes are also discussed. The dynamical motions are dependent on the type of plasma inhomogeneity represented by four different kinds of initial conditions in our numerical simulation. The perturbation present in the magnetic field gets the energy from the pump DAWs. As the waves propagate, magnetic coherent structures are generated when there is a balance between the wave diffraction and nonlinearity effects resulting from plasma inhomogeneity profile. The collapse of the DAW wave packets takes place when this balance is x no more, thereby leading to the transfer of energy from the waves to the particles in the plasma such as electrons and ions. This transfer of energy at perpendicular wavevector is more for uniform initial pump KAWs rather than those for non-uniform initial pump waves of Gaussian wavefronts. The transfer of energy at kinetic small scales when the wavenumber is less than ion gyroradius and comparable to electron inertial length causes solar wind turbulence and heating of the plasma. In our study, the power spectral index follows Kolmogorov scale of −5/3 in the inertial range followed by deeper index varying from -2.5 to -8 in the kinetic dissipation range. The scaling anisotropy of turbulent power spectra in the kinetic scales of plasma particles can importantly influence the plasma heating and turbulent energy transfer processes. For the heating of plasma particles via the wave-particle interactions, in general, the electric power spectra of the turbulent waves are more important than the magnetic power spectra. For the fluctuating electric/magnetic fields, the distribution function of the charged particles satisfies the Fokker-Plank equation. By solving this distribution function in steady state condition, we show that the extension of the distribution thermal tail depends on the wavenumber spectral indices of the electric/magnetic field power spectra. Therefore, charged particles at the end of the distribution function thermal tail have higher velocity and thereby energizing the solar coronal or auroral plasmas. Since the formation of magnetic filaments and it’s collapse are considered as one of the faster way to transport energy, our present study may provide some clues to understand the phenomena of energy distributio