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State-of-the-art MHD calculations reveal acceptable agreement with observational data for the height profile of the temperature $T(h)$ in the transition region of solar corona. Simultaneously, the velocity of the solar wind $U(h)$ has also been calculated. The developed method gives the possibility at given frequency dependent spectral density of Alfven waves (AW) coming from chromosphere $mathcal{W}(omega)$ to calculate both height profiles $T(h)$ and $U(h)$. In agreement with the concepts of the self-induced opacity of plasma with respect of AW, the narrow width $lambda$ of the transition region is determined by the fast temperature increase of the viscosity $eta(T,B)$. After more than 70 years of development of Solar physics, the Alfven hypothesis of heating of the solar corona by AW has remained without alternatives; none of other mechanisms can explain $ab$ $initio$ the value of $lambda$. The performed MHD analysis explains the height dependence of the non-thermal broadening of the chromospheric spectral lines and predicts angular dependence of this broadening with respect of position in solar disc. One can expect significant impact of MHD analysis in the interpretation of the long expected data from Parker Solar Probe.
A three-dimensional MHD model for the propagation and dissipation of Alfven waves in a coronal loop is developed. The model includes the lower atmospheres at the two ends of the loop. The waves originate on small spatial scales (less than 100 km) ins
We perform 2.5D hybrid simulations with massless fluid electrons and kinetic particle-in-cell ions to study the temporal evolution of ion temperatures, temperature anisotropies and velocity distribution functions in relation to the dissipation and tu
We solve numerically the ideal MHD equations with an external gravitational field in 2D in order to study the effects of impulsively generated linear and non-linear Alfven waves into isolated solar arcades and coronal funnels. We analyze the region c
The solar corona is a complex system, with nonisothermal plasma and being in the self-gravitating field of the Sun. So the corona plasma is not only a nonequilibrium system but also a nonextensive one. We estimate the parameter of describing the degr
To properly describe heating in weakly collisional turbulent plasmas such as the solar wind, inter-particle collisions should be taken into account. Collisions can convert ordered energy into heat by means of irreversible relaxation towards the therm