Field-Lines-Threaded Model for: (1) the Low Solar Corona; (2) Electrons in the Transition Region; and (3) Solar Energetic Particle Acceleration and Transport

In numerical simulations of the solar corona, both for the ambient state and especially for dynamical processes the most computational resources are spent for maintaining the numerical solution in the Low Solar Corona and in the transition region, where the temperature gradients are very sharp and the magnetic field has a complicated topology. The degraded computational efficiency is caused by the need in a highest resolution as well as the use of the fully three-dimensional implicit solver for electron heat conduction. On the other hand, the physical nature of the processes involved is rather simple (which still does not facilitate the numerical methods) as long as the heat fluxes as well as slow plasma motional velocities are aligned with the magnetic field. The Alfven wave turbulence, which is often believed to be the main driver of the solar wind and the main source of the coronal heating, is characterized by the Poynting flux of the waves, which is also aligned with the magnetic field. Therefore, the plasma state in any point of the three-dimensional grid in the Low Solar Corona can be found by solving a set of one-dimensional equations for the magnetic field line ('thread'), which passes through this point and connects it to the chromosphere and to the global Solar Corona. In the present paper we describe an innovative computational technology based upon the use of the magnetic-field-line-threads to find the local solution. We present the development of the AWSoM code of the University of Michigan with the field-lines-threaded Low Solar Corona. In the transition region, where the essentially kinetic description of the electron energy fluxes is required, we solve the Fokker-Plank equation on the system of threads, to achieve the physically consistent description of chromosphere evaporation. The third application for the field-lines-treaded model is the Solar Energetic Particle (SEP) acceleration and transport. Being the natural extension of the Field-Line-Advection Model for Particle Acceleration (FLAMPA), earlier suggested for a single magnetic field line advected with the plasma motion, the multiple-field-lines model allows us to simulate the SEP fluxes at multiple points of possible observation (at the Earth location, at STEREOs, at Mercury).