Basic consents of plasma physics and their application to processes in the solar atmosphere. Kinetic, two-fluid and MHD description of plasmas: (single-)fluid model as an approximation and limits of its usability. Generalized Ohm’s law and anomalous (effective) electrical resistivity. Coupling of macro- and micro-scales in solar plasmas.

Macroscopic structures of magnetic field in the solar atmosphere: Loops, flux ropes, and arcades. Magnetic field extrapolations: linear and non-linear force-free fields.

Basics of solar magneto-hydrostatics (MHS): Example calculations of MHS equilibria - prominences/filaments, vertical slabs and tubes. Magneto/hydrodynamic waves in wave-guides: Classification of the wave-modes, MHS structures in the solar atmosphere as wave-guides, applications - coronal seismology.

Magnetic-field topology and its changes. Topological skeleton of the magnetic field: Null points, separators, separatrix surfaces and quasi-separatrix layers (QSLs). Helicity. Topological changes of the magnetic field - magnetic field-line reconnection.

Magnetic reconnection - deeper look: current-layer (in)stability (tearing mode), classical reconnection models (Sweet-Parker, Petchek) and their limitations, non-linear stage of the tearing-mode instability - formation of magnetic islands/plasmoids. Plasmoid instability in highly-conductive plasmas. Dimensionality aspects: 2D vs. 3D reconnection. Magnetic configurations prone to formation of the current concentrations (current sheets): Null points, separators, (quasi)separatrix layers. (Turbulent) Energy cascades in the magnetic reconnection. Different reconnection regimes - parametric “phase diagram” of reconnection.

Occurrence and meaning of magnetic reconnection in the solar and astrophysical plasmas. Application of the MHD-instabilities theory and reconnection physics in solar research: Solar eruptive flares and CMEs.

Modeling of macroscopic processes in plasmas. Structure of the MHD equations: Energetics of the MHD processes and MHD equations in the conservative form. Approximative solution of the Riemann problem in MHD. Basic approaches to the numerical MHD modeling: Finite differences (FDM), volumes (FVM), and elements (FEM) methods of discretisation. Introduction to advanced techniques: Adaptive Mesh Refinement (AMR), parallelisation (MPI, CUDA) of numerical algorithms and high-performance computing (HPC).

Micro-scale kinetic processes in plasmas. Cascading energy transfer towards micro-scales and MHD turbulence. Particle acceleration, formation of non-Maxwellian distribution functions. Plasma micro-instabilities: Plasma+particle-beam systems and other non-Maxwellian configurations, generation of high-frequency plasma waves.

Analytical description of driven/damped waves in plasmas - quasi-linear (QL) approximation. Generalized plasma dielectric tensor. Kinetic equations for QL approximation. Energetics in the waves, absorption and emission coefficients. Stimulated emission vs. Landau damping. Feedback of plasma micro-physics to (effective) transport coefficients (e.g. resistivity) - scale coupling.

Numerical approaches to modeling of small-scale (kinetic) processes in the solar plasmas: Particle codes - Test particle (TP) and Particle-in-Cell (PIC), Vlasov simulations, gyro-kinetic approximation.

Modern multi-wavelength observations as a remote diagnostics of solar plasmas and test of our models. Relations between model and observation - forward fitting and inversion methods. Significance of the diagnostic layer above numerical models - calculation of observables from the state variables of the simulated system. Numerical simulations with observation-driven boundary conditions. Cascade of consecutive simulations for the space weather predictions - CACTUS.

Magnetic field structures. Magnetohydrodynamic waves.

Magnetic field reconnection. Helicity. Emission process in plasmas. Quasilinear theory. Coherent process. Acceleration of particles. Particle beams and their instabilities.. Numerical MHD and particle codes. Solar radio bursts. Solar flares and coronal mass ejection.