Dimensionless scaling approaches to the solar and heliospheric processes

The paper presents the review of dimensionless parameters met in solar and heliospheric plasma physics. Kinetic and macroscopic regimes are delimited mainly by the values of large (small) Knudsen numbers correspondingly. The magneto-hydrodynamic (MHD) description with dissipation and radiation generates well-known parameters like Mach (M), Mach-Alfvén (MA), Strouhal (S) and several other numbers. They play the important role and often used in literature, but others, like ‘velocity-emission’ ratios (Ve), Trieste (T) and Faraday (F) numbers are still not so common and remain poorly evaluated quantities. We demonstrate several examples when these ‘new’ parameters, respectively, allow clear quantitative delimitation and classification of flare-like and CME-like events on the Sun, physically open and closed systems against the energy, momentum and mass transports in the case of quiescent and eruptive prominences, inductive and Coulomb dominated plasma regimes in electric and magnetic fields. Dimensionless scaling is very helpful in complicated turbulent situations, when the application of other analytical methods is difficult.