Hall effect is known to be especially significant for compressible plasmas with flows that are usual for the present-day fusion experiments. Hall effect is able to change a behavior of the plasma parameters typical for ideal magnetohydrodynamics (MHD), e.g., it produces nonmonotonic density profile, current eddies, and modifies plasma stability conditions. The existence of the Hall effect was verified both experimentally and computationally. However, still now there is no general formalism, which would allow to analyse plasma stability accounting for the Hall effect in the systems of rather general geometry.

The formalism developed is aimed to present a variational stability criterion similar to the energy principle, which is well known for static equilibrium in the frame of ideal MHD. The most relevant hydrodynamic model accounting for both Hall effect and plasma flows, namely, Hall MHD, is figured out. The variational approach is appeared to be fruitful due to accounting for all the principal conservation laws inherent in the model equations. The method is based on the regular procedure of finding the variational symmetries of partial differential equations.