Extended symmetries of the kinetic plasma theory models
Extended symmetries of the kinetic plasma theory models. Abstract: In recent decades the Lie group method has been applied to explore many physically interesting
nonlinear problems in gas dynamics, plasma physics etc. Furthermore, extensions of the classical Lie algorithm to the integro-differential systems of equations of kinetic theory were proposed. It was shown that Lie symmetry group of the integro-differential equations of kinetic plasma theory is larger than that of its hydrodynamic approximations based on the partial differential equations. For the collisionless plasmas containing components with equal charge to mass ratio of particles, this result was first obtained by an indirect algorithm which allows us to built symmetries of the integro-differential kinetic equations via the symmetries of an infinite set of partial differential equations for the moments of distribution functions. Even more large symmetries were obtained by explicit symmetry exploration methods working directly with integro-differential equations of the kinetic models. Unfortunately, these additional symmetry extensions are incompatible with the existence of charge and current density integrals present in Maxwell field equations. It must be noted that the above mentioned indirect algorithm is free of these incompatibility problems.