The pseudosymmetry principle being used for hot plasma confinement magnetic systems design could provide the realization of all the ability of magnetic confinement for reactor construction. In particular, it enables hot plasma confinement at steady state operational mode with a 'tokamak' level of confinement time and a high average β value (plasma pressure to 'vacuum' magnetic field pressure ratio). High β operation provides the possibility of thinking of advanced fuels (D–3He, D–D) use.It is proposed to check the main idea and the results of a preliminary theoretical study experimentally in the frame of the EPSILON project—closed mirror magnetic trap with extremely small rotational transform and with poloidal pseudosymmetry. The EPSILON system consists of two (or more) multimirror traps, closed with curvilinear equilibrium elements. Mirror field, MHD stability and plasma cleaning are provided by axially symmetric divertors with zero magnetic field at the separatrix displaced along the multimirror traps.