In the present work the status of the open systen studies at the Novosibirsk Institute ofNuclear Physics (INP) is described.For the heating of dense plasnas in open systens of the multi-mirror type the possibility isbeing studied to use high-current relativistic electron beans (REBS). At ne 3 - 1015 cm-3,jb ~ 2.5 kA/cm2, the experiments indicate that for fields up to B = 5 T the interaction efficiency sbstantially increases with increasing field strength. With the above aim in view, thework being performed at the Institute concerns the construction of high power generators ofmicrosecond REBS. At the generator U-1 a beam with 130 kJ energy content was produced. The construction of the generator U-2 is finished. In this generator, a foilless diode with a band geometry beam has been employed. In a similar geometry, the beams from several generators can beinjected sequentially into the same magnetic track.The results, obtained on a gas-dynamical trap (GDT) with large mirror ratio (R > 80) for thecase when the ion mean free path λii satisfied the inequality: L > λii(lnR/R) (L is thelongitudinal size of the system), have shown that the plasma dynamics in the trap is consistentwith gas-dynamical estimations. At the stage of GDT filling, the plasma in it proves to bestable. At a favourable curvature of the magnetic field lines in expanders the plasma turns outto be MHD stable with the plasma source switched off as well. In the latter case the plasmadecay time is in reasonable agreement with the gas-dynanical estimation: τ ~ LR/vTi.The project of an ambipolar trap (tanden mirror) with axisymmetrical magnetic field has beendeveloped. For MHD stabilization on the outside of the end plugs, two semi cusps with hot ionplasma (T = 15 keV) are planned to be mounted. High mode number MHD modes are assumed to bestabilized by the finite Larmor radius (FLR) effect, while the mode m = 1 will be stabilized bya favourable curvature of the magnetic field. The basic parameters of the central mirror trapare: L = 14 m, B = 0.45 T, ne = 1013 cm-3. The end plugs have the following paraneters:Lp = 1.8 m, R = 4, Bmax = 6 T, ne = 3 × 1013 cm-3.