The main results obtained by studying astrophysical plasma under extreme conditions are associated with interpretation of the observed spectral and temporal peculiarities of emissions of various compact objects, diagnostics of physical conditions in their vicinity, analysis of the kinetic processes in the plasma of relativistic jets and shock waves, and construction of the models of accretion disks, sources of gamma bursts, micro- quasars, and active galactic nuclei. A great contribution to these studies was made by V. V. Zheleznyakov, V. V. Kocharovsky, Vl. V. Kocharovsky, and E. V. Derishev. The following can be listed among the recent achievements in this research field.
The theory of radiation transfer in the plasma of white dwarfs and neutron stars, whose magnetic fields determine the decisive role of cyclotron scattering and magnetization of vacuum in the radiation transfer and even in plasma dynamics, has been developed. Contrary to earlier notions, it has been shown that redistribution of photons with respect to their frequencies in the cyclotron line increases the probability of the photons' release from great optical depths by several orders of magnitude, which makes the formation of cyclotron singularities considerably nonlocal and allows one to judge about the structure and parameters of rather deep layers of the atmosphere of compact stars.
The range of atmospheric parameters of white dwarfs and neutron stars, where the cyclotron wind can arise, has been determined, and the mass loss rate of these stars has been estimated. The obtained results indicate that the cyclotron wind can arise in a wide range of parameters of the magnetized plasma corresponding to many actually observed astronomical objects, in which the predicted mass loss rate allows one to expect considerable readjustments of their magnetospheres and formation of so-called discons.
Physical models of relativistic jets in the sources of gamma bursts and active galactic nuclei have been constructed. The developed mechanisms of particle acceleration in the jet plasma, which are matched with the generated accompanying radiation, allow one to explain many observed features of spectra and light curves, as well as demonstrate possible properties of the radiation in the X-ray, MeV, and GeV energy ranges.

Scheme of evolution of the Lorentz factor in gamma burst sources as a function of the distance between them and the source center. The plasma component is shown, i.e., the relativistic jet proper (red curve), as well as two neutron component differing in their velocities (green and blue curves), which propagate independently starting at some distance, and interact with the plasma jet after decay of neutrons, thus causing a secondary shock wave

Main properties of the off-axis radiation of relativistic jet blazars and microquazars in the gamma range have been predicted, and the method for determination of the relative content of cold electrons in the blazar plasma from the polarization of their synchronous radiation has been developed.
The significant role of free neutrons in the dynamics of relativistic plasma in gamma burst sources has been found out, and the theory of neutron radiation of these sources has been developed, which includes the possibility of effective deceleration of relativistic jets due to emission of neutrinos by decaying pions.
A wide class of solutions for stationary current layers and filaments in collision-free multi-component plasma, both relativistic and nonrelativistic, has been constructed analytically. They serve as a foundation for the unified description of the dynamics of the self-consistent current and the magnetic field in different astrophysical objects and collision-free shock waves with an arbitrary particle energy distribution. It is shown that in the specific case of the angle-averaged energy distribution function, under certain conditions in the spectrum of synchronous radiation of the particles, which form self-consistent current layers and filaments, there exist characteristic singularities in the form of knees and/or extremums. Observation of such singularities can allow one to obtain information about the parameters of such current structures.
IAP researchers continued developing the earlier proposed conversion mechanism of acceleration of charged particles during their motion in inhomogeneous relativistic plasma flows under the conditions of multiple transformations (e.g., photoinduced ones) of the particles from charged particles (proton or electron/positron) to neutrals (neutron or photon) and back. Peculiarities of the origin of space rays with superhigh energies (up to ~10²¹ eV) have been identified.
The features of formation of the dynamic spectrum and propagation of low-frequency radiation, as well as its dynamic (ponderomotive) action on the plasma in the magnetospheres of neutron stars and in relativistic jets have been analyzed theoretically.
The kinetic and radiation processes inside the leading edge of the shock wave propagating in very dense and hot plasma, e.g., a shock wave in a supernova during its explosion, have been studied. As a result, it was demonstrated that the regime of the radiation-dominated shock front (where the width of the edge is determined by the radiation pressure) can transform to the regime of the viscous edge (where the width is determined by the free path length of the particles), which is accompanied by a sharp increase in the temperature of the plasma behind the shock front and generation of a high-power pulse of high-energy neutrinos.
The model of binary star systems including a massive star and a compact object, which are sources of hard gamma radiation, has been developed. This model offers a satisfactory explanation to observations and is based on the positive feedback effect, when electrons and positrons accelerated at the leading edge of the shock wave between the pulsar and star wind generate synchronous radiation, which increases the number of electron-positron pairs due to their two-photon birth inside the relativistic pulsar wind.
The promising fields of the fundamental space plasma physics, which are currently being developed at IAP intensely, include:

• formation of dynamic spectra of the natural electromagnetic radiation: effects of generation, propagation, and linear and nonlinear interaction of various waves in non-equilibrium space plasma;
• self-consistent cyclotron and synchrotron interaction of high-power electromagnetic radiation with inhomogeneous moving plasma allowing for its nonequilibrium state, which is a result of the action of radiation on particles;
• acceleration of charged particles and collective processes in multi-component plasma including the conditions of efficient mutual transformation of particles and/or photons;
• plasma phenomena at the interface between magnetohydrodynamic and kinetic processes in inhomogeneous media with particle flows and well-developed electromagnetic radiation.