Yu. N. Orlov

Conservation laws for polynomial Hamiltonians and for discrete models of the Boltzmann equation

Conservation laws that are linear with respect to the number of particles are constructed for classical and quantum Hamiltonians. A class of relaxation models generalizing discrete models of the Boltzmann equation are also considered. Conservation laws are written for these models in the same form as for the Hamiltonians.

Feynman formulas as a method of averaging random Hamiltonians

We propose a method for finding the mathematical expectation of random unbounded operators in a Hilbert space. The method is based on averaging random one-parameter semigroups by means of the Feynman-Chernoff formula. We also consider an application of this method to the description of various operations that assign quantum Hamiltonians to the classical Hamilton functions.

Power plant design and accelerator technology for heavy ion inertial fusion energy

The concept of a power plant for fast-ignition heavy ion fusion is developed. It is based on repetitive detonation of a cylindrical direct-drive target, producing 750 MJ of fusion yield in each microexplosion. A heavy-ion driver system providing consequent compression and ignition of the cylindrical DT target is described. Data on energy fluxes generated by the microexplosion are given. The design of the thin liquid wall reactor chamber is presented. The behaviour of the liquid film at the first wall and the blanket coolant and material under a pulsed energy flux loading is analysed. The energy conversion thermal scheme and power plant output parameters are presented. The state of the art at the ITEP-TWAC experimental accelerator is described.

Evaluation of a power plant concept for fast ignition heavy ion fusion

The characteristics of a fast ignition heavy ion fusion (FIHIF) power plant are preliminarily evaluated. The reactor chamber consists of two sections: The upper smaller part is the microexplosion section proper; the lower bigger part is the condensation section, in which sprayed jets of coolant are injected. The first surface of the blanket is of generally accepted wetted porous design. The coolant is lithium-lead eutectic with an initial surface temperature of 820 K. The mass of the evaporated coolant just after the explosion is evaluated as 4 kg. Computation of neutronics results in blanket energy deposition with maximum density of the order of 10 8 J/m 3 at the first wall. The heat conversion system consisting of three coolant loops provides a net efficiency of the FIHIF power plant of 0.37.

BBGKY-hierarchies and Vlasov's equations in postgalilean approximation

The so-called “no interaction theorem” of D.G. Currie, T.F. Jordan and E.C. Sudarschan make it possible to construct relativistic quasiclassical dynamics and based on it statistical mechanics in the postgalilean approximation only. This paper deals with constructing equilibrium and non-equilibrium BBGKY-hierarchies, equilibrium one-body distributions and Vlasovs kinetic equations in this approximation. The results are obtained for particles of arbitrary contravariant tensor valency in both Lagrange and Hamilton variables.

Development of a fusion and fission power system based on direct-action microtargets and a high-power heavy-ion driver

A concept for a power system based on cylindrical direct-action microtargets and a high-power heavy-ion driver and using fusion and fission processes is examined. Combining fusion and fission makes it possible to utilize most efficiently the conditions of shock-free compression with cylindrical cumulation and to increase the burnup of thermonuclear fuel substantially.

Energy conversion in a reactor chamber for fast ignition heavy ion fusion

The concept of a power plant for a fast ignition heavy ion fusion is briefly reviewed. The reactor chamber response to x-ray irradiation, ion debris and neutron flux is considered. Ablation of a thin liquid film at the first wall is simulated by means of a one-dimensional hydrodynamic code. Ion debris reheating of the vaporized coolant is evaluated. Vaporization and subsequent condensation of the coolant is computed with the use of a kinetic model of fast condensation. Heating of the blanket due to neutron deposition and corresponding generation of pressure and stress waves are simulated by means of the Monte Carlo (MCNP) code and by the strength media mechanics code, respectively.

Equilibrium correlation function in post-Galilean approximation of a scalar field

The exact formula for the equilibrium one-dimensional binary distribution function for scalar particles, interacting by the potential 1/r, is obtained in the post-Galilean approximation. To take into account the post-Galilean corrections (i.e. the values of the order of O(c−2), where c is the velocity of light), the temperature shift is suggested. It means that in this relativistic approximation we can use the classical coordinate distribution function with the shifted temperature parameter.

Quantum BBGKY-hierarchies and Wigner's equation in postgalilean approximation

Abstract The so-called “no interaction theorem” of D.G. Currie, T.F. Jordan and E.C. Sudarschan makes it possible to construct relativistic quasiclassical dynamics and based on it statistical mechanics in the postgalilean approximation only. The transition to the quantum mechanics must be realized through the quantization law that can be developed in an infinite number of ways. This paper deals with construcing quantum BBGKY-hierarchies and Wigners equation in the postgalilean approximation. The relation between Wigners and Vlasovs equations is examined. This investigation is carried out in addition to our previous paper which concerned non-quantum postgalilean BBGKY-hierarchies and Vlasovs equation.

Feynman—Chernoff Iterations and Their Applications in Quantum Dynamics

The notion of Chernoff equivalence for operator-valued functions is generalized to the solutions of quantum evolution equations with respect to the density matrix. A semigroup is constructed that is Chernoff equivalent to the operator function arising as the mean value of random semigroups. As applied to the problems of quantum optics, an operator is constructed that is Chernoff equivalent to a translation operator generating coherent states.