The effect of a parameter in a boundary condition on the stability of difference schemes

A nonlocal difference scheme for the heat conduction equation with a real parameter γ > 1 or γ < 0 in the boundary condition is considered. Thus, the analysis of this problem is generalized to all real values of the parameter in the boundary condition. The spectrum of the spatial operator of the scheme is studied. The results obtained are used to formulate a stability criterion for the difference scheme. The case γ = ?1 proves to be special, because the system of eigenfunctions of the operator does not form a basis in the space of grid functions.     

Stability of a nonlocal difference problem with a complex parameter

We consider a difference scheme for the heat equation with nonlocal boundary conditions containing a complex parameter γ. We single out stability domains in the complex γ-plane and derive a criterion for stability with respect to the initial data in the form of a condition on γ and the grid increments.     

Dynamics of neutralized charged particle beams in external magnetic and self fields

The dynamics of charged particle beams under the influence of their self-magnetic field and an external magnetic field is examined on the basis of equations for the trajectory of a boundary particle. A study is made of the change in the dynamics of fast particles due to the influence of the electric field of the partially neutralized space charge of the beam, the stationary electric field, and the field of the oscillations in the quasineutral beam plasma. Changes in the total beam energy caused by the self-electric field and in the longitudinal velocity owing to the self-magnetic field are taken into account. Zh. Tekh. Fiz. 68, 106–109 (August 1998)     

Difference scheme for the Samarskii-Ionkin problem with a parameter

We consider a weighted difference scheme approximating the heat equation with the nonlocal boundary conditions

$$u(0,t) = 0, \frac{{\partial u}}{{\partial x}}(0,t) + \frac{{\partial u}}{{\partial x}}(1,t) = 0$$

. We show that in this case the system of eigenfunctions of the main difference operator is not a basis but can be supplemented with associated functions to form a basis. Using the method of expansions in the basis of eigenfunctions and associated functions, we find a necessary and sufficient condition for stability with respect to the initial data in some energy norm. We show that this stability condition cannot be weakened by choosing a different norm. The above-mentioned energy norm is shown to be equivalent to the grid L ₂-norm.

     

Experimental setup for ground-based measurements in preparing cosmic experiments to study nuclear planetology

An experimental laboratory setup combining various gamma spectrometers and neutron generators that is intended for operating at the experimental nuclear-planetology facility deployed at the Joint Institute for Nuclear Research (Dubna, Russia) in order to perform physical calibrations of active gamma and neutron spectrometers is described.     

The LUE-200 accelerator at the IREN facility: Current status and development

The general scheme and current status of an electron linear accelerator with an S-band travelling wave (f = 2856 MHz) accelerating structure—a driver for a pulsed neutron source (the Intense Resonance Neutron source (IREN)) at the Frank Laboratory of Neutron Physics of the Joint Institute for Nuclear Research—are presented. The parameters of the accelerating system and the measured parameters of the electron beam—pulse-beam current, duration of the current pulse, repetition rate, electron-energy spectrum, and loading characteristics of the accelerating structure—are given. The beginning of the implementation of the project of the second stage of the IREN facility, which forms the basis for the development of the accelerator aimed at increasing its beam power, is reported. Technical solutions underlying the modernization of the accelerator’s electrophysical systems are discussed: accelerating system, RF power supplies, and modulators.     

Multifractal Properties of Copper Sulfide Film Formed in Self-Organizing Chemical System

The growth of fractal films of copper sulfide formed during the oxidation of ascorbic acid by aerial oxygen in the presence of a copper coordination compound and sodium sulfide has been studied. The process of growth of the film can be divided into three parts: 1) generation of CuS centers of growth; 2) growth of CuS according to the diffusion limitation of aggregation mechanism; and 3) in the final stage the structure of the film does not change. A method is developed to obtain films with uniform fractal dimensions, but different values of fractal divergence.     

Electric strength of an accelerating gap in a plasma source of charged particles

An investigation is performed on the electric strength of accelerating gaps of plasma sources of electrons and ions in the presence of beam plasma behind the accelerating electrode. For the bipolar mode, when the gas ionization in the accelerating gas may be ignored, the conditions of bridging the gap of plasma discharge of a source with beam plasma and of disruption of emission current are found.