Faculty of Physics
M.V.Lomonosov Moscow State University

## Ultrahigh-energy cosmic rays

### S.N. Vernov, G.B. Khristiansen

Moscow University Physics Bulletin 1982. 37. N 6. P. 1

We present the results of a study of the primary very-high-energy cosmic radiation carried out at the Moscow State University and in Yakutsk. We briefly explain the new methods which were realized at these establishments. Particular attention is given to the results on the high energy spectrum of primary cosmic radiation in the interval of energies 10$^{15}$-10$^{19}$ eV. We discuss the role of galactic cosmic rays of metagalactic origin, and also new mechanisms which ensure the acceleration of particles to energy of the order or more than 10$^{19}$ eV.

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## Metastable electron states in doped alloys Pb$_{1-x}$Sn$_{x}$Te

### B.A. Akimov, N.В. Brandt, L.I. Ryabova

Moscow University Physics Bulletin 1982. 37. N 6. P. 12

We present the results of an Investigation of nonequilibrium states and long-lived relaxation processes which occur in doped alloys Pb$_{1-x}$Sn$_{x}$Te at temperatures T≤20К when the system is brought, our of equilibrium by a quantizing magnetic field, IR illumination, or by a strong electric field. The obtained results Indicate that the energy spectrum of the alloys studied here contain electron metastable states.

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## On the variation of e/m ratio in five-dimentional field theory

Moscow University Physics Bulletin 1982. 37. N 6. P. 19

We present the main equations of the unified five-dimensional theory of gravitation, electromagnetism and scalar field. We discussed one of the consequences of the theory, namely the dependence of the ratio of the electric charge to the mass of a probe particle, on the value of the fundamental scalar field in a given point. This last quantity is determined by the solution of the system of Einstein, Maxwell and Klein -Рок equations. In particular, this field changes in the sun-Earth system for an observer on the earth, as a result of the ellopticity of the Earth's orbit. We obtained a formula which describes the change of e/m. We present data on the measurement of the Josephson frequency ω$_{J}$= 2e/h, which show a dependence on the time of year (the distance from the Earth to the sun), which makes it desirable to carry out direct experiments to test the stability of the ratio e/m.

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## Extention of convergation region of iterative method for the inverse problem of refraction

### S.V. Baykov, V.A. Burov, A.A. Gоrуunоv, A.V. Saskоvets

Moscow University Physics Bulletin 1982. 37. N 6. P. 24

We consider the determination of the inhomogeneity of the velocity of propagation of waves in a medium, from the data on the field scattered from this inhomogeneity. We present a multistage iteration algorithm for the solution of the problem which is free from limitations of the region of convergence, and can also be used for scattering from strong inhomogeneity for which the scattered field exceeds the incident field. This extension of the region of convergence is achieved by solving only a small fraction of -the scattered field at each stage, and the obtained Intermediate estimates of the inhomogeneity are used in the calculation of the Green function for the following iteration stage. A computer experiment is used to illustrate the results.

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## On the ultimate accuracy of gravity gradients measurements

### V.S. Nazarenkо

Moscow University Physics Bulletin 1982. 37. N 6. P. 29

We consider the static, dynamic and modulation methods of measurement of the second derivatives of the gravitational potential by using a high-quality mass-quadrupole oscillator. It is assumed that the useful signal is masked by the noise of the displacement indicator, or by the Brownian oscillations of the oscillator. We present algorithms for the analysis of the output signals which correspond to the method of maximum of a probability function, and we obtain formulae for the dispersion of estimates of the second derivatives of the potential,i.e., for the instrumental and thermal limits of accuracy of various methods of measurements. The obtained results make it possible to make conclusions about the advantages of the modulation method.

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## The influence of large-scale turbulence on the structure of the density current boundary layer

### В.I. Samolubov, A.Yu. Pyrkin

Moscow University Physics Bulletin 1982. 37. N 6. P. 36

The results of complex natural measurements in the upper contact zone of near-floor density flow are used to analyze the repeating cyclic transformations of the structure of the boundary layer of the flow which were observed by registrations lasting several hours. We establish the interdependence of the appearance of fine structure elements of the mixed layer in the stratified flow, such as the lens of translucent liquid, temperature inversions, minima in the velocity profiles, and of the root-mean-square values of its fluctuations. An analysis of the results of discrete and continuous measurements of the profiles of velocity, concentration of suspension and temperature, and aslo the use of spectral analysis, make it possible to interpret the observed phenomena as the effects of generation and dissipation of outer-scale turbulent formations on the vertical structure of the boundary layer. This interpretation is confirmed by quantitative estimates, and agrees well with the main stages of the real process.

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## Calculation of the frequency spectrum of the electron beam in klystron with premodulation

### Yu.K. Alexeev, A.I. Kostienko

Moscow University Physics Bulletin 1982. 37. N 6. P. 43

The example of transit clystron is used to consider a combined perturbation of a one-dimensional electron beam. At the beginning, the current density is amplitude modulated (static control) and, subsequently, the electron velocities are modulated (dynamic control). For large ratios of the control frequencies, a computer was used to calculate the spectral characteristics of the convection current at the entrance to the power takeoff device. The calculations show that it is possible to use a low-frequency amplitude premodulation to increase the electron efficiency of clystron-type pulsed devices which operate in the amplification or frequency multiplication regimes.

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## The anomalous passage of X-and gamma-rays beams by the three waves difraction

### A.V. Andreev, V.E. Gorshkov, Yu.A. Ilyinskii

Moscow University Physics Bulletin 1982. 37. N 6. P. 49

We consider a three-wave dynamical problem of the diffraction of x- and gamma rays in the case of non-coplanar diffraction, when the two reflected waves do not interact directly with each other. We obtain approximate equations which describe the propagation of confined beams during three-wave diffraction in perfect crystals. We estimate the conditions of applicability of plane-wave approximation, and present numerical estimates.

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## Surface light wave diffraction in planar waveguide on a surface acoustic wave

### V.N. Parygin, N.S. Tankovski

Moscow University Physics Bulletin 1982. 37. N 6. P. 55

We formulate a general equation for the interaction of light in the planar surface-acoustic-wave lightguide and obtain a solution of this equation which determines the intensity of light in all possible modes and diffraction orders. We show an analogy between the diffraction of light in a multi-mode lightguide and in an anisotropic medium.

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## Polarization effects in the bremsstrahlung production of massive measons in magnetic field

### I.M. Ternov, V.N. Rodionov, V.G. Zhulego, A.I. Studenikin

Moscow University Physics Bulletin 1982. 37. N 6. P. 60

We obtain the probabilities of bremsstrahlung creation of the massive vector Weinberg-Salam meson in a magnetic field. We study the dependence of the total probability on the axial component of the transition current, and on the spin orientation of.the initial electron. It is shown that the sign of the spin correction can change with the relative magnitude of the axial component of the current.

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## Mechanisms of magnetic losses in fine-grain Ni—Zn ferrites

### V.G. Efremov, E.V. Lebedeva, M.A. Kharinskaya

Moscow University Physics Bulletin 1982. 37. N 6. P. 65

Polycrystalline samples of nickel-zinc ferrites were used to study the dependence of the excitation threshold of spin waves on the grain size. The measurements were carried out on two series of samples. In the first, the zinc concentration was varied to change the anisotropy field, and in the second, the level of internal losses was varied by the introduction of small addition of cobalt ions. It is shown that, as the anisotropy field decreases (the coupling between grains increases) the increase of the threshold field with decreasing grain size becomes weaker. When cobalt ions are introduced, the dependence of the threshold field on the grain size disappears in the region of large grains, and the larger the cobalt-ion concentration the smaller is the grain size starting from which the threshold field ceases to depend on the grain size.

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## Radiation damping of waves in cold magnetized plasma

### L.S. Kuz'menkov, P.B. Podosenov, P.A. Polyakov

Moscow University Physics Bulletin 1982. 37. N 6. P. 71

We study the dispersion and radiation damping of waves in a cold magnetized plasma. We give the appropriate analytical formulae for various frequency cases. It is shown that in a strong magnetic field, the decrement of radiation damping of electromagnetic waves with the righthand circular polarization and the decrement of oscillations near the cyclotron and hybrid frequencies, are proportional to the square of the cyclotron frequency. In a weak magnetic field, the radiation damping decrements of all modes are proportional to the square of the plasma frequency.

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## On the theory of spatial resolution enhancement in the SEM functioning in the beta-conductive mode

### G.V. Saparin, V.V. Filimоnоv, A.V. Сhivilev

Moscow University Physics Bulletin 1982. 37. N 6. P. 76

We consider a problem aimed at increasing the resolution of the scanning electron microscope in the beta-conductivity regime. It is shown that the full analysis of the problem requires investigation of the following aspects of the signal formation in the scanning electron microscope operating in the beta-conductivity regime. Firstly, one needs to calculate the region of scattering of the probe electrons in the volume of the semiconductor in the presence of tangential electric fields. Secondly, one has to study the dynamics of the volume of minority carriers generated by the electron probe as a result of diffusion under the action of electric fields in the object, in the presence of surface recombination. By using a number of assumptions, we analyse the equations for the diffusion of carriers, calculate the concentration for various values of the E field'and surface recombination rate during the pulse of electron current. It is shown that the volume taken up by the electron-hole pairs (the signal volume) depends strongly on the values of the E field and the surface recombination rate. We note that, by using the stroboscopic regime in the scanning electron microscope, one can increase the resolution in the case of beta-conductivity by a factor of 2 - 3.

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## Quasi-classical spin theory

### I.M. Ternov, V.A. Bordovitsyn

Moscow University Physics Bulletin 1982. 37. N 6. P. 84

The proper-time Dirac equation (τ-equation) is used to develop a quasiclassical theory of spin of the Dirac particles.

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## High multiplicity interaction in photoemulsion

### V.A. Sobinyakov, Ch.A. Tretjakova, V.Ya. Shestoperov

Moscow University Physics Bulletin 1982. N 6. P. 89

We present the results of measurements of angles of 527 relativlstic particles which are created in the interaction of an aluminum nucleus with the nucleus of the photoemulsion.

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## Beam solitons in slowing down systems

### V.K. Grishin, E.N. Shaposhnikova

Moscow University Physics Bulletin 1982. 37. N 6. P. 91

We consider the possibility of propagation of short beams of charged particles (beam solitons) in a retarding system. By using a selfconsistent analysis of the nonlinear kinetic equation and the Maxwell equations, we obtain the conditions under which the particles which propagate in a dielectric waveguide are confined by the proper longitudinal field. We discuss the possibility of compression of the beam to durations shorter than one nanosecond by using a transformation of the beam parameters.

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## Diffuse scattering of electrons in the alloy Ti$_{50}$Ni$_{46}$Nb$_{4}$ during the pre-precipitation of the X-phase

### A.G. Khundzhua, M.I. Zakharova

Moscow University Physics Bulletin 1982. 37. N 6. P. 94

The method of diffraction electron microscopy is used to study the fine crystalline structure of the B2 solid solution in the alloy Ti$_{50}$Ni$_{46}$Nb$_{4}$. During an isothermal anneal at 550°C the X-phase with the face-centered cubic structure and lattice constant a$_{x}$= 2√7a$_{B2}$=15,8A precipitates. Immediately after hardening of the alloy at 1100°C the body-centered cubic B2 lattice contains regions with crystal structure close to the structure of the X-phase, which are responsible for the characteristic configuration of the intense diffuse electron scattering.

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## Absorption of microwaves during resonant heating of plasma with a high concentration of electrons inside a waveguide

### P.S. Bulkin, S.A. Dvinin, G.S. Solntsev

Moscow University Physics Bulletin 1982. 37. N 6. P. 98

We show the role of resonant absorption and redistribution of a microwave field along the force lines during the interaction of the field with a confined plasma with above-critical electron concentration at low gas pressure. We calculate, and compare with experiments, the absorption and reflection coefficients of microwaves by a plasma column in a waveguide. We show that the kinetic processes in the plasma can be controlled effectively by a pulsed microwave heating.

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## Iteration algorithm for the solution of the inverse scattering problem

### V.A. Burov, A.A. Goryunov, A.V. Saskovets

Moscow University Physics Bulletin 1982. 37. N 6. P. 102

We develop an effective iteration algorithm for the solution of the inverse scattering problem. We estimate the rate and region of convergence.

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## Averaging method for scatterers estimation in tomography

### V.A. Burov, A.A. Goryunov, A.V. Saskovets

Moscow University Physics Bulletin 1982. 37. N 6. P. 105

We give an estimate for the error in the determination of reemission coefficients of discrete scatterers in the solution of the inverse scattering problem by the averaging method. We present the results of a model experiment which confirm the theoretical estimates of the accuracy of the solution.

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## On the method of synthesis of optical films using the necessary conditions of optimum

### A.V. Tiknhоnravоv

Moscow University Physics Bulletin 1982. 37. N 6. P. 108

The study of necessary conditions for a minimum of the estimator functional in the problem of synthesis of optical coverings, leads to a result which is analogous to the Pontryagin principle of the maximum. It is shown that these results can be used for the construction of solution of the synthesis problem.

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