# Journal in journal

## LASER ACCELERATION OF HEAVY ION BEAMS IN VACUUM

The possibility of heavy ion additional acceleration in laser beams is investigated. The main observation is the existence of a big variety of acceleration modes due to many ﬁtting parameters even for only one Gaussian beam and for crossed ones even more so. An essentially non-monotonic dependence of energy gain on relevant variables such as initial velocity or pulse duration is found which makes the search for the most eﬀective acceleration modus very complex. There is a threshold level for the intensity (» 1025W/cm2) when the ion moves in the capture mode in one direction.

## POPULATION DYNAMICS IN A HYDROGEN ATOM UNDER THE ACTION OF AN ULTRA-SHORT PULSE OF LASER RADIATION

Population dynamics of highly excited states of a hydrogen atom under the action of an ultra-short intense laser pulse is studied by means of direct numerical solution of Schr¨ edinger equation in the ﬁnite basis of eigenstates of the discrete and continuous energy spectrum. The essential role of continuous spectrum states is demonstrated. Formation of localized wave packets of Rydberg states is discussed.

## DYNAMICS OF PROBABILITY AMPLITUDES IN HYDROGEN-LIKE ATOMS UNDER THE ACTION OF STRONG VARIABLE ELECTRIC FIELD OF ELECTROMAGNETIC WAVE ACCOUNTING TRANSITIONS TO CONTINUUM

The dynamics of populations of 4s and 3p states in hydrogen atom is investigated under the action of ultra high laser single frequency linear-polarized pulse at one-, two- and three-photon resonance and at large detuning out of frame of perturbation theory and rotating wave approximation. It was shown the existence of low frequency modulation of optical oscillations,which frequency becomes zero at some values of laser ﬁeld amplitude.

## THE EIGENWAVES OF THE ANISOTROPIC PHOTONIC CRYSTALS: THE CALCULATION METHOD AND ITS FEATURES, THE SYMMETRY OF THE DISPERSION SURFACE OF THE 2D CRYSTAL

Fully vectorial plane wave method is presented aimed the calculation of the electromagnetic eigenwaves in periodical dielectric media having arbitrary geometry and dimension with both isotropic and anisotropic elements. Using this method the eﬀect of the reorientation of molecules of anisotropic material in photonic crystal on the dispersion surface is investigated.

## SUPERCONTINUUM SPECTRUM SMOOTHING IN THE MICROSTRUCTURE FIBERS WITH PERIODICALLY MODULATED DIAMETER

The results of numerical modelling of the supercontinuum generation in microstructure ﬁbers excited by femtosecond multi-soliton pulses are presented. Pulse dynamics is modelled using the extended Schrodinger equation, in which the dispersion and nonlinear coeﬃcient for given ﬁber are calculated by plane wave method. It is more easy to achieve the phase-matching conditions for the dispersive wave generation in the ﬁbers with periodical modulated diameter.

## SYNCHRONIZATION OF TWO COUPLED KLYSTRON ACTIVE OSCILLATORS WITH DELAYED FEEDBACK

Results of experimental research of synchronization of two coupled almost identical resonance microwave active oscillators on multicavity klystrons in the modes of periodic and chaotic oscillations are presented. It is shown that depending on type of coupling it is possible to realize a mode of mutual frequency capture, synchronization by means of chaos full elimination by outer harmonic signal, and full synchronization mode. A possibility of using the chaos elimination eﬀect for generation of sequence of chaotic radio pulses is shown.

## STUDYING OF SPATIAL TRANSITION TO TEMPORAL CHAOS IN ACTIVE MEDIUM WITH UNIDIRECTIONAL COUPLING

In the work a new model of a continuous active medium with unidirectional coupling of active elements is proposed. The Anishchenko–Astakhov oscillator was selected as an active element. The model shows both regular and chaotic in time regimes. The results obtained for the medium are compared with the results for a chain of Anishchenko–Astakhov oscillators. The problem of conformity between the discrete model and the continuous medium is analyzed.

## STATISTICAL PROPERTIES OF PHASE SYNCHRONIZATION COEFFICIENT ESTIMATOR

A phase synchronization coeﬃcient estimate, obtained from a time series, can take a high value even for uncoupled oscillators in the case of short signals and close basic frequencies. Since such situations are widespread in practice, it is necessary to detect them to avoid false conclusions about the presence of coupling. We investigate statistical properties of the estimator with the use of an exemplary system – uncoupled phase oscillators. Conditions leading to high probability to get big values of the estimator are determined quantitatively.

## PECULIARITIES OF CALCULATION OF THE LYAPUNOV EXPONENTS SET IN DISTRIBUTED SELE-OSCILLATED SISTEMS WITH DELAYED FEEDBACK

The numerical scheme for calculation the set of Lyapunov exponents in distributed systems with delayed feedback based on a modiﬁcation of Benettine algorithm is described. The results of numerical simulation of two such systems (active oscillator with cubic nonlinearity and active oscillator of klystron type) are presented. The sets of Lyapunov exponents in diﬀerent regimes, particularly in regimes of «weak» and «developed» chaos are analyzed. The calculation peculiarities of the set of Lyapunov exponents in the systems with delayed feedback are discussed.

## SYNCHRONIZATION OF TWO-FREQUENCY QUASI-PERIODIC OSCILLATIONS

In present paper we study the eﬀect of synchronization of two-frequency quasiperiodic oscillations. We analyze both external and mutual synchronization. The peculiarities of synchronization of a resonant limit cycle on a two-dimensional torus are established. It is shown that in general case, one and then another one of the basic frequencies is locked. The results of computer simulation are conﬁrmed experimentally.