I. V. Amirkhanov

The generalized continuous analog of Newton’s method for the numerical study of some nonlinear quantum-field models

A numerical method for studying nonlinear problems arising in mathematical models of physics is systematically described in this review. The unified basis for the development of numerical schemes is a generalization of the continuous analog of Newton’s method, which represents a qualitatively new development of the Newtonian evolution process on the basis of the integration of concepts from perturbation theory and the theory of evolution in parameters. The results are presented of numerical studies of quantum-field models of the polaron, the solvated electron, the binucleon, and also QCD potential models for some commonly used potentials.

Sputtering of solids by heavy ions and temperature effects in electronic and lattice subsystems

The results of sputtering coefficient measurements for pure metals, alloys, amorphous alloys, semiconductors, and highly oriented pyrolytic graphite under irradiation by high energy ions are considered. The possible mechanisms of strong sputtering of materials with high defect concentrations are discussed. The three-dimensional thermal spike model (“hot ion track”) with the temperature dependence of thermodynamic parameters (specific heat thermal conductivity) is formulated for single-layer mono-and polycrystals and multilayer systems (materials). The results of a numerical solution to the introduced system of partial differential equations are considered for the lattice and electronic subsystem temperatures around and along the fast heavy ion trajectory as a function of the time t, as well as radial r and longitudinal z coordinates, taking into account possible phase transitions such as melting and evaporation. The results obtained are discussed.

A nonlinear thermal spike model for pyrolytic graphite under irradiation with 86Kr and 209Bi high-energy heavy ions

The temperature dependences of the specific heat capacity and thermal conductivity are introduced for a highly oriented pyrolytic graphite; i.e., the nonlinear model of a thermal spike is considered and a comparative analysis of the obtained results and those for the linear model of a thermal spike is performed. The temperature effects observed in the highly oriented pyrolytic graphite with a change in the electron-phonon interaction coefficient g are investigated in detail. It is shown that, under irradiation of the highly oriented pyrolytic graphite by bismuth ions with an energy of 710 MeV, the temperature on the surface of the target within the framework of the nonlinear model can exceed the sublimation temperature, whereas the temperature on the surface of the target under irradiation by krypton ions with an energy of 253 MeV does not exceed the sublimation temperature. The characteristic range of variations in the electron-phonon interaction coefficient g is evaluated. For values of g in this range, the thermal spike model explains the experimental data on the presence of structures in the form of hillocks with craters at their centers on the surface of the highly oriented pyrolytic graphite exposed to irradiation by 209Bi ions and on the absence of such structures in the case of irradiation by 86Kr ions.

Investigation of thermal processes in one-and two-layer materials under irradiation with high-energy heavy ions within the thermal peak model

A system of equations for the electron and lattice temperatures around and along the path of a 700-MeV heavy (uranium) ion in nickel (one-layer material) is solved numerically in the axially symmetric cylindrical coordinate system under the assumption of temperature-dependent specific heat and thermal conductivity. The obtained dependences of the lattice temperature on the radius (distance from the ion path) and depth suggest that the ionization energy loss of a 700-MeV uranium ion in nickel is sufficient to melt the material. A comparative analysis with the linear model is performed and the maximum radius and depth of the region where the target material can melt is estimated. Then, the initial system of equations is solved for the region around and along the path of a 710-MeV heavy (bismuth 209Bi) ion in the two-layer material Ni(2 μm)-W with constant thermophysical parameters. The obtained dependences of the lattice temperature on the radius and depth show that the ionization energy loss of a 710-MeV bismuth ion in this two-layer material is sufficient for melting. The maximum radius and depth of the regions in the target material where phase transitions may occur are estimated.

Model description of thermoelastic stress in materials under bombardment by heavy ions

In our previous papers, the processes of formation and evolution of thermoelastic waves produced in metals under the action of powerful pulsed beams of small-energy ions were studied using the system of thermoelasticity equations. In this paper, the detailed numerical study of thermoelasticity processes taking into account temperature effects in the electronic and lattice subsystems is carried out using a temperature model of the thermal peak and the system of thermoelasticity equations in the case of propagation of a heavy ion through a condensed medium. New data and dependences are obtained. An analysis involving the comparison between the obtained results and the results of previous papers is presented.

Numerical study of the phase transitions occurring in metals under the action of pulsed ion beams within the framework of the thermal spike model

Phase transitions occur in materials under the action of high-current high-power beams of charged particles. As a rule, such problems are solved within the framework of the heat-conduction equation. In this paper, studies of phase transitions are carried out within the framework of the thermal spike model, and both models are analyzed and compared. It is established that taking the electron gas into account significantly affects the dynamics of the crystal-lattice temperature and the dynamics of the phase transition.

Application of the thermal spike model for explanation of variations of surface structure of highly oriented pyrolytic graphite under bombardment by 86Kr and 209Bi fast ions with high ionization energy loss

Temperature effects in the highly oriented pyrolytic graphite (HOPG) under bombardment by 86Kr (253 MeV) and 209Bi (710 MeV) heavy ions are studied in the framework of a three-dimensional thermal spike model. It is shown that the surface temperature of an HOPG target under bombardment by bismuth ions can exceed the sublimation temperature at particular values of the electron-phonon interaction coefficient. At the same time, the temperature at the target surface during bombardment of HOPG by krypton ions does not exceed the sublimation temperature over a wide range of variations in the electron-phonon interaction belongs. The calculations allow the explanation of the observed changes in the surface structure of HOPG single crystal under bombardment by 209Bi and 86Kr ions.

A modified thermal peak model with the source function dependent on ion velocity for materials bombarded by heavy ions

A modified thermal spike model is proposed. In contrast to the previous model, this scheme involves a source function dependent on ion energy losses determined by the penetration depth of a target and the characteristic time of ion penetration until comes to a complete stop. Such an approach is especially significant for confirming its applicability for track formation processes observed in materials because, as is shown, characteristic times appreciably exceed the periods of phonon oscillations with frequencies of 1013 Hz or more. The performed calculations make it possible to infer that the source function of the modified model describes thermal processes differently than does the commonly used source function. It is established that the temperature of a material exceeds the solid-liquid transition temperature in the cylindrical regions with sizes that are smaller than those calculated without allowance for ion motion.

Numerical investigation of temperature effects in materials irradiated by high-energy heavy ions in the framework of heat conduction equation for electrons and lattice

A system of equations for electron gas and lattice around and along the trajectory of a heavy uranium ion with an energy of 700 MeV in nickel at constant heat capacity and heat conduction taken at room temperature is solved numerically in an axially symmetric cylindrical coordinate system. On the basis of the lattice temperature obtained as a function of radius around the ion trajectory and depth, a conclusion is made that the ionization energy losses of a uranium ion in nickel are sufficient for melting and evaporating the material from the surface. The maximum radius and depth of the region in which melting and evaporation take place are estimated.

Investigation of thermal processes in single crystals irradiated with high-energy heavy ions

The thermal processes arising in InP and GaAs single crystals irradiated with high-energy heavy ions are investigated with the help of a thermal peak model. Numerical simulation is used to estimate the sizes of regions where the melting process can occur and the structural changes arising in the irradiated materials are observed.