Features of Excitation of Linear and Nonlinear Thermal Waves in Dielectric Films on a Substrate Under Irradiation With a Harmonically Modulated Ion Beam

Abstract

A mathematical model has been formulated for the problem of generating linear and nonlinear thermal waves in dielectric films attached to a substrate and in the air by means of a harmonically frequency-modulated ion beam. To solve the formulated problem, a system of nonlinear heat conduction equations is used for two layers of the sample and the substrate. The temperature dependence of the thermophysical quantities of both parts of the sample and, as well as the heat transfer coefficient and emissivity degree, is taken in linear form using thermal coefficients. Temperature disturbances are presented as the sum of stationary and oscillatory components, and the oscillatory part as the sum of linear and nonlinear. In turn, the nonlinear part consists of the sum of oscillations at the fundamental and second harmonics. Due to the fact that the temporary change in the heat source due to the absorption of the ion flow has a harmonic form, the time dependence of the temperature fluctuation in the original equations is also presented in a harmonic form. By solving the boundary value problem, an explicit form of expression was obtained for all parts of the oscillatory component of the temperature disturbance. It was discovered that the frequency dependence of the amplitude of the linear component of the excited thermal wave in the irradiated layer, while for the non-irradiated layer and substrate