Solution to the Problem of the Evolution of a Weak Perturbation Induced at the Boundary of a Hot Coronal Loop in a Strong Magnetic Field

Magnetoacoustic waves are actively used as a means of diagnosing plasma parameters and processes occurring in it. In this paper, we study the problem of the evolution of a weak perturbation specified at the base of a coronal loop. The analysis is carried out under the assumption that the plasma is in a strong magnetic field, such that the evolution of slow magnetoacoustic and entropy modes can be described within the framework of gas dynamics equations with a high degree of accuracy. The spectrum of the waves in question is assumed to be such that the main source of dispersion and dissipation of the waves is the thermal conduction of the medium. Within the framework of the specified approximations, an exact solution to the boundary value problem for the linear evolution equation is found using the Fourier method and Duhamel’s principle. The obtained exact analytical solution can be used to interpret the observation results, as well as numerical modeling of slow magnetoacoustic and entropy waves in the solar corona.