Magnetoacoustic waves in diagnostics of the flare current sheets

Abstract

Aims. To obtain diagnostics tools for solar flare current sheets, we numerically studied impulsively generated magnetoacoustic waves in the Harris current sheet. Methods. We used two-dimensional (2-D) magnetohydrodynamic (MHD) and wave dispersion models. Tests of these models were performed for waves in the density slab, where analytical solutions are known. In the MHD model, we solved the full set of ideal MHD equations by means of the modified two-step Lax-Wendroff algorithm. The initial perturbation was chosen to generate preferentially the fast sausage magnetoacoustic waves. To determine the dispersion characteristics of MHD waves in the Harris current sheet, we numerically solved the equation of plasma motions by means of the Runge-Kutta fourth order method together with the bisection iteration one. To establish some diagnostics of these waves and their corresponding flare current sheets, we used the wavelet analysis method. Results. We find that the results of tests of our 2-D MHD and wave dispersion models for the density slab are in good agreement with analytical results. We analyze the magnetoacoustic waves in the current sheet and compare them with those in the density slab. In both cases, for similar geometrical and plasma parameters, we find that wave trains were generated and propagated in a similar way. Their signals registered at selected locations of the Harris current sheet and density slab are also similar. Nevertheless, a dependence of the period of the magnetoacoustic waves on the width of the Harris current sheet differs from that for the density slab. The form of the wave front inside the current sheet similarly differs from that in the density slab. We find that the wavelet spectra of the signals of incoming magnetoacoustic waves at selected locations in the current sheet have the form of wavelet tadpoles. We distinguish that the form of these wavelet tadpoles becomes longer and the heads of the wavelet tadpoles are detected later in time as the distance of the detection point from that of the initial wave perturbation increases. We also find that the wavelet tadpole period depends on the plasma beta parameter. The results are discussed from the point of view of their use as diagnostics of the flare current sheets or flare loops.