On the propagation of magnetohydrodynamic perturbations in a Harris‐type current sheet 1. Propagation on discrete modes and signal reconstruction

Abstract

We propose a study of the propagation of magnetohydrodynamic linear perturbations in a 1‐D model of the magnetotail current sheet. Starting from a mathematical analysis of the impulsive linear response of a Harris sheet to external excitations, we study the propagation of the different types of perturbations in the sheet. The structure of the discrete modes of propagation is analyzed, and their coupling to the initial perturbation is discussed. Using various types of initial perturbations (with different characteristic temporal and spatial scales, centered on the neutral sheet or shifted toward the lobe), we reconstruct the full spatial–temporal evolution of the magnetic, velocity, and pressure perturbations. We thus completely determined the perturbations that would be detected by a spacecraft in the tail if the propagation of the perturbations obeys to the ideal linear MHD equations. For example, it is shown that pulse‐like initial perturbations result in the propagation of long quasi‐monochromatic wave packets. The typical period is of the order of 1 min with a maximum amplitude for both the magnetic and thermal pressure perturbations that reach at maximum a few percent of the static value (for an initial pulse with maximum amplitude of the order of the total equilibrium pressure). The highest amplitudes are obtained with initial pulse with spatial scales of the order of the current sheet width.