The successive formation and disappearance of density structures in simple expanding systems

Abstract

The Lagrangian fluid description is employed to solve the initial value problem for one-dimensional, compressible fluid flows represented by the Euler–Poisson system. Exact nonlinear and time-dependent solutions are obtained, which exhibit a variety of transient phenomena such as a density collapse in finite space–time or the appearance and, for the first time, a successive dissolution of wavelet structures during the same event. The latter are superimposed on the gross density pattern in the course of the uni-directional expansion of an initially localized density hump. Whereas self-gravitating fluids will always experience collapse, neutral fluids and fluids with repulsive forces, such as a non-neutral, pure electron fluid, can exhibit an evolution of the second type, being determined by the initial conditions. For an electron fluid, being embedded in a neutralizing ion background, these nonlinearities are, however, strongly diminished due to the omnipresent plasma oscillations, which weaken and alternatively change the sign of the collective force.