Nonlinear evolution of a cold non-relativistic electron-ion plasma with an arbitrary initial density profile: A phase mixing perspective

Using a perturbative approach, an evolution equation for the space charge density, correct up to the third order, is deduced for arbitrary initial density profiles of the electron and ion fluids in a cold nonrelativistic plasma. The evolution equation is solved to reproduce known results pertaining to the phase mixing time in the immobile ion limit as well as in the case of mobile ions, for a homogeneous plasma as well as for a plasma with a periodic inhomogeneity. The case of non-periodic plasma inhomogeneity, as in a finite-size plasma, is also discussed and some insights are given which are well supported by fluid simulation observations.