One-Dimensional Free Expansion of a Collisionless Plasma

The free expansion of a plasma is usually pictured as a combination of free-streaming ions and an oscillating electron fluid. This conjecture is tested for the one-dimensional expansion of a collisionless plasma initially in thermal equilibrium and confined between two perfectly reflecting planes and then with the right one removed. Two methods of solution are used. The first is an approximate method based on Vlasov's equations and the second is a computer experiment employing the sheet model. The two methods show good agreement in the zeroth-order motion to the end of the computer run which is about 4 electron plasma periods or 0.75 ion plasma period for the mass ratio used. The behavior of the ion follows the center of mass of the plasma which is acted on by the sum of electron and ion pressures. The electron follows a damped sine wave at the electron plasma frequency, with the amount of damping dependent upon the decrease in the pressure at the left boundary.