Rescaling methods and plasma expansions into vacuum

The problem of a two-component, collisionless plasma expansion into vacuum is investigated from the viewpoint of the Vlasov–Poisson model. The set of equations is treated both analytically (through the rescaling transformations) and numerically, using a one-dimensional Eulerian code. In planar geometry, the rescaling allows to conjecture the existence of a self-similar expansion over long times. Numerical results subsequently confirm the conjecture and show that the plasma becomes neutral over a smaller and smaller scale. A few thermodynamical properties are studied: the temperature is shown to decrease as t−2; the polytropic relation (d/dt)(pn−γ)=0 (with γ=3) is verified asymptotically via a semianalytical argument. Finally, the same problem is studied in a spherical one-dimensional geometry. The time-asymptotic solution is again self-similar. Numerical simulations show that a non-neutral, multiple-layer structure appears, which is proved to be stable over long times.