Evolution of small perturbations of system consisting of a gas piston, which accelerates thin shell

Small perturbation technique is used to consider linear stability of a thin shell that is accelerated by gaseous piston while working of heavy-ion fusion target.
The analytical investigation established that the finite density of gas of piston stabilizes (i.e. decreases the increments of perturbation growth) the unstable modes of perturbations as compared with the case of zero density.
The investigation proves that the problem of calculation of perturbation in gaseous piston can be reduced to the well-known Laplace’s equation with the Neumann boundary conditions.
The results are applied to the examples of typical cylindrical targets used for computer modeling of heavy ion fusion.