A particular setup of the two-stage gun is described that is capable of smoothing the acceleration of cryogenic pellets used for tokamak refueling. The mathematical approach describes with sufficient accuracy the most important physical effects, with substantial improvements over an earlier model Experimental data are used to “tune” such parameters as the coefficients governing piston friction, heat losses in the pump tube, and gas friction along the barrel The available experimental results are correctly simulated by numerical calculations. Numerical results show that, under certain conditions, the two-piston version provides smoother pellet acceleration for the desired final velocity.