Optimal energy and mass input into an electro-thermal launcher

The problem of the optimization of heat and mass input into the channel of an ET-launcher with energy losses and different physical effects taken into account, is solved with the use of Pontryagin's maximum principle. The quantity of energy spent to obtain the given outlet velocity is the minimized functional, intensities of heat and mass sources are the control parameters. In general, the control consists of the intervals of maximal heating, minimal, and of the singular extremal. The analytical solution for the case of unlimited heat source power is obtained, in particular, for power loss law. An ET-launcher operation with mass input from the outer source and due to the destruction of the special inner ablator and/or channel walls is considered. The character of the optimal mass input into the working channel, optimal values of the initial mass and ablation coefficient are determined. It is shown that there is no necessity to input mass during acceleration and the initial gas mass only is to be optimized. The numerical results for a case of limited control are presented.