on optimal nozzle shapes of gas-dynamic lasers

pontryagin's principle is used to study the shape of the supersonic part of the nozzle of a carbon dioxide gas-dynamic laser whose gain is maximal. the exact shape is obtained for the uncoupled approximation of anderson's bimodal model. in this case, if sharp corners are allowed, the ceiling of the supersonic part consists of a slant rectangular sheet followed by a horizontal one; otherwise, a parabolic cylinder joins the two sheets smoothly. pontryagin's principle reduces the optimal control problem to a multifactor optimal problem of the types treated by s.a. losev, v.n. makarov, n.m. reddy, and v. shanmugasundaram