Optimization of efficiency using a gradient search in function space

Summary form only given. In high-power microwave tubes, it is almost always important to operate at the largest possible efficiency. Typically the efficiency depends on a number of continuous parameters, e.g., the magnetic field, B(z), and the wall radius, r/sub w/(z). It would be highly desirable to optimize efficiency with respect to these or some other continuous parameters. A technique has been developed for computing the functional derivative /spl deltaspl eta/spl deltaspl alpha/(z) where /spl alpha/(z) is any continuous parameter (e.g., B(z) or r/sub w/(z)). Combining this technique with a gradient search guarantees that a local maximum of the efficiency can be found in the function space /spl alpha/(z). Computation of the derivative /spl deltaspl eta/spl deltaspl alpha/(z) is performed by integrating the linearized particle and wave equations along unperturbed orbits, and as such is easily implemented in most models of microwave devices. Results have been obtained for the gyrotwistron.