Relativistic travelling-wave-tube-O (TWT-O) with an irregular moderating system

The optimization of the profile of the decelerating system (DS) of a relativistic O-type traveling wave tube (O-TWT) is a very difficult nonlinear problem, which in addition is multidimensional (due to the necessity to apply the method of large particles), The form of the DS boundary surface under optimization is quasiperiodic and, as a rule, has a large number of periods (20-100). Obviously, the method of representation of the desired optimal boundary determines to a great degree the success of solving the optimization problem. Such problems can be rather efficiently solved with the use of atomic functions, which have the best approximating properties among other finite infinitely differentiable functions. In the present work, atomic functions are used for approximating the profile of a nonregular DS of a relativistic O-TWT under optimization. We use the general theory of interaction of a relativistic electron flow with the field of the E(01) wave of an irregular waveguide, developed in Zakalyukin and Kuraev (1989).