Iterative solution of two matrix equations

We study iterative methods for finding the maximal Hermitian positive definite solutions of the matrix equations and , where is Hermitian positive definite. General convergence results are given for the basic fixed point iteration for both equations. Newton's method and inversion free variants of the basic fixed point iteration are discussed in some detail for the first equation. Numerical results are reported to illustrate the convergence behaviour of various algorithms.

     

Super-reltron theory and experiments

A highly efficient, high-power microwave tube called super-reltron is reported. The authors have achieved operation at >400 MW with ~50% efficiency at 1 GHz, and 250 MW with 40% efficiency at 3 GHz. The RF pulse durations are typically a few hundred nanoseconds. These compact lightweight tubes do not require an external magnetic field. The RF output coupling is straightforward and delivers the power directly via the fundamental TE₁₀ wave in a rectangular waveguide without a mode converter. The key features of the tube include (i) generation of a well-modulated electron beam by periodic virtual cathode formation, (ii) postacceleration of the modulated beam to reduce the relative electron energy spread, and (iii) a multicavity output section that efficiently extracts power without RF breakdown. Various theoretical aspects of the device are discussed and the experimental results are summarized