A simplified geometric approach for space charge limiting current analysis in interaction region

Summary form only given. A major limitation on the generation of high power microwaves is due to the space charge limiting (SCL) current in the beam wave interaction region of a microwave source which is supported by a particular geometry. Operating above this limit results in formation of virtual cathode and reduction in transmitted current¹. There have been efforts to derive the SCL current for different variants of a beam moving axially inside a coaxial cylindrical drift tube using conventional nonlinear differential equation approach for individual geometry under consideration¹.This work presents a much simple and unified geometrical approach as compared to the conventional approaches to derive the SCL current analytically for different variants of a beam moving axially inside a coaxial cylindrical drift tube. The radial and axial variation of beam potential and formation of virtual cathode is studied with 2D geometrical variations. This has helped in simplifying the analysis. The dependency of SCL current obtained from the proposed simplified approach on geometry has been numerically plotted for different geometrical variables and a critical limit is noted for a practical feasible case. Also, the physical significance of the variation of SCL current with different parameters, such as, beam geometry, drift tube geometry and beam energy is brought forward based on the obtained results. For plasma assisted microwave sources, the influence of plasma on SCL current is worked out and hence the equations are suitably modified. The increment in the SCL current forms the basis for increased output microwave power in plasma filled microwave sources2,3. Results of these efforts will be presented.