Electrostatic field management and electrodynamic modeling of switched quarter-wave oscillators

Quarter-wave switched oscillators (SWOs), sometimes referred to as MATRIX oscillators, are an important technology for the generation of high-power, moderate bandwidth (mesoband) waveforms. The use of SWOs in high power microwave sources has been discussed for the past 10 years but a detailed discussion of the design of this type of oscillators for particular waveforms has been lacking. In this work a design methodology for a realization of SWOs is developed. A key element in the design of SWOs is the self-breakdown switch, which is created by a large electric field. In order for the switch to close as expected from the design, it is essential to manage the electrostatic field distribution inside the oscillator during the charging time. This enforces geometric constraints on the shape of the conductors inside the oscillator. At the same time, the electrodynamic operation of the system is dependent on the geometry of the structure. In order to generate a geometry that satisfies both the electrostatic and electrodynamic constraints, a new approach is developed to generate this geometry using iterative solutions to the 2-D static Laplace equation, subject to a particular set of boundary conditions. These boundary conditions are manipulated to generate equipotential lines with specific dimensions that satisfy the electrodynamic constraints. Meanwhile, these equipotential lines naturally support an electrostatic field distribution that meets the requirements for the field enhancement. To study the electrodynamic aspects of SWOs, three different (but inter-related) numerical models are built. Depending on the assumptions made in each model, different information about the electrodynamic properties of the designed SWO are obtained. In addition, the agreement and consistency between the different models, validate and give confidence in the calculated results.