Perturbation technique as applied to space-varying and time-varying electromagnetic systems

The word "perturb" means to disturb or change slightly. Perturbation techniques are useful for calculating changes in a quantity due to small changes in the problem. This technique could be applied to time-varying and space-varying electromagnetic systems and is illustrated through one example of each in this dissertation. These examples surfaced in the process of doing research in complex media by our research group.; The space-varying system is a double ridge waveguide that consists of 2 trough regions and one gap region. The cutoff frequency and the different fields inside the different regions are known. Outward perturbation is performed by chamfering each of the 4 ridges. The cutoff frequency of the new chamfered double ridge waveguide is obtained. HFSS is used as a simulation tool to verify results. The importance of the cutoff frequency comes in the calculation of the waveguide bandwidth, defined as the difference between cutoff frequency of first and second mode.; The time-varying system is a one-dimensional cavity consisting of 2 PEC plates and separated by a small distance d. The cavity medium is initially free space and is then converted to a lossy magnetoplasma. Transverse modes are considered. Theoretical derivation of the zero-order electric and magnetic fields as well as the current densities when the medium is suddenly switched in time are obtained. It was shown that the switching would result in transformation of the original source wave into 3 new waves, each having unique frequency, amplitude and phase. One of these modes is a DC component of zero frequency called the wiggler mode having a wiggler electric as well as a wiggler magnetic field component. The wiggler electric field is the unique aspect of this study.; The sudden switching case is the ideal scenario and cannot be easily achieved in reality. Thus Finite-Difference-Time-Domain (FDTD) numerical technique is used to find the fields of the modes for more practical plasma profiles. A linear plasma profile with a finite rise time is considered and the fields are computed during and after the switching is complete. Perturbation technique is then used to find the new fields of the modes. This technique requires the development of a Green's function for the problem. Using the zero-order solution and the Green's function, the first-order correction of the fields is obtained. Results of the FDTD technique are compared to those of the perturbation technique and are in good agreement for small rise time. Thus, both techniques are valid. For large rise times, higher order perturbation terms can be calculated in an iterative process.