Transient evolution of eigenmodes in dynamic cavities and time-varying media

Abstract

In this paper, we investigate the perturbation of natural eigenmodes of dynamic cavities with boundaries moving at quasi-static speeds relative to the wave velocity. For an arbitrarily shaped source-free cavity, the amplitude of the irrotational mode is modeled as a damped harmonic oscillator with time-varying eigenfrequency, i.e., a parametric oscillator. It is found that the effect of the pure Doppler shift of the resonance frequencies of the eigenmodes is small at nonrelativistic speeds. However, it is known that any spectrum of eigenenergies that is perturbed by a space-and/or time-fluctuating medium can develop frequency shifts of arbitrary magnitude. By using a linear dynamic (time-dependent) shift for the cavity broad resonances, we find that Doppler-like large shifts result in a mere frequency modulation of the total (resultant) field amplitude, while nonuniform red or blue shift can create a hybrid amplitude and frequency modulation. Interestingly, the combined action of red and blue shifts of uniform magnitude can also create a hybrid modulation. If the angle between modal wave vector and stirrer speed is accounted for in the static (time-independent) shift, the resulting red and blue shifts lead to irregular hybrid modulations. This can occur even for regular perturbations in regular cavities. In addition, owing to the stochastic nature of mode-stirred cavities, the effect of random Doppler-like shifts is also investigated, leading to a Fokker-Planck equation whose diffusion coefficient shows quadratic dependence on the mode amplitude. Thus, the analysis of random perturbations offers an effective framework for observed instantaneous Doppler effects in closed electromagnetic environments. The mathematical framework obtained in terms of stochastic differential equations is useful to predict the nonstationary response of dynamic cavities with complicated or unknown boundary geometry.

Mode-stirred reverberation chambers: A paradigm for spatio-temporal complexity in dynamic electromagnetic environments

“…Physically, the instantaneous nonstationary field evolves through a sequence of ''slipping'' stir states [61,62], and it can be modeled physically as a random-walk process with continuously relaxing phases and magnitudes (with average time constant τ ) as its steps, defined by the parameters of the time-varying plane-wave components. The temporal evolution of the transition PDF (TPDF)…”

A novel time domain analysis of the modes perturbed by a lossy material in a cavity

“…The analysis, based on the Evolutionary Approach to Electromagnetics (EAE), provides exact solutions, ensuring compliance with the principle of causality. Understanding and accurately modeling these intricate systems are crucial for both theoretical insights and practical applications in electronic circuit design, as demonstrated in previous studies utilizing various methods [23][24][25][26][27][28][29][30].…”

Pulse Jitter, Delay Spread, and Doppler Shift in Mode-Stirred Reverberation

“…This paper extends previous work on early-time characterization of pulses in quasi-static chambers [11], harmonic or pulse modulated excitation of nonstationary chambers [12], [13,Sec. 10.2.3], and a study of more general wave diffusion in nonstationary EMEs [14], [15]. Short-, medium-and longterm characterization of power decay and steady state in static and quasi-static reverberant rooms has typically focused on amplitude-based characterization and has a long history, e.g., [16]- [19].…”