# Average Linear and Angular Momentum and Power of Random Fields Near a Perfectly Conducting Boundary

## TL;DR

This paper analyzes how a perfect conducting boundary influences the average linear and angular momentum and power of a random electromagnetic field, revealing oscillatory behavior and implications for sensor placement and chamber design.

## Contribution

It provides analytical expressions and simulation validation for the boundary effects on electromagnetic momentum and power, and explores applications in reverberation chambers and multiphysics systems.

## Key findings

- Average LM and AM are purely imaginary and oscillate with distance from the boundary.
- At specific distances and frequencies, the averages match free-space values.
- Supports applications in sensor placement and chamber design.

## Abstract

The effect of a perfectly conducting planar boundary on the average linear momentum (LM), angular (momentum (AM), and power of a time-harmonic statistically isotropic random field is analyzed. These averages are purely imaginary and their magnitude decreases in a damped oscillatory manner with distance from the boundary. At discrete quasi-periodic distances and frequencies, the average LM and AM attain their free-space value. Implications for the optimal placement or tuning of power and field sensors are analyzed. Conservation of the flux of the mean LM and AM with respect to the difference of the average electric and magnetic energies and the radiation stresses via the Maxwell stress dyadic is demonstrated. The second-order spatial derivatives of differential radiation stress can be directly linked to the electromagnetic energy imbalance. Analytical results are supported by Monte Carlo simulation results. As an application, performance based estimates for the working volume of a reverberation chamber are obtained. In the context of multiphysics compatibility, mechanical self-stirred reverberation is proposed as an exploitation of electromagnetic stress.