The law of momentum conservation in free microwave cavities containing coherent radiation

TL;DR

This paper investigates the electromagnetic momentum in free microwave cavities with coherent radiation, revealing conditions where momentum transfer to the cavity's mechanical body can occur, but likely remains unobserved in current experiments.

Contribution

It derives expressions for electromagnetic momentum in microwave cavities and shows conditions under which this momentum can cause mechanical displacement, highlighting the transient nature of the effect.

Findings

Electromagnetic momentum can be transferred to the cavity's mechanical body.

The effect is transient and shorter than current experimental measurement times.

Non-zero momentum conditions are demonstrated for asymmetric cavity shapes.

Abstract

Using classical electrodynamics, this work analyzes the dynamics of a closed microwave cavity as a function of its center of energy. Starting from the principle of momentum conservation, expressions for the maximum electromagnetic momentum stored in a free microwave cavity are obtained. Next, it is shown that, for coherent fields and special shape conditions, this momentum component may not completely average out to zero when the fields change in the transient regime. Non-zero conditions are illustrated for the asymmetric conical frustum whose exact modes can not be calculated analytically. One concludes that the electromagnetic momentum can be imparted to the mechanical body so as to displace it in relation to the original center of energy. However, the average time range of the effect is much shorter than any time regime of the experimental tests performed to measure presently, suggesting it has not been observed yet in copper-made resonators.