Initial heating rate of a droplet in a spherical microwave cavity

A simple analytical relationship for the Q of a resonant spherical cavity with a central droplet is derived assuming superconducting cavity walls. In this case Q = (ω × stored energy)/((power loss) where power loss refers to the energy rate delivered to the central droplet. It is assumed that the skin depth δ is small compared with the droplet radius a, and that the wavelength, λ = 2πc/ω, be small compared with the cavity radius b, and large compared with the droplet radius. The equation is Q = (bc2) / (a2δω2). It is shown that in the case of conducting cavity walls a short wavelength minimizes the wall losses.