Non-Dimensional Analysis of Thermal Effect on Skin Exposure to an Electromagnetic Beam

Abstract

We consider the problem of inducing withdrawal reflex on a test subject by exposing the subject’s skin to an electromagnetic beam. Heat-sensitive nociceptors in the skin are activated wherever the temperature is above the activation temperature. Withdrawal reflex occurs when the activated volume reaches a threshold. We non-dimensionalize the problem to write the temperature as the product of a parameter-free function of non-dimensional variables and a function of beam parameters. This formulation allows studying beam parameters without knowing skin material parameters. We examine the effects of spot size, total power and distribution type of the electromagnetic beam on 3 quantities at reflex: 1) the time to reflex, 2) the maximum temperature increase, and 3) the total energy consumption. We find that the flat-top beam is the best, with the lowest energy consumption and the smallest maximum temperature increase. The Super-Gaussian beam is only slightly inferior to the flat-top. The Gaussian beam has by far the worst performance among these three.