Scaling of low-aspect ratio HID lamps

This is an effort to characterize the lowest possible order approximation to how HID lamps of different wattages should scale. We are looking for broad, simple relationships that connect a lamp's power to its dimensions for ceramic HID lamps of constant low-aspect ratio. We consider a class of lamps in which the arc-tube size and power vary together over an arbitrary range, but the operating pressure, temperature profiles and gas chemistries are all as identical as possible throughout the range. For this class of lamps, we characterize the scaling relationships between the rated power P and the arc-tube inner radius R. Corresponding wall-loading expressions are also derived