Numerical simulation of a vertically held metal-halide lamp ͑Hg/Na/Sc system͒ is presented. The lamp was driven by an ac current of 60 Hz. The model took convection and diffusion of various species into account. A method for rapid calculation of optically thick radiation power was developed. Density of scandium ions and sodium ions has a minimum on the central axis due to radial ambipolar diffusion. Density of metallic atoms and ions and metal iodine molecules decreases with increasing axial

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... tance from the bottom of the tube. This tendency was explained by convection and diffusion. The density of scandium ions depends on the direction of the current; the density was greater at upward current than at downward current.