Focused Beam Ray Tracing for Laser Fusion

A method for modeling the finite size focal spot of a high intensity laser beam in terms of rays and a procedure for tracing the rays are described. The rays, which represent the beam, are normally distributed over the spot via a random walk prescription. The paths traveled by these rays in vacuum are given in terms of the cyclindrical coordinates r and z. We then describe a two-step procedure for tracing the rays in three dimensions in a cylindrically symmetric medium. The first step determines r and z along each path, giving the entrance and exit points for each zone through which the ray passes. The second step gives an approximation to the three-dimensional path in each zone. Each step reduces to a two-dimensional problem yielding simple and computationally fast answers.