Laser line transport with refraction

Extensive studies were completed of numerical methods for the treatment of refraction in laser line transport. A stable method which provides acceptable accuracy now resides in the three dimensional laser transport code BEAM3. By way of review, the numerical method employed by BEAM3 is an extension to three dimensions of a technique tested extensively in a one-dimensional model of a laser rod. At each time step, this method involves sweeping back and forth along the rod axis z, solving for the forward propagating intensity while holding the back-propagating beam fixed. The sweeps continue until convergence is achieved. On each sweep, the nonlinear transport equation is solved by the method of Newton Raphson, for the intensity J(sub k), at each slice z(sub k) along the rod. At slice z(sub k), on a sweep over increasing values of k, the upwind intensity value is known at z(sub k-1), z(sub k-2), ..., z(sub 2), z(sub 1). To solve the transport equation at z(sub k) the ray of propagation is extended upwind until it intersects either the coordinate boundary z(sub k-1), or the previous time value, ct(sub n-1). Therefore, for sub-Courant time steps, the upwind conditions couple to the unknown slice as well as the upwind slice.