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The effect of the air space on self-focusing instability growth rates has been considered for glass laser systems. The situation may be viewed as a min-max problem in which the air space may be adjusted to minimize the fastest growing instability. A solution exists to the min-max problem which reduces the problem to the solution of a single transcendental equation. Solutions to this equation indicate that, at most, a 10-percent reduction in the effective value of the non-linear index of refraction can occur.
Elliott et al. (Sat,) studied this question.