Theory of induced spatial incoherence

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Abstract
This paper describes theoretical and experimental investigations of induced spatial incoherence (ISI), a technique for achieving the smooth and controllable target beam profiles required for direct‐drive laser fusion. In conventional ISI, a broadband laser beam (coherence time tc=1/Δν≪tpulse) is sliced into an array of mutually incoherent beamlets by echelon structures that impose successive time delay increments Δt>tc. A focusing lens then overlaps those beamlets onto the target, which is usually located at the far field. Here, we evaluate the ideal target beam profiles for practical ISI focusing configurations, and examine the perturbing effects of transient interference, laser aberration, and plasma filamentation. Analytic and numerical calculations show that nonuniformities due to interference among the beamlets are smoothed by both thermal diffusion and temporal averaging. Under laser‐plasma conditions of interest to inertial confinement fusion (ICF), average ablation pressure nonuniformities ∼1% should be readily attainable. We also investigate a partial ISI scheme, which allows widely spaced beamlets to remain mutually coherent; the resulting high spatial frequency interference structure can be effectively smoothed by thermal diffusion alone. A perturbation analysis shows that the average target profile 〈I(x)〉 remains relatively insensitive to laser beam aberration when the scale length of that aberration is larger than the initial beamlet width. This aberration will tend to broaden and smooth 〈I(x)〉, rather than introduce any small‐scale structure. The broadening is largely controllable because it depends only upon spatial averages of the aberrated quantities over the entire laser aperture; the uncontrollable perturbations can be reduced to ∼1% in practical cases. Filamentation in the underdense plasma has been studied numerically using a 2D propagation/hydro code selfoct, which includes both ponderomotive and thermal effects. For 0.25‐μm light, this code predicts that ISI should suppress filamentation in plasmas of interest to ICF. We review recent planar target experiments carried out at the Naval Research Laboratory using 1.054‐ and 0.527‐μm light, which show that the combination of ISI and shorter wavelength substantially reduces all evidence of plasma instabilities. Finally, we review a promising alternative technique for achieving ISI in KrF lasers without using echelons.