We present high-dynamic-range images of circumstellar dust around HR 4796A that were obtained with MIRLIN at the Keck II telescope at lambda = 7.9, 10.3, 12.5 and 24.5 um. We also present a new continuum measurement at 350 um obtained at the Caltech Submillimeter Observatory. Emission is resolved in Keck images at 12.5 and 24.5 um with PSF FWHMs of 0.37 and 0.55, respectively, and confirms the presence of an outer ring centered at 70 AU. Unresolved excess infrared emission is also detected at the stellar position and must originate well within 13 AU of the star. A model of dust emission fit to flux densities at 12.5, 20.8, and 24.5 um indicates dust grains are located 4(+3/-2) AU from the star with effective size, 28+/-6 um, and an associated temperature of 260+/-40 K. We simulate all extant data with a simple model of exozodiacal dust and an outer exo-Kuiper ring. A two-component outer ring is necessary to fit both Keck thermal infrared and HST scattered-light images. Bayesian parameter estimates yield a total cross-sectional area of 0.055 AU^2 for grains roughly 4 AU from the star and an outer-dust disk composed of a narrow large-grain ring embedded within a wider ring of smaller grains. The narrow ring is 14+/-1 AU wide with inner radius 66+/-1 AU and total cross-sectional area 245 AU^2. The outer ring is 80+/-15 AU wide with inner radius 45+/-5 AU and total cross-sectional area 90 AU^2. Dust grains in the narrow ring are about 10 times larger and have lower albedos than those in the wider ring. These properties are consistent with a picture in which radiation pressure dominates the dispersal of an exo-Kuiper belt.
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