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Gravitationally lensed extragalactic sources are often subject to statisticalmicrolensing by stars in the galaxy or cluster lens. Accurate models of theflux statistics are required for inferring source and lens properties from fluxobservations. We derive an accurate semi-analytic approximation for calculatingthe mean and variance of the magnification factor, which are applicable toGaussian source profiles and arbitrary non-uniform macro lens models, and hencecan save the need to perform expensive numerical simulations. The results aregiven as single and double lens-plane integrals with simple, non-oscillatoryintegrands, and hence are fast computable using common Monte Carlo integrators.Employing numerical ray-shooting experiments, we examine the case of a highlymagnified source near a macro fold caustic, and demonstrate the excellentaccuracy of this semi-analytic approximation in the regime of multiple microimages. Additionally, we point out how the maximum persistent magnificationachievable near a macro caustic is fundamentally limited by the masses andnumber density of the foreground microlenses, in addition to the source'sphysical size.

New Approximation of Magnification Statistics for Random Microlensing of Magnified Sources