We derive the luminosity function of high-redshift Lyman alpha emitting sources from a deep, blind, spectroscopic survey that utilized strong-lensing magnification by intermediate-redshift clusters of galaxies. We observed carefully selected regions near 9 clusters, consistent with magnification factors generally greater than 10 for the redshift range 4.5<z<6.7. Eleven emission-line candidates were located in the range 2.2<z<5.6 whose identification we justify as Lyman alpha, in most cases via further spectroscopic observations. The selection function we constructed for our survey takes into account our varying intrinsic Lyman alpha line sensitivity as a function of wavelength and sky position. By virtue of the strong magnification factor, we provide constraints on the Lyman alpha luminosity function to unprecedented limits of 10^40 erg/s, corresponding to a star-formation rate of 0.01 Msun/yr. Our cumulative z=5 Lyman alpha luminosity function is consistent with a power law form, n(>L) proportional to L^-1 over 10^41 to 10^42.5 erg/s. When combined with the results of other surveys, limited at higher luminosities, our results suggest evidence for the suppression of star formation in low-mass halos, as predicted in popular models of galaxy formation.
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