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The rapid proper motion of the alpha Cen pair (3.7 arcsec/yr) and itslocation close to the galactic plane on a rich stellar background combine tomake them excellent candidates for stellar conjunctions with distant stars.Adding new astrometry to archival data, we have refined the orbital parameters,barycentric proper motion and parallax of alpha Cen and compute its apparenttrajectory on sky over the coming decades. We present a catalog of the expectedclose conjunctions until 2050. An exceptional event will take place in earlyMay 2028, when alpha Cen A will come within 0.015 +/- 0.135 arcseconds of themK = 7.8 star 2MASS 14392160-6049528 (hereafter S5). In terms of impactparameter and contrast, this is the most favorable stellar conjunction of alphaCen within at least the next three decades. With an angular diameter of LD =0.47 +/- 0.05 mas, it is likely that S5 is a red giant or supergiant located atseveral kiloparsecs. The approached stars will act as moving light probes intransmission through the environment of alpha Cen. The observation of theseclose conjunctions holds great promises to search for planets and other lowmass objects in the alpha Cen system using photometry and astrometry. Therelativistic deflection of the approached star images will be in themilliarcsecond range. The small impact parameter of the conjunction with S5means that this star has a probability of 45% of entering the Einstein ring ofalpha Cen A. The gravitational amplification of the flux of S5 could reach afactor five for the combination of the two lensed images. The proper motion,orbital parameters and parallax of alpha Cen will be measurable with an extremeaccuracy from differential astrometry with the S stars. This will be valuable,for example to prepare the Breakthrough Starshot initiative to sendinterstellar nanocrafts to alpha Centauri.

Close stellar conjunctions of alpha Centauri A and B until 2050 - An mK = 7.8 star may enter the Einstein ring of alpha Cen A in 2028