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(NotedoublePoint this is the HST part of a joint Chandra-HST projectdoublePoint the original Chandra proposal abstract follows.) Chandra has been tracking coronal activity cycles of late-type stars via high-contrast soft X-rays comma jointly with HST to capture UV tracers. Objective is to provide fundamental observational constraints for contemporary and future studies of the underlying magnetic Dynamo comma whose inner workings remain elusive. The Sun.s high-energy modulations play an important d_commaSpace Weatherd_comma role in our heliosphere comma as do stellar counterparts for their exoplanets. 3-year time-domain campaign (jointly with HST) is proposed for iconic Alpha Centauri comma already followed by HRC-I since 2006. The Alpha Cen field also is rich in serendipitous sources comma including flaring red dwarfs and several possibly cycling F-K stars.