"Keep me informed" module
The way I would do this is with a Notification module.  There is a page at Drupal.org that lists the notification modules that exist.  You may want to look at that page to find a module that suits you.

One particular module I would like to suggest (since I maintain it :-) is the one named Notify.  


  The notify module allows users to subscribe to periodic emails which include all new or revised content and/or comments of specific content types, much like the daily news letters sent by some websites.


You can set it up so that users become automatically subscribed to notifications when they register at the site.  You may notify about all new content or only specific content types.  I.e. you can create a special content type named "Site updates" and use that to post site updates about your alpha site. Then, all your subscribed users will receive an e-mail update update whenever you post new content of the type "Site updates".