Bluish is completely right about this, you can't do it through Ajax because JavaScript cannot save files directly to a user's computer (out of security concerns). Unfortunately pointing the main window's URL at your file download means you have little control over what the user experience is when a file download occurs.
I created jQuery File Download which allows for an "Ajax like" experience with file downloads complete with OnSuccess and OnFailure callbacks to provide for a better user experience. Take a look at my blog post on the common problem that the plugin solves and some ways to use it and also a demo of jQuery File Download in action