The search fields in the Content and Admin perspectives support using the Enter key to submit the search. When the search result is shown, the cursor remains in the search field, but is placed before the term. It would be a small delight if the cursor would appear in the same position as where it was in the term.
If the cursor was at the end, place it there again after the ajax callback. But if it was for example in the middle ("ad2|min"), place it again there, so users can immediately re-edit on the same location ("ad3|min").