You're missing the concatenation operator . and you've got your quotes mixed up:
echo "<td><a target='_blank' href='http://alpha.bug.corp.com/show_bug.cgi?id=" . $ticket_id . "'>" . $ticket_id . "</a></td>";
To be clear, using double quotes you can leave your variables inside them, but I personally don't like doing it. Variables inside double quotes will be interpreted and parsed by PHP. This would work fine too:
echo "<td><a target='_blank' href='http://alpha.bug.corp.com/show_bug.cgi?id=$ticket_id'>$ticket_id</a></td>";
You could do this:
echo "<td>" . "<a href...
...but it's pointless in almost all cases except where you want to switch to the other type of quote. You might do this so you don't have to escape quotes, or so that variables will (double quotes) or won't (single quotes) be parsed in certain segments.
echo "<td>" . '<a href="">I can use double quotes now!</a>' . "</td>";
Another common use would be for new lines in a <pre> block where \n characters are not processed inside single quotes:
echo 'Your test is going here, Mary said: "Hello Bob!"' . "\n";