add this code to the bottom of your success page:
<?php
session_start();
if (isset($_COOKIE[session_name()])) {
setcookie(session_name(), '', time()-42000, '/');
}
session_destroy();
?>
the session id is the value of session_id:
function.session-id.php
if you want to regenerate that value it appears you can use:
session_regenerate_id
function.session-regenerate-id.php