PHP で非同期ファイルのダウンロードを実現するにはどうすればよいですか?

function csv(){
    $ajaxRequest = ajax();//ajax() initializes XML HTTP Requests
    $postdata = "data=" + document.getElementById("id").value;
    $ajaxRequest.onreadystatechange = function(){
        $ajaxDisplay = document.getElementById('ajaxDiv');
        if($ajaxRequest.readyState == 4 && $ajaxRequest.status==200){
            $ajaxDisplay.innerHTML = $ajaxRequest.responseText;
        }
    }
    $ajaxRequest.open("POST","csv.php",false);
    $ajaxRequest.setRequestHeader('Content-Type', 'application/x-www-form-urlencoded');
    $ajaxRequest.send($postdata);
}

$fileName = 'file.csv';
$downloadFileName = 'newfile.csv';
if (file_exists($fileName)) {
    header('Content-Description: File Transfer');
    header('Content-Type: text/csv');
    header('Content-Disposition: attachment; filename='.$downloadFileName);
    ob_clean();
    flush();
    readfile($fileName);
    exit;
}
echo "done";

window.open('download.php?file=' . $fileName, '_blank');

// or

document.location = 'download.php?file=' . $fileName;